(** Heavily annotated for a tutorial introduction. *)
(** First, import the entire Floyd proof automation system, which includes ** the VeriC program logic and the MSL theory of separation logic**)
(** Import the [reverse.v] file, which is produced by CompCert's clightgen ** from reverse.c.   The file reverse.v defines abbreviations for identifiers ** (variable names, etc.) of the C program, such as _head, _reverse. ** It also defines "prog", which is the entire abstract syntax tree ** of the C program *)
(* The C programming language has a special namespace for struct ** and union identifiers, e.g., "struct foo {...}".  Some type-based operators ** in the program logic need access to an interpretation of this namespace, ** i.e., the meaning of each struct-identifier such as "foo".  The next ** line (which looks identical for any program) builds this ** interpretation, called "CompSpecs" *)
Instance CompSpecs : compspecs. make_compspecs prog. Defined.
(** Calculate the "types-of-global-variables" specification ** directly from the program *)
Definition Vprog : varspecs. mk_varspecs prog. Defined.
(** A convenience definition *)
Definition t_struct_list := Tstruct _list noattr.
(** Inductive definition of linked lists *)
Fixpoint listrep (sigma: list val) (x: val) : mpred :=
match sigma with
| h::hs =>
EX y:val,
data_at Tsh t_struct_list (h,y) x  *  listrep hs y
| nil =>
!! (x = nullval) && emp
end.
Fixpoint lsegrec (sigma: list val) (x z: val) : mpred :=
match sigma with
| h::hs =>
EX y:val,
data_at Tsh t_struct_list (h,y) x  *  lsegrec hs y z
| nil =>
!! (x = z) && emp
end.
(* This file is only to demonstrate object language induction. *)
(* induction rule *)

Lemma list_ind_in_logc: forall {A: Type} (P: mpred) (Q: list A -> mpred),
P |-- Q nil ->
P |-- ALL a: A, (ALL l: list A, Q l --> Q (a :: l)) ->
P |-- ALL l: list A, Q l.