(** * Abstract syntax *)

(** RTL is organized as instructions, functions and programs.
  Instructions correspond roughly to elementary instructions of the
  target processor, but take their arguments and leave their results
  in pseudo-registers (also called temporaries in textbooks).
  Infinitely many pseudo-registers are available, and each function
  has its own set of pseudo-registers, unaffected by function calls.

  Instructions are organized as a control-flow graph: a function is
  a finite map from ``nodes'' (abstract program points) to instructions,
  and each instruction lists explicitly the nodes of its successors.
*)

Definition node := positive.Inductive instruction: Type :=
  | Inop: node -> instruction
      (** No operation -- just branch to the successor. *)
  | Iop: operation -> list reg -> reg -> node -> instruction
      (** [Iop op args dest succ] performs the arithmetic operation [op]
          over the values of registers [args], stores the result in [dest],
          and branches to [succ]. *)
  | Iload: memory_chunk -> addressing -> list reg -> reg -> node -> instruction
      (** [Iload chunk addr args dest succ] loads a [chunk] quantity from
          the address determined by the addressing mode [addr] and the
          values of the [args] registers, stores the quantity just read
          into [dest], and branches to [succ]. *)
  | Istore: memory_chunk -> addressing -> list reg -> reg -> node -> instruction
      (** [Istore chunk addr args src succ] stores the value of register
          [src] in the [chunk] quantity at the
          the address determined by the addressing mode [addr] and the
          values of the [args] registers, then branches to [succ]. *)
  | Icall: signature -> reg + ident -> list reg -> reg -> node -> instruction
      (** [Icall sig fn args dest succ] invokes the function determined by
          [fn] (either a function pointer found in a register or a
          function name), giving it the values of registers [args]
          as arguments.  It stores the return value in [dest] and branches
          to [succ]. *)
  | Itailcall: signature -> reg + ident -> list reg -> instruction
      (** [Itailcall sig fn args] performs a function invocation
          in tail-call position.  *)
  | Ibuiltin: external_function -> list (builtin_arg reg) -> builtin_res reg -> node -> instruction
      (** [Ibuiltin ef args dest succ] calls the built-in function
          identified by [ef], giving it the values of [args] as arguments.
          It stores the return value in [dest] and branches to [succ]. *)
  | Icond: condition -> list reg -> node -> node -> instruction
      (** [Icond cond args ifso ifnot] evaluates the boolean condition
          [cond] over the values of registers [args].  If the condition
          is true, it transitions to [ifso].  If the condition is false,
          it transitions to [ifnot]. *)
  | Ijumptable: reg -> list node -> instruction
      (** [Ijumptable arg tbl] transitions to the node that is the [n]-th
          element of the list [tbl], where [n] is the signed integer
          value of register [arg]. *)
  | Ireturn: option reg -> instruction.Inductive instruction: Type :=
  | Inop: node -> instruction
      (** No operation -- just branch to the successor. *)
  | Iop: operation -> list reg -> reg -> node -> instruction
      (** [Iop op args dest succ] performs the arithmetic operation [op]
          over the values of registers [args], stores the result in [dest],
          and branches to [succ]. *)
  | Iload: memory_chunk -> addressing -> list reg -> reg -> node -> instruction
      (** [Iload chunk addr args dest succ] loads a [chunk] quantity from
          the address determined by the addressing mode [addr] and the
          values of the [args] registers, stores the quantity just read
          into [dest], and branches to [succ]. *)
  | Istore: memory_chunk -> addressing -> list reg -> reg -> node -> instruction
      (** [Istore chunk addr args src succ] stores the value of register
          [src] in the [chunk] quantity at the
          the address determined by the addressing mode [addr] and the
          values of the [args] registers, then branches to [succ]. *)
  | Icall: signature -> reg + ident -> list reg -> reg -> node -> instruction
      (** [Icall sig fn args dest succ] invokes the function determined by
          [fn] (either a function pointer found in a register or a
          function name), giving it the values of registers [args]
          as arguments.  It stores the return value in [dest] and branches
          to [succ]. *)
  | Itailcall: signature -> reg + ident -> list reg -> instruction
      (** [Itailcall sig fn args] performs a function invocation
          in tail-call position.  *)
  | Ibuiltin: external_function -> list (builtin_arg reg) -> builtin_res reg -> node -> instruction
      (** [Ibuiltin ef args dest succ] calls the built-in function
          identified by [ef], giving it the values of [args] as arguments.
          It stores the return value in [dest] and branches to [succ]. *)
  | Icond: condition -> list reg -> node -> node -> instruction
      (** [Icond cond args ifso ifnot] evaluates the boolean condition
          [cond] over the values of registers [args].  If the condition
          is true, it transitions to [ifso].  If the condition is false,
          it transitions to [ifnot]. *)
  | Ijumptable: reg -> list node -> instruction
      (** [Ijumptable arg tbl] transitions to the node that is the [n]-th
          element of the list [tbl], where [n] is the signed integer
          value of register [arg]. *)
  | Ireturn: option reg -> instruction.Inductive instruction: Type :=
  | Inop: node -> instruction
      (** No operation -- just branch to the successor. *)
  | Iop: operation -> list reg -> reg -> node -> instruction
      (** [Iop op args dest succ] performs the arithmetic operation [op]
          over the values of registers [args], stores the result in [dest],
          and branches to [succ]. *)
  | Iload: memory_chunk -> addressing -> list reg -> reg -> node -> instruction
      (** [Iload chunk addr args dest succ] loads a [chunk] quantity from
          the address determined by the addressing mode [addr] and the
          values of the [args] registers, stores the quantity just read
          into [dest], and branches to [succ]. *)
  | Istore: memory_chunk -> addressing -> list reg -> reg -> node -> instruction
      (** [Istore chunk addr args src succ] stores the value of register
          [src] in the [chunk] quantity at the
          the address determined by the addressing mode [addr] and the
          values of the [args] registers, then branches to [succ]. *)
  | Icall: signature -> reg + ident -> list reg -> reg -> node -> instruction
      (** [Icall sig fn args dest succ] invokes the function determined by
          [fn] (either a function pointer found in a register or a
          function name), giving it the values of registers [args]
          as arguments.  It stores the return value in [dest] and branches
          to [succ]. *)
  | Itailcall: signature -> reg + ident -> list reg -> instruction
      (** [Itailcall sig fn args] performs a function invocation
          in tail-call position.  *)
  | Ibuiltin: external_function -> list (builtin_arg reg) -> builtin_res reg -> node -> instruction
      (** [Ibuiltin ef args dest succ] calls the built-in function
          identified by [ef], giving it the values of [args] as arguments.
          It stores the return value in [dest] and branches to [succ]. *)
  | Icond: condition -> list reg -> node -> node -> instruction
      (** [Icond cond args ifso ifnot] evaluates the boolean condition
          [cond] over the values of registers [args].  If the condition
          is true, it transitions to [ifso].  If the condition is false,
          it transitions to [ifnot]. *)
  | Ijumptable: reg -> list node -> instruction
      (** [Ijumptable arg tbl] transitions to the node that is the [n]-th
          element of the list [tbl], where [n] is the signed integer
          value of register [arg]. *)
  | Ireturn: option reg -> instruction.Inductive instruction: Type :=
  | Inop: node -> instruction
      (** No operation -- just branch to the successor. *)
  | Iop: operation -> list reg -> reg -> node -> instruction
      (** [Iop op args dest succ] performs the arithmetic operation [op]
          over the values of registers [args], stores the result in [dest],
          and branches to [succ]. *)
  | Iload: memory_chunk -> addressing -> list reg -> reg -> node -> instruction
      (** [Iload chunk addr args dest succ] loads a [chunk] quantity from
          the address determined by the addressing mode [addr] and the
          values of the [args] registers, stores the quantity just read
          into [dest], and branches to [succ]. *)
  | Istore: memory_chunk -> addressing -> list reg -> reg -> node -> instruction
      (** [Istore chunk addr args src succ] stores the value of register
          [src] in the [chunk] quantity at the
          the address determined by the addressing mode [addr] and the
          values of the [args] registers, then branches to [succ]. *)
  | Icall: signature -> reg + ident -> list reg -> reg -> node -> instruction
      (** [Icall sig fn args dest succ] invokes the function determined by
          [fn] (either a function pointer found in a register or a
          function name), giving it the values of registers [args]
          as arguments.  It stores the return value in [dest] and branches
          to [succ]. *)
  | Itailcall: signature -> reg + ident -> list reg -> instruction
      (** [Itailcall sig fn args] performs a function invocation
          in tail-call position.  *)
  | Ibuiltin: external_function -> list (builtin_arg reg) -> builtin_res reg -> node -> instruction
      (** [Ibuiltin ef args dest succ] calls the built-in function
          identified by [ef], giving it the values of [args] as arguments.
          It stores the return value in [dest] and branches to [succ]. *)
  | Icond: condition -> list reg -> node -> node -> instruction
      (** [Icond cond args ifso ifnot] evaluates the boolean condition
          [cond] over the values of registers [args].  If the condition
          is true, it transitions to [ifso].  If the condition is false,
          it transitions to [ifnot]. *)
  | Ijumptable: reg -> list node -> instruction
      (** [Ijumptable arg tbl] transitions to the node that is the [n]-th
          element of the list [tbl], where [n] is the signed integer
          value of register [arg]. *)
  | Ireturn: option reg -> instruction.Inductive instruction: Type :=
  | Inop: node -> instruction
      (** No operation -- just branch to the successor. *)
  | Iop: operation -> list reg -> reg -> node -> instruction
      (** [Iop op args dest succ] performs the arithmetic operation [op]
          over the values of registers [args], stores the result in [dest],
          and branches to [succ]. *)
  | Iload: memory_chunk -> addressing -> list reg -> reg -> node -> instruction
      (** [Iload chunk addr args dest succ] loads a [chunk] quantity from
          the address determined by the addressing mode [addr] and the
          values of the [args] registers, stores the quantity just read
          into [dest], and branches to [succ]. *)
  | Istore: memory_chunk -> addressing -> list reg -> reg -> node -> instruction
      (** [Istore chunk addr args src succ] stores the value of register
          [src] in the [chunk] quantity at the
          the address determined by the addressing mode [addr] and the
          values of the [args] registers, then branches to [succ]. *)
  | Icall: signature -> reg + ident -> list reg -> reg -> node -> instruction
      (** [Icall sig fn args dest succ] invokes the function determined by
          [fn] (either a function pointer found in a register or a
          function name), giving it the values of registers [args]
          as arguments.  It stores the return value in [dest] and branches
          to [succ]. *)
  | Itailcall: signature -> reg + ident -> list reg -> instruction
      (** [Itailcall sig fn args] performs a function invocation
          in tail-call position.  *)
  | Ibuiltin: external_function -> list (builtin_arg reg) -> builtin_res reg -> node -> instruction
      (** [Ibuiltin ef args dest succ] calls the built-in function
          identified by [ef], giving it the values of [args] as arguments.
          It stores the return value in [dest] and branches to [succ]. *)
  | Icond: condition -> list reg -> node -> node -> instruction
      (** [Icond cond args ifso ifnot] evaluates the boolean condition
          [cond] over the values of registers [args].  If the condition
          is true, it transitions to [ifso].  If the condition is false,
          it transitions to [ifnot]. *)
  | Ijumptable: reg -> list node -> instruction
      (** [Ijumptable arg tbl] transitions to the node that is the [n]-th
          element of the list [tbl], where [n] is the signed integer
          value of register [arg]. *)
  | Ireturn: option reg -> instruction.Inductive instruction: Type :=
  | Inop: node -> instruction
      (** No operation -- just branch to the successor. *)
  | Iop: operation -> list reg -> reg -> node -> instruction
      (** [Iop op args dest succ] performs the arithmetic operation [op]
          over the values of registers [args], stores the result in [dest],
          and branches to [succ]. *)
  | Iload: memory_chunk -> addressing -> list reg -> reg -> node -> instruction
      (** [Iload chunk addr args dest succ] loads a [chunk] quantity from
          the address determined by the addressing mode [addr] and the
          values of the [args] registers, stores the quantity just read
          into [dest], and branches to [succ]. *)
  | Istore: memory_chunk -> addressing -> list reg -> reg -> node -> instruction
      (** [Istore chunk addr args src succ] stores the value of register
          [src] in the [chunk] quantity at the
          the address determined by the addressing mode [addr] and the
          values of the [args] registers, then branches to [succ]. *)
  | Icall: signature -> reg + ident -> list reg -> reg -> node -> instruction
      (** [Icall sig fn args dest succ] invokes the function determined by
          [fn] (either a function pointer found in a register or a
          function name), giving it the values of registers [args]
          as arguments.  It stores the return value in [dest] and branches
          to [succ]. *)
  | Itailcall: signature -> reg + ident -> list reg -> instruction
      (** [Itailcall sig fn args] performs a function invocation
          in tail-call position.  *)
  | Ibuiltin: external_function -> list (builtin_arg reg) -> builtin_res reg -> node -> instruction
      (** [Ibuiltin ef args dest succ] calls the built-in function
          identified by [ef], giving it the values of [args] as arguments.
          It stores the return value in [dest] and branches to [succ]. *)
  | Icond: condition -> list reg -> node -> node -> instruction
      (** [Icond cond args ifso ifnot] evaluates the boolean condition
          [cond] over the values of registers [args].  If the condition
          is true, it transitions to [ifso].  If the condition is false,
          it transitions to [ifnot]. *)
  | Ijumptable: reg -> list node -> instruction
      (** [Ijumptable arg tbl] transitions to the node that is the [n]-th
          element of the list [tbl], where [n] is the signed integer
          value of register [arg]. *)
  | Ireturn: option reg -> instruction.Inductive instruction: Type :=
  | Inop: node -> instruction
      (** No operation -- just branch to the successor. *)
  | Iop: operation -> list reg -> reg -> node -> instruction
      (** [Iop op args dest succ] performs the arithmetic operation [op]
          over the values of registers [args], stores the result in [dest],
          and branches to [succ]. *)
  | Iload: memory_chunk -> addressing -> list reg -> reg -> node -> instruction
      (** [Iload chunk addr args dest succ] loads a [chunk] quantity from
          the address determined by the addressing mode [addr] and the
          values of the [args] registers, stores the quantity just read
          into [dest], and branches to [succ]. *)
  | Istore: memory_chunk -> addressing -> list reg -> reg -> node -> instruction
      (** [Istore chunk addr args src succ] stores the value of register
          [src] in the [chunk] quantity at the
          the address determined by the addressing mode [addr] and the
          values of the [args] registers, then branches to [succ]. *)
  | Icall: signature -> reg + ident -> list reg -> reg -> node -> instruction
      (** [Icall sig fn args dest succ] invokes the function determined by
          [fn] (either a function pointer found in a register or a
          function name), giving it the values of registers [args]
          as arguments.  It stores the return value in [dest] and branches
          to [succ]. *)
  | Itailcall: signature -> reg + ident -> list reg -> instruction
      (** [Itailcall sig fn args] performs a function invocation
          in tail-call position.  *)
  | Ibuiltin: external_function -> list (builtin_arg reg) -> builtin_res reg -> node -> instruction
      (** [Ibuiltin ef args dest succ] calls the built-in function
          identified by [ef], giving it the values of [args] as arguments.
          It stores the return value in [dest] and branches to [succ]. *)
  | Icond: condition -> list reg -> node -> node -> instruction
      (** [Icond cond args ifso ifnot] evaluates the boolean condition
          [cond] over the values of registers [args].  If the condition
          is true, it transitions to [ifso].  If the condition is false,
          it transitions to [ifnot]. *)
  | Ijumptable: reg -> list node -> instruction
      (** [Ijumptable arg tbl] transitions to the node that is the [n]-th
          element of the list [tbl], where [n] is the signed integer
          value of register [arg]. *)
  | Ireturn: option reg -> instruction.Inductive instruction: Type :=
  | Inop: node -> instruction
      (** No operation -- just branch to the successor. *)
  | Iop: operation -> list reg -> reg -> node -> instruction
      (** [Iop op args dest succ] performs the arithmetic operation [op]
          over the values of registers [args], stores the result in [dest],
          and branches to [succ]. *)
  | Iload: memory_chunk -> addressing -> list reg -> reg -> node -> instruction
      (** [Iload chunk addr args dest succ] loads a [chunk] quantity from
          the address determined by the addressing mode [addr] and the
          values of the [args] registers, stores the quantity just read
          into [dest], and branches to [succ]. *)
  | Istore: memory_chunk -> addressing -> list reg -> reg -> node -> instruction
      (** [Istore chunk addr args src succ] stores the value of register
          [src] in the [chunk] quantity at the
          the address determined by the addressing mode [addr] and the
          values of the [args] registers, then branches to [succ]. *)
  | Icall: signature -> reg + ident -> list reg -> reg -> node -> instruction
      (** [Icall sig fn args dest succ] invokes the function determined by
          [fn] (either a function pointer found in a register or a
          function name), giving it the values of registers [args]
          as arguments.  It stores the return value in [dest] and branches
          to [succ]. *)
  | Itailcall: signature -> reg + ident -> list reg -> instruction
      (** [Itailcall sig fn args] performs a function invocation
          in tail-call position.  *)
  | Ibuiltin: external_function -> list (builtin_arg reg) -> builtin_res reg -> node -> instruction
      (** [Ibuiltin ef args dest succ] calls the built-in function
          identified by [ef], giving it the values of [args] as arguments.
          It stores the return value in [dest] and branches to [succ]. *)
  | Icond: condition -> list reg -> node -> node -> instruction
      (** [Icond cond args ifso ifnot] evaluates the boolean condition
          [cond] over the values of registers [args].  If the condition
          is true, it transitions to [ifso].  If the condition is false,
          it transitions to [ifnot]. *)
  | Ijumptable: reg -> list node -> instruction
      (** [Ijumptable arg tbl] transitions to the node that is the [n]-th
          element of the list [tbl], where [n] is the signed integer
          value of register [arg]. *)
  | Ireturn: option reg -> instruction.Inductive instruction: Type :=
  | Inop: node -> instruction
      (** No operation -- just branch to the successor. *)
  | Iop: operation -> list reg -> reg -> node -> instruction
      (** [Iop op args dest succ] performs the arithmetic operation [op]
          over the values of registers [args], stores the result in [dest],
          and branches to [succ]. *)
  | Iload: memory_chunk -> addressing -> list reg -> reg -> node -> instruction
      (** [Iload chunk addr args dest succ] loads a [chunk] quantity from
          the address determined by the addressing mode [addr] and the
          values of the [args] registers, stores the quantity just read
          into [dest], and branches to [succ]. *)
  | Istore: memory_chunk -> addressing -> list reg -> reg -> node -> instruction
      (** [Istore chunk addr args src succ] stores the value of register
          [src] in the [chunk] quantity at the
          the address determined by the addressing mode [addr] and the
          values of the [args] registers, then branches to [succ]. *)
  | Icall: signature -> reg + ident -> list reg -> reg -> node -> instruction
      (** [Icall sig fn args dest succ] invokes the function determined by
          [fn] (either a function pointer found in a register or a
          function name), giving it the values of registers [args]
          as arguments.  It stores the return value in [dest] and branches
          to [succ]. *)
  | Itailcall: signature -> reg + ident -> list reg -> instruction
      (** [Itailcall sig fn args] performs a function invocation
          in tail-call position.  *)
  | Ibuiltin: external_function -> list (builtin_arg reg) -> builtin_res reg -> node -> instruction
      (** [Ibuiltin ef args dest succ] calls the built-in function
          identified by [ef], giving it the values of [args] as arguments.
          It stores the return value in [dest] and branches to [succ]. *)
  | Icond: condition -> list reg -> node -> node -> instruction
      (** [Icond cond args ifso ifnot] evaluates the boolean condition
          [cond] over the values of registers [args].  If the condition
          is true, it transitions to [ifso].  If the condition is false,
          it transitions to [ifnot]. *)
  | Ijumptable: reg -> list node -> instruction
      (** [Ijumptable arg tbl] transitions to the node that is the [n]-th
          element of the list [tbl], where [n] is the signed integer
          value of register [arg]. *)
  | Ireturn: option reg -> instruction.Inductive instruction: Type :=
  | Inop: node -> instruction
      (** No operation -- just branch to the successor. *)
  | Iop: operation -> list reg -> reg -> node -> instruction
      (** [Iop op args dest succ] performs the arithmetic operation [op]
          over the values of registers [args], stores the result in [dest],
          and branches to [succ]. *)
  | Iload: memory_chunk -> addressing -> list reg -> reg -> node -> instruction
      (** [Iload chunk addr args dest succ] loads a [chunk] quantity from
          the address determined by the addressing mode [addr] and the
          values of the [args] registers, stores the quantity just read
          into [dest], and branches to [succ]. *)
  | Istore: memory_chunk -> addressing -> list reg -> reg -> node -> instruction
      (** [Istore chunk addr args src succ] stores the value of register
          [src] in the [chunk] quantity at the
          the address determined by the addressing mode [addr] and the
          values of the [args] registers, then branches to [succ]. *)
  | Icall: signature -> reg + ident -> list reg -> reg -> node -> instruction
      (** [Icall sig fn args dest succ] invokes the function determined by
          [fn] (either a function pointer found in a register or a
          function name), giving it the values of registers [args]
          as arguments.  It stores the return value in [dest] and branches
          to [succ]. *)
  | Itailcall: signature -> reg + ident -> list reg -> instruction
      (** [Itailcall sig fn args] performs a function invocation
          in tail-call position.  *)
  | Ibuiltin: external_function -> list (builtin_arg reg) -> builtin_res reg -> node -> instruction
      (** [Ibuiltin ef args dest succ] calls the built-in function
          identified by [ef], giving it the values of [args] as arguments.
          It stores the return value in [dest] and branches to [succ]. *)
  | Icond: condition -> list reg -> node -> node -> instruction
      (** [Icond cond args ifso ifnot] evaluates the boolean condition
          [cond] over the values of registers [args].  If the condition
          is true, it transitions to [ifso].  If the condition is false,
          it transitions to [ifnot]. *)
  | Ijumptable: reg -> list node -> instruction
      (** [Ijumptable arg tbl] transitions to the node that is the [n]-th
          element of the list [tbl], where [n] is the signed integer
          value of register [arg]. *)
  | Ireturn: option reg -> instruction.Inductive instruction: Type :=
  | Inop: node -> instruction
      (** No operation -- just branch to the successor. *)
  | Iop: operation -> list reg -> reg -> node -> instruction
      (** [Iop op args dest succ] performs the arithmetic operation [op]
          over the values of registers [args], stores the result in [dest],
          and branches to [succ]. *)
  | Iload: memory_chunk -> addressing -> list reg -> reg -> node -> instruction
      (** [Iload chunk addr args dest succ] loads a [chunk] quantity from
          the address determined by the addressing mode [addr] and the
          values of the [args] registers, stores the quantity just read
          into [dest], and branches to [succ]. *)
  | Istore: memory_chunk -> addressing -> list reg -> reg -> node -> instruction
      (** [Istore chunk addr args src succ] stores the value of register
          [src] in the [chunk] quantity at the
          the address determined by the addressing mode [addr] and the
          values of the [args] registers, then branches to [succ]. *)
  | Icall: signature -> reg + ident -> list reg -> reg -> node -> instruction
      (** [Icall sig fn args dest succ] invokes the function determined by
          [fn] (either a function pointer found in a register or a
          function name), giving it the values of registers [args]
          as arguments.  It stores the return value in [dest] and branches
          to [succ]. *)
  | Itailcall: signature -> reg + ident -> list reg -> instruction
      (** [Itailcall sig fn args] performs a function invocation
          in tail-call position.  *)
  | Ibuiltin: external_function -> list (builtin_arg reg) -> builtin_res reg -> node -> instruction
      (** [Ibuiltin ef args dest succ] calls the built-in function
          identified by [ef], giving it the values of [args] as arguments.
          It stores the return value in [dest] and branches to [succ]. *)
  | Icond: condition -> list reg -> node -> node -> instruction
      (** [Icond cond args ifso ifnot] evaluates the boolean condition
          [cond] over the values of registers [args].  If the condition
          is true, it transitions to [ifso].  If the condition is false,
          it transitions to [ifnot]. *)
  | Ijumptable: reg -> list node -> instruction
      (** [Ijumptable arg tbl] transitions to the node that is the [n]-th
          element of the list [tbl], where [n] is the signed integer
          value of register [arg]. *)
  | Ireturn: option reg -> instruction.(** [Ireturn] terminates the execution of the current function
          (it has no successor).  It returns the value of the given
          register, or [Vundef] if none is given. *)

Definition code: Type := PTree.t instruction.Record function: Type := mkfunction {
  fn_sig: signature;
  fn_params: list reg;
  fn_stacksize: Z;
  fn_code: code;
  fn_entrypoint: node
}.Record function: Type := mkfunction {
  fn_sig: signature;
  fn_params: list reg;
  fn_stacksize: Z;
  fn_code: code;
  fn_entrypoint: node
}.Record function: Type := mkfunction {
  fn_sig: signature;
  fn_params: list reg;
  fn_stacksize: Z;
  fn_code: code;
  fn_entrypoint: node
}.Record function: Type := mkfunction {
  fn_sig: signature;
  fn_params: list reg;
  fn_stacksize: Z;
  fn_code: code;
  fn_entrypoint: node
}.Record function: Type := mkfunction {
  fn_sig: signature;
  fn_params: list reg;
  fn_stacksize: Z;
  fn_code: code;
  fn_entrypoint: node
}.Record function: Type := mkfunction {
  fn_sig: signature;
  fn_params: list reg;
  fn_stacksize: Z;
  fn_code: code;
  fn_entrypoint: node
}.Record function: Type := mkfunction {
  fn_sig: signature;
  fn_params: list reg;
  fn_stacksize: Z;
  fn_code: code;
  fn_entrypoint: node
}.(** A function description comprises a control-flow graph (CFG) [fn_code]
    (a partial finite mapping from nodes to instructions).  As in Cminor,
    [fn_sig] is the function signature and [fn_stacksize] the number of bytes
    for its stack-allocated activation record.  [fn_params] is the list
    of registers that are bound to the values of arguments at call time.
    [fn_entrypoint] is the node of the first instruction of the function
    in the CFG. *)

Definition fundef := AST.fundef function.Definition program := AST.program fundef unit.Definition funsig (fd: fundef) :=
  match fd with
  | Internal f => fn_sig f
  | External ef => ef_sig ef
  end.(** * Operational semantics *)

Definition genv := Genv.t fundef unit.Definition regset := Regmap.t val.Fixpoint init_regs (vl: list val) (rl: list reg) {struct rl} : regset :=
  match rl, vl with
  | r1 :: rs, v1 :: vs => Regmap.set r1 v1 (init_regs vs rs)
  | _, _ => Regmap.init Vundef
  end.(** The dynamic semantics of RTL is given in small-step style, as a
  set of transitions between states.  A state captures the current
  point in the execution.  Three kinds of states appear in the transitions:

- [State cs f sp pc rs m] describes an execution point within a function.
  [f] is the current function.
  [sp] is the pointer to the stack block for its current activation
     (as in Cminor).
  [pc] is the current program point (CFG node) within the code [c].
  [rs] gives the current values for the pseudo-registers.
  [m] is the current memory state.
- [Callstate cs f args m] is an intermediate state that appears during
  function calls.
  [f] is the function definition that we are calling.
  [args] (a list of values) are the arguments for this call.
  [m] is the current memory state.
- [Returnstate cs v m] is an intermediate state that appears when a
  function terminates and returns to its caller.
  [v] is the return value and [m] the current memory state.

In all three kinds of states, the [cs] parameter represents the call stack.
It is a list of frames [Stackframe res f sp pc rs].  Each frame represents
a function call in progress.
[res] is the pseudo-register that will receive the result of the call.
[f] is the calling function.
[sp] is its stack pointer.
[pc] is the program point for the instruction that follows the call.
[rs] is the state of registers in the calling function.
*)

Inductive stackframe : Type :=
  | Stackframe:
      forall (res: reg)            (**r where to store the result *)
             (f: function)         (**r calling function *)
             (sp: val)             (**r stack pointer in calling function *)
             (pc: node)            (**r program point in calling function *)
             (rs: regset),         (**r register state in calling function *)
      stackframe.(** The dynamic semantics of RTL is given in small-step style, as a
  set of transitions between states.  A state captures the current
  point in the execution.  Three kinds of states appear in the transitions:

- [State cs f sp pc rs m] describes an execution point within a function.
  [f] is the current function.
  [sp] is the pointer to the stack block for its current activation
     (as in Cminor).
  [pc] is the current program point (CFG node) within the code [c].
  [rs] gives the current values for the pseudo-registers.
  [m] is the current memory state.
- [Callstate cs f args m] is an intermediate state that appears during
  function calls.
  [f] is the function definition that we are calling.
  [args] (a list of values) are the arguments for this call.
  [m] is the current memory state.
- [Returnstate cs v m] is an intermediate state that appears when a
  function terminates and returns to its caller.
  [v] is the return value and [m] the current memory state.

In all three kinds of states, the [cs] parameter represents the call stack.
It is a list of frames [Stackframe res f sp pc rs].  Each frame represents
a function call in progress.
[res] is the pseudo-register that will receive the result of the call.
[f] is the calling function.
[sp] is its stack pointer.
[pc] is the program point for the instruction that follows the call.
[rs] is the state of registers in the calling function.
*)

Inductive stackframe : Type :=
  | Stackframe:
      forall (res: reg)            (**r where to store the result *)
             (f: function)         (**r calling function *)
             (sp: val)             (**r stack pointer in calling function *)
             (pc: node)            (**r program point in calling function *)
             (rs: regset),         (**r register state in calling function *)
      stackframe.Inductive state : Type :=
  | State:
      forall (stack: list stackframe) (**r call stack *)
             (f: function)            (**r current function *)
             (sp: val)                (**r stack pointer *)
             (pc: node)               (**r current program point in [c] *)
             (rs: regset)             (**r register state *)
             (m: mem),                (**r memory state *)
      state
  | Callstate:
      forall (stack: list stackframe) (**r call stack *)
             (f: fundef)              (**r function to call *)
             (args: list val)         (**r arguments to the call *)
             (m: mem),                (**r memory state *)
      state
  | Returnstate:
      forall (stack: list stackframe) (**r call stack *)
             (v: val)                 (**r return value for the call *)
             (m: mem),                (**r memory state *)
      state.Inductive state : Type :=
  | State:
      forall (stack: list stackframe) (**r call stack *)
             (f: function)            (**r current function *)
             (sp: val)                (**r stack pointer *)
             (pc: node)               (**r current program point in [c] *)
             (rs: regset)             (**r register state *)
             (m: mem),                (**r memory state *)
      state
  | Callstate:
      forall (stack: list stackframe) (**r call stack *)
             (f: fundef)              (**r function to call *)
             (args: list val)         (**r arguments to the call *)
             (m: mem),                (**r memory state *)
      state
  | Returnstate:
      forall (stack: list stackframe) (**r call stack *)
             (v: val)                 (**r return value for the call *)
             (m: mem),                (**r memory state *)
      state.Inductive state : Type :=
  | State:
      forall (stack: list stackframe) (**r call stack *)
             (f: function)            (**r current function *)
             (sp: val)                (**r stack pointer *)
             (pc: node)               (**r current program point in [c] *)
             (rs: regset)             (**r register state *)
             (m: mem),                (**r memory state *)
      state
  | Callstate:
      forall (stack: list stackframe) (**r call stack *)
             (f: fundef)              (**r function to call *)
             (args: list val)         (**r arguments to the call *)
             (m: mem),                (**r memory state *)
      state
  | Returnstate:
      forall (stack: list stackframe) (**r call stack *)
             (v: val)                 (**r return value for the call *)
             (m: mem),                (**r memory state *)
      state.Inductive state : Type :=
  | State:
      forall (stack: list stackframe) (**r call stack *)
             (f: function)            (**r current function *)
             (sp: val)                (**r stack pointer *)
             (pc: node)               (**r current program point in [c] *)
             (rs: regset)             (**r register state *)
             (m: mem),                (**r memory state *)
      state
  | Callstate:
      forall (stack: list stackframe) (**r call stack *)
             (f: fundef)              (**r function to call *)
             (args: list val)         (**r arguments to the call *)
             (m: mem),                (**r memory state *)
      state
  | Returnstate:
      forall (stack: list stackframe) (**r call stack *)
             (v: val)                 (**r return value for the call *)
             (m: mem),                (**r memory state *)
      state.(** Execution of whole programs are described as sequences of transitions
  from an initial state to a final state.  An initial state is a [Callstate]
  corresponding to the invocation of the ``main'' function of the program
  without arguments and with an empty call stack. *)

Inductive initial_state (p: program): state -> Prop :=
  | initial_state_intro: forall b f m0,
      let ge := Genv.globalenv p in
      Genv.init_mem p = Some m0 ->
      Genv.find_symbol ge p.(prog_main) = Some b ->
      Genv.find_funct_ptr ge b = Some f ->
      funsig f = signature_main ->
      initial_state p (Callstate nil f nil m0).(** Execution of whole programs are described as sequences of transitions
  from an initial state to a final state.  An initial state is a [Callstate]
  corresponding to the invocation of the ``main'' function of the program
  without arguments and with an empty call stack. *)

Inductive initial_state (p: program): state -> Prop :=
  | initial_state_intro: forall b f m0,
      let ge := Genv.globalenv p in
      Genv.init_mem p = Some m0 ->
      Genv.find_symbol ge p.(prog_main) = Some b ->
      Genv.find_funct_ptr ge b = Some f ->
      funsig f = signature_main ->
      initial_state p (Callstate nil f nil m0).(** Execution of whole programs are described as sequences of transitions
  from an initial state to a final state.  An initial state is a [Callstate]
  corresponding to the invocation of the ``main'' function of the program
  without arguments and with an empty call stack. *)

Inductive initial_state (p: program): state -> Prop :=
  | initial_state_intro: forall b f m0,
      let ge := Genv.globalenv p in
      Genv.init_mem p = Some m0 ->
      Genv.find_symbol ge p.(prog_main) = Some b ->
      Genv.find_funct_ptr ge b = Some f ->
      funsig f = signature_main ->
      initial_state p (Callstate nil f nil m0).(** A final state is a [Returnstate] with an empty call stack. *)

Inductive final_state: state -> int -> Prop :=
  | final_state_intro: forall r m,
      final_state (Returnstate nil (Vint r) m) r.(** A final state is a [Returnstate] with an empty call stack. *)

Inductive final_state: state -> int -> Prop :=
  | final_state_intro: forall r m,
      final_state (Returnstate nil (Vint r) m) r.(** The small-step semantics for a program. *)

Definition semantics (p: program) :=
  Semantics step (initial_state p) final_state (Genv.globalenv p).

Lemma semantics_receptive: forall (p: program), receptive (semantics p).