(** * Syntax of operators. *)

Inductive unary_operation : Type :=
  | Onotbool : unary_operation          (**r boolean negation ([!] in C) *)
  | Onotint : unary_operation           (**r integer complement ([~] in C) *)
  | Oneg : unary_operation              (**r opposite (unary [-]) *)
  | Oabsfloat : unary_operation.(** * Syntax of operators. *)

Inductive unary_operation : Type :=
  | Onotbool : unary_operation          (**r boolean negation ([!] in C) *)
  | Onotint : unary_operation           (**r integer complement ([~] in C) *)
  | Oneg : unary_operation              (**r opposite (unary [-]) *)
  | Oabsfloat : unary_operation.(** * Syntax of operators. *)

Inductive unary_operation : Type :=
  | Onotbool : unary_operation          (**r boolean negation ([!] in C) *)
  | Onotint : unary_operation           (**r integer complement ([~] in C) *)
  | Oneg : unary_operation              (**r opposite (unary [-]) *)
  | Oabsfloat : unary_operation.(** * Syntax of operators. *)

Inductive unary_operation : Type :=
  | Onotbool : unary_operation          (**r boolean negation ([!] in C) *)
  | Onotint : unary_operation           (**r integer complement ([~] in C) *)
  | Oneg : unary_operation              (**r opposite (unary [-]) *)
  | Oabsfloat : unary_operation.(** * Syntax of operators. *)

Inductive unary_operation : Type :=
  | Onotbool : unary_operation          (**r boolean negation ([!] in C) *)
  | Onotint : unary_operation           (**r integer complement ([~] in C) *)
  | Oneg : unary_operation              (**r opposite (unary [-]) *)
  | Oabsfloat : unary_operation.(**r floating-point absolute value *)

Inductive binary_operation : Type :=
  | Oadd : binary_operation             (**r addition (binary [+]) *)
  | Osub : binary_operation             (**r subtraction (binary [-]) *)
  | Omul : binary_operation             (**r multiplication (binary [*]) *)
  | Odiv : binary_operation             (**r division ([/]) *)
  | Omod : binary_operation             (**r remainder ([%]) *)
  | Oand : binary_operation             (**r bitwise and ([&]) *)
  | Oor : binary_operation              (**r bitwise or ([|]) *)
  | Oxor : binary_operation             (**r bitwise xor ([^]) *)
  | Oshl : binary_operation             (**r left shift ([<<]) *)
  | Oshr : binary_operation             (**r right shift ([>>]) *)
  | Oeq: binary_operation               (**r comparison ([==]) *)
  | One: binary_operation               (**r comparison ([!=]) *)
  | Olt: binary_operation               (**r comparison ([<]) *)
  | Ogt: binary_operation               (**r comparison ([>]) *)
  | Ole: binary_operation               (**r comparison ([<=]) *)
  | Oge: binary_operation.(**r floating-point absolute value *)

Inductive binary_operation : Type :=
  | Oadd : binary_operation             (**r addition (binary [+]) *)
  | Osub : binary_operation             (**r subtraction (binary [-]) *)
  | Omul : binary_operation             (**r multiplication (binary [*]) *)
  | Odiv : binary_operation             (**r division ([/]) *)
  | Omod : binary_operation             (**r remainder ([%]) *)
  | Oand : binary_operation             (**r bitwise and ([&]) *)
  | Oor : binary_operation              (**r bitwise or ([|]) *)
  | Oxor : binary_operation             (**r bitwise xor ([^]) *)
  | Oshl : binary_operation             (**r left shift ([<<]) *)
  | Oshr : binary_operation             (**r right shift ([>>]) *)
  | Oeq: binary_operation               (**r comparison ([==]) *)
  | One: binary_operation               (**r comparison ([!=]) *)
  | Olt: binary_operation               (**r comparison ([<]) *)
  | Ogt: binary_operation               (**r comparison ([>]) *)
  | Ole: binary_operation               (**r comparison ([<=]) *)
  | Oge: binary_operation.(**r floating-point absolute value *)

Inductive binary_operation : Type :=
  | Oadd : binary_operation             (**r addition (binary [+]) *)
  | Osub : binary_operation             (**r subtraction (binary [-]) *)
  | Omul : binary_operation             (**r multiplication (binary [*]) *)
  | Odiv : binary_operation             (**r division ([/]) *)
  | Omod : binary_operation             (**r remainder ([%]) *)
  | Oand : binary_operation             (**r bitwise and ([&]) *)
  | Oor : binary_operation              (**r bitwise or ([|]) *)
  | Oxor : binary_operation             (**r bitwise xor ([^]) *)
  | Oshl : binary_operation             (**r left shift ([<<]) *)
  | Oshr : binary_operation             (**r right shift ([>>]) *)
  | Oeq: binary_operation               (**r comparison ([==]) *)
  | One: binary_operation               (**r comparison ([!=]) *)
  | Olt: binary_operation               (**r comparison ([<]) *)
  | Ogt: binary_operation               (**r comparison ([>]) *)
  | Ole: binary_operation               (**r comparison ([<=]) *)
  | Oge: binary_operation.(**r floating-point absolute value *)

Inductive binary_operation : Type :=
  | Oadd : binary_operation             (**r addition (binary [+]) *)
  | Osub : binary_operation             (**r subtraction (binary [-]) *)
  | Omul : binary_operation             (**r multiplication (binary [*]) *)
  | Odiv : binary_operation             (**r division ([/]) *)
  | Omod : binary_operation             (**r remainder ([%]) *)
  | Oand : binary_operation             (**r bitwise and ([&]) *)
  | Oor : binary_operation              (**r bitwise or ([|]) *)
  | Oxor : binary_operation             (**r bitwise xor ([^]) *)
  | Oshl : binary_operation             (**r left shift ([<<]) *)
  | Oshr : binary_operation             (**r right shift ([>>]) *)
  | Oeq: binary_operation               (**r comparison ([==]) *)
  | One: binary_operation               (**r comparison ([!=]) *)
  | Olt: binary_operation               (**r comparison ([<]) *)
  | Ogt: binary_operation               (**r comparison ([>]) *)
  | Ole: binary_operation               (**r comparison ([<=]) *)
  | Oge: binary_operation.(**r floating-point absolute value *)

Inductive binary_operation : Type :=
  | Oadd : binary_operation             (**r addition (binary [+]) *)
  | Osub : binary_operation             (**r subtraction (binary [-]) *)
  | Omul : binary_operation             (**r multiplication (binary [*]) *)
  | Odiv : binary_operation             (**r division ([/]) *)
  | Omod : binary_operation             (**r remainder ([%]) *)
  | Oand : binary_operation             (**r bitwise and ([&]) *)
  | Oor : binary_operation              (**r bitwise or ([|]) *)
  | Oxor : binary_operation             (**r bitwise xor ([^]) *)
  | Oshl : binary_operation             (**r left shift ([<<]) *)
  | Oshr : binary_operation             (**r right shift ([>>]) *)
  | Oeq: binary_operation               (**r comparison ([==]) *)
  | One: binary_operation               (**r comparison ([!=]) *)
  | Olt: binary_operation               (**r comparison ([<]) *)
  | Ogt: binary_operation               (**r comparison ([>]) *)
  | Ole: binary_operation               (**r comparison ([<=]) *)
  | Oge: binary_operation.(**r floating-point absolute value *)

Inductive binary_operation : Type :=
  | Oadd : binary_operation             (**r addition (binary [+]) *)
  | Osub : binary_operation             (**r subtraction (binary [-]) *)
  | Omul : binary_operation             (**r multiplication (binary [*]) *)
  | Odiv : binary_operation             (**r division ([/]) *)
  | Omod : binary_operation             (**r remainder ([%]) *)
  | Oand : binary_operation             (**r bitwise and ([&]) *)
  | Oor : binary_operation              (**r bitwise or ([|]) *)
  | Oxor : binary_operation             (**r bitwise xor ([^]) *)
  | Oshl : binary_operation             (**r left shift ([<<]) *)
  | Oshr : binary_operation             (**r right shift ([>>]) *)
  | Oeq: binary_operation               (**r comparison ([==]) *)
  | One: binary_operation               (**r comparison ([!=]) *)
  | Olt: binary_operation               (**r comparison ([<]) *)
  | Ogt: binary_operation               (**r comparison ([>]) *)
  | Ole: binary_operation               (**r comparison ([<=]) *)
  | Oge: binary_operation.(**r floating-point absolute value *)

Inductive binary_operation : Type :=
  | Oadd : binary_operation             (**r addition (binary [+]) *)
  | Osub : binary_operation             (**r subtraction (binary [-]) *)
  | Omul : binary_operation             (**r multiplication (binary [*]) *)
  | Odiv : binary_operation             (**r division ([/]) *)
  | Omod : binary_operation             (**r remainder ([%]) *)
  | Oand : binary_operation             (**r bitwise and ([&]) *)
  | Oor : binary_operation              (**r bitwise or ([|]) *)
  | Oxor : binary_operation             (**r bitwise xor ([^]) *)
  | Oshl : binary_operation             (**r left shift ([<<]) *)
  | Oshr : binary_operation             (**r right shift ([>>]) *)
  | Oeq: binary_operation               (**r comparison ([==]) *)
  | One: binary_operation               (**r comparison ([!=]) *)
  | Olt: binary_operation               (**r comparison ([<]) *)
  | Ogt: binary_operation               (**r comparison ([>]) *)
  | Ole: binary_operation               (**r comparison ([<=]) *)
  | Oge: binary_operation.(**r floating-point absolute value *)

Inductive binary_operation : Type :=
  | Oadd : binary_operation             (**r addition (binary [+]) *)
  | Osub : binary_operation             (**r subtraction (binary [-]) *)
  | Omul : binary_operation             (**r multiplication (binary [*]) *)
  | Odiv : binary_operation             (**r division ([/]) *)
  | Omod : binary_operation             (**r remainder ([%]) *)
  | Oand : binary_operation             (**r bitwise and ([&]) *)
  | Oor : binary_operation              (**r bitwise or ([|]) *)
  | Oxor : binary_operation             (**r bitwise xor ([^]) *)
  | Oshl : binary_operation             (**r left shift ([<<]) *)
  | Oshr : binary_operation             (**r right shift ([>>]) *)
  | Oeq: binary_operation               (**r comparison ([==]) *)
  | One: binary_operation               (**r comparison ([!=]) *)
  | Olt: binary_operation               (**r comparison ([<]) *)
  | Ogt: binary_operation               (**r comparison ([>]) *)
  | Ole: binary_operation               (**r comparison ([<=]) *)
  | Oge: binary_operation.(**r floating-point absolute value *)

Inductive binary_operation : Type :=
  | Oadd : binary_operation             (**r addition (binary [+]) *)
  | Osub : binary_operation             (**r subtraction (binary [-]) *)
  | Omul : binary_operation             (**r multiplication (binary [*]) *)
  | Odiv : binary_operation             (**r division ([/]) *)
  | Omod : binary_operation             (**r remainder ([%]) *)
  | Oand : binary_operation             (**r bitwise and ([&]) *)
  | Oor : binary_operation              (**r bitwise or ([|]) *)
  | Oxor : binary_operation             (**r bitwise xor ([^]) *)
  | Oshl : binary_operation             (**r left shift ([<<]) *)
  | Oshr : binary_operation             (**r right shift ([>>]) *)
  | Oeq: binary_operation               (**r comparison ([==]) *)
  | One: binary_operation               (**r comparison ([!=]) *)
  | Olt: binary_operation               (**r comparison ([<]) *)
  | Ogt: binary_operation               (**r comparison ([>]) *)
  | Ole: binary_operation               (**r comparison ([<=]) *)
  | Oge: binary_operation.(**r floating-point absolute value *)

Inductive binary_operation : Type :=
  | Oadd : binary_operation             (**r addition (binary [+]) *)
  | Osub : binary_operation             (**r subtraction (binary [-]) *)
  | Omul : binary_operation             (**r multiplication (binary [*]) *)
  | Odiv : binary_operation             (**r division ([/]) *)
  | Omod : binary_operation             (**r remainder ([%]) *)
  | Oand : binary_operation             (**r bitwise and ([&]) *)
  | Oor : binary_operation              (**r bitwise or ([|]) *)
  | Oxor : binary_operation             (**r bitwise xor ([^]) *)
  | Oshl : binary_operation             (**r left shift ([<<]) *)
  | Oshr : binary_operation             (**r right shift ([>>]) *)
  | Oeq: binary_operation               (**r comparison ([==]) *)
  | One: binary_operation               (**r comparison ([!=]) *)
  | Olt: binary_operation               (**r comparison ([<]) *)
  | Ogt: binary_operation               (**r comparison ([>]) *)
  | Ole: binary_operation               (**r comparison ([<=]) *)
  | Oge: binary_operation.(**r floating-point absolute value *)

Inductive binary_operation : Type :=
  | Oadd : binary_operation             (**r addition (binary [+]) *)
  | Osub : binary_operation             (**r subtraction (binary [-]) *)
  | Omul : binary_operation             (**r multiplication (binary [*]) *)
  | Odiv : binary_operation             (**r division ([/]) *)
  | Omod : binary_operation             (**r remainder ([%]) *)
  | Oand : binary_operation             (**r bitwise and ([&]) *)
  | Oor : binary_operation              (**r bitwise or ([|]) *)
  | Oxor : binary_operation             (**r bitwise xor ([^]) *)
  | Oshl : binary_operation             (**r left shift ([<<]) *)
  | Oshr : binary_operation             (**r right shift ([>>]) *)
  | Oeq: binary_operation               (**r comparison ([==]) *)
  | One: binary_operation               (**r comparison ([!=]) *)
  | Olt: binary_operation               (**r comparison ([<]) *)
  | Ogt: binary_operation               (**r comparison ([>]) *)
  | Ole: binary_operation               (**r comparison ([<=]) *)
  | Oge: binary_operation.(**r floating-point absolute value *)

Inductive binary_operation : Type :=
  | Oadd : binary_operation             (**r addition (binary [+]) *)
  | Osub : binary_operation             (**r subtraction (binary [-]) *)
  | Omul : binary_operation             (**r multiplication (binary [*]) *)
  | Odiv : binary_operation             (**r division ([/]) *)
  | Omod : binary_operation             (**r remainder ([%]) *)
  | Oand : binary_operation             (**r bitwise and ([&]) *)
  | Oor : binary_operation              (**r bitwise or ([|]) *)
  | Oxor : binary_operation             (**r bitwise xor ([^]) *)
  | Oshl : binary_operation             (**r left shift ([<<]) *)
  | Oshr : binary_operation             (**r right shift ([>>]) *)
  | Oeq: binary_operation               (**r comparison ([==]) *)
  | One: binary_operation               (**r comparison ([!=]) *)
  | Olt: binary_operation               (**r comparison ([<]) *)
  | Ogt: binary_operation               (**r comparison ([>]) *)
  | Ole: binary_operation               (**r comparison ([<=]) *)
  | Oge: binary_operation.(**r floating-point absolute value *)

Inductive binary_operation : Type :=
  | Oadd : binary_operation             (**r addition (binary [+]) *)
  | Osub : binary_operation             (**r subtraction (binary [-]) *)
  | Omul : binary_operation             (**r multiplication (binary [*]) *)
  | Odiv : binary_operation             (**r division ([/]) *)
  | Omod : binary_operation             (**r remainder ([%]) *)
  | Oand : binary_operation             (**r bitwise and ([&]) *)
  | Oor : binary_operation              (**r bitwise or ([|]) *)
  | Oxor : binary_operation             (**r bitwise xor ([^]) *)
  | Oshl : binary_operation             (**r left shift ([<<]) *)
  | Oshr : binary_operation             (**r right shift ([>>]) *)
  | Oeq: binary_operation               (**r comparison ([==]) *)
  | One: binary_operation               (**r comparison ([!=]) *)
  | Olt: binary_operation               (**r comparison ([<]) *)
  | Ogt: binary_operation               (**r comparison ([>]) *)
  | Ole: binary_operation               (**r comparison ([<=]) *)
  | Oge: binary_operation.(**r floating-point absolute value *)

Inductive binary_operation : Type :=
  | Oadd : binary_operation             (**r addition (binary [+]) *)
  | Osub : binary_operation             (**r subtraction (binary [-]) *)
  | Omul : binary_operation             (**r multiplication (binary [*]) *)
  | Odiv : binary_operation             (**r division ([/]) *)
  | Omod : binary_operation             (**r remainder ([%]) *)
  | Oand : binary_operation             (**r bitwise and ([&]) *)
  | Oor : binary_operation              (**r bitwise or ([|]) *)
  | Oxor : binary_operation             (**r bitwise xor ([^]) *)
  | Oshl : binary_operation             (**r left shift ([<<]) *)
  | Oshr : binary_operation             (**r right shift ([>>]) *)
  | Oeq: binary_operation               (**r comparison ([==]) *)
  | One: binary_operation               (**r comparison ([!=]) *)
  | Olt: binary_operation               (**r comparison ([<]) *)
  | Ogt: binary_operation               (**r comparison ([>]) *)
  | Ole: binary_operation               (**r comparison ([<=]) *)
  | Oge: binary_operation.(**r floating-point absolute value *)

Inductive binary_operation : Type :=
  | Oadd : binary_operation             (**r addition (binary [+]) *)
  | Osub : binary_operation             (**r subtraction (binary [-]) *)
  | Omul : binary_operation             (**r multiplication (binary [*]) *)
  | Odiv : binary_operation             (**r division ([/]) *)
  | Omod : binary_operation             (**r remainder ([%]) *)
  | Oand : binary_operation             (**r bitwise and ([&]) *)
  | Oor : binary_operation              (**r bitwise or ([|]) *)
  | Oxor : binary_operation             (**r bitwise xor ([^]) *)
  | Oshl : binary_operation             (**r left shift ([<<]) *)
  | Oshr : binary_operation             (**r right shift ([>>]) *)
  | Oeq: binary_operation               (**r comparison ([==]) *)
  | One: binary_operation               (**r comparison ([!=]) *)
  | Olt: binary_operation               (**r comparison ([<]) *)
  | Ogt: binary_operation               (**r comparison ([>]) *)
  | Ole: binary_operation               (**r comparison ([<=]) *)
  | Oge: binary_operation.(**r floating-point absolute value *)

Inductive binary_operation : Type :=
  | Oadd : binary_operation             (**r addition (binary [+]) *)
  | Osub : binary_operation             (**r subtraction (binary [-]) *)
  | Omul : binary_operation             (**r multiplication (binary [*]) *)
  | Odiv : binary_operation             (**r division ([/]) *)
  | Omod : binary_operation             (**r remainder ([%]) *)
  | Oand : binary_operation             (**r bitwise and ([&]) *)
  | Oor : binary_operation              (**r bitwise or ([|]) *)
  | Oxor : binary_operation             (**r bitwise xor ([^]) *)
  | Oshl : binary_operation             (**r left shift ([<<]) *)
  | Oshr : binary_operation             (**r right shift ([>>]) *)
  | Oeq: binary_operation               (**r comparison ([==]) *)
  | One: binary_operation               (**r comparison ([!=]) *)
  | Olt: binary_operation               (**r comparison ([<]) *)
  | Ogt: binary_operation               (**r comparison ([>]) *)
  | Ole: binary_operation               (**r comparison ([<=]) *)
  | Oge: binary_operation.(**r floating-point absolute value *)

Inductive binary_operation : Type :=
  | Oadd : binary_operation             (**r addition (binary [+]) *)
  | Osub : binary_operation             (**r subtraction (binary [-]) *)
  | Omul : binary_operation             (**r multiplication (binary [*]) *)
  | Odiv : binary_operation             (**r division ([/]) *)
  | Omod : binary_operation             (**r remainder ([%]) *)
  | Oand : binary_operation             (**r bitwise and ([&]) *)
  | Oor : binary_operation              (**r bitwise or ([|]) *)
  | Oxor : binary_operation             (**r bitwise xor ([^]) *)
  | Oshl : binary_operation             (**r left shift ([<<]) *)
  | Oshr : binary_operation             (**r right shift ([>>]) *)
  | Oeq: binary_operation               (**r comparison ([==]) *)
  | One: binary_operation               (**r comparison ([!=]) *)
  | Olt: binary_operation               (**r comparison ([<]) *)
  | Ogt: binary_operation               (**r comparison ([>]) *)
  | Ole: binary_operation               (**r comparison ([<=]) *)
  | Oge: binary_operation.(**r comparison ([>=]) *)

Inductive incr_or_decr : Type := Incr | Decr.(**r comparison ([>=]) *)

Inductive incr_or_decr : Type := Incr | Decr.(**r comparison ([>=]) *)

Inductive incr_or_decr : Type := Incr | Decr.(** * Type classification and semantics of operators. *)

(** Most C operators are overloaded (they apply to arguments of various
  types) and their semantics depend on the types of their arguments.
  The following [classify_*] functions take as arguments the types
  of the arguments of an operation.  They return enough information
  to resolve overloading for this operator applications, such as
  ``both arguments are floats'', or ``the first is a pointer
  and the second is an integer''.  This classification is used in the
  compiler (module [Cshmgen]) to resolve overloading statically.

  The [sem_*] functions below compute the result of an operator
  application.  Since operators are overloaded, the result depends
  both on the static types of the arguments and on their run-time values.
  The corresponding [classify_*] function is first called on the
  types of the arguments to resolve static overloading.  It is then
  followed by a case analysis on the values of the arguments. *)

(** ** Casts and truth values *)

Inductive classify_cast_cases : Type :=
  | cast_case_pointer                              (**r between pointer types or intptr_t types *)
  | cast_case_i2i (sz2:intsize) (si2:signedness)   (**r int -> int *)
  | cast_case_f2f                                  (**r double -> double *)
  | cast_case_s2s                                  (**r single -> single *)
  | cast_case_f2s                                  (**r double -> single *)
  | cast_case_s2f                                  (**r single -> double *)
  | cast_case_i2f (si1: signedness)                (**r int -> double *)
  | cast_case_i2s (si1: signedness)                (**r int -> single *)
  | cast_case_f2i (sz2:intsize) (si2:signedness)   (**r double -> int *)
  | cast_case_s2i (sz2:intsize) (si2:signedness)   (**r single -> int *)
  | cast_case_l2l                       (**r long -> long *)
  | cast_case_i2l (si1: signedness)     (**r int -> long *)
  | cast_case_l2i (sz2: intsize) (si2: signedness) (**r long -> int *)
  | cast_case_l2f (si1: signedness)                (**r long -> double *)
  | cast_case_l2s (si1: signedness)                (**r long -> single *)
  | cast_case_f2l (si2:signedness)                 (**r double -> long *)
  | cast_case_s2l (si2:signedness)                 (**r single -> long *)
  | cast_case_i2bool                               (**r int -> bool *)
  | cast_case_l2bool                               (**r long -> bool *)
  | cast_case_f2bool                               (**r double -> bool *)
  | cast_case_s2bool                               (**r single -> bool *)
  | cast_case_struct (id1 id2: ident)              (**r struct -> struct *)
  | cast_case_union  (id1 id2: ident)              (**r union -> union *)
  | cast_case_void                                 (**r any -> void *)
  | cast_case_default.(** * Type classification and semantics of operators. *)

(** Most C operators are overloaded (they apply to arguments of various
  types) and their semantics depend on the types of their arguments.
  The following [classify_*] functions take as arguments the types
  of the arguments of an operation.  They return enough information
  to resolve overloading for this operator applications, such as
  ``both arguments are floats'', or ``the first is a pointer
  and the second is an integer''.  This classification is used in the
  compiler (module [Cshmgen]) to resolve overloading statically.

  The [sem_*] functions below compute the result of an operator
  application.  Since operators are overloaded, the result depends
  both on the static types of the arguments and on their run-time values.
  The corresponding [classify_*] function is first called on the
  types of the arguments to resolve static overloading.  It is then
  followed by a case analysis on the values of the arguments. *)

(** ** Casts and truth values *)

Inductive classify_cast_cases : Type :=
  | cast_case_pointer                              (**r between pointer types or intptr_t types *)
  | cast_case_i2i (sz2:intsize) (si2:signedness)   (**r int -> int *)
  | cast_case_f2f                                  (**r double -> double *)
  | cast_case_s2s                                  (**r single -> single *)
  | cast_case_f2s                                  (**r double -> single *)
  | cast_case_s2f                                  (**r single -> double *)
  | cast_case_i2f (si1: signedness)                (**r int -> double *)
  | cast_case_i2s (si1: signedness)                (**r int -> single *)
  | cast_case_f2i (sz2:intsize) (si2:signedness)   (**r double -> int *)
  | cast_case_s2i (sz2:intsize) (si2:signedness)   (**r single -> int *)
  | cast_case_l2l                       (**r long -> long *)
  | cast_case_i2l (si1: signedness)     (**r int -> long *)
  | cast_case_l2i (sz2: intsize) (si2: signedness) (**r long -> int *)
  | cast_case_l2f (si1: signedness)                (**r long -> double *)
  | cast_case_l2s (si1: signedness)                (**r long -> single *)
  | cast_case_f2l (si2:signedness)                 (**r double -> long *)
  | cast_case_s2l (si2:signedness)                 (**r single -> long *)
  | cast_case_i2bool                               (**r int -> bool *)
  | cast_case_l2bool                               (**r long -> bool *)
  | cast_case_f2bool                               (**r double -> bool *)
  | cast_case_s2bool                               (**r single -> bool *)
  | cast_case_struct (id1 id2: ident)              (**r struct -> struct *)
  | cast_case_union  (id1 id2: ident)              (**r union -> union *)
  | cast_case_void                                 (**r any -> void *)
  | cast_case_default.(** * Type classification and semantics of operators. *)

(** Most C operators are overloaded (they apply to arguments of various
  types) and their semantics depend on the types of their arguments.
  The following [classify_*] functions take as arguments the types
  of the arguments of an operation.  They return enough information
  to resolve overloading for this operator applications, such as
  ``both arguments are floats'', or ``the first is a pointer
  and the second is an integer''.  This classification is used in the
  compiler (module [Cshmgen]) to resolve overloading statically.

  The [sem_*] functions below compute the result of an operator
  application.  Since operators are overloaded, the result depends
  both on the static types of the arguments and on their run-time values.
  The corresponding [classify_*] function is first called on the
  types of the arguments to resolve static overloading.  It is then
  followed by a case analysis on the values of the arguments. *)

(** ** Casts and truth values *)

Inductive classify_cast_cases : Type :=
  | cast_case_pointer                              (**r between pointer types or intptr_t types *)
  | cast_case_i2i (sz2:intsize) (si2:signedness)   (**r int -> int *)
  | cast_case_f2f                                  (**r double -> double *)
  | cast_case_s2s                                  (**r single -> single *)
  | cast_case_f2s                                  (**r double -> single *)
  | cast_case_s2f                                  (**r single -> double *)
  | cast_case_i2f (si1: signedness)                (**r int -> double *)
  | cast_case_i2s (si1: signedness)                (**r int -> single *)
  | cast_case_f2i (sz2:intsize) (si2:signedness)   (**r double -> int *)
  | cast_case_s2i (sz2:intsize) (si2:signedness)   (**r single -> int *)
  | cast_case_l2l                       (**r long -> long *)
  | cast_case_i2l (si1: signedness)     (**r int -> long *)
  | cast_case_l2i (sz2: intsize) (si2: signedness) (**r long -> int *)
  | cast_case_l2f (si1: signedness)                (**r long -> double *)
  | cast_case_l2s (si1: signedness)                (**r long -> single *)
  | cast_case_f2l (si2:signedness)                 (**r double -> long *)
  | cast_case_s2l (si2:signedness)                 (**r single -> long *)
  | cast_case_i2bool                               (**r int -> bool *)
  | cast_case_l2bool                               (**r long -> bool *)
  | cast_case_f2bool                               (**r double -> bool *)
  | cast_case_s2bool                               (**r single -> bool *)
  | cast_case_struct (id1 id2: ident)              (**r struct -> struct *)
  | cast_case_union  (id1 id2: ident)              (**r union -> union *)
  | cast_case_void                                 (**r any -> void *)
  | cast_case_default.(** * Type classification and semantics of operators. *)

(** Most C operators are overloaded (they apply to arguments of various
  types) and their semantics depend on the types of their arguments.
  The following [classify_*] functions take as arguments the types
  of the arguments of an operation.  They return enough information
  to resolve overloading for this operator applications, such as
  ``both arguments are floats'', or ``the first is a pointer
  and the second is an integer''.  This classification is used in the
  compiler (module [Cshmgen]) to resolve overloading statically.

  The [sem_*] functions below compute the result of an operator
  application.  Since operators are overloaded, the result depends
  both on the static types of the arguments and on their run-time values.
  The corresponding [classify_*] function is first called on the
  types of the arguments to resolve static overloading.  It is then
  followed by a case analysis on the values of the arguments. *)

(** ** Casts and truth values *)

Inductive classify_cast_cases : Type :=
  | cast_case_pointer                              (**r between pointer types or intptr_t types *)
  | cast_case_i2i (sz2:intsize) (si2:signedness)   (**r int -> int *)
  | cast_case_f2f                                  (**r double -> double *)
  | cast_case_s2s                                  (**r single -> single *)
  | cast_case_f2s                                  (**r double -> single *)
  | cast_case_s2f                                  (**r single -> double *)
  | cast_case_i2f (si1: signedness)                (**r int -> double *)
  | cast_case_i2s (si1: signedness)                (**r int -> single *)
  | cast_case_f2i (sz2:intsize) (si2:signedness)   (**r double -> int *)
  | cast_case_s2i (sz2:intsize) (si2:signedness)   (**r single -> int *)
  | cast_case_l2l                       (**r long -> long *)
  | cast_case_i2l (si1: signedness)     (**r int -> long *)
  | cast_case_l2i (sz2: intsize) (si2: signedness) (**r long -> int *)
  | cast_case_l2f (si1: signedness)                (**r long -> double *)
  | cast_case_l2s (si1: signedness)                (**r long -> single *)
  | cast_case_f2l (si2:signedness)                 (**r double -> long *)
  | cast_case_s2l (si2:signedness)                 (**r single -> long *)
  | cast_case_i2bool                               (**r int -> bool *)
  | cast_case_l2bool                               (**r long -> bool *)
  | cast_case_f2bool                               (**r double -> bool *)
  | cast_case_s2bool                               (**r single -> bool *)
  | cast_case_struct (id1 id2: ident)              (**r struct -> struct *)
  | cast_case_union  (id1 id2: ident)              (**r union -> union *)
  | cast_case_void                                 (**r any -> void *)
  | cast_case_default.(** * Type classification and semantics of operators. *)

(** Most C operators are overloaded (they apply to arguments of various
  types) and their semantics depend on the types of their arguments.
  The following [classify_*] functions take as arguments the types
  of the arguments of an operation.  They return enough information
  to resolve overloading for this operator applications, such as
  ``both arguments are floats'', or ``the first is a pointer
  and the second is an integer''.  This classification is used in the
  compiler (module [Cshmgen]) to resolve overloading statically.

  The [sem_*] functions below compute the result of an operator
  application.  Since operators are overloaded, the result depends
  both on the static types of the arguments and on their run-time values.
  The corresponding [classify_*] function is first called on the
  types of the arguments to resolve static overloading.  It is then
  followed by a case analysis on the values of the arguments. *)

(** ** Casts and truth values *)

Inductive classify_cast_cases : Type :=
  | cast_case_pointer                              (**r between pointer types or intptr_t types *)
  | cast_case_i2i (sz2:intsize) (si2:signedness)   (**r int -> int *)
  | cast_case_f2f                                  (**r double -> double *)
  | cast_case_s2s                                  (**r single -> single *)
  | cast_case_f2s                                  (**r double -> single *)
  | cast_case_s2f                                  (**r single -> double *)
  | cast_case_i2f (si1: signedness)                (**r int -> double *)
  | cast_case_i2s (si1: signedness)                (**r int -> single *)
  | cast_case_f2i (sz2:intsize) (si2:signedness)   (**r double -> int *)
  | cast_case_s2i (sz2:intsize) (si2:signedness)   (**r single -> int *)
  | cast_case_l2l                       (**r long -> long *)
  | cast_case_i2l (si1: signedness)     (**r int -> long *)
  | cast_case_l2i (sz2: intsize) (si2: signedness) (**r long -> int *)
  | cast_case_l2f (si1: signedness)                (**r long -> double *)
  | cast_case_l2s (si1: signedness)                (**r long -> single *)
  | cast_case_f2l (si2:signedness)                 (**r double -> long *)
  | cast_case_s2l (si2:signedness)                 (**r single -> long *)
  | cast_case_i2bool                               (**r int -> bool *)
  | cast_case_l2bool                               (**r long -> bool *)
  | cast_case_f2bool                               (**r double -> bool *)
  | cast_case_s2bool                               (**r single -> bool *)
  | cast_case_struct (id1 id2: ident)              (**r struct -> struct *)
  | cast_case_union  (id1 id2: ident)              (**r union -> union *)
  | cast_case_void                                 (**r any -> void *)
  | cast_case_default.(** * Type classification and semantics of operators. *)

(** Most C operators are overloaded (they apply to arguments of various
  types) and their semantics depend on the types of their arguments.
  The following [classify_*] functions take as arguments the types
  of the arguments of an operation.  They return enough information
  to resolve overloading for this operator applications, such as
  ``both arguments are floats'', or ``the first is a pointer
  and the second is an integer''.  This classification is used in the
  compiler (module [Cshmgen]) to resolve overloading statically.

  The [sem_*] functions below compute the result of an operator
  application.  Since operators are overloaded, the result depends
  both on the static types of the arguments and on their run-time values.
  The corresponding [classify_*] function is first called on the
  types of the arguments to resolve static overloading.  It is then
  followed by a case analysis on the values of the arguments. *)

(** ** Casts and truth values *)

Inductive classify_cast_cases : Type :=
  | cast_case_pointer                              (**r between pointer types or intptr_t types *)
  | cast_case_i2i (sz2:intsize) (si2:signedness)   (**r int -> int *)
  | cast_case_f2f                                  (**r double -> double *)
  | cast_case_s2s                                  (**r single -> single *)
  | cast_case_f2s                                  (**r double -> single *)
  | cast_case_s2f                                  (**r single -> double *)
  | cast_case_i2f (si1: signedness)                (**r int -> double *)
  | cast_case_i2s (si1: signedness)                (**r int -> single *)
  | cast_case_f2i (sz2:intsize) (si2:signedness)   (**r double -> int *)
  | cast_case_s2i (sz2:intsize) (si2:signedness)   (**r single -> int *)
  | cast_case_l2l                       (**r long -> long *)
  | cast_case_i2l (si1: signedness)     (**r int -> long *)
  | cast_case_l2i (sz2: intsize) (si2: signedness) (**r long -> int *)
  | cast_case_l2f (si1: signedness)                (**r long -> double *)
  | cast_case_l2s (si1: signedness)                (**r long -> single *)
  | cast_case_f2l (si2:signedness)                 (**r double -> long *)
  | cast_case_s2l (si2:signedness)                 (**r single -> long *)
  | cast_case_i2bool                               (**r int -> bool *)
  | cast_case_l2bool                               (**r long -> bool *)
  | cast_case_f2bool                               (**r double -> bool *)
  | cast_case_s2bool                               (**r single -> bool *)
  | cast_case_struct (id1 id2: ident)              (**r struct -> struct *)
  | cast_case_union  (id1 id2: ident)              (**r union -> union *)
  | cast_case_void                                 (**r any -> void *)
  | cast_case_default.(** * Type classification and semantics of operators. *)

(** Most C operators are overloaded (they apply to arguments of various
  types) and their semantics depend on the types of their arguments.
  The following [classify_*] functions take as arguments the types
  of the arguments of an operation.  They return enough information
  to resolve overloading for this operator applications, such as
  ``both arguments are floats'', or ``the first is a pointer
  and the second is an integer''.  This classification is used in the
  compiler (module [Cshmgen]) to resolve overloading statically.

  The [sem_*] functions below compute the result of an operator
  application.  Since operators are overloaded, the result depends
  both on the static types of the arguments and on their run-time values.
  The corresponding [classify_*] function is first called on the
  types of the arguments to resolve static overloading.  It is then
  followed by a case analysis on the values of the arguments. *)

(** ** Casts and truth values *)

Inductive classify_cast_cases : Type :=
  | cast_case_pointer                              (**r between pointer types or intptr_t types *)
  | cast_case_i2i (sz2:intsize) (si2:signedness)   (**r int -> int *)
  | cast_case_f2f                                  (**r double -> double *)
  | cast_case_s2s                                  (**r single -> single *)
  | cast_case_f2s                                  (**r double -> single *)
  | cast_case_s2f                                  (**r single -> double *)
  | cast_case_i2f (si1: signedness)                (**r int -> double *)
  | cast_case_i2s (si1: signedness)                (**r int -> single *)
  | cast_case_f2i (sz2:intsize) (si2:signedness)   (**r double -> int *)
  | cast_case_s2i (sz2:intsize) (si2:signedness)   (**r single -> int *)
  | cast_case_l2l                       (**r long -> long *)
  | cast_case_i2l (si1: signedness)     (**r int -> long *)
  | cast_case_l2i (sz2: intsize) (si2: signedness) (**r long -> int *)
  | cast_case_l2f (si1: signedness)                (**r long -> double *)
  | cast_case_l2s (si1: signedness)                (**r long -> single *)
  | cast_case_f2l (si2:signedness)                 (**r double -> long *)
  | cast_case_s2l (si2:signedness)                 (**r single -> long *)
  | cast_case_i2bool                               (**r int -> bool *)
  | cast_case_l2bool                               (**r long -> bool *)
  | cast_case_f2bool                               (**r double -> bool *)
  | cast_case_s2bool                               (**r single -> bool *)
  | cast_case_struct (id1 id2: ident)              (**r struct -> struct *)
  | cast_case_union  (id1 id2: ident)              (**r union -> union *)
  | cast_case_void                                 (**r any -> void *)
  | cast_case_default.(** * Type classification and semantics of operators. *)

(** Most C operators are overloaded (they apply to arguments of various
  types) and their semantics depend on the types of their arguments.
  The following [classify_*] functions take as arguments the types
  of the arguments of an operation.  They return enough information
  to resolve overloading for this operator applications, such as
  ``both arguments are floats'', or ``the first is a pointer
  and the second is an integer''.  This classification is used in the
  compiler (module [Cshmgen]) to resolve overloading statically.

  The [sem_*] functions below compute the result of an operator
  application.  Since operators are overloaded, the result depends
  both on the static types of the arguments and on their run-time values.
  The corresponding [classify_*] function is first called on the
  types of the arguments to resolve static overloading.  It is then
  followed by a case analysis on the values of the arguments. *)

(** ** Casts and truth values *)

Inductive classify_cast_cases : Type :=
  | cast_case_pointer                              (**r between pointer types or intptr_t types *)
  | cast_case_i2i (sz2:intsize) (si2:signedness)   (**r int -> int *)
  | cast_case_f2f                                  (**r double -> double *)
  | cast_case_s2s                                  (**r single -> single *)
  | cast_case_f2s                                  (**r double -> single *)
  | cast_case_s2f                                  (**r single -> double *)
  | cast_case_i2f (si1: signedness)                (**r int -> double *)
  | cast_case_i2s (si1: signedness)                (**r int -> single *)
  | cast_case_f2i (sz2:intsize) (si2:signedness)   (**r double -> int *)
  | cast_case_s2i (sz2:intsize) (si2:signedness)   (**r single -> int *)
  | cast_case_l2l                       (**r long -> long *)
  | cast_case_i2l (si1: signedness)     (**r int -> long *)
  | cast_case_l2i (sz2: intsize) (si2: signedness) (**r long -> int *)
  | cast_case_l2f (si1: signedness)                (**r long -> double *)
  | cast_case_l2s (si1: signedness)                (**r long -> single *)
  | cast_case_f2l (si2:signedness)                 (**r double -> long *)
  | cast_case_s2l (si2:signedness)                 (**r single -> long *)
  | cast_case_i2bool                               (**r int -> bool *)
  | cast_case_l2bool                               (**r long -> bool *)
  | cast_case_f2bool                               (**r double -> bool *)
  | cast_case_s2bool                               (**r single -> bool *)
  | cast_case_struct (id1 id2: ident)              (**r struct -> struct *)
  | cast_case_union  (id1 id2: ident)              (**r union -> union *)
  | cast_case_void                                 (**r any -> void *)
  | cast_case_default.(** * Type classification and semantics of operators. *)

(** Most C operators are overloaded (they apply to arguments of various
  types) and their semantics depend on the types of their arguments.
  The following [classify_*] functions take as arguments the types
  of the arguments of an operation.  They return enough information
  to resolve overloading for this operator applications, such as
  ``both arguments are floats'', or ``the first is a pointer
  and the second is an integer''.  This classification is used in the
  compiler (module [Cshmgen]) to resolve overloading statically.

  The [sem_*] functions below compute the result of an operator
  application.  Since operators are overloaded, the result depends
  both on the static types of the arguments and on their run-time values.
  The corresponding [classify_*] function is first called on the
  types of the arguments to resolve static overloading.  It is then
  followed by a case analysis on the values of the arguments. *)

(** ** Casts and truth values *)

Inductive classify_cast_cases : Type :=
  | cast_case_pointer                              (**r between pointer types or intptr_t types *)
  | cast_case_i2i (sz2:intsize) (si2:signedness)   (**r int -> int *)
  | cast_case_f2f                                  (**r double -> double *)
  | cast_case_s2s                                  (**r single -> single *)
  | cast_case_f2s                                  (**r double -> single *)
  | cast_case_s2f                                  (**r single -> double *)
  | cast_case_i2f (si1: signedness)                (**r int -> double *)
  | cast_case_i2s (si1: signedness)                (**r int -> single *)
  | cast_case_f2i (sz2:intsize) (si2:signedness)   (**r double -> int *)
  | cast_case_s2i (sz2:intsize) (si2:signedness)   (**r single -> int *)
  | cast_case_l2l                       (**r long -> long *)
  | cast_case_i2l (si1: signedness)     (**r int -> long *)
  | cast_case_l2i (sz2: intsize) (si2: signedness) (**r long -> int *)
  | cast_case_l2f (si1: signedness)                (**r long -> double *)
  | cast_case_l2s (si1: signedness)                (**r long -> single *)
  | cast_case_f2l (si2:signedness)                 (**r double -> long *)
  | cast_case_s2l (si2:signedness)                 (**r single -> long *)
  | cast_case_i2bool                               (**r int -> bool *)
  | cast_case_l2bool                               (**r long -> bool *)
  | cast_case_f2bool                               (**r double -> bool *)
  | cast_case_s2bool                               (**r single -> bool *)
  | cast_case_struct (id1 id2: ident)              (**r struct -> struct *)
  | cast_case_union  (id1 id2: ident)              (**r union -> union *)
  | cast_case_void                                 (**r any -> void *)
  | cast_case_default.(** * Type classification and semantics of operators. *)

(** Most C operators are overloaded (they apply to arguments of various
  types) and their semantics depend on the types of their arguments.
  The following [classify_*] functions take as arguments the types
  of the arguments of an operation.  They return enough information
  to resolve overloading for this operator applications, such as
  ``both arguments are floats'', or ``the first is a pointer
  and the second is an integer''.  This classification is used in the
  compiler (module [Cshmgen]) to resolve overloading statically.

  The [sem_*] functions below compute the result of an operator
  application.  Since operators are overloaded, the result depends
  both on the static types of the arguments and on their run-time values.
  The corresponding [classify_*] function is first called on the
  types of the arguments to resolve static overloading.  It is then
  followed by a case analysis on the values of the arguments. *)

(** ** Casts and truth values *)

Inductive classify_cast_cases : Type :=
  | cast_case_pointer                              (**r between pointer types or intptr_t types *)
  | cast_case_i2i (sz2:intsize) (si2:signedness)   (**r int -> int *)
  | cast_case_f2f                                  (**r double -> double *)
  | cast_case_s2s                                  (**r single -> single *)
  | cast_case_f2s                                  (**r double -> single *)
  | cast_case_s2f                                  (**r single -> double *)
  | cast_case_i2f (si1: signedness)                (**r int -> double *)
  | cast_case_i2s (si1: signedness)                (**r int -> single *)
  | cast_case_f2i (sz2:intsize) (si2:signedness)   (**r double -> int *)
  | cast_case_s2i (sz2:intsize) (si2:signedness)   (**r single -> int *)
  | cast_case_l2l                       (**r long -> long *)
  | cast_case_i2l (si1: signedness)     (**r int -> long *)
  | cast_case_l2i (sz2: intsize) (si2: signedness) (**r long -> int *)
  | cast_case_l2f (si1: signedness)                (**r long -> double *)
  | cast_case_l2s (si1: signedness)                (**r long -> single *)
  | cast_case_f2l (si2:signedness)                 (**r double -> long *)
  | cast_case_s2l (si2:signedness)                 (**r single -> long *)
  | cast_case_i2bool                               (**r int -> bool *)
  | cast_case_l2bool                               (**r long -> bool *)
  | cast_case_f2bool                               (**r double -> bool *)
  | cast_case_s2bool                               (**r single -> bool *)
  | cast_case_struct (id1 id2: ident)              (**r struct -> struct *)
  | cast_case_union  (id1 id2: ident)              (**r union -> union *)
  | cast_case_void                                 (**r any -> void *)
  | cast_case_default.(** * Type classification and semantics of operators. *)

(** Most C operators are overloaded (they apply to arguments of various
  types) and their semantics depend on the types of their arguments.
  The following [classify_*] functions take as arguments the types
  of the arguments of an operation.  They return enough information
  to resolve overloading for this operator applications, such as
  ``both arguments are floats'', or ``the first is a pointer
  and the second is an integer''.  This classification is used in the
  compiler (module [Cshmgen]) to resolve overloading statically.

  The [sem_*] functions below compute the result of an operator
  application.  Since operators are overloaded, the result depends
  both on the static types of the arguments and on their run-time values.
  The corresponding [classify_*] function is first called on the
  types of the arguments to resolve static overloading.  It is then
  followed by a case analysis on the values of the arguments. *)

(** ** Casts and truth values *)

Inductive classify_cast_cases : Type :=
  | cast_case_pointer                              (**r between pointer types or intptr_t types *)
  | cast_case_i2i (sz2:intsize) (si2:signedness)   (**r int -> int *)
  | cast_case_f2f                                  (**r double -> double *)
  | cast_case_s2s                                  (**r single -> single *)
  | cast_case_f2s                                  (**r double -> single *)
  | cast_case_s2f                                  (**r single -> double *)
  | cast_case_i2f (si1: signedness)                (**r int -> double *)
  | cast_case_i2s (si1: signedness)                (**r int -> single *)
  | cast_case_f2i (sz2:intsize) (si2:signedness)   (**r double -> int *)
  | cast_case_s2i (sz2:intsize) (si2:signedness)   (**r single -> int *)
  | cast_case_l2l                       (**r long -> long *)
  | cast_case_i2l (si1: signedness)     (**r int -> long *)
  | cast_case_l2i (sz2: intsize) (si2: signedness) (**r long -> int *)
  | cast_case_l2f (si1: signedness)                (**r long -> double *)
  | cast_case_l2s (si1: signedness)                (**r long -> single *)
  | cast_case_f2l (si2:signedness)                 (**r double -> long *)
  | cast_case_s2l (si2:signedness)                 (**r single -> long *)
  | cast_case_i2bool                               (**r int -> bool *)
  | cast_case_l2bool                               (**r long -> bool *)
  | cast_case_f2bool                               (**r double -> bool *)
  | cast_case_s2bool                               (**r single -> bool *)
  | cast_case_struct (id1 id2: ident)              (**r struct -> struct *)
  | cast_case_union  (id1 id2: ident)              (**r union -> union *)
  | cast_case_void                                 (**r any -> void *)
  | cast_case_default.(** * Type classification and semantics of operators. *)

(** Most C operators are overloaded (they apply to arguments of various
  types) and their semantics depend on the types of their arguments.
  The following [classify_*] functions take as arguments the types
  of the arguments of an operation.  They return enough information
  to resolve overloading for this operator applications, such as
  ``both arguments are floats'', or ``the first is a pointer
  and the second is an integer''.  This classification is used in the
  compiler (module [Cshmgen]) to resolve overloading statically.

  The [sem_*] functions below compute the result of an operator
  application.  Since operators are overloaded, the result depends
  both on the static types of the arguments and on their run-time values.
  The corresponding [classify_*] function is first called on the
  types of the arguments to resolve static overloading.  It is then
  followed by a case analysis on the values of the arguments. *)

(** ** Casts and truth values *)

Inductive classify_cast_cases : Type :=
  | cast_case_pointer                              (**r between pointer types or intptr_t types *)
  | cast_case_i2i (sz2:intsize) (si2:signedness)   (**r int -> int *)
  | cast_case_f2f                                  (**r double -> double *)
  | cast_case_s2s                                  (**r single -> single *)
  | cast_case_f2s                                  (**r double -> single *)
  | cast_case_s2f                                  (**r single -> double *)
  | cast_case_i2f (si1: signedness)                (**r int -> double *)
  | cast_case_i2s (si1: signedness)                (**r int -> single *)
  | cast_case_f2i (sz2:intsize) (si2:signedness)   (**r double -> int *)
  | cast_case_s2i (sz2:intsize) (si2:signedness)   (**r single -> int *)
  | cast_case_l2l                       (**r long -> long *)
  | cast_case_i2l (si1: signedness)     (**r int -> long *)
  | cast_case_l2i (sz2: intsize) (si2: signedness) (**r long -> int *)
  | cast_case_l2f (si1: signedness)                (**r long -> double *)
  | cast_case_l2s (si1: signedness)                (**r long -> single *)
  | cast_case_f2l (si2:signedness)                 (**r double -> long *)
  | cast_case_s2l (si2:signedness)                 (**r single -> long *)
  | cast_case_i2bool                               (**r int -> bool *)
  | cast_case_l2bool                               (**r long -> bool *)
  | cast_case_f2bool                               (**r double -> bool *)
  | cast_case_s2bool                               (**r single -> bool *)
  | cast_case_struct (id1 id2: ident)              (**r struct -> struct *)
  | cast_case_union  (id1 id2: ident)              (**r union -> union *)
  | cast_case_void                                 (**r any -> void *)
  | cast_case_default.(** * Type classification and semantics of operators. *)

(** Most C operators are overloaded (they apply to arguments of various
  types) and their semantics depend on the types of their arguments.
  The following [classify_*] functions take as arguments the types
  of the arguments of an operation.  They return enough information
  to resolve overloading for this operator applications, such as
  ``both arguments are floats'', or ``the first is a pointer
  and the second is an integer''.  This classification is used in the
  compiler (module [Cshmgen]) to resolve overloading statically.

  The [sem_*] functions below compute the result of an operator
  application.  Since operators are overloaded, the result depends
  both on the static types of the arguments and on their run-time values.
  The corresponding [classify_*] function is first called on the
  types of the arguments to resolve static overloading.  It is then
  followed by a case analysis on the values of the arguments. *)

(** ** Casts and truth values *)

Inductive classify_cast_cases : Type :=
  | cast_case_pointer                              (**r between pointer types or intptr_t types *)
  | cast_case_i2i (sz2:intsize) (si2:signedness)   (**r int -> int *)
  | cast_case_f2f                                  (**r double -> double *)
  | cast_case_s2s                                  (**r single -> single *)
  | cast_case_f2s                                  (**r double -> single *)
  | cast_case_s2f                                  (**r single -> double *)
  | cast_case_i2f (si1: signedness)                (**r int -> double *)
  | cast_case_i2s (si1: signedness)                (**r int -> single *)
  | cast_case_f2i (sz2:intsize) (si2:signedness)   (**r double -> int *)
  | cast_case_s2i (sz2:intsize) (si2:signedness)   (**r single -> int *)
  | cast_case_l2l                       (**r long -> long *)
  | cast_case_i2l (si1: signedness)     (**r int -> long *)
  | cast_case_l2i (sz2: intsize) (si2: signedness) (**r long -> int *)
  | cast_case_l2f (si1: signedness)                (**r long -> double *)
  | cast_case_l2s (si1: signedness)                (**r long -> single *)
  | cast_case_f2l (si2:signedness)                 (**r double -> long *)
  | cast_case_s2l (si2:signedness)                 (**r single -> long *)
  | cast_case_i2bool                               (**r int -> bool *)
  | cast_case_l2bool                               (**r long -> bool *)
  | cast_case_f2bool                               (**r double -> bool *)
  | cast_case_s2bool                               (**r single -> bool *)
  | cast_case_struct (id1 id2: ident)              (**r struct -> struct *)
  | cast_case_union  (id1 id2: ident)              (**r union -> union *)
  | cast_case_void                                 (**r any -> void *)
  | cast_case_default.(** * Type classification and semantics of operators. *)

(** Most C operators are overloaded (they apply to arguments of various
  types) and their semantics depend on the types of their arguments.
  The following [classify_*] functions take as arguments the types
  of the arguments of an operation.  They return enough information
  to resolve overloading for this operator applications, such as
  ``both arguments are floats'', or ``the first is a pointer
  and the second is an integer''.  This classification is used in the
  compiler (module [Cshmgen]) to resolve overloading statically.

  The [sem_*] functions below compute the result of an operator
  application.  Since operators are overloaded, the result depends
  both on the static types of the arguments and on their run-time values.
  The corresponding [classify_*] function is first called on the
  types of the arguments to resolve static overloading.  It is then
  followed by a case analysis on the values of the arguments. *)

(** ** Casts and truth values *)

Inductive classify_cast_cases : Type :=
  | cast_case_pointer                              (**r between pointer types or intptr_t types *)
  | cast_case_i2i (sz2:intsize) (si2:signedness)   (**r int -> int *)
  | cast_case_f2f                                  (**r double -> double *)
  | cast_case_s2s                                  (**r single -> single *)
  | cast_case_f2s                                  (**r double -> single *)
  | cast_case_s2f                                  (**r single -> double *)
  | cast_case_i2f (si1: signedness)                (**r int -> double *)
  | cast_case_i2s (si1: signedness)                (**r int -> single *)
  | cast_case_f2i (sz2:intsize) (si2:signedness)   (**r double -> int *)
  | cast_case_s2i (sz2:intsize) (si2:signedness)   (**r single -> int *)
  | cast_case_l2l                       (**r long -> long *)
  | cast_case_i2l (si1: signedness)     (**r int -> long *)
  | cast_case_l2i (sz2: intsize) (si2: signedness) (**r long -> int *)
  | cast_case_l2f (si1: signedness)                (**r long -> double *)
  | cast_case_l2s (si1: signedness)                (**r long -> single *)
  | cast_case_f2l (si2:signedness)                 (**r double -> long *)
  | cast_case_s2l (si2:signedness)                 (**r single -> long *)
  | cast_case_i2bool                               (**r int -> bool *)
  | cast_case_l2bool                               (**r long -> bool *)
  | cast_case_f2bool                               (**r double -> bool *)
  | cast_case_s2bool                               (**r single -> bool *)
  | cast_case_struct (id1 id2: ident)              (**r struct -> struct *)
  | cast_case_union  (id1 id2: ident)              (**r union -> union *)
  | cast_case_void                                 (**r any -> void *)
  | cast_case_default.(** * Type classification and semantics of operators. *)

(** Most C operators are overloaded (they apply to arguments of various
  types) and their semantics depend on the types of their arguments.
  The following [classify_*] functions take as arguments the types
  of the arguments of an operation.  They return enough information
  to resolve overloading for this operator applications, such as
  ``both arguments are floats'', or ``the first is a pointer
  and the second is an integer''.  This classification is used in the
  compiler (module [Cshmgen]) to resolve overloading statically.

  The [sem_*] functions below compute the result of an operator
  application.  Since operators are overloaded, the result depends
  both on the static types of the arguments and on their run-time values.
  The corresponding [classify_*] function is first called on the
  types of the arguments to resolve static overloading.  It is then
  followed by a case analysis on the values of the arguments. *)

(** ** Casts and truth values *)

Inductive classify_cast_cases : Type :=
  | cast_case_pointer                              (**r between pointer types or intptr_t types *)
  | cast_case_i2i (sz2:intsize) (si2:signedness)   (**r int -> int *)
  | cast_case_f2f                                  (**r double -> double *)
  | cast_case_s2s                                  (**r single -> single *)
  | cast_case_f2s                                  (**r double -> single *)
  | cast_case_s2f                                  (**r single -> double *)
  | cast_case_i2f (si1: signedness)                (**r int -> double *)
  | cast_case_i2s (si1: signedness)                (**r int -> single *)
  | cast_case_f2i (sz2:intsize) (si2:signedness)   (**r double -> int *)
  | cast_case_s2i (sz2:intsize) (si2:signedness)   (**r single -> int *)
  | cast_case_l2l                       (**r long -> long *)
  | cast_case_i2l (si1: signedness)     (**r int -> long *)
  | cast_case_l2i (sz2: intsize) (si2: signedness) (**r long -> int *)
  | cast_case_l2f (si1: signedness)                (**r long -> double *)
  | cast_case_l2s (si1: signedness)                (**r long -> single *)
  | cast_case_f2l (si2:signedness)                 (**r double -> long *)
  | cast_case_s2l (si2:signedness)                 (**r single -> long *)
  | cast_case_i2bool                               (**r int -> bool *)
  | cast_case_l2bool                               (**r long -> bool *)
  | cast_case_f2bool                               (**r double -> bool *)
  | cast_case_s2bool                               (**r single -> bool *)
  | cast_case_struct (id1 id2: ident)              (**r struct -> struct *)
  | cast_case_union  (id1 id2: ident)              (**r union -> union *)
  | cast_case_void                                 (**r any -> void *)
  | cast_case_default.(** * Type classification and semantics of operators. *)

(** Most C operators are overloaded (they apply to arguments of various
  types) and their semantics depend on the types of their arguments.
  The following [classify_*] functions take as arguments the types
  of the arguments of an operation.  They return enough information
  to resolve overloading for this operator applications, such as
  ``both arguments are floats'', or ``the first is a pointer
  and the second is an integer''.  This classification is used in the
  compiler (module [Cshmgen]) to resolve overloading statically.

  The [sem_*] functions below compute the result of an operator
  application.  Since operators are overloaded, the result depends
  both on the static types of the arguments and on their run-time values.
  The corresponding [classify_*] function is first called on the
  types of the arguments to resolve static overloading.  It is then
  followed by a case analysis on the values of the arguments. *)

(** ** Casts and truth values *)

Inductive classify_cast_cases : Type :=
  | cast_case_pointer                              (**r between pointer types or intptr_t types *)
  | cast_case_i2i (sz2:intsize) (si2:signedness)   (**r int -> int *)
  | cast_case_f2f                                  (**r double -> double *)
  | cast_case_s2s                                  (**r single -> single *)
  | cast_case_f2s                                  (**r double -> single *)
  | cast_case_s2f                                  (**r single -> double *)
  | cast_case_i2f (si1: signedness)                (**r int -> double *)
  | cast_case_i2s (si1: signedness)                (**r int -> single *)
  | cast_case_f2i (sz2:intsize) (si2:signedness)   (**r double -> int *)
  | cast_case_s2i (sz2:intsize) (si2:signedness)   (**r single -> int *)
  | cast_case_l2l                       (**r long -> long *)
  | cast_case_i2l (si1: signedness)     (**r int -> long *)
  | cast_case_l2i (sz2: intsize) (si2: signedness) (**r long -> int *)
  | cast_case_l2f (si1: signedness)                (**r long -> double *)
  | cast_case_l2s (si1: signedness)                (**r long -> single *)
  | cast_case_f2l (si2:signedness)                 (**r double -> long *)
  | cast_case_s2l (si2:signedness)                 (**r single -> long *)
  | cast_case_i2bool                               (**r int -> bool *)
  | cast_case_l2bool                               (**r long -> bool *)
  | cast_case_f2bool                               (**r double -> bool *)
  | cast_case_s2bool                               (**r single -> bool *)
  | cast_case_struct (id1 id2: ident)              (**r struct -> struct *)
  | cast_case_union  (id1 id2: ident)              (**r union -> union *)
  | cast_case_void                                 (**r any -> void *)
  | cast_case_default.(** * Type classification and semantics of operators. *)

(** Most C operators are overloaded (they apply to arguments of various
  types) and their semantics depend on the types of their arguments.
  The following [classify_*] functions take as arguments the types
  of the arguments of an operation.  They return enough information
  to resolve overloading for this operator applications, such as
  ``both arguments are floats'', or ``the first is a pointer
  and the second is an integer''.  This classification is used in the
  compiler (module [Cshmgen]) to resolve overloading statically.

  The [sem_*] functions below compute the result of an operator
  application.  Since operators are overloaded, the result depends
  both on the static types of the arguments and on their run-time values.
  The corresponding [classify_*] function is first called on the
  types of the arguments to resolve static overloading.  It is then
  followed by a case analysis on the values of the arguments. *)

(** ** Casts and truth values *)

Inductive classify_cast_cases : Type :=
  | cast_case_pointer                              (**r between pointer types or intptr_t types *)
  | cast_case_i2i (sz2:intsize) (si2:signedness)   (**r int -> int *)
  | cast_case_f2f                                  (**r double -> double *)
  | cast_case_s2s                                  (**r single -> single *)
  | cast_case_f2s                                  (**r double -> single *)
  | cast_case_s2f                                  (**r single -> double *)
  | cast_case_i2f (si1: signedness)                (**r int -> double *)
  | cast_case_i2s (si1: signedness)                (**r int -> single *)
  | cast_case_f2i (sz2:intsize) (si2:signedness)   (**r double -> int *)
  | cast_case_s2i (sz2:intsize) (si2:signedness)   (**r single -> int *)
  | cast_case_l2l                       (**r long -> long *)
  | cast_case_i2l (si1: signedness)     (**r int -> long *)
  | cast_case_l2i (sz2: intsize) (si2: signedness) (**r long -> int *)
  | cast_case_l2f (si1: signedness)                (**r long -> double *)
  | cast_case_l2s (si1: signedness)                (**r long -> single *)
  | cast_case_f2l (si2:signedness)                 (**r double -> long *)
  | cast_case_s2l (si2:signedness)                 (**r single -> long *)
  | cast_case_i2bool                               (**r int -> bool *)
  | cast_case_l2bool                               (**r long -> bool *)
  | cast_case_f2bool                               (**r double -> bool *)
  | cast_case_s2bool                               (**r single -> bool *)
  | cast_case_struct (id1 id2: ident)              (**r struct -> struct *)
  | cast_case_union  (id1 id2: ident)              (**r union -> union *)
  | cast_case_void                                 (**r any -> void *)
  | cast_case_default.(** * Type classification and semantics of operators. *)

(** Most C operators are overloaded (they apply to arguments of various
  types) and their semantics depend on the types of their arguments.
  The following [classify_*] functions take as arguments the types
  of the arguments of an operation.  They return enough information
  to resolve overloading for this operator applications, such as
  ``both arguments are floats'', or ``the first is a pointer
  and the second is an integer''.  This classification is used in the
  compiler (module [Cshmgen]) to resolve overloading statically.

  The [sem_*] functions below compute the result of an operator
  application.  Since operators are overloaded, the result depends
  both on the static types of the arguments and on their run-time values.
  The corresponding [classify_*] function is first called on the
  types of the arguments to resolve static overloading.  It is then
  followed by a case analysis on the values of the arguments. *)

(** ** Casts and truth values *)

Inductive classify_cast_cases : Type :=
  | cast_case_pointer                              (**r between pointer types or intptr_t types *)
  | cast_case_i2i (sz2:intsize) (si2:signedness)   (**r int -> int *)
  | cast_case_f2f                                  (**r double -> double *)
  | cast_case_s2s                                  (**r single -> single *)
  | cast_case_f2s                                  (**r double -> single *)
  | cast_case_s2f                                  (**r single -> double *)
  | cast_case_i2f (si1: signedness)                (**r int -> double *)
  | cast_case_i2s (si1: signedness)                (**r int -> single *)
  | cast_case_f2i (sz2:intsize) (si2:signedness)   (**r double -> int *)
  | cast_case_s2i (sz2:intsize) (si2:signedness)   (**r single -> int *)
  | cast_case_l2l                       (**r long -> long *)
  | cast_case_i2l (si1: signedness)     (**r int -> long *)
  | cast_case_l2i (sz2: intsize) (si2: signedness) (**r long -> int *)
  | cast_case_l2f (si1: signedness)                (**r long -> double *)
  | cast_case_l2s (si1: signedness)                (**r long -> single *)
  | cast_case_f2l (si2:signedness)                 (**r double -> long *)
  | cast_case_s2l (si2:signedness)                 (**r single -> long *)
  | cast_case_i2bool                               (**r int -> bool *)
  | cast_case_l2bool                               (**r long -> bool *)
  | cast_case_f2bool                               (**r double -> bool *)
  | cast_case_s2bool                               (**r single -> bool *)
  | cast_case_struct (id1 id2: ident)              (**r struct -> struct *)
  | cast_case_union  (id1 id2: ident)              (**r union -> union *)
  | cast_case_void                                 (**r any -> void *)
  | cast_case_default.(** * Type classification and semantics of operators. *)

(** Most C operators are overloaded (they apply to arguments of various
  types) and their semantics depend on the types of their arguments.
  The following [classify_*] functions take as arguments the types
  of the arguments of an operation.  They return enough information
  to resolve overloading for this operator applications, such as
  ``both arguments are floats'', or ``the first is a pointer
  and the second is an integer''.  This classification is used in the
  compiler (module [Cshmgen]) to resolve overloading statically.

  The [sem_*] functions below compute the result of an operator
  application.  Since operators are overloaded, the result depends
  both on the static types of the arguments and on their run-time values.
  The corresponding [classify_*] function is first called on the
  types of the arguments to resolve static overloading.  It is then
  followed by a case analysis on the values of the arguments. *)

(** ** Casts and truth values *)

Inductive classify_cast_cases : Type :=
  | cast_case_pointer                              (**r between pointer types or intptr_t types *)
  | cast_case_i2i (sz2:intsize) (si2:signedness)   (**r int -> int *)
  | cast_case_f2f                                  (**r double -> double *)
  | cast_case_s2s                                  (**r single -> single *)
  | cast_case_f2s                                  (**r double -> single *)
  | cast_case_s2f                                  (**r single -> double *)
  | cast_case_i2f (si1: signedness)                (**r int -> double *)
  | cast_case_i2s (si1: signedness)                (**r int -> single *)
  | cast_case_f2i (sz2:intsize) (si2:signedness)   (**r double -> int *)
  | cast_case_s2i (sz2:intsize) (si2:signedness)   (**r single -> int *)
  | cast_case_l2l                       (**r long -> long *)
  | cast_case_i2l (si1: signedness)     (**r int -> long *)
  | cast_case_l2i (sz2: intsize) (si2: signedness) (**r long -> int *)
  | cast_case_l2f (si1: signedness)                (**r long -> double *)
  | cast_case_l2s (si1: signedness)                (**r long -> single *)
  | cast_case_f2l (si2:signedness)                 (**r double -> long *)
  | cast_case_s2l (si2:signedness)                 (**r single -> long *)
  | cast_case_i2bool                               (**r int -> bool *)
  | cast_case_l2bool                               (**r long -> bool *)
  | cast_case_f2bool                               (**r double -> bool *)
  | cast_case_s2bool                               (**r single -> bool *)
  | cast_case_struct (id1 id2: ident)              (**r struct -> struct *)
  | cast_case_union  (id1 id2: ident)              (**r union -> union *)
  | cast_case_void                                 (**r any -> void *)
  | cast_case_default.(** * Type classification and semantics of operators. *)

(** Most C operators are overloaded (they apply to arguments of various
  types) and their semantics depend on the types of their arguments.
  The following [classify_*] functions take as arguments the types
  of the arguments of an operation.  They return enough information
  to resolve overloading for this operator applications, such as
  ``both arguments are floats'', or ``the first is a pointer
  and the second is an integer''.  This classification is used in the
  compiler (module [Cshmgen]) to resolve overloading statically.

  The [sem_*] functions below compute the result of an operator
  application.  Since operators are overloaded, the result depends
  both on the static types of the arguments and on their run-time values.
  The corresponding [classify_*] function is first called on the
  types of the arguments to resolve static overloading.  It is then
  followed by a case analysis on the values of the arguments. *)

(** ** Casts and truth values *)

Inductive classify_cast_cases : Type :=
  | cast_case_pointer                              (**r between pointer types or intptr_t types *)
  | cast_case_i2i (sz2:intsize) (si2:signedness)   (**r int -> int *)
  | cast_case_f2f                                  (**r double -> double *)
  | cast_case_s2s                                  (**r single -> single *)
  | cast_case_f2s                                  (**r double -> single *)
  | cast_case_s2f                                  (**r single -> double *)
  | cast_case_i2f (si1: signedness)                (**r int -> double *)
  | cast_case_i2s (si1: signedness)                (**r int -> single *)
  | cast_case_f2i (sz2:intsize) (si2:signedness)   (**r double -> int *)
  | cast_case_s2i (sz2:intsize) (si2:signedness)   (**r single -> int *)
  | cast_case_l2l                       (**r long -> long *)
  | cast_case_i2l (si1: signedness)     (**r int -> long *)
  | cast_case_l2i (sz2: intsize) (si2: signedness) (**r long -> int *)
  | cast_case_l2f (si1: signedness)                (**r long -> double *)
  | cast_case_l2s (si1: signedness)                (**r long -> single *)
  | cast_case_f2l (si2:signedness)                 (**r double -> long *)
  | cast_case_s2l (si2:signedness)                 (**r single -> long *)
  | cast_case_i2bool                               (**r int -> bool *)
  | cast_case_l2bool                               (**r long -> bool *)
  | cast_case_f2bool                               (**r double -> bool *)
  | cast_case_s2bool                               (**r single -> bool *)
  | cast_case_struct (id1 id2: ident)              (**r struct -> struct *)
  | cast_case_union  (id1 id2: ident)              (**r union -> union *)
  | cast_case_void                                 (**r any -> void *)
  | cast_case_default.(** * Type classification and semantics of operators. *)

(** Most C operators are overloaded (they apply to arguments of various
  types) and their semantics depend on the types of their arguments.
  The following [classify_*] functions take as arguments the types
  of the arguments of an operation.  They return enough information
  to resolve overloading for this operator applications, such as
  ``both arguments are floats'', or ``the first is a pointer
  and the second is an integer''.  This classification is used in the
  compiler (module [Cshmgen]) to resolve overloading statically.

  The [sem_*] functions below compute the result of an operator
  application.  Since operators are overloaded, the result depends
  both on the static types of the arguments and on their run-time values.
  The corresponding [classify_*] function is first called on the
  types of the arguments to resolve static overloading.  It is then
  followed by a case analysis on the values of the arguments. *)

(** ** Casts and truth values *)

Inductive classify_cast_cases : Type :=
  | cast_case_pointer                              (**r between pointer types or intptr_t types *)
  | cast_case_i2i (sz2:intsize) (si2:signedness)   (**r int -> int *)
  | cast_case_f2f                                  (**r double -> double *)
  | cast_case_s2s                                  (**r single -> single *)
  | cast_case_f2s                                  (**r double -> single *)
  | cast_case_s2f                                  (**r single -> double *)
  | cast_case_i2f (si1: signedness)                (**r int -> double *)
  | cast_case_i2s (si1: signedness)                (**r int -> single *)
  | cast_case_f2i (sz2:intsize) (si2:signedness)   (**r double -> int *)
  | cast_case_s2i (sz2:intsize) (si2:signedness)   (**r single -> int *)
  | cast_case_l2l                       (**r long -> long *)
  | cast_case_i2l (si1: signedness)     (**r int -> long *)
  | cast_case_l2i (sz2: intsize) (si2: signedness) (**r long -> int *)
  | cast_case_l2f (si1: signedness)                (**r long -> double *)
  | cast_case_l2s (si1: signedness)                (**r long -> single *)
  | cast_case_f2l (si2:signedness)                 (**r double -> long *)
  | cast_case_s2l (si2:signedness)                 (**r single -> long *)
  | cast_case_i2bool                               (**r int -> bool *)
  | cast_case_l2bool                               (**r long -> bool *)
  | cast_case_f2bool                               (**r double -> bool *)
  | cast_case_s2bool                               (**r single -> bool *)
  | cast_case_struct (id1 id2: ident)              (**r struct -> struct *)
  | cast_case_union  (id1 id2: ident)              (**r union -> union *)
  | cast_case_void                                 (**r any -> void *)
  | cast_case_default.(** * Type classification and semantics of operators. *)

(** Most C operators are overloaded (they apply to arguments of various
  types) and their semantics depend on the types of their arguments.
  The following [classify_*] functions take as arguments the types
  of the arguments of an operation.  They return enough information
  to resolve overloading for this operator applications, such as
  ``both arguments are floats'', or ``the first is a pointer
  and the second is an integer''.  This classification is used in the
  compiler (module [Cshmgen]) to resolve overloading statically.

  The [sem_*] functions below compute the result of an operator
  application.  Since operators are overloaded, the result depends
  both on the static types of the arguments and on their run-time values.
  The corresponding [classify_*] function is first called on the
  types of the arguments to resolve static overloading.  It is then
  followed by a case analysis on the values of the arguments. *)

(** ** Casts and truth values *)

Inductive classify_cast_cases : Type :=
  | cast_case_pointer                              (**r between pointer types or intptr_t types *)
  | cast_case_i2i (sz2:intsize) (si2:signedness)   (**r int -> int *)
  | cast_case_f2f                                  (**r double -> double *)
  | cast_case_s2s                                  (**r single -> single *)
  | cast_case_f2s                                  (**r double -> single *)
  | cast_case_s2f                                  (**r single -> double *)
  | cast_case_i2f (si1: signedness)                (**r int -> double *)
  | cast_case_i2s (si1: signedness)                (**r int -> single *)
  | cast_case_f2i (sz2:intsize) (si2:signedness)   (**r double -> int *)
  | cast_case_s2i (sz2:intsize) (si2:signedness)   (**r single -> int *)
  | cast_case_l2l                       (**r long -> long *)
  | cast_case_i2l (si1: signedness)     (**r int -> long *)
  | cast_case_l2i (sz2: intsize) (si2: signedness) (**r long -> int *)
  | cast_case_l2f (si1: signedness)                (**r long -> double *)
  | cast_case_l2s (si1: signedness)                (**r long -> single *)
  | cast_case_f2l (si2:signedness)                 (**r double -> long *)
  | cast_case_s2l (si2:signedness)                 (**r single -> long *)
  | cast_case_i2bool                               (**r int -> bool *)
  | cast_case_l2bool                               (**r long -> bool *)
  | cast_case_f2bool                               (**r double -> bool *)
  | cast_case_s2bool                               (**r single -> bool *)
  | cast_case_struct (id1 id2: ident)              (**r struct -> struct *)
  | cast_case_union  (id1 id2: ident)              (**r union -> union *)
  | cast_case_void                                 (**r any -> void *)
  | cast_case_default.(** * Type classification and semantics of operators. *)

(** Most C operators are overloaded (they apply to arguments of various
  types) and their semantics depend on the types of their arguments.
  The following [classify_*] functions take as arguments the types
  of the arguments of an operation.  They return enough information
  to resolve overloading for this operator applications, such as
  ``both arguments are floats'', or ``the first is a pointer
  and the second is an integer''.  This classification is used in the
  compiler (module [Cshmgen]) to resolve overloading statically.

  The [sem_*] functions below compute the result of an operator
  application.  Since operators are overloaded, the result depends
  both on the static types of the arguments and on their run-time values.
  The corresponding [classify_*] function is first called on the
  types of the arguments to resolve static overloading.  It is then
  followed by a case analysis on the values of the arguments. *)

(** ** Casts and truth values *)

Inductive classify_cast_cases : Type :=
  | cast_case_pointer                              (**r between pointer types or intptr_t types *)
  | cast_case_i2i (sz2:intsize) (si2:signedness)   (**r int -> int *)
  | cast_case_f2f                                  (**r double -> double *)
  | cast_case_s2s                                  (**r single -> single *)
  | cast_case_f2s                                  (**r double -> single *)
  | cast_case_s2f                                  (**r single -> double *)
  | cast_case_i2f (si1: signedness)                (**r int -> double *)
  | cast_case_i2s (si1: signedness)                (**r int -> single *)
  | cast_case_f2i (sz2:intsize) (si2:signedness)   (**r double -> int *)
  | cast_case_s2i (sz2:intsize) (si2:signedness)   (**r single -> int *)
  | cast_case_l2l                       (**r long -> long *)
  | cast_case_i2l (si1: signedness)     (**r int -> long *)
  | cast_case_l2i (sz2: intsize) (si2: signedness) (**r long -> int *)
  | cast_case_l2f (si1: signedness)                (**r long -> double *)
  | cast_case_l2s (si1: signedness)                (**r long -> single *)
  | cast_case_f2l (si2:signedness)                 (**r double -> long *)
  | cast_case_s2l (si2:signedness)                 (**r single -> long *)
  | cast_case_i2bool                               (**r int -> bool *)
  | cast_case_l2bool                               (**r long -> bool *)
  | cast_case_f2bool                               (**r double -> bool *)
  | cast_case_s2bool                               (**r single -> bool *)
  | cast_case_struct (id1 id2: ident)              (**r struct -> struct *)
  | cast_case_union  (id1 id2: ident)              (**r union -> union *)
  | cast_case_void                                 (**r any -> void *)
  | cast_case_default.(** * Type classification and semantics of operators. *)

(** Most C operators are overloaded (they apply to arguments of various
  types) and their semantics depend on the types of their arguments.
  The following [classify_*] functions take as arguments the types
  of the arguments of an operation.  They return enough information
  to resolve overloading for this operator applications, such as
  ``both arguments are floats'', or ``the first is a pointer
  and the second is an integer''.  This classification is used in the
  compiler (module [Cshmgen]) to resolve overloading statically.

  The [sem_*] functions below compute the result of an operator
  application.  Since operators are overloaded, the result depends
  both on the static types of the arguments and on their run-time values.
  The corresponding [classify_*] function is first called on the
  types of the arguments to resolve static overloading.  It is then
  followed by a case analysis on the values of the arguments. *)

(** ** Casts and truth values *)

Inductive classify_cast_cases : Type :=
  | cast_case_pointer                              (**r between pointer types or intptr_t types *)
  | cast_case_i2i (sz2:intsize) (si2:signedness)   (**r int -> int *)
  | cast_case_f2f                                  (**r double -> double *)
  | cast_case_s2s                                  (**r single -> single *)
  | cast_case_f2s                                  (**r double -> single *)
  | cast_case_s2f                                  (**r single -> double *)
  | cast_case_i2f (si1: signedness)                (**r int -> double *)
  | cast_case_i2s (si1: signedness)                (**r int -> single *)
  | cast_case_f2i (sz2:intsize) (si2:signedness)   (**r double -> int *)
  | cast_case_s2i (sz2:intsize) (si2:signedness)   (**r single -> int *)
  | cast_case_l2l                       (**r long -> long *)
  | cast_case_i2l (si1: signedness)     (**r int -> long *)
  | cast_case_l2i (sz2: intsize) (si2: signedness) (**r long -> int *)
  | cast_case_l2f (si1: signedness)                (**r long -> double *)
  | cast_case_l2s (si1: signedness)                (**r long -> single *)
  | cast_case_f2l (si2:signedness)                 (**r double -> long *)
  | cast_case_s2l (si2:signedness)                 (**r single -> long *)
  | cast_case_i2bool                               (**r int -> bool *)
  | cast_case_l2bool                               (**r long -> bool *)
  | cast_case_f2bool                               (**r double -> bool *)
  | cast_case_s2bool                               (**r single -> bool *)
  | cast_case_struct (id1 id2: ident)              (**r struct -> struct *)
  | cast_case_union  (id1 id2: ident)              (**r union -> union *)
  | cast_case_void                                 (**r any -> void *)
  | cast_case_default.(** * Type classification and semantics of operators. *)

(** Most C operators are overloaded (they apply to arguments of various
  types) and their semantics depend on the types of their arguments.
  The following [classify_*] functions take as arguments the types
  of the arguments of an operation.  They return enough information
  to resolve overloading for this operator applications, such as
  ``both arguments are floats'', or ``the first is a pointer
  and the second is an integer''.  This classification is used in the
  compiler (module [Cshmgen]) to resolve overloading statically.

  The [sem_*] functions below compute the result of an operator
  application.  Since operators are overloaded, the result depends
  both on the static types of the arguments and on their run-time values.
  The corresponding [classify_*] function is first called on the
  types of the arguments to resolve static overloading.  It is then
  followed by a case analysis on the values of the arguments. *)

(** ** Casts and truth values *)

Inductive classify_cast_cases : Type :=
  | cast_case_pointer                              (**r between pointer types or intptr_t types *)
  | cast_case_i2i (sz2:intsize) (si2:signedness)   (**r int -> int *)
  | cast_case_f2f                                  (**r double -> double *)
  | cast_case_s2s                                  (**r single -> single *)
  | cast_case_f2s                                  (**r double -> single *)
  | cast_case_s2f                                  (**r single -> double *)
  | cast_case_i2f (si1: signedness)                (**r int -> double *)
  | cast_case_i2s (si1: signedness)                (**r int -> single *)
  | cast_case_f2i (sz2:intsize) (si2:signedness)   (**r double -> int *)
  | cast_case_s2i (sz2:intsize) (si2:signedness)   (**r single -> int *)
  | cast_case_l2l                       (**r long -> long *)
  | cast_case_i2l (si1: signedness)     (**r int -> long *)
  | cast_case_l2i (sz2: intsize) (si2: signedness) (**r long -> int *)
  | cast_case_l2f (si1: signedness)                (**r long -> double *)
  | cast_case_l2s (si1: signedness)                (**r long -> single *)
  | cast_case_f2l (si2:signedness)                 (**r double -> long *)
  | cast_case_s2l (si2:signedness)                 (**r single -> long *)
  | cast_case_i2bool                               (**r int -> bool *)
  | cast_case_l2bool                               (**r long -> bool *)
  | cast_case_f2bool                               (**r double -> bool *)
  | cast_case_s2bool                               (**r single -> bool *)
  | cast_case_struct (id1 id2: ident)              (**r struct -> struct *)
  | cast_case_union  (id1 id2: ident)              (**r union -> union *)
  | cast_case_void                                 (**r any -> void *)
  | cast_case_default.(** * Type classification and semantics of operators. *)

(** Most C operators are overloaded (they apply to arguments of various
  types) and their semantics depend on the types of their arguments.
  The following [classify_*] functions take as arguments the types
  of the arguments of an operation.  They return enough information
  to resolve overloading for this operator applications, such as
  ``both arguments are floats'', or ``the first is a pointer
  and the second is an integer''.  This classification is used in the
  compiler (module [Cshmgen]) to resolve overloading statically.

  The [sem_*] functions below compute the result of an operator
  application.  Since operators are overloaded, the result depends
  both on the static types of the arguments and on their run-time values.
  The corresponding [classify_*] function is first called on the
  types of the arguments to resolve static overloading.  It is then
  followed by a case analysis on the values of the arguments. *)

(** ** Casts and truth values *)

Inductive classify_cast_cases : Type :=
  | cast_case_pointer                              (**r between pointer types or intptr_t types *)
  | cast_case_i2i (sz2:intsize) (si2:signedness)   (**r int -> int *)
  | cast_case_f2f                                  (**r double -> double *)
  | cast_case_s2s                                  (**r single -> single *)
  | cast_case_f2s                                  (**r double -> single *)
  | cast_case_s2f                                  (**r single -> double *)
  | cast_case_i2f (si1: signedness)                (**r int -> double *)
  | cast_case_i2s (si1: signedness)                (**r int -> single *)
  | cast_case_f2i (sz2:intsize) (si2:signedness)   (**r double -> int *)
  | cast_case_s2i (sz2:intsize) (si2:signedness)   (**r single -> int *)
  | cast_case_l2l                       (**r long -> long *)
  | cast_case_i2l (si1: signedness)     (**r int -> long *)
  | cast_case_l2i (sz2: intsize) (si2: signedness) (**r long -> int *)
  | cast_case_l2f (si1: signedness)                (**r long -> double *)
  | cast_case_l2s (si1: signedness)                (**r long -> single *)
  | cast_case_f2l (si2:signedness)                 (**r double -> long *)
  | cast_case_s2l (si2:signedness)                 (**r single -> long *)
  | cast_case_i2bool                               (**r int -> bool *)
  | cast_case_l2bool                               (**r long -> bool *)
  | cast_case_f2bool                               (**r double -> bool *)
  | cast_case_s2bool                               (**r single -> bool *)
  | cast_case_struct (id1 id2: ident)              (**r struct -> struct *)
  | cast_case_union  (id1 id2: ident)              (**r union -> union *)
  | cast_case_void                                 (**r any -> void *)
  | cast_case_default.Definition classify_cast (tfrom tto: type) : classify_cast_cases :=
  match tto, tfrom with
  (* To [void] *)
  | Tvoid, _ => cast_case_void
  (* To [_Bool] *)
  | Tint IBool _ _, Tint _ _ _ => cast_case_i2bool
  | Tint IBool _ _, Tlong _ _ => cast_case_l2bool
  | Tint IBool _ _, Tfloat F64 _ => cast_case_f2bool
  | Tint IBool _ _, Tfloat F32 _ => cast_case_s2bool
  | Tint IBool _ _, (Tpointer _ _ | Tarray _ _ _ | Tfunction _ _ _) => 
      if Archi.ptr64 then cast_case_l2bool else cast_case_i2bool
  (* To [int] other than [_Bool] *)
  | Tint sz2 si2 _, Tint _ _ _ =>
      if Archi.ptr64 then cast_case_i2i sz2 si2
      else if intsize_eq sz2 I32 then cast_case_pointer
      else cast_case_i2i sz2 si2
  | Tint sz2 si2 _, Tlong _ _ => cast_case_l2i sz2 si2
  | Tint sz2 si2 _, Tfloat F64 _ => cast_case_f2i sz2 si2
  | Tint sz2 si2 _, Tfloat F32 _ => cast_case_s2i sz2 si2
  | Tint sz2 si2 _, (Tpointer _ _ | Tarray _ _ _ | Tfunction _ _ _) =>
      if Archi.ptr64 then cast_case_l2i sz2 si2
      else if intsize_eq sz2 I32 then cast_case_pointer
      else cast_case_i2i sz2 si2
  (* To [long] *)
  | Tlong _ _, Tlong _ _ =>
      if Archi.ptr64 then cast_case_pointer else cast_case_l2l
  | Tlong _ _, Tint sz1 si1 _ => cast_case_i2l si1
  | Tlong si2 _, Tfloat F64 _ => cast_case_f2l si2
  | Tlong si2 _, Tfloat F32 _ => cast_case_s2l si2
  | Tlong si2 _, (Tpointer _ _ | Tarray _ _ _ | Tfunction _ _ _) =>
      if Archi.ptr64 then cast_case_pointer else cast_case_i2l si2
  (* To [float] *)
  | Tfloat F64 _, Tint sz1 si1 _ => cast_case_i2f si1
  | Tfloat F32 _, Tint sz1 si1 _ => cast_case_i2s si1
  | Tfloat F64 _, Tlong si1 _ => cast_case_l2f si1
  | Tfloat F32 _, Tlong si1 _ => cast_case_l2s si1
  | Tfloat F64 _, Tfloat F64 _ => cast_case_f2f
  | Tfloat F32 _, Tfloat F32 _ => cast_case_s2s
  | Tfloat F64 _, Tfloat F32 _ => cast_case_s2f
  | Tfloat F32 _, Tfloat F64 _ => cast_case_f2s
  (* To pointer types *)
  | Tpointer _ _, Tint _ _ _ =>
      if Archi.ptr64 then cast_case_i2l Unsigned else cast_case_pointer
  | Tpointer _ _, Tlong _ _ =>
      if Archi.ptr64 then cast_case_pointer else cast_case_l2i I32 Unsigned
  | Tpointer _ _, (Tpointer _ _ | Tarray _ _ _ | Tfunction _ _ _) => cast_case_pointer
  (* To struct or union types *)
  | Tstruct id2 _, Tstruct id1 _ => cast_case_struct id1 id2
  | Tunion id2 _, Tunion id1 _ => cast_case_union id1 id2
  (* Catch-all *)
  | _, _ => cast_case_default
  end.(** Semantics of casts.  [sem_cast v1 t1 t2 m = Some v2] if value [v1],
  viewed with static type [t1], can be converted  to type [t2],
  resulting in value [v2].  *)

Definition cast_int_int (sz: intsize) (sg: signedness) (i: int) : int :=
  match sz, sg with
  | I8, Signed => Int.sign_ext 8 i
  | I8, Unsigned => Int.zero_ext 8 i
  | I16, Signed => Int.sign_ext 16 i
  | I16, Unsigned => Int.zero_ext 16 i
  | I32, _ => i
  | IBool, _ => if Int.eq i Int.zero then Int.zero else Int.one
  end.Definition cast_int_float (si: signedness) (i: int) : float :=
  match si with
  | Signed => Float.of_int i
  | Unsigned => Float.of_intu i
  end.Definition cast_float_int (si : signedness) (f: float) : option int :=
  match si with
  | Signed => Float.to_int f
  | Unsigned => Float.to_intu f
  end.Definition cast_int_single (si: signedness) (i: int) : float32 :=
  match si with
  | Signed => Float32.of_int i
  | Unsigned => Float32.of_intu i
  end.Definition cast_single_int (si : signedness) (f: float32) : option int :=
  match si with
  | Signed => Float32.to_int f
  | Unsigned => Float32.to_intu f
  end.Definition cast_int_long (si: signedness) (i: int) : int64 :=
  match si with
  | Signed => Int64.repr (Int.signed i)
  | Unsigned => Int64.repr (Int.unsigned i)
  end.Definition cast_long_float (si: signedness) (i: int64) : float :=
  match si with
  | Signed => Float.of_long i
  | Unsigned => Float.of_longu i
  end.Definition cast_long_single (si: signedness) (i: int64) : float32 :=
  match si with
  | Signed => Float32.of_long i
  | Unsigned => Float32.of_longu i
  end.Definition cast_float_long (si : signedness) (f: float) : option int64 :=
  match si with
  | Signed => Float.to_long f
  | Unsigned => Float.to_longu f
  end.Definition cast_single_long (si : signedness) (f: float32) : option int64 :=
  match si with
  | Signed => Float32.to_long f
  | Unsigned => Float32.to_longu f
  end.Definition sem_cast (v: val) (t1 t2: type) (m: mem): option val :=
  match classify_cast t1 t2 with
  | cast_case_pointer =>
      match v with
      | Vptr _ _ => Some v
      | Vint _ => if Archi.ptr64 then None else Some v
      | Vlong _ => if Archi.ptr64 then Some v else None
      | _ => None
      end
  | cast_case_i2i sz2 si2 =>
      match v with
      | Vint i => Some (Vint (cast_int_int sz2 si2 i))
      | _ => None
      end
  | cast_case_f2f =>
      match v with
      | Vfloat f => Some (Vfloat f)
      | _ => None
      end
  | cast_case_s2s =>
      match v with
      | Vsingle f => Some (Vsingle f)
      | _ => None
      end
  | cast_case_s2f =>
      match v with
      | Vsingle f => Some (Vfloat (Float.of_single f))
      | _ => None
      end
  | cast_case_f2s =>
      match v with
      | Vfloat f => Some (Vsingle (Float.to_single f))
      | _ => None
      end
  | cast_case_i2f si1 =>
      match v with
      | Vint i => Some (Vfloat (cast_int_float si1 i))
      | _ => None
      end
  | cast_case_i2s si1 =>
      match v with
      | Vint i => Some (Vsingle (cast_int_single si1 i))
      | _ => None
      end
  | cast_case_f2i sz2 si2 =>
      match v with
      | Vfloat f =>
          match cast_float_int si2 f with
          | Some i => Some (Vint (cast_int_int sz2 si2 i))
          | None => None
          end
      | _ => None
      end
  | cast_case_s2i sz2 si2 =>
      match v with
      | Vsingle f =>
          match cast_single_int si2 f with
          | Some i => Some (Vint (cast_int_int sz2 si2 i))
          | None => None
          end
      | _ => None
      end
  | cast_case_i2bool =>
      match v with
      | Vint n =>
          Some(Vint(if Int.eq n Int.zero then Int.zero else Int.one))
      | Vptr b ofs =>
          if Archi.ptr64 then None else
          if Mem.weak_valid_pointer m b (Ptrofs.unsigned ofs) then Some Vone else None
      | _ => None
      end
  | cast_case_l2bool =>
      match v with
      | Vlong n =>
          Some(Vint(if Int64.eq n Int64.zero then Int.zero else Int.one))
      | Vptr b ofs =>
          if negb Archi.ptr64 then None else
          if Mem.weak_valid_pointer m b (Ptrofs.unsigned ofs) then Some Vone else None

      | _ => None
      end
  | cast_case_f2bool =>
      match v with
      | Vfloat f =>
          Some(Vint(if Float.cmp Ceq f Float.zero then Int.zero else Int.one))
      | _ => None
      end
  | cast_case_s2bool =>
      match v with
      | Vsingle f =>
          Some(Vint(if Float32.cmp Ceq f Float32.zero then Int.zero else Int.one))
      | _ => None
      end
  | cast_case_l2l =>
      match v with
      | Vlong n => Some (Vlong n)
      | _ => None
      end
  | cast_case_i2l si =>
      match v with
      | Vint n => Some(Vlong (cast_int_long si n))
      | _ => None
      end
  | cast_case_l2i sz si =>
      match v with
      | Vlong n => Some(Vint (cast_int_int sz si (Int.repr (Int64.unsigned n))))
      | _ => None
      end
  | cast_case_l2f si1 =>
      match v with
      | Vlong i => Some (Vfloat (cast_long_float si1 i))
      | _ => None
      end
  | cast_case_l2s si1 =>
      match v with
      | Vlong i => Some (Vsingle (cast_long_single si1 i))
      | _ => None
      end
  | cast_case_f2l si2 =>
      match v with
      | Vfloat f =>
          match cast_float_long si2 f with
          | Some i => Some (Vlong i)
          | None => None
          end
      | _ => None
      end
  | cast_case_s2l si2 =>
      match v with
      | Vsingle f =>
          match cast_single_long si2 f with
          | Some i => Some (Vlong i)
          | None => None
          end
      | _ => None
      end
  | cast_case_struct id1 id2 =>
      match v with
      | Vptr b ofs =>
          if ident_eq id1 id2 then Some v else None
      | _ => None
      end
  | cast_case_union id1 id2 =>
      match v with
      | Vptr b ofs =>
          if ident_eq id1 id2 then Some v else None
      | _ => None
      end
  | cast_case_void =>
      Some v
  | cast_case_default =>
      None
  end.(** The following describes types that can be interpreted as a boolean:
  integers, floats, pointers.  It is used for the semantics of
  the [!] and [?] operators, as well as the [if], [while],
  and [for] statements. *)

Inductive classify_bool_cases : Type :=
  | bool_case_i                           (**r integer *)
  | bool_case_l                           (**r long *)
  | bool_case_f                           (**r double float *)
  | bool_case_s                           (**r single float *)
  | bool_default.(** The following describes types that can be interpreted as a boolean:
  integers, floats, pointers.  It is used for the semantics of
  the [!] and [?] operators, as well as the [if], [while],
  and [for] statements. *)

Inductive classify_bool_cases : Type :=
  | bool_case_i                           (**r integer *)
  | bool_case_l                           (**r long *)
  | bool_case_f                           (**r double float *)
  | bool_case_s                           (**r single float *)
  | bool_default.(** The following describes types that can be interpreted as a boolean:
  integers, floats, pointers.  It is used for the semantics of
  the [!] and [?] operators, as well as the [if], [while],
  and [for] statements. *)

Inductive classify_bool_cases : Type :=
  | bool_case_i                           (**r integer *)
  | bool_case_l                           (**r long *)
  | bool_case_f                           (**r double float *)
  | bool_case_s                           (**r single float *)
  | bool_default.(** The following describes types that can be interpreted as a boolean:
  integers, floats, pointers.  It is used for the semantics of
  the [!] and [?] operators, as well as the [if], [while],
  and [for] statements. *)

Inductive classify_bool_cases : Type :=
  | bool_case_i                           (**r integer *)
  | bool_case_l                           (**r long *)
  | bool_case_f                           (**r double float *)
  | bool_case_s                           (**r single float *)
  | bool_default.(** The following describes types that can be interpreted as a boolean:
  integers, floats, pointers.  It is used for the semantics of
  the [!] and [?] operators, as well as the [if], [while],
  and [for] statements. *)

Inductive classify_bool_cases : Type :=
  | bool_case_i                           (**r integer *)
  | bool_case_l                           (**r long *)
  | bool_case_f                           (**r double float *)
  | bool_case_s                           (**r single float *)
  | bool_default.(** The following describes types that can be interpreted as a boolean:
  integers, floats, pointers.  It is used for the semantics of
  the [!] and [?] operators, as well as the [if], [while],
  and [for] statements. *)

Inductive classify_bool_cases : Type :=
  | bool_case_i                           (**r integer *)
  | bool_case_l                           (**r long *)
  | bool_case_f                           (**r double float *)
  | bool_case_s                           (**r single float *)
  | bool_default.Definition classify_bool (ty: type) : classify_bool_cases :=
  match typeconv ty with
  | Tint _ _ _ => bool_case_i
  | Tpointer _ _ => if Archi.ptr64 then bool_case_l else bool_case_i
  | Tfloat F64 _ => bool_case_f
  | Tfloat F32 _ => bool_case_s
  | Tlong _ _ => bool_case_l
  | _ => bool_default
  end.(** Interpretation of values as truth values.
  Non-zero integers, non-zero floats and non-null pointers are
  considered as true.  The integer zero (which also represents
  the null pointer) and the float 0.0 are false. *)

Definition bool_val (v: val) (t: type) (m: mem) : option bool :=
  match classify_bool t with
  | bool_case_i =>
      match v with
      | Vint n => Some (negb (Int.eq n Int.zero))
      | Vptr b ofs =>
          if Archi.ptr64 then None else
          if Mem.weak_valid_pointer m b (Ptrofs.unsigned ofs) then Some true else None
      | _ => None
      end
  | bool_case_l =>
      match v with
      | Vlong n => Some (negb (Int64.eq n Int64.zero))
      | Vptr b ofs =>
          if negb Archi.ptr64 then None else
          if Mem.weak_valid_pointer m b (Ptrofs.unsigned ofs) then Some true else None
      | _ => None
      end
  | bool_case_f =>
      match v with
      | Vfloat f => Some (negb (Float.cmp Ceq f Float.zero))
      | _ => None
      end
  | bool_case_s =>
      match v with
      | Vsingle f => Some (negb (Float32.cmp Ceq f Float32.zero))
      | _ => None
      end
  | bool_default => None
  end.(** ** Unary operators *)

(** *** Boolean negation *)

Definition sem_notbool (v: val) (ty: type) (m: mem): option val :=
  option_map (fun b => Val.of_bool (negb b)) (bool_val v ty m).(** *** Opposite and absolute value *)

Inductive classify_neg_cases : Type :=
  | neg_case_i(s: signedness)              (**r int *)
  | neg_case_f                             (**r double float *)
  | neg_case_s                             (**r single float *)
  | neg_case_l(s: signedness)              (**r long *)
  | neg_default.(** *** Opposite and absolute value *)

Inductive classify_neg_cases : Type :=
  | neg_case_i(s: signedness)              (**r int *)
  | neg_case_f                             (**r double float *)
  | neg_case_s                             (**r single float *)
  | neg_case_l(s: signedness)              (**r long *)
  | neg_default.(** *** Opposite and absolute value *)

Inductive classify_neg_cases : Type :=
  | neg_case_i(s: signedness)              (**r int *)
  | neg_case_f                             (**r double float *)
  | neg_case_s                             (**r single float *)
  | neg_case_l(s: signedness)              (**r long *)
  | neg_default.(** *** Opposite and absolute value *)

Inductive classify_neg_cases : Type :=
  | neg_case_i(s: signedness)              (**r int *)
  | neg_case_f                             (**r double float *)
  | neg_case_s                             (**r single float *)
  | neg_case_l(s: signedness)              (**r long *)
  | neg_default.(** *** Opposite and absolute value *)

Inductive classify_neg_cases : Type :=
  | neg_case_i(s: signedness)              (**r int *)
  | neg_case_f                             (**r double float *)
  | neg_case_s                             (**r single float *)
  | neg_case_l(s: signedness)              (**r long *)
  | neg_default.(** *** Opposite and absolute value *)

Inductive classify_neg_cases : Type :=
  | neg_case_i(s: signedness)              (**r int *)
  | neg_case_f                             (**r double float *)
  | neg_case_s                             (**r single float *)
  | neg_case_l(s: signedness)              (**r long *)
  | neg_default.Definition classify_neg (ty: type) : classify_neg_cases :=
  match ty with
  | Tint I32 Unsigned _ => neg_case_i Unsigned
  | Tint _ _ _ => neg_case_i Signed
  | Tfloat F64 _ => neg_case_f
  | Tfloat F32 _ => neg_case_s
  | Tlong si _ => neg_case_l si
  | _ => neg_default
  end.Definition sem_neg (v: val) (ty: type) : option val :=
  match classify_neg ty with
  | neg_case_i sg =>
      match v with
      | Vint n => Some (Vint (Int.neg n))
      | _ => None
      end
  | neg_case_f =>
      match v with
      | Vfloat f => Some (Vfloat (Float.neg f))
      | _ => None
      end
  | neg_case_s =>
      match v with
      | Vsingle f => Some (Vsingle (Float32.neg f))
      | _ => None
      end
  | neg_case_l sg =>
      match v with
      | Vlong n => Some (Vlong (Int64.neg n))
      | _ => None
      end
  | neg_default => None
  end.Definition sem_absfloat (v: val) (ty: type) : option val :=
  match classify_neg ty with
  | neg_case_i sg =>
      match v with
      | Vint n => Some (Vfloat (Float.abs (cast_int_float sg n)))
      | _ => None
      end
  | neg_case_f =>
      match v with
      | Vfloat f => Some (Vfloat (Float.abs f))
      | _ => None
      end
  | neg_case_s =>
      match v with
      | Vsingle f => Some (Vfloat (Float.abs (Float.of_single f)))
      | _ => None
      end
  | neg_case_l sg =>
      match v with
      | Vlong n => Some (Vfloat (Float.abs (cast_long_float sg n)))
      | _ => None
      end
  | neg_default => None
  end.(** *** Bitwise complement *)

Inductive classify_notint_cases : Type :=
  | notint_case_i(s: signedness)              (**r int *)
  | notint_case_l(s: signedness)              (**r long *)
  | notint_default.(** *** Bitwise complement *)

Inductive classify_notint_cases : Type :=
  | notint_case_i(s: signedness)              (**r int *)
  | notint_case_l(s: signedness)              (**r long *)
  | notint_default.(** *** Bitwise complement *)

Inductive classify_notint_cases : Type :=
  | notint_case_i(s: signedness)              (**r int *)
  | notint_case_l(s: signedness)              (**r long *)
  | notint_default.(** *** Bitwise complement *)

Inductive classify_notint_cases : Type :=
  | notint_case_i(s: signedness)              (**r int *)
  | notint_case_l(s: signedness)              (**r long *)
  | notint_default.Definition classify_notint (ty: type) : classify_notint_cases :=
  match ty with
  | Tint I32 Unsigned _ => notint_case_i Unsigned
  | Tint _ _ _ => notint_case_i Signed
  | Tlong si _ => notint_case_l si
  | _ => notint_default
  end.Definition sem_notint (v: val) (ty: type): option val :=
  match classify_notint ty with
  | notint_case_i sg =>
      match v with
      | Vint n => Some (Vint (Int.not n))
      | _ => None
      end
  | notint_case_l sg =>
      match v with
      | Vlong n => Some (Vlong (Int64.not n))
      | _ => None
      end
  | notint_default => None
  end.(** ** Binary operators *)

(** For binary operations, the "usual binary conversions" consist in
- determining the type at which the operation is to be performed
  (a form of least upper bound of the types of the two arguments);
- casting the two arguments to this common type;
- performing the operation at that type.
*)

Inductive binarith_cases: Type :=
  | bin_case_i (s: signedness)         (**r at int type *)
  | bin_case_l (s: signedness)         (**r at long int type *)
  | bin_case_f                         (**r at double float type *)
  | bin_case_s                         (**r at single float type *)
  | bin_default.(** ** Binary operators *)

(** For binary operations, the "usual binary conversions" consist in
- determining the type at which the operation is to be performed
  (a form of least upper bound of the types of the two arguments);
- casting the two arguments to this common type;
- performing the operation at that type.
*)

Inductive binarith_cases: Type :=
  | bin_case_i (s: signedness)         (**r at int type *)
  | bin_case_l (s: signedness)         (**r at long int type *)
  | bin_case_f                         (**r at double float type *)
  | bin_case_s                         (**r at single float type *)
  | bin_default.(** ** Binary operators *)

(** For binary operations, the "usual binary conversions" consist in
- determining the type at which the operation is to be performed
  (a form of least upper bound of the types of the two arguments);
- casting the two arguments to this common type;
- performing the operation at that type.
*)

Inductive binarith_cases: Type :=
  | bin_case_i (s: signedness)         (**r at int type *)
  | bin_case_l (s: signedness)         (**r at long int type *)
  | bin_case_f                         (**r at double float type *)
  | bin_case_s                         (**r at single float type *)
  | bin_default.(** ** Binary operators *)

(** For binary operations, the "usual binary conversions" consist in
- determining the type at which the operation is to be performed
  (a form of least upper bound of the types of the two arguments);
- casting the two arguments to this common type;
- performing the operation at that type.
*)

Inductive binarith_cases: Type :=
  | bin_case_i (s: signedness)         (**r at int type *)
  | bin_case_l (s: signedness)         (**r at long int type *)
  | bin_case_f                         (**r at double float type *)
  | bin_case_s                         (**r at single float type *)
  | bin_default.(** ** Binary operators *)

(** For binary operations, the "usual binary conversions" consist in
- determining the type at which the operation is to be performed
  (a form of least upper bound of the types of the two arguments);
- casting the two arguments to this common type;
- performing the operation at that type.
*)

Inductive binarith_cases: Type :=
  | bin_case_i (s: signedness)         (**r at int type *)
  | bin_case_l (s: signedness)         (**r at long int type *)
  | bin_case_f                         (**r at double float type *)
  | bin_case_s                         (**r at single float type *)
  | bin_default.(** ** Binary operators *)

(** For binary operations, the "usual binary conversions" consist in
- determining the type at which the operation is to be performed
  (a form of least upper bound of the types of the two arguments);
- casting the two arguments to this common type;
- performing the operation at that type.
*)

Inductive binarith_cases: Type :=
  | bin_case_i (s: signedness)         (**r at int type *)
  | bin_case_l (s: signedness)         (**r at long int type *)
  | bin_case_f                         (**r at double float type *)
  | bin_case_s                         (**r at single float type *)
  | bin_default.(**r error *)

Definition classify_binarith (ty1: type) (ty2: type) : binarith_cases :=
  match ty1, ty2 with
  | Tint I32 Unsigned _, Tint _ _ _ => bin_case_i Unsigned
  | Tint _ _ _, Tint I32 Unsigned _ => bin_case_i Unsigned
  | Tint _ _ _, Tint _ _ _ => bin_case_i Signed
  | Tlong Signed _, Tlong Signed _ => bin_case_l Signed
  | Tlong _ _, Tlong _ _ => bin_case_l Unsigned
  | Tlong sg _, Tint _ _ _ => bin_case_l sg
  | Tint _ _ _, Tlong sg _ => bin_case_l sg
  | Tfloat F32 _, Tfloat F32 _ => bin_case_s
  | Tfloat _ _, Tfloat _ _ => bin_case_f
  | Tfloat F64 _, (Tint _ _ _ | Tlong _ _) => bin_case_f
  | (Tint _ _ _ | Tlong _ _), Tfloat F64 _ => bin_case_f
  | Tfloat F32 _, (Tint _ _ _ | Tlong _ _) => bin_case_s
  | (Tint _ _ _ | Tlong _ _), Tfloat F32 _ => bin_case_s
  | _, _ => bin_default
  end.(** The static type of the result. Both arguments are converted to this type
    before the actual computation. *)

Definition binarith_type (c: binarith_cases) : type :=
  match c with
  | bin_case_i sg => Tint I32 sg noattr
  | bin_case_l sg => Tlong sg noattr
  | bin_case_f    => Tfloat F64 noattr
  | bin_case_s    => Tfloat F32 noattr
  | bin_default   => Tvoid
  end.Definition sem_binarith
    (sem_int: signedness -> int -> int -> option val)
    (sem_long: signedness -> int64 -> int64 -> option val)
    (sem_float: float -> float -> option val)
    (sem_single: float32 -> float32 -> option val)
    (v1: val) (t1: type) (v2: val) (t2: type) (m: mem): option val :=
  let c := classify_binarith t1 t2 in
  let t := binarith_type c in
  match sem_cast v1 t1 t m with
  | None => None
  | Some v1' =>
  match sem_cast v2 t2 t m with
  | None => None
  | Some v2' =>
  match c with
  | bin_case_i sg =>
      match v1', v2' with
      | Vint n1, Vint n2 => sem_int sg n1 n2
      | _,  _ => None
      end
  | bin_case_f =>
      match v1', v2' with
      | Vfloat n1, Vfloat n2 => sem_float n1 n2
      | _,  _ => None
      end
  | bin_case_s =>
      match v1', v2' with
      | Vsingle n1, Vsingle n2 => sem_single n1 n2
      | _,  _ => None
      end
  | bin_case_l sg =>
      match v1', v2' with
      | Vlong n1, Vlong n2 => sem_long sg n1 n2
      | _,  _ => None
      end
  | bin_default => None
  end end end.(** *** Addition *)

Inductive classify_add_cases : Type :=
  | add_case_pi (ty: type) (si: signedness)     (**r pointer, int *)
  | add_case_pl (ty: type)     (**r pointer, long *)
  | add_case_ip (si: signedness) (ty: type)     (**r int, pointer *)
  | add_case_lp (ty: type)     (**r long, pointer *)
  | add_default.(** *** Addition *)

Inductive classify_add_cases : Type :=
  | add_case_pi (ty: type) (si: signedness)     (**r pointer, int *)
  | add_case_pl (ty: type)     (**r pointer, long *)
  | add_case_ip (si: signedness) (ty: type)     (**r int, pointer *)
  | add_case_lp (ty: type)     (**r long, pointer *)
  | add_default.(** *** Addition *)

Inductive classify_add_cases : Type :=
  | add_case_pi (ty: type) (si: signedness)     (**r pointer, int *)
  | add_case_pl (ty: type)     (**r pointer, long *)
  | add_case_ip (si: signedness) (ty: type)     (**r int, pointer *)
  | add_case_lp (ty: type)     (**r long, pointer *)
  | add_default.(** *** Addition *)

Inductive classify_add_cases : Type :=
  | add_case_pi (ty: type) (si: signedness)     (**r pointer, int *)
  | add_case_pl (ty: type)     (**r pointer, long *)
  | add_case_ip (si: signedness) (ty: type)     (**r int, pointer *)
  | add_case_lp (ty: type)     (**r long, pointer *)
  | add_default.(** *** Addition *)

Inductive classify_add_cases : Type :=
  | add_case_pi (ty: type) (si: signedness)     (**r pointer, int *)
  | add_case_pl (ty: type)     (**r pointer, long *)
  | add_case_ip (si: signedness) (ty: type)     (**r int, pointer *)
  | add_case_lp (ty: type)     (**r long, pointer *)
  | add_default.(** *** Addition *)

Inductive classify_add_cases : Type :=
  | add_case_pi (ty: type) (si: signedness)     (**r pointer, int *)
  | add_case_pl (ty: type)     (**r pointer, long *)
  | add_case_ip (si: signedness) (ty: type)     (**r int, pointer *)
  | add_case_lp (ty: type)     (**r long, pointer *)
  | add_default.(**r numerical type, numerical type *)

Definition classify_add (ty1: type) (ty2: type) :=
  match typeconv ty1, typeconv ty2 with
  | Tpointer ty _, Tint _ si _ => add_case_pi ty si
  | Tpointer ty _, Tlong _ _ => add_case_pl ty
  | Tint _ si _, Tpointer ty _ => add_case_ip si ty
  | Tlong _ _, Tpointer ty _ => add_case_lp ty
  | _, _ => add_default
  end.Definition ptrofs_of_int (si: signedness) (n: int) : ptrofs :=
  match si with
  | Signed => Ptrofs.of_ints n
  | Unsigned => Ptrofs.of_intu n
  end.Definition sem_add_ptr_int (cenv: composite_env) (ty: type) (si: signedness) (v1 v2: val): option val :=
  match v1, v2 with
  | Vptr b1 ofs1, Vint n2 =>
      let n2 := ptrofs_of_int si n2 in
      Some (Vptr b1 (Ptrofs.add ofs1 (Ptrofs.mul (Ptrofs.repr (sizeof cenv ty)) n2)))
  | Vint n1, Vint n2 =>
      if Archi.ptr64 then None else Some (Vint (Int.add n1 (Int.mul (Int.repr (sizeof cenv ty)) n2)))
  | Vlong n1, Vint n2 =>
      let n2 := cast_int_long si n2 in
      if Archi.ptr64 then Some (Vlong (Int64.add n1 (Int64.mul (Int64.repr (sizeof cenv ty)) n2))) else None
  | _,  _ => None
  end.Definition sem_add_ptr_long (cenv: composite_env) (ty: type) (v1 v2: val): option val :=
  match v1, v2 with
  | Vptr b1 ofs1, Vlong n2 =>
      let n2 := Ptrofs.of_int64 n2 in
      Some (Vptr b1 (Ptrofs.add ofs1 (Ptrofs.mul (Ptrofs.repr (sizeof cenv ty)) n2)))
  | Vint n1, Vlong n2 =>
      let n2 := Int.repr (Int64.unsigned n2) in
      if Archi.ptr64 then None else Some (Vint (Int.add n1 (Int.mul (Int.repr (sizeof cenv ty)) n2)))
  | Vlong n1, Vlong n2 =>
      if Archi.ptr64 then Some (Vlong (Int64.add n1 (Int64.mul (Int64.repr (sizeof cenv ty)) n2))) else None
  | _,  _ => None
  end.Definition sem_add (cenv: composite_env) (v1:val) (t1:type) (v2: val) (t2:type) (m: mem): option val :=
  match classify_add t1 t2 with
  | add_case_pi ty si =>             (**r pointer plus integer *)
      sem_add_ptr_int cenv ty si v1 v2
  | add_case_pl ty =>                (**r pointer plus long *)
      sem_add_ptr_long cenv ty v1 v2
  | add_case_ip si ty =>             (**r integer plus pointer *)
      sem_add_ptr_int cenv ty si v2 v1
  | add_case_lp ty =>                (**r long plus pointer *)
      sem_add_ptr_long cenv ty v2 v1
  | add_default =>
      sem_binarith
        (fun sg n1 n2 => Some(Vint(Int.add n1 n2)))
        (fun sg n1 n2 => Some(Vlong(Int64.add n1 n2)))
        (fun n1 n2 => Some(Vfloat(Float.add n1 n2)))
        (fun n1 n2 => Some(Vsingle(Float32.add n1 n2)))
        v1 t1 v2 t2 m
  end.(** *** Subtraction *)

Inductive classify_sub_cases : Type :=
  | sub_case_pi (ty: type) (si: signedness)  (**r pointer, int *)
  | sub_case_pp (ty: type)               (**r pointer, pointer *)
  | sub_case_pl (ty: type)               (**r pointer, long *)
  | sub_default.(** *** Subtraction *)

Inductive classify_sub_cases : Type :=
  | sub_case_pi (ty: type) (si: signedness)  (**r pointer, int *)
  | sub_case_pp (ty: type)               (**r pointer, pointer *)
  | sub_case_pl (ty: type)               (**r pointer, long *)
  | sub_default.(** *** Subtraction *)

Inductive classify_sub_cases : Type :=
  | sub_case_pi (ty: type) (si: signedness)  (**r pointer, int *)
  | sub_case_pp (ty: type)               (**r pointer, pointer *)
  | sub_case_pl (ty: type)               (**r pointer, long *)
  | sub_default.(** *** Subtraction *)

Inductive classify_sub_cases : Type :=
  | sub_case_pi (ty: type) (si: signedness)  (**r pointer, int *)
  | sub_case_pp (ty: type)               (**r pointer, pointer *)
  | sub_case_pl (ty: type)               (**r pointer, long *)
  | sub_default.(** *** Subtraction *)

Inductive classify_sub_cases : Type :=
  | sub_case_pi (ty: type) (si: signedness)  (**r pointer, int *)
  | sub_case_pp (ty: type)               (**r pointer, pointer *)
  | sub_case_pl (ty: type)               (**r pointer, long *)
  | sub_default.(**r numerical type, numerical type *)

Definition classify_sub (ty1: type) (ty2: type) :=
  match typeconv ty1, typeconv ty2 with
  | Tpointer ty _, Tint _ si _ => sub_case_pi ty si
  | Tpointer ty _ , Tpointer _ _ => sub_case_pp ty
  | Tpointer ty _, Tlong _ _ => sub_case_pl ty
  | _, _ => sub_default
  end.Definition sem_sub (cenv: composite_env) (v1:val) (t1:type) (v2: val) (t2:type) (m:mem): option val :=
  match classify_sub t1 t2 with
  | sub_case_pi ty si =>            (**r pointer minus integer *)
      match v1, v2 with
      | Vptr b1 ofs1, Vint n2 =>
          let n2 := ptrofs_of_int si n2 in
          Some (Vptr b1 (Ptrofs.sub ofs1 (Ptrofs.mul (Ptrofs.repr (sizeof cenv ty)) n2)))
      | Vint n1, Vint n2 =>
          if Archi.ptr64 then None else Some (Vint (Int.sub n1 (Int.mul (Int.repr (sizeof cenv ty)) n2)))
      | Vlong n1, Vint n2 =>
          let n2 := cast_int_long si n2 in
          if Archi.ptr64 then Some (Vlong (Int64.sub n1 (Int64.mul (Int64.repr (sizeof cenv ty)) n2))) else None
      | _,  _ => None
      end
  | sub_case_pl ty =>            (**r pointer minus long *)
      match v1, v2 with
      | Vptr b1 ofs1, Vlong n2 =>
          let n2 := Ptrofs.of_int64 n2 in
          Some (Vptr b1 (Ptrofs.sub ofs1 (Ptrofs.mul (Ptrofs.repr (sizeof cenv ty)) n2)))
      | Vint n1, Vlong n2 =>
          let n2 := Int.repr (Int64.unsigned n2) in
          if Archi.ptr64 then None else Some (Vint (Int.sub n1 (Int.mul (Int.repr (sizeof cenv ty)) n2)))
      | Vlong n1, Vlong n2 =>
          if Archi.ptr64 then Some (Vlong (Int64.sub n1 (Int64.mul (Int64.repr (sizeof cenv ty)) n2))) else None
      | _,  _ => None
      end
  | sub_case_pp ty =>          (**r pointer minus pointer *)
      match v1,v2 with
      | Vptr b1 ofs1, Vptr b2 ofs2 =>
          if eq_block b1 b2 then
            let sz := sizeof cenv ty in
            if zlt 0 sz && zle sz Ptrofs.max_signed
            then Some (Vptrofs (Ptrofs.divs (Ptrofs.sub ofs1 ofs2) (Ptrofs.repr sz)))
            else None
          else None
      | _, _ => None
      end
  | sub_default =>
      sem_binarith
        (fun sg n1 n2 => Some(Vint(Int.sub n1 n2)))
        (fun sg n1 n2 => Some(Vlong(Int64.sub n1 n2)))
        (fun n1 n2 => Some(Vfloat(Float.sub n1 n2)))
        (fun n1 n2 => Some(Vsingle(Float32.sub n1 n2)))
        v1 t1 v2 t2 m
  end.(** *** Multiplication, division, modulus *)

Definition sem_mul (v1:val) (t1:type) (v2: val) (t2:type) (m:mem) : option val :=
  sem_binarith
    (fun sg n1 n2 => Some(Vint(Int.mul n1 n2)))
    (fun sg n1 n2 => Some(Vlong(Int64.mul n1 n2)))
    (fun n1 n2 => Some(Vfloat(Float.mul n1 n2)))
    (fun n1 n2 => Some(Vsingle(Float32.mul n1 n2)))
    v1 t1 v2 t2 m.Definition sem_div (v1:val) (t1:type) (v2: val) (t2:type) (m:mem) : option val :=
  sem_binarith
    (fun sg n1 n2 =>
      match sg with
      | Signed =>
          if Int.eq n2 Int.zero
          || Int.eq n1 (Int.repr Int.min_signed) && Int.eq n2 Int.mone
          then None else Some(Vint(Int.divs n1 n2))
      | Unsigned =>
          if Int.eq n2 Int.zero
          then None else Some(Vint(Int.divu n1 n2))
      end)
    (fun sg n1 n2 =>
      match sg with
      | Signed =>
          if Int64.eq n2 Int64.zero
          || Int64.eq n1 (Int64.repr Int64.min_signed) && Int64.eq n2 Int64.mone
          then None else Some(Vlong(Int64.divs n1 n2))
      | Unsigned =>
          if Int64.eq n2 Int64.zero
          then None else Some(Vlong(Int64.divu n1 n2))
      end)
    (fun n1 n2 => Some(Vfloat(Float.div n1 n2)))
    (fun n1 n2 => Some(Vsingle(Float32.div n1 n2)))
    v1 t1 v2 t2 m.Definition sem_mod (v1:val) (t1:type) (v2: val) (t2:type) (m:mem) : option val :=
  sem_binarith
    (fun sg n1 n2 =>
      match sg with
      | Signed =>
          if Int.eq n2 Int.zero
          || Int.eq n1 (Int.repr Int.min_signed) && Int.eq n2 Int.mone
          then None else Some(Vint(Int.mods n1 n2))
      | Unsigned =>
          if Int.eq n2 Int.zero
          then None else Some(Vint(Int.modu n1 n2))
      end)
    (fun sg n1 n2 =>
      match sg with
      | Signed =>
          if Int64.eq n2 Int64.zero
          || Int64.eq n1 (Int64.repr Int64.min_signed) && Int64.eq n2 Int64.mone
          then None else Some(Vlong(Int64.mods n1 n2))
      | Unsigned =>
          if Int64.eq n2 Int64.zero
          then None else Some(Vlong(Int64.modu n1 n2))
      end)
    (fun n1 n2 => None)
    (fun n1 n2 => None)
    v1 t1 v2 t2 m.Definition sem_and (v1:val) (t1:type) (v2: val) (t2:type) (m:mem) : option val :=
  sem_binarith
    (fun sg n1 n2 => Some(Vint(Int.and n1 n2)))
    (fun sg n1 n2 => Some(Vlong(Int64.and n1 n2)))
    (fun n1 n2 => None)
    (fun n1 n2 => None)
    v1 t1 v2 t2 m.Definition sem_or (v1:val) (t1:type) (v2: val) (t2:type) (m:mem) : option val :=
  sem_binarith
    (fun sg n1 n2 => Some(Vint(Int.or n1 n2)))
    (fun sg n1 n2 => Some(Vlong(Int64.or n1 n2)))
    (fun n1 n2 => None)
    (fun n1 n2 => None)
    v1 t1 v2 t2 m.Definition sem_xor (v1:val) (t1:type) (v2: val) (t2:type) (m:mem) : option val :=
  sem_binarith
    (fun sg n1 n2 => Some(Vint(Int.xor n1 n2)))
    (fun sg n1 n2 => Some(Vlong(Int64.xor n1 n2)))
    (fun n1 n2 => None)
    (fun n1 n2 => None)
    v1 t1 v2 t2 m.(** *** Shifts *)

(** Shifts do not perform the usual binary conversions.  Instead,
  each argument is converted independently, and the signedness
  of the result is always that of the first argument. *)

Inductive classify_shift_cases : Type:=
  | shift_case_ii(s: signedness)         (**r int , int *)
  | shift_case_ll(s: signedness)         (**r long, long *)
  | shift_case_il(s: signedness)         (**r int, long *)
  | shift_case_li(s: signedness)         (**r long, int *)
  | shift_default.(** *** Shifts *)

(** Shifts do not perform the usual binary conversions.  Instead,
  each argument is converted independently, and the signedness
  of the result is always that of the first argument. *)

Inductive classify_shift_cases : Type:=
  | shift_case_ii(s: signedness)         (**r int , int *)
  | shift_case_ll(s: signedness)         (**r long, long *)
  | shift_case_il(s: signedness)         (**r int, long *)
  | shift_case_li(s: signedness)         (**r long, int *)
  | shift_default.(** *** Shifts *)

(** Shifts do not perform the usual binary conversions.  Instead,
  each argument is converted independently, and the signedness
  of the result is always that of the first argument. *)

Inductive classify_shift_cases : Type:=
  | shift_case_ii(s: signedness)         (**r int , int *)
  | shift_case_ll(s: signedness)         (**r long, long *)
  | shift_case_il(s: signedness)         (**r int, long *)
  | shift_case_li(s: signedness)         (**r long, int *)
  | shift_default.(** *** Shifts *)

(** Shifts do not perform the usual binary conversions.  Instead,
  each argument is converted independently, and the signedness
  of the result is always that of the first argument. *)

Inductive classify_shift_cases : Type:=
  | shift_case_ii(s: signedness)         (**r int , int *)
  | shift_case_ll(s: signedness)         (**r long, long *)
  | shift_case_il(s: signedness)         (**r int, long *)
  | shift_case_li(s: signedness)         (**r long, int *)
  | shift_default.(** *** Shifts *)

(** Shifts do not perform the usual binary conversions.  Instead,
  each argument is converted independently, and the signedness
  of the result is always that of the first argument. *)

Inductive classify_shift_cases : Type:=
  | shift_case_ii(s: signedness)         (**r int , int *)
  | shift_case_ll(s: signedness)         (**r long, long *)
  | shift_case_il(s: signedness)         (**r int, long *)
  | shift_case_li(s: signedness)         (**r long, int *)
  | shift_default.(** *** Shifts *)

(** Shifts do not perform the usual binary conversions.  Instead,
  each argument is converted independently, and the signedness
  of the result is always that of the first argument. *)

Inductive classify_shift_cases : Type:=
  | shift_case_ii(s: signedness)         (**r int , int *)
  | shift_case_ll(s: signedness)         (**r long, long *)
  | shift_case_il(s: signedness)         (**r int, long *)
  | shift_case_li(s: signedness)         (**r long, int *)
  | shift_default.Definition classify_shift (ty1: type) (ty2: type) :=
  match typeconv ty1, typeconv ty2 with
  | Tint I32 Unsigned _, Tint _ _ _ => shift_case_ii Unsigned
  | Tint _ _ _, Tint _ _ _ => shift_case_ii Signed
  | Tint I32 Unsigned _, Tlong _ _ => shift_case_il Unsigned
  | Tint _ _ _, Tlong _ _ => shift_case_il Signed
  | Tlong s _, Tint _ _ _ => shift_case_li s
  | Tlong s _, Tlong _ _ => shift_case_ll s
  | _,_  => shift_default
  end.Definition sem_shift
    (sem_int: signedness -> int -> int -> int)
    (sem_long: signedness -> int64 -> int64 -> int64)
    (v1: val) (t1: type) (v2: val) (t2: type) : option val :=
  match classify_shift t1 t2 with
  | shift_case_ii sg =>
      match v1, v2 with
      | Vint n1, Vint n2 =>
          if Int.ltu n2 Int.iwordsize
          then Some(Vint(sem_int sg n1 n2)) else None
      | _, _ => None
      end
  | shift_case_il sg =>
      match v1, v2 with
      | Vint n1, Vlong n2 =>
          if Int64.ltu n2 (Int64.repr 32)
          then Some(Vint(sem_int sg n1 (Int64.loword n2))) else None
      | _, _ => None
      end
  | shift_case_li sg =>
      match v1, v2 with
      | Vlong n1, Vint n2 =>
          if Int.ltu n2 Int64.iwordsize'
          then Some(Vlong(sem_long sg n1 (Int64.repr (Int.unsigned n2)))) else None
      | _, _ => None
      end
  | shift_case_ll sg =>
      match v1, v2 with
      | Vlong n1, Vlong n2 =>
          if Int64.ltu n2 Int64.iwordsize
          then Some(Vlong(sem_long sg n1 n2)) else None
      | _, _ => None
      end
  | shift_default => None
  end.Definition sem_shl (v1:val) (t1:type) (v2: val) (t2:type) : option val :=
  sem_shift
    (fun sg n1 n2 => Int.shl n1 n2)
    (fun sg n1 n2 => Int64.shl n1 n2)
    v1 t1 v2 t2.Definition sem_shr (v1:val) (t1:type) (v2: val) (t2:type) : option val :=
  sem_shift
    (fun sg n1 n2 => match sg with Signed => Int.shr n1 n2 | Unsigned => Int.shru n1 n2 end)
    (fun sg n1 n2 => match sg with Signed => Int64.shr n1 n2 | Unsigned => Int64.shru n1 n2 end)
    v1 t1 v2 t2.(** *** Comparisons *)

Inductive classify_cmp_cases : Type :=
  | cmp_case_pp                       (**r pointer, pointer *)
  | cmp_case_pi (si: signedness)      (**r pointer, int *)
  | cmp_case_ip (si: signedness)      (**r int, pointer *)
  | cmp_case_pl                       (**r pointer, long *)
  | cmp_case_lp                       (**r long, pointer *)
  | cmp_default.(** *** Comparisons *)

Inductive classify_cmp_cases : Type :=
  | cmp_case_pp                       (**r pointer, pointer *)
  | cmp_case_pi (si: signedness)      (**r pointer, int *)
  | cmp_case_ip (si: signedness)      (**r int, pointer *)
  | cmp_case_pl                       (**r pointer, long *)
  | cmp_case_lp                       (**r long, pointer *)
  | cmp_default.(** *** Comparisons *)

Inductive classify_cmp_cases : Type :=
  | cmp_case_pp                       (**r pointer, pointer *)
  | cmp_case_pi (si: signedness)      (**r pointer, int *)
  | cmp_case_ip (si: signedness)      (**r int, pointer *)
  | cmp_case_pl                       (**r pointer, long *)
  | cmp_case_lp                       (**r long, pointer *)
  | cmp_default.(** *** Comparisons *)

Inductive classify_cmp_cases : Type :=
  | cmp_case_pp                       (**r pointer, pointer *)
  | cmp_case_pi (si: signedness)      (**r pointer, int *)
  | cmp_case_ip (si: signedness)      (**r int, pointer *)
  | cmp_case_pl                       (**r pointer, long *)
  | cmp_case_lp                       (**r long, pointer *)
  | cmp_default.(** *** Comparisons *)

Inductive classify_cmp_cases : Type :=
  | cmp_case_pp                       (**r pointer, pointer *)
  | cmp_case_pi (si: signedness)      (**r pointer, int *)
  | cmp_case_ip (si: signedness)      (**r int, pointer *)
  | cmp_case_pl                       (**r pointer, long *)
  | cmp_case_lp                       (**r long, pointer *)
  | cmp_default.(** *** Comparisons *)

Inductive classify_cmp_cases : Type :=
  | cmp_case_pp                       (**r pointer, pointer *)
  | cmp_case_pi (si: signedness)      (**r pointer, int *)
  | cmp_case_ip (si: signedness)      (**r int, pointer *)
  | cmp_case_pl                       (**r pointer, long *)
  | cmp_case_lp                       (**r long, pointer *)
  | cmp_default.(** *** Comparisons *)

Inductive classify_cmp_cases : Type :=
  | cmp_case_pp                       (**r pointer, pointer *)
  | cmp_case_pi (si: signedness)      (**r pointer, int *)
  | cmp_case_ip (si: signedness)      (**r int, pointer *)
  | cmp_case_pl                       (**r pointer, long *)
  | cmp_case_lp                       (**r long, pointer *)
  | cmp_default.(**r numerical, numerical *)

Definition classify_cmp (ty1: type) (ty2: type) :=
  match typeconv ty1, typeconv ty2 with
  | Tpointer _ _ , Tpointer _ _ => cmp_case_pp
  | Tpointer _ _ , Tint _ si _ => cmp_case_pi si
  | Tint _ si _, Tpointer _ _ => cmp_case_ip si
  | Tpointer _ _ , Tlong _ _ => cmp_case_pl
  | Tlong _ _ , Tpointer _ _ => cmp_case_lp
  | _, _ => cmp_default
  end.Definition cmp_ptr (m: mem) (c: comparison) (v1 v2: val): option val :=
  option_map Val.of_bool
   (if Archi.ptr64
    then Val.cmplu_bool (Mem.valid_pointer m) c v1 v2
    else Val.cmpu_bool (Mem.valid_pointer m) c v1 v2).Definition sem_cmp (c:comparison)
                  (v1: val) (t1: type) (v2: val) (t2: type)
                  (m: mem): option val :=
  match classify_cmp t1 t2 with
  | cmp_case_pp =>
      cmp_ptr m c v1 v2
  | cmp_case_pi si =>
      match v2 with
      | Vint n2 =>
          let v2' := Vptrofs (ptrofs_of_int si n2) in
          cmp_ptr m c v1 v2'
      | Vptr b ofs =>
          if Archi.ptr64 then None else cmp_ptr m c v1 v2
      | _ =>
          None
      end
  | cmp_case_ip si =>
      match v1 with
      | Vint n1 =>
          let v1' := Vptrofs (ptrofs_of_int si n1) in
          cmp_ptr m c v1' v2
      | Vptr b ofs =>
          if Archi.ptr64 then None else cmp_ptr m c v1 v2
      | _ =>
          None
      end
  | cmp_case_pl =>
      match v2 with
      | Vlong n2 =>
          let v2' := Vptrofs (Ptrofs.of_int64 n2) in
          cmp_ptr m c v1 v2'
      | Vptr b ofs =>
          if Archi.ptr64 then cmp_ptr m c v1 v2 else None
      | _ =>
          None
      end
  | cmp_case_lp =>
      match v1 with
      | Vlong n1 =>
          let v1' := Vptrofs (Ptrofs.of_int64 n1) in
          cmp_ptr m c v1' v2
      | Vptr b ofs =>
          if Archi.ptr64 then cmp_ptr m c v1 v2 else None
      | _ =>
          None
      end
  | cmp_default =>
      sem_binarith
        (fun sg n1 n2 =>
            Some(Val.of_bool(match sg with Signed => Int.cmp c n1 n2 | Unsigned => Int.cmpu c n1 n2 end)))
        (fun sg n1 n2 =>
            Some(Val.of_bool(match sg with Signed => Int64.cmp c n1 n2 | Unsigned => Int64.cmpu c n1 n2 end)))
        (fun n1 n2 =>
            Some(Val.of_bool(Float.cmp c n1 n2)))
        (fun n1 n2 =>
            Some(Val.of_bool(Float32.cmp c n1 n2)))
        v1 t1 v2 t2 m
  end.(** ** Function applications *)

Inductive classify_fun_cases : Type :=
  | fun_case_f (targs: typelist) (tres: type) (cc: calling_convention) (**r (pointer to) function *)
  | fun_default.(** ** Function applications *)

Inductive classify_fun_cases : Type :=
  | fun_case_f (targs: typelist) (tres: type) (cc: calling_convention) (**r (pointer to) function *)
  | fun_default.(** ** Function applications *)

Inductive classify_fun_cases : Type :=
  | fun_case_f (targs: typelist) (tres: type) (cc: calling_convention) (**r (pointer to) function *)
  | fun_default.Definition classify_fun (ty: type) :=
  match ty with
  | Tfunction args res cc => fun_case_f args res cc
  | Tpointer (Tfunction args res cc) _ => fun_case_f args res cc
  | _ => fun_default
  end.(** ** Argument of a [switch] statement *)

Inductive classify_switch_cases : Type :=
  | switch_case_i
  | switch_case_l
  | switch_default.(** ** Argument of a [switch] statement *)

Inductive classify_switch_cases : Type :=
  | switch_case_i
  | switch_case_l
  | switch_default.(** ** Argument of a [switch] statement *)

Inductive classify_switch_cases : Type :=
  | switch_case_i
  | switch_case_l
  | switch_default.(** ** Argument of a [switch] statement *)

Inductive classify_switch_cases : Type :=
  | switch_case_i
  | switch_case_l
  | switch_default.Definition classify_switch (ty: type) :=
  match ty with
  | Tint _ _ _ => switch_case_i
  | Tlong _ _ => switch_case_l
  | _ => switch_default
  end.Definition sem_switch_arg (v: val) (ty: type): option Z :=
  match classify_switch ty with
  | switch_case_i =>
      match v with Vint n => Some(Int.unsigned n) | _ => None end
  | switch_case_l =>
      match v with Vlong n => Some(Int64.unsigned n) | _ => None end
  | switch_default =>
      None
  end.(** * Combined semantics of unary and binary operators *)

Definition sem_unary_operation
            (op: unary_operation) (v: val) (ty: type) (m: mem): option val :=
  match op with
  | Onotbool => sem_notbool v ty m
  | Onotint => sem_notint v ty
  | Oneg => sem_neg v ty
  | Oabsfloat => sem_absfloat v ty
  end.Definition sem_binary_operation
    (cenv: composite_env)
    (op: binary_operation)
    (v1: val) (t1: type) (v2: val) (t2:type)
    (m: mem): option val :=
  match op with
  | Oadd => sem_add cenv v1 t1 v2 t2 m
  | Osub => sem_sub cenv v1 t1 v2 t2 m
  | Omul => sem_mul v1 t1 v2 t2 m
  | Omod => sem_mod v1 t1 v2 t2 m
  | Odiv => sem_div v1 t1 v2 t2 m
  | Oand => sem_and v1 t1 v2 t2 m
  | Oor  => sem_or v1 t1 v2 t2 m
  | Oxor  => sem_xor v1 t1 v2 t2 m
  | Oshl => sem_shl v1 t1 v2 t2
  | Oshr  => sem_shr v1 t1 v2 t2
  | Oeq => sem_cmp Ceq v1 t1 v2 t2 m
  | One => sem_cmp Cne v1 t1 v2 t2 m
  | Olt => sem_cmp Clt v1 t1 v2 t2 m
  | Ogt => sem_cmp Cgt v1 t1 v2 t2 m
  | Ole => sem_cmp Cle v1 t1 v2 t2 m
  | Oge => sem_cmp Cge v1 t1 v2 t2 m
  end.Definition sem_incrdecr (cenv: composite_env) (id: incr_or_decr) (v: val) (ty: type) (m: mem) :=
  match id with
  | Incr => sem_add cenv v ty (Vint Int.one) type_int32s m
  | Decr => sem_sub cenv v ty (Vint Int.one) type_int32s m
  end.Definition incrdecr_type (ty: type) :=
  match typeconv ty with
  | Tpointer ty a => Tpointer ty a
  | Tint sz sg a => Tint sz sg noattr
  | Tlong sg a => Tlong sg noattr
  | Tfloat sz a => Tfloat sz noattr
  | _ => Tvoid
  end.Remark val_inject_vtrue: forall f, Val.inject f Vtrue Vtrue.Remark val_inject_vfalse: forall f, Val.inject f Vfalse Vfalse.Remark val_inject_of_bool: forall f b, Val.inject f (Val.of_bool b) (Val.of_bool b).Remark val_inject_vptrofs: forall n, Val.inject f (Vptrofs n) (Vptrofs n).Ltac TrivialInject :=
  match goal with
  | [ H: None = Some _ |- _ ] => discriminate
  | [ H: Some _ = Some _ |- _ ] => inv H; TrivialInject
  | [ H: match ?x with Some _ => _ | None => _ end = Some _ |- _ ] => destruct x; TrivialInject
  | [ H: match ?x with true => _ | false => _ end = Some _ |- _ ] => destruct x eqn:?; TrivialInject
  | [ |- exists v', Some ?v = Some v' /\ _ ] => exists v; split; auto
  | _ => idtac
  end.

(* Specifications: *)
Lemma sem_cast_inj: forall v1 ty1 ty v tv1, sem_cast v1 ty1 ty m = Some v -> Val.inject f v1 tv1 -> exists tv, sem_cast tv1 ty1 ty m'= Some tv /\ Val.inject f v tv.
Lemma bool_val_inj: forall v ty b tv, bool_val v ty m = Some b -> Val.inject f v tv -> bool_val tv ty m' = Some b.
Lemma sem_unary_operation_inj: forall op v1 ty v tv1, sem_unary_operation op v1 ty m = Some v -> Val.inject f v1 tv1 -> exists tv, sem_unary_operation op tv1 ty m' = Some tv /\ Val.inject f v tv.