Commit 319c0954 authored by Sylvain Dailler's avatar Sylvain Dailler
Browse files

Simplification of strong induction principle

parent f02b7674
......@@ -20,8 +20,8 @@ open Args_wrapper
(* Documentation of induction:
From task [delta, x: int, delta'(x) |- G(x)], variable x and term bound, builds the tasks:
[delta, x: int, x <= bound, delta'(x) |- G(x)] and
[delta, x: int, x >= bound, (delta'(x) -> G(x)), delta'(x+1) |- G(x+1)]
[delta, x: int, x < bound, delta'(x) |- G(x)] and
[delta, x: int, x >= bound, (forall n, n < x -> delta'(n) -> G(n)), delta'(x) |- G(x)]
x cannot occur in delta as it can only appear after its declaration (by
construction of the task). Also, G is not part of delta'.
......@@ -129,7 +129,7 @@ let collect_lsymbol s (d: decl) =
(* s is a set of variables, g is a term. If d contains one of the elements of s
then all variables of d are added to s and the declaration is prepended to g.
let revert_only_stuff (g, s) (d: decl) =
let revert_chosen_decls (g, s) (d: decl) =
let d_set = collect_lsymbol Sls.empty d in
let interp = Sls.inter s d_set in
if Sls.equal interp Sls.empty then
......@@ -140,10 +140,10 @@ let revert_only_stuff (g, s) (d: decl) =
(* Build a term that generalizes all the declarations that were given in l and
that contains at least one of the variables in the set s. Actually, only
revert what is necessary to build a correct term. *)
let revert_only_stuff_list s (l: decl list) (g: decl) (t: term) =
let revert_chosen_decls_list s (l: decl list) (g: decl) (t: term) =
(* The goal is a special case, we collect its variable independantly *)
let s = collect_lsymbol s g in
fst (List.fold_left revert_only_stuff (t, s) l)
fst (List.fold_left revert_chosen_decls (t, s) l)
let induction x bound env =
(* Default bound is 0 if not given *)
......@@ -160,9 +160,7 @@ let induction x bound env =
(* Loading of needed symbols from int theory *)
let th = Env.read_theory env ["int"] "Int" in
let le_int = Theory.ns_find_ls th.Theory.th_export ["infix <="] in
let plus_int = Theory.ns_find_ls th.Theory.th_export ["infix +"] in
let one_int =
Term.t_const (Number.ConstInt (Number.int_const_dec "1")) Ty.ty_int in
let lt_int = Theory.ns_find_ls th.Theory.th_export ["infix <"] in
(* Symbol associated to term x *)
let lsx =
......@@ -192,12 +190,12 @@ let induction x bound env =
raise (Arg_trans "induction")
let t_delta' =
revert_only_stuff_list (Sls.add lsx Sls.empty) !delta' d t in
revert_chosen_decls_list (Sls.add lsx Sls.empty) !delta' d t in
let n = Term.create_vsymbol (Ident.id_fresh "n") Ty.ty_int in
(* t_delta' = forall n, n <= x -> t_delta'[x <- n] *)
(* t_delta' = forall n, n < x -> t_delta'[x <- n] *)
let t_delta' =
t_forall_close [n] []
(t_implies (Term.t_app_infer le_int [t_var n; x]) (t_replace x (t_var n) t_delta'))
(t_implies (Term.t_app_infer lt_int [t_var n; x]) (t_replace x (t_var n) t_delta'))
(* x_ge_bound = bound <= x *)
......@@ -205,19 +203,14 @@ let induction x bound env =
let x_ge_bound =
create_prop_decl Paxiom (Decl.create_prsymbol (gen_ident "Init")) x_ge_bound_t in
let rec_pr = create_prsymbol (gen_ident "Hrec") in
let new_pr = create_prsymbol (gen_ident "G") in
(* new_goal: G[x <- x + 1] *)
let new_goal =
create_prop_decl Pgoal new_pr
(replace_in_term x (t_app_infer plus_int [x; one_int]) t) in
let hrec = create_prop_decl Paxiom rec_pr t_delta' in
[x_ge_bound; hrec; new_goal]
| Dprop (p, pr, t) ->
[x_ge_bound; hrec; d]
| Dprop (_p, _pr, _t) ->
if !x_is_passed then
delta' := d :: !delta';
(* d [x <- x + 1] *)
[create_prop_decl p pr (replace_in_term x (t_app_infer plus_int [x; one_int]) t)]
(* d [x <- x] *)
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