Section TRANSF.
Variable transf: node -> instruction -> instruction.
Definition transf_function (f: function) : function :=
mkfunction
f.(fn_sig)
f.(fn_params)
f.(fn_stacksize)
(PTree.map transf f.(fn_code))
f.(fn_entrypoint).
End TRANSF.
(** Computation of the possible successors of an instruction. This is used in particular for dataflow analyses. *)
Definition successors_instr (i: instruction) : list node :=
match i with
| Inop s => s :: nil
| Iop op args res s => s :: nil
| Iload chunk addr args dst s => s :: nil
| Istore chunk addr args src s => s :: nil
| Icall sig ros args res s => s :: nil
| Itailcall sig ros args => nil
| Ibuiltin ef args res s => s :: nil
| Icond cond args ifso ifnot => ifso :: ifnot :: nil
| Ijumptable arg tbl => tbl
| Ireturn optarg => nil
end.
Definition successors_map (f: function) : PTree.t (list node) :=
PTree.map1 successors_instr f.(fn_code).
(** The registers used by an instruction *)
Definition instr_uses (i: instruction) : list reg :=
match i with
| Inop s => nil
| Iop op args res s => args
| Iload chunk addr args dst s => args
| Istore chunk addr args src s => src :: args
| Icall sig (inl r) args res s => r :: args
| Icall sig (inr id) args res s => args
| Itailcall sig (inl r) args => r :: args
| Itailcall sig (inr id) args => args
| Ibuiltin ef args res s => params_of_builtin_args args
| Icond cond args ifso ifnot => args
| Ijumptable arg tbl => arg :: nil
| Ireturn None => nil
| Ireturn (Some arg) => arg :: nil
end.
(** The register defined by an instruction, if any *)
Definition instr_defs (i: instruction) : option reg :=
match i with
| Inop s => None
| Iop op args res s => Some res
| Iload chunk addr args dst s => Some dst
| Istore chunk addr args src s => None
| Icall sig ros args res s => Some res
| Itailcall sig ros args => None
| Ibuiltin ef args res s =>
match res with BR r => Some r | _ => None end
| Icond cond args ifso ifnot => None
| Ijumptable arg tbl => None
| Ireturn optarg => None
end.
(** Maximum PC (node number) in the CFG of a function.  All nodes of the CFG of [f] are between 1 and [max_pc_function f] (inclusive). *)
Definition max_pc_function (f: function) :=
PTree.fold (fun m pc i => Pos.max m pc) f.(fn_code) 1%positive.

Lemma max_pc_function_sound:
forall f pc i, f.(fn_code)!pc = Some i -> Ple pc (max_pc_function f).