(** Heavily annotated for a tutorial introduction. ** See the Makefile for how to strip the annotations **)
(** First, import the entire Floyd proof automation system, which ** includes the VeriC program logic and the MSL theory of separation logic **)
(** Import the theory of list segments.  This is not, strictly speaking, ** part of the Floyd system.  In principle, any user of Floyd can build ** theories of new data structures (list segments, trees, doubly linked ** lists, trees with cross edges, etc.).  We emphasize this by putting ** list_dt in the progs directory.   "dt" stands for "dependent types", ** as the theory uses Coq's dependent types to handle user-defined ** record fields. **)
(** 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 in the reverse.c file. **)
(* 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.
Definition Vprog : varspecs. mk_varspecs prog. Defined.
(** The reverse.c program uses the linked list structure [struct list]. ** This satisfies the linked-list pattern, in that it has one self-reference ** field (in this case, called [tail]) and arbitrary other fields.  The [Instance] ** explains (and proves) how [struct list] satisfies the [listspec] pattern. **)
Instance LS: listspec _list _tail (fun _ _ => emp).
(** Here's a loop invariant for use in the body_sumlist proof *)
Definition sumlist_Inv (sh: share) (contents: list int) (p: val) : environ->mpred :=
(EX cts1: list int, EX cts2: list int, EX t: val,
PROP (contents = cts1++cts2)
LOCAL (temp _t t; temp _s (Vint (sum_int cts1)))
SEP ( lseg LS sh (map Vint cts1) p t ; lseg LS sh (map Vint cts2) t nullval)).

Lemma sum_int_app:
forall a b, sum_int (a++b) = Int.add (sum_int a) (sum_int b).