(** * External functions *)

(** For most languages, the functions composing the program are either
  internal functions, defined within the language, or external functions,
  defined outside.  External functions include system calls but also
  compiler built-in functions.  We define a type for external functions
  and associated operations. *)

Inductive external_function : Type :=
  | EF_external (name: string) (sg: signature)
     (** A system call or library function.  Produces an event
         in the trace. *)
  | EF_builtin (name: string) (sg: signature)
     (** A compiler built-in function.  Behaves like an external, but
         can be inlined by the compiler. *)
  | EF_runtime (name: string) (sg: signature)
     (** A function from the run-time library.  Behaves like an
         external, but must not be redefined. *)
  | EF_vload (chunk: memory_chunk)
     (** A volatile read operation.  If the adress given as first argument
         points within a volatile global variable, generate an
         event and return the value found in this event.  Otherwise,
         produce no event and behave like a regular memory load. *)
  | EF_vstore (chunk: memory_chunk)
     (** A volatile store operation.   If the adress given as first argument
         points within a volatile global variable, generate an event.
         Otherwise, produce no event and behave like a regular memory store. *)
  | EF_malloc
     (** Dynamic memory allocation.  Takes the requested size in bytes
         as argument; returns a pointer to a fresh block of the given size.
         Produces no observable event. *)
  | EF_free
     (** Dynamic memory deallocation.  Takes a pointer to a block
         allocated by an [EF_malloc] external call and frees the
         corresponding block.
         Produces no observable event. *)
  | EF_memcpy (sz: Z) (al: Z)
     (** Block copy, of [sz] bytes, between addresses that are [al]-aligned. *)
  | EF_annot (kind: positive) (text: string) (targs: list typ)
     (** A programmer-supplied annotation.  Takes zero, one or several arguments,
         produces an event carrying the text and the values of these arguments,
         and returns no value. *)
  | EF_annot_val (kind: positive) (text: string) (targ: typ)
     (** Another form of annotation that takes one argument, produces
         an event carrying the text and the value of this argument,
         and returns the value of the argument. *)
  | EF_inline_asm (text: string) (sg: signature) (clobbers: list string)
     (** Inline [asm] statements.  Semantically, treated like an
         annotation with no parameters ([EF_annot text nil]).  To be
         used with caution, as it can invalidate the semantic
         preservation theorem.  Generated only if [-finline-asm] is
         given. *)
  | EF_debug (kind: positive) (text: ident) (targs: list typ).(** * External functions *)

(** For most languages, the functions composing the program are either
  internal functions, defined within the language, or external functions,
  defined outside.  External functions include system calls but also
  compiler built-in functions.  We define a type for external functions
  and associated operations. *)

Inductive external_function : Type :=
  | EF_external (name: string) (sg: signature)
     (** A system call or library function.  Produces an event
         in the trace. *)
  | EF_builtin (name: string) (sg: signature)
     (** A compiler built-in function.  Behaves like an external, but
         can be inlined by the compiler. *)
  | EF_runtime (name: string) (sg: signature)
     (** A function from the run-time library.  Behaves like an
         external, but must not be redefined. *)
  | EF_vload (chunk: memory_chunk)
     (** A volatile read operation.  If the adress given as first argument
         points within a volatile global variable, generate an
         event and return the value found in this event.  Otherwise,
         produce no event and behave like a regular memory load. *)
  | EF_vstore (chunk: memory_chunk)
     (** A volatile store operation.   If the adress given as first argument
         points within a volatile global variable, generate an event.
         Otherwise, produce no event and behave like a regular memory store. *)
  | EF_malloc
     (** Dynamic memory allocation.  Takes the requested size in bytes
         as argument; returns a pointer to a fresh block of the given size.
         Produces no observable event. *)
  | EF_free
     (** Dynamic memory deallocation.  Takes a pointer to a block
         allocated by an [EF_malloc] external call and frees the
         corresponding block.
         Produces no observable event. *)
  | EF_memcpy (sz: Z) (al: Z)
     (** Block copy, of [sz] bytes, between addresses that are [al]-aligned. *)
  | EF_annot (kind: positive) (text: string) (targs: list typ)
     (** A programmer-supplied annotation.  Takes zero, one or several arguments,
         produces an event carrying the text and the values of these arguments,
         and returns no value. *)
  | EF_annot_val (kind: positive) (text: string) (targ: typ)
     (** Another form of annotation that takes one argument, produces
         an event carrying the text and the value of this argument,
         and returns the value of the argument. *)
  | EF_inline_asm (text: string) (sg: signature) (clobbers: list string)
     (** Inline [asm] statements.  Semantically, treated like an
         annotation with no parameters ([EF_annot text nil]).  To be
         used with caution, as it can invalidate the semantic
         preservation theorem.  Generated only if [-finline-asm] is
         given. *)
  | EF_debug (kind: positive) (text: ident) (targs: list typ).(** * External functions *)

(** For most languages, the functions composing the program are either
  internal functions, defined within the language, or external functions,
  defined outside.  External functions include system calls but also
  compiler built-in functions.  We define a type for external functions
  and associated operations. *)

Inductive external_function : Type :=
  | EF_external (name: string) (sg: signature)
     (** A system call or library function.  Produces an event
         in the trace. *)
  | EF_builtin (name: string) (sg: signature)
     (** A compiler built-in function.  Behaves like an external, but
         can be inlined by the compiler. *)
  | EF_runtime (name: string) (sg: signature)
     (** A function from the run-time library.  Behaves like an
         external, but must not be redefined. *)
  | EF_vload (chunk: memory_chunk)
     (** A volatile read operation.  If the adress given as first argument
         points within a volatile global variable, generate an
         event and return the value found in this event.  Otherwise,
         produce no event and behave like a regular memory load. *)
  | EF_vstore (chunk: memory_chunk)
     (** A volatile store operation.   If the adress given as first argument
         points within a volatile global variable, generate an event.
         Otherwise, produce no event and behave like a regular memory store. *)
  | EF_malloc
     (** Dynamic memory allocation.  Takes the requested size in bytes
         as argument; returns a pointer to a fresh block of the given size.
         Produces no observable event. *)
  | EF_free
     (** Dynamic memory deallocation.  Takes a pointer to a block
         allocated by an [EF_malloc] external call and frees the
         corresponding block.
         Produces no observable event. *)
  | EF_memcpy (sz: Z) (al: Z)
     (** Block copy, of [sz] bytes, between addresses that are [al]-aligned. *)
  | EF_annot (kind: positive) (text: string) (targs: list typ)
     (** A programmer-supplied annotation.  Takes zero, one or several arguments,
         produces an event carrying the text and the values of these arguments,
         and returns no value. *)
  | EF_annot_val (kind: positive) (text: string) (targ: typ)
     (** Another form of annotation that takes one argument, produces
         an event carrying the text and the value of this argument,
         and returns the value of the argument. *)
  | EF_inline_asm (text: string) (sg: signature) (clobbers: list string)
     (** Inline [asm] statements.  Semantically, treated like an
         annotation with no parameters ([EF_annot text nil]).  To be
         used with caution, as it can invalidate the semantic
         preservation theorem.  Generated only if [-finline-asm] is
         given. *)
  | EF_debug (kind: positive) (text: ident) (targs: list typ).(** * External functions *)

(** For most languages, the functions composing the program are either
  internal functions, defined within the language, or external functions,
  defined outside.  External functions include system calls but also
  compiler built-in functions.  We define a type for external functions
  and associated operations. *)

Inductive external_function : Type :=
  | EF_external (name: string) (sg: signature)
     (** A system call or library function.  Produces an event
         in the trace. *)
  | EF_builtin (name: string) (sg: signature)
     (** A compiler built-in function.  Behaves like an external, but
         can be inlined by the compiler. *)
  | EF_runtime (name: string) (sg: signature)
     (** A function from the run-time library.  Behaves like an
         external, but must not be redefined. *)
  | EF_vload (chunk: memory_chunk)
     (** A volatile read operation.  If the adress given as first argument
         points within a volatile global variable, generate an
         event and return the value found in this event.  Otherwise,
         produce no event and behave like a regular memory load. *)
  | EF_vstore (chunk: memory_chunk)
     (** A volatile store operation.   If the adress given as first argument
         points within a volatile global variable, generate an event.
         Otherwise, produce no event and behave like a regular memory store. *)
  | EF_malloc
     (** Dynamic memory allocation.  Takes the requested size in bytes
         as argument; returns a pointer to a fresh block of the given size.
         Produces no observable event. *)
  | EF_free
     (** Dynamic memory deallocation.  Takes a pointer to a block
         allocated by an [EF_malloc] external call and frees the
         corresponding block.
         Produces no observable event. *)
  | EF_memcpy (sz: Z) (al: Z)
     (** Block copy, of [sz] bytes, between addresses that are [al]-aligned. *)
  | EF_annot (kind: positive) (text: string) (targs: list typ)
     (** A programmer-supplied annotation.  Takes zero, one or several arguments,
         produces an event carrying the text and the values of these arguments,
         and returns no value. *)
  | EF_annot_val (kind: positive) (text: string) (targ: typ)
     (** Another form of annotation that takes one argument, produces
         an event carrying the text and the value of this argument,
         and returns the value of the argument. *)
  | EF_inline_asm (text: string) (sg: signature) (clobbers: list string)
     (** Inline [asm] statements.  Semantically, treated like an
         annotation with no parameters ([EF_annot text nil]).  To be
         used with caution, as it can invalidate the semantic
         preservation theorem.  Generated only if [-finline-asm] is
         given. *)
  | EF_debug (kind: positive) (text: ident) (targs: list typ).(** * External functions *)

(** For most languages, the functions composing the program are either
  internal functions, defined within the language, or external functions,
  defined outside.  External functions include system calls but also
  compiler built-in functions.  We define a type for external functions
  and associated operations. *)

Inductive external_function : Type :=
  | EF_external (name: string) (sg: signature)
     (** A system call or library function.  Produces an event
         in the trace. *)
  | EF_builtin (name: string) (sg: signature)
     (** A compiler built-in function.  Behaves like an external, but
         can be inlined by the compiler. *)
  | EF_runtime (name: string) (sg: signature)
     (** A function from the run-time library.  Behaves like an
         external, but must not be redefined. *)
  | EF_vload (chunk: memory_chunk)
     (** A volatile read operation.  If the adress given as first argument
         points within a volatile global variable, generate an
         event and return the value found in this event.  Otherwise,
         produce no event and behave like a regular memory load. *)
  | EF_vstore (chunk: memory_chunk)
     (** A volatile store operation.   If the adress given as first argument
         points within a volatile global variable, generate an event.
         Otherwise, produce no event and behave like a regular memory store. *)
  | EF_malloc
     (** Dynamic memory allocation.  Takes the requested size in bytes
         as argument; returns a pointer to a fresh block of the given size.
         Produces no observable event. *)
  | EF_free
     (** Dynamic memory deallocation.  Takes a pointer to a block
         allocated by an [EF_malloc] external call and frees the
         corresponding block.
         Produces no observable event. *)
  | EF_memcpy (sz: Z) (al: Z)
     (** Block copy, of [sz] bytes, between addresses that are [al]-aligned. *)
  | EF_annot (kind: positive) (text: string) (targs: list typ)
     (** A programmer-supplied annotation.  Takes zero, one or several arguments,
         produces an event carrying the text and the values of these arguments,
         and returns no value. *)
  | EF_annot_val (kind: positive) (text: string) (targ: typ)
     (** Another form of annotation that takes one argument, produces
         an event carrying the text and the value of this argument,
         and returns the value of the argument. *)
  | EF_inline_asm (text: string) (sg: signature) (clobbers: list string)
     (** Inline [asm] statements.  Semantically, treated like an
         annotation with no parameters ([EF_annot text nil]).  To be
         used with caution, as it can invalidate the semantic
         preservation theorem.  Generated only if [-finline-asm] is
         given. *)
  | EF_debug (kind: positive) (text: ident) (targs: list typ).(** * External functions *)

(** For most languages, the functions composing the program are either
  internal functions, defined within the language, or external functions,
  defined outside.  External functions include system calls but also
  compiler built-in functions.  We define a type for external functions
  and associated operations. *)

Inductive external_function : Type :=
  | EF_external (name: string) (sg: signature)
     (** A system call or library function.  Produces an event
         in the trace. *)
  | EF_builtin (name: string) (sg: signature)
     (** A compiler built-in function.  Behaves like an external, but
         can be inlined by the compiler. *)
  | EF_runtime (name: string) (sg: signature)
     (** A function from the run-time library.  Behaves like an
         external, but must not be redefined. *)
  | EF_vload (chunk: memory_chunk)
     (** A volatile read operation.  If the adress given as first argument
         points within a volatile global variable, generate an
         event and return the value found in this event.  Otherwise,
         produce no event and behave like a regular memory load. *)
  | EF_vstore (chunk: memory_chunk)
     (** A volatile store operation.   If the adress given as first argument
         points within a volatile global variable, generate an event.
         Otherwise, produce no event and behave like a regular memory store. *)
  | EF_malloc
     (** Dynamic memory allocation.  Takes the requested size in bytes
         as argument; returns a pointer to a fresh block of the given size.
         Produces no observable event. *)
  | EF_free
     (** Dynamic memory deallocation.  Takes a pointer to a block
         allocated by an [EF_malloc] external call and frees the
         corresponding block.
         Produces no observable event. *)
  | EF_memcpy (sz: Z) (al: Z)
     (** Block copy, of [sz] bytes, between addresses that are [al]-aligned. *)
  | EF_annot (kind: positive) (text: string) (targs: list typ)
     (** A programmer-supplied annotation.  Takes zero, one or several arguments,
         produces an event carrying the text and the values of these arguments,
         and returns no value. *)
  | EF_annot_val (kind: positive) (text: string) (targ: typ)
     (** Another form of annotation that takes one argument, produces
         an event carrying the text and the value of this argument,
         and returns the value of the argument. *)
  | EF_inline_asm (text: string) (sg: signature) (clobbers: list string)
     (** Inline [asm] statements.  Semantically, treated like an
         annotation with no parameters ([EF_annot text nil]).  To be
         used with caution, as it can invalidate the semantic
         preservation theorem.  Generated only if [-finline-asm] is
         given. *)
  | EF_debug (kind: positive) (text: ident) (targs: list typ).(** * External functions *)

(** For most languages, the functions composing the program are either
  internal functions, defined within the language, or external functions,
  defined outside.  External functions include system calls but also
  compiler built-in functions.  We define a type for external functions
  and associated operations. *)

Inductive external_function : Type :=
  | EF_external (name: string) (sg: signature)
     (** A system call or library function.  Produces an event
         in the trace. *)
  | EF_builtin (name: string) (sg: signature)
     (** A compiler built-in function.  Behaves like an external, but
         can be inlined by the compiler. *)
  | EF_runtime (name: string) (sg: signature)
     (** A function from the run-time library.  Behaves like an
         external, but must not be redefined. *)
  | EF_vload (chunk: memory_chunk)
     (** A volatile read operation.  If the adress given as first argument
         points within a volatile global variable, generate an
         event and return the value found in this event.  Otherwise,
         produce no event and behave like a regular memory load. *)
  | EF_vstore (chunk: memory_chunk)
     (** A volatile store operation.   If the adress given as first argument
         points within a volatile global variable, generate an event.
         Otherwise, produce no event and behave like a regular memory store. *)
  | EF_malloc
     (** Dynamic memory allocation.  Takes the requested size in bytes
         as argument; returns a pointer to a fresh block of the given size.
         Produces no observable event. *)
  | EF_free
     (** Dynamic memory deallocation.  Takes a pointer to a block
         allocated by an [EF_malloc] external call and frees the
         corresponding block.
         Produces no observable event. *)
  | EF_memcpy (sz: Z) (al: Z)
     (** Block copy, of [sz] bytes, between addresses that are [al]-aligned. *)
  | EF_annot (kind: positive) (text: string) (targs: list typ)
     (** A programmer-supplied annotation.  Takes zero, one or several arguments,
         produces an event carrying the text and the values of these arguments,
         and returns no value. *)
  | EF_annot_val (kind: positive) (text: string) (targ: typ)
     (** Another form of annotation that takes one argument, produces
         an event carrying the text and the value of this argument,
         and returns the value of the argument. *)
  | EF_inline_asm (text: string) (sg: signature) (clobbers: list string)
     (** Inline [asm] statements.  Semantically, treated like an
         annotation with no parameters ([EF_annot text nil]).  To be
         used with caution, as it can invalidate the semantic
         preservation theorem.  Generated only if [-finline-asm] is
         given. *)
  | EF_debug (kind: positive) (text: ident) (targs: list typ).(** * External functions *)

(** For most languages, the functions composing the program are either
  internal functions, defined within the language, or external functions,
  defined outside.  External functions include system calls but also
  compiler built-in functions.  We define a type for external functions
  and associated operations. *)

Inductive external_function : Type :=
  | EF_external (name: string) (sg: signature)
     (** A system call or library function.  Produces an event
         in the trace. *)
  | EF_builtin (name: string) (sg: signature)
     (** A compiler built-in function.  Behaves like an external, but
         can be inlined by the compiler. *)
  | EF_runtime (name: string) (sg: signature)
     (** A function from the run-time library.  Behaves like an
         external, but must not be redefined. *)
  | EF_vload (chunk: memory_chunk)
     (** A volatile read operation.  If the adress given as first argument
         points within a volatile global variable, generate an
         event and return the value found in this event.  Otherwise,
         produce no event and behave like a regular memory load. *)
  | EF_vstore (chunk: memory_chunk)
     (** A volatile store operation.   If the adress given as first argument
         points within a volatile global variable, generate an event.
         Otherwise, produce no event and behave like a regular memory store. *)
  | EF_malloc
     (** Dynamic memory allocation.  Takes the requested size in bytes
         as argument; returns a pointer to a fresh block of the given size.
         Produces no observable event. *)
  | EF_free
     (** Dynamic memory deallocation.  Takes a pointer to a block
         allocated by an [EF_malloc] external call and frees the
         corresponding block.
         Produces no observable event. *)
  | EF_memcpy (sz: Z) (al: Z)
     (** Block copy, of [sz] bytes, between addresses that are [al]-aligned. *)
  | EF_annot (kind: positive) (text: string) (targs: list typ)
     (** A programmer-supplied annotation.  Takes zero, one or several arguments,
         produces an event carrying the text and the values of these arguments,
         and returns no value. *)
  | EF_annot_val (kind: positive) (text: string) (targ: typ)
     (** Another form of annotation that takes one argument, produces
         an event carrying the text and the value of this argument,
         and returns the value of the argument. *)
  | EF_inline_asm (text: string) (sg: signature) (clobbers: list string)
     (** Inline [asm] statements.  Semantically, treated like an
         annotation with no parameters ([EF_annot text nil]).  To be
         used with caution, as it can invalidate the semantic
         preservation theorem.  Generated only if [-finline-asm] is
         given. *)
  | EF_debug (kind: positive) (text: ident) (targs: list typ).(** * External functions *)

(** For most languages, the functions composing the program are either
  internal functions, defined within the language, or external functions,
  defined outside.  External functions include system calls but also
  compiler built-in functions.  We define a type for external functions
  and associated operations. *)

Inductive external_function : Type :=
  | EF_external (name: string) (sg: signature)
     (** A system call or library function.  Produces an event
         in the trace. *)
  | EF_builtin (name: string) (sg: signature)
     (** A compiler built-in function.  Behaves like an external, but
         can be inlined by the compiler. *)
  | EF_runtime (name: string) (sg: signature)
     (** A function from the run-time library.  Behaves like an
         external, but must not be redefined. *)
  | EF_vload (chunk: memory_chunk)
     (** A volatile read operation.  If the adress given as first argument
         points within a volatile global variable, generate an
         event and return the value found in this event.  Otherwise,
         produce no event and behave like a regular memory load. *)
  | EF_vstore (chunk: memory_chunk)
     (** A volatile store operation.   If the adress given as first argument
         points within a volatile global variable, generate an event.
         Otherwise, produce no event and behave like a regular memory store. *)
  | EF_malloc
     (** Dynamic memory allocation.  Takes the requested size in bytes
         as argument; returns a pointer to a fresh block of the given size.
         Produces no observable event. *)
  | EF_free
     (** Dynamic memory deallocation.  Takes a pointer to a block
         allocated by an [EF_malloc] external call and frees the
         corresponding block.
         Produces no observable event. *)
  | EF_memcpy (sz: Z) (al: Z)
     (** Block copy, of [sz] bytes, between addresses that are [al]-aligned. *)
  | EF_annot (kind: positive) (text: string) (targs: list typ)
     (** A programmer-supplied annotation.  Takes zero, one or several arguments,
         produces an event carrying the text and the values of these arguments,
         and returns no value. *)
  | EF_annot_val (kind: positive) (text: string) (targ: typ)
     (** Another form of annotation that takes one argument, produces
         an event carrying the text and the value of this argument,
         and returns the value of the argument. *)
  | EF_inline_asm (text: string) (sg: signature) (clobbers: list string)
     (** Inline [asm] statements.  Semantically, treated like an
         annotation with no parameters ([EF_annot text nil]).  To be
         used with caution, as it can invalidate the semantic
         preservation theorem.  Generated only if [-finline-asm] is
         given. *)
  | EF_debug (kind: positive) (text: ident) (targs: list typ).(** * External functions *)

(** For most languages, the functions composing the program are either
  internal functions, defined within the language, or external functions,
  defined outside.  External functions include system calls but also
  compiler built-in functions.  We define a type for external functions
  and associated operations. *)

Inductive external_function : Type :=
  | EF_external (name: string) (sg: signature)
     (** A system call or library function.  Produces an event
         in the trace. *)
  | EF_builtin (name: string) (sg: signature)
     (** A compiler built-in function.  Behaves like an external, but
         can be inlined by the compiler. *)
  | EF_runtime (name: string) (sg: signature)
     (** A function from the run-time library.  Behaves like an
         external, but must not be redefined. *)
  | EF_vload (chunk: memory_chunk)
     (** A volatile read operation.  If the adress given as first argument
         points within a volatile global variable, generate an
         event and return the value found in this event.  Otherwise,
         produce no event and behave like a regular memory load. *)
  | EF_vstore (chunk: memory_chunk)
     (** A volatile store operation.   If the adress given as first argument
         points within a volatile global variable, generate an event.
         Otherwise, produce no event and behave like a regular memory store. *)
  | EF_malloc
     (** Dynamic memory allocation.  Takes the requested size in bytes
         as argument; returns a pointer to a fresh block of the given size.
         Produces no observable event. *)
  | EF_free
     (** Dynamic memory deallocation.  Takes a pointer to a block
         allocated by an [EF_malloc] external call and frees the
         corresponding block.
         Produces no observable event. *)
  | EF_memcpy (sz: Z) (al: Z)
     (** Block copy, of [sz] bytes, between addresses that are [al]-aligned. *)
  | EF_annot (kind: positive) (text: string) (targs: list typ)
     (** A programmer-supplied annotation.  Takes zero, one or several arguments,
         produces an event carrying the text and the values of these arguments,
         and returns no value. *)
  | EF_annot_val (kind: positive) (text: string) (targ: typ)
     (** Another form of annotation that takes one argument, produces
         an event carrying the text and the value of this argument,
         and returns the value of the argument. *)
  | EF_inline_asm (text: string) (sg: signature) (clobbers: list string)
     (** Inline [asm] statements.  Semantically, treated like an
         annotation with no parameters ([EF_annot text nil]).  To be
         used with caution, as it can invalidate the semantic
         preservation theorem.  Generated only if [-finline-asm] is
         given. *)
  | EF_debug (kind: positive) (text: ident) (targs: list typ).(** * External functions *)

(** For most languages, the functions composing the program are either
  internal functions, defined within the language, or external functions,
  defined outside.  External functions include system calls but also
  compiler built-in functions.  We define a type for external functions
  and associated operations. *)

Inductive external_function : Type :=
  | EF_external (name: string) (sg: signature)
     (** A system call or library function.  Produces an event
         in the trace. *)
  | EF_builtin (name: string) (sg: signature)
     (** A compiler built-in function.  Behaves like an external, but
         can be inlined by the compiler. *)
  | EF_runtime (name: string) (sg: signature)
     (** A function from the run-time library.  Behaves like an
         external, but must not be redefined. *)
  | EF_vload (chunk: memory_chunk)
     (** A volatile read operation.  If the adress given as first argument
         points within a volatile global variable, generate an
         event and return the value found in this event.  Otherwise,
         produce no event and behave like a regular memory load. *)
  | EF_vstore (chunk: memory_chunk)
     (** A volatile store operation.   If the adress given as first argument
         points within a volatile global variable, generate an event.
         Otherwise, produce no event and behave like a regular memory store. *)
  | EF_malloc
     (** Dynamic memory allocation.  Takes the requested size in bytes
         as argument; returns a pointer to a fresh block of the given size.
         Produces no observable event. *)
  | EF_free
     (** Dynamic memory deallocation.  Takes a pointer to a block
         allocated by an [EF_malloc] external call and frees the
         corresponding block.
         Produces no observable event. *)
  | EF_memcpy (sz: Z) (al: Z)
     (** Block copy, of [sz] bytes, between addresses that are [al]-aligned. *)
  | EF_annot (kind: positive) (text: string) (targs: list typ)
     (** A programmer-supplied annotation.  Takes zero, one or several arguments,
         produces an event carrying the text and the values of these arguments,
         and returns no value. *)
  | EF_annot_val (kind: positive) (text: string) (targ: typ)
     (** Another form of annotation that takes one argument, produces
         an event carrying the text and the value of this argument,
         and returns the value of the argument. *)
  | EF_inline_asm (text: string) (sg: signature) (clobbers: list string)
     (** Inline [asm] statements.  Semantically, treated like an
         annotation with no parameters ([EF_annot text nil]).  To be
         used with caution, as it can invalidate the semantic
         preservation theorem.  Generated only if [-finline-asm] is
         given. *)
  | EF_debug (kind: positive) (text: ident) (targs: list typ).(** * External functions *)

(** For most languages, the functions composing the program are either
  internal functions, defined within the language, or external functions,
  defined outside.  External functions include system calls but also
  compiler built-in functions.  We define a type for external functions
  and associated operations. *)

Inductive external_function : Type :=
  | EF_external (name: string) (sg: signature)
     (** A system call or library function.  Produces an event
         in the trace. *)
  | EF_builtin (name: string) (sg: signature)
     (** A compiler built-in function.  Behaves like an external, but
         can be inlined by the compiler. *)
  | EF_runtime (name: string) (sg: signature)
     (** A function from the run-time library.  Behaves like an
         external, but must not be redefined. *)
  | EF_vload (chunk: memory_chunk)
     (** A volatile read operation.  If the adress given as first argument
         points within a volatile global variable, generate an
         event and return the value found in this event.  Otherwise,
         produce no event and behave like a regular memory load. *)
  | EF_vstore (chunk: memory_chunk)
     (** A volatile store operation.   If the adress given as first argument
         points within a volatile global variable, generate an event.
         Otherwise, produce no event and behave like a regular memory store. *)
  | EF_malloc
     (** Dynamic memory allocation.  Takes the requested size in bytes
         as argument; returns a pointer to a fresh block of the given size.
         Produces no observable event. *)
  | EF_free
     (** Dynamic memory deallocation.  Takes a pointer to a block
         allocated by an [EF_malloc] external call and frees the
         corresponding block.
         Produces no observable event. *)
  | EF_memcpy (sz: Z) (al: Z)
     (** Block copy, of [sz] bytes, between addresses that are [al]-aligned. *)
  | EF_annot (kind: positive) (text: string) (targs: list typ)
     (** A programmer-supplied annotation.  Takes zero, one or several arguments,
         produces an event carrying the text and the values of these arguments,
         and returns no value. *)
  | EF_annot_val (kind: positive) (text: string) (targ: typ)
     (** Another form of annotation that takes one argument, produces
         an event carrying the text and the value of this argument,
         and returns the value of the argument. *)
  | EF_inline_asm (text: string) (sg: signature) (clobbers: list string)
     (** Inline [asm] statements.  Semantically, treated like an
         annotation with no parameters ([EF_annot text nil]).  To be
         used with caution, as it can invalidate the semantic
         preservation theorem.  Generated only if [-finline-asm] is
         given. *)
  | EF_debug (kind: positive) (text: ident) (targs: list typ).(** * External functions *)

(** For most languages, the functions composing the program are either
  internal functions, defined within the language, or external functions,
  defined outside.  External functions include system calls but also
  compiler built-in functions.  We define a type for external functions
  and associated operations. *)

Inductive external_function : Type :=
  | EF_external (name: string) (sg: signature)
     (** A system call or library function.  Produces an event
         in the trace. *)
  | EF_builtin (name: string) (sg: signature)
     (** A compiler built-in function.  Behaves like an external, but
         can be inlined by the compiler. *)
  | EF_runtime (name: string) (sg: signature)
     (** A function from the run-time library.  Behaves like an
         external, but must not be redefined. *)
  | EF_vload (chunk: memory_chunk)
     (** A volatile read operation.  If the adress given as first argument
         points within a volatile global variable, generate an
         event and return the value found in this event.  Otherwise,
         produce no event and behave like a regular memory load. *)
  | EF_vstore (chunk: memory_chunk)
     (** A volatile store operation.   If the adress given as first argument
         points within a volatile global variable, generate an event.
         Otherwise, produce no event and behave like a regular memory store. *)
  | EF_malloc
     (** Dynamic memory allocation.  Takes the requested size in bytes
         as argument; returns a pointer to a fresh block of the given size.
         Produces no observable event. *)
  | EF_free
     (** Dynamic memory deallocation.  Takes a pointer to a block
         allocated by an [EF_malloc] external call and frees the
         corresponding block.
         Produces no observable event. *)
  | EF_memcpy (sz: Z) (al: Z)
     (** Block copy, of [sz] bytes, between addresses that are [al]-aligned. *)
  | EF_annot (kind: positive) (text: string) (targs: list typ)
     (** A programmer-supplied annotation.  Takes zero, one or several arguments,
         produces an event carrying the text and the values of these arguments,
         and returns no value. *)
  | EF_annot_val (kind: positive) (text: string) (targ: typ)
     (** Another form of annotation that takes one argument, produces
         an event carrying the text and the value of this argument,
         and returns the value of the argument. *)
  | EF_inline_asm (text: string) (sg: signature) (clobbers: list string)
     (** Inline [asm] statements.  Semantically, treated like an
         annotation with no parameters ([EF_annot text nil]).  To be
         used with caution, as it can invalidate the semantic
         preservation theorem.  Generated only if [-finline-asm] is
         given. *)
  | EF_debug (kind: positive) (text: ident) (targs: list typ).(** Transport debugging information from the front-end to the generated
         assembly.  Takes zero, one or several arguments like [EF_annot].
         Unlike [EF_annot], produces no observable event. *)

(** The type signature of an external function. *)

Definition ef_sig (ef: external_function): signature :=
  match ef with
  | EF_external name sg => sg
  | EF_builtin name sg => sg
  | EF_runtime name sg => sg
  | EF_vload chunk => mksignature (Tptr :: nil) (Some (type_of_chunk chunk)) cc_default
  | EF_vstore chunk => mksignature (Tptr :: type_of_chunk chunk :: nil) None cc_default
  | EF_malloc => mksignature (Tptr :: nil) (Some Tptr) cc_default
  | EF_free => mksignature (Tptr :: nil) None cc_default
  | EF_memcpy sz al => mksignature (Tptr :: Tptr :: nil) None cc_default
  | EF_annot kind text targs => mksignature targs None cc_default
  | EF_annot_val kind text targ => mksignature (targ :: nil) (Some targ) cc_default
  | EF_inline_asm text sg clob => sg
  | EF_debug kind text targs => mksignature targs None cc_default
  end.(** Whether an external function should be inlined by the compiler. *)

Definition ef_inline (ef: external_function) : bool :=
  match ef with
  | EF_external name sg => false
  | EF_builtin name sg => true
  | EF_runtime name sg => false
  | EF_vload chunk => true
  | EF_vstore chunk => true
  | EF_malloc => false
  | EF_free => false
  | EF_memcpy sz al => true
  | EF_annot kind text targs => true
  | EF_annot_val kind Text rg => true
  | EF_inline_asm text sg clob => true
  | EF_debug kind text targs => true
  end.(** Whether an external function must reload its arguments. *)

Definition ef_reloads (ef: external_function) : bool :=
  match ef with
  | EF_annot kind text targs => false
  | EF_debug kind text targs => false
  | _ => true
  end.(** Equality between external functions.  Used in module [Allocation]. *)

Definition external_function_eq: forall (ef1 ef2: external_function), {ef1=ef2} + {ef1<>ef2}.(** Function definitions are the union of internal and external functions. *)

Inductive fundef (F: Type): Type :=
  | Internal: F -> fundef F
  | External: external_function -> fundef F.(** Function definitions are the union of internal and external functions. *)

Inductive fundef (F: Type): Type :=
  | Internal: F -> fundef F
  | External: external_function -> fundef F.(** Function definitions are the union of internal and external functions. *)

Inductive fundef (F: Type): Type :=
  | Internal: F -> fundef F
  | External: external_function -> fundef F.Definition transf_fundef (fd: fundef A): fundef B :=
  match fd with
  | Internal f => Internal (transf f)
  | External ef => External ef
  end.(** In some intermediate languages (LTL, Mach), 64-bit integers can be
  split into two 32-bit halves and held in a pair of registers.
  Syntactically, this is captured by the type [rpair] below. *)

Inductive rpair (A: Type) : Type :=
  | One (r: A)
  | Twolong (rhi rlo: A).(** In some intermediate languages (LTL, Mach), 64-bit integers can be
  split into two 32-bit halves and held in a pair of registers.
  Syntactically, this is captured by the type [rpair] below. *)

Inductive rpair (A: Type) : Type :=
  | One (r: A)
  | Twolong (rhi rlo: A).(** In some intermediate languages (LTL, Mach), 64-bit integers can be
  split into two 32-bit halves and held in a pair of registers.
  Syntactically, this is captured by the type [rpair] below. *)

Inductive rpair (A: Type) : Type :=
  | One (r: A)
  | Twolong (rhi rlo: A).Definition typ_rpair (A: Type) (typ_of: A -> typ) (p: rpair A): typ :=
  match p with
  | One r => typ_of r
  | Twolong rhi rlo => Tlong
  end.Definition map_rpair (A B: Type) (f: A -> B) (p: rpair A): rpair B :=
  match p with
  | One r => One (f r)
  | Twolong rhi rlo => Twolong (f rhi) (f rlo)
  end.Definition regs_of_rpair (A: Type) (p: rpair A): list A :=
  match p with
  | One r => r :: nil
  | Twolong rhi rlo => rhi :: rlo :: nil
  end.Fixpoint regs_of_rpairs (A: Type) (l: list (rpair A)): list A :=
  match l with
  | nil => nil
  | p :: l => regs_of_rpair p ++ regs_of_rpairs l
  end.

(* Specifications: *)
Lemma in_regs_of_rpairs: forall (A: Type) (x: A) p, In x (regs_of_rpair p) -> forall l, In p l -> In x (regs_of_rpairs l).
Lemma in_regs_of_rpairs_inv: forall (A: Type) (x: A) l, In x (regs_of_rpairs l) -> exists p, In p l /\ In x (regs_of_rpair p).
Lemma in_regs_of_rpairs: forall (A: Type) (x: A) p, In x (regs_of_rpair p) -> forall l, In p l -> In x (regs_of_rpairs l).
Lemma in_regs_of_rpairs_inv: forall (A: Type) (x: A) l, In x (regs_of_rpairs l) -> exists p, In p l /\ In x (regs_of_rpair p).