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|
(***********************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
(* \VV/ *************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(***********************************************************************)
(* $Id$ *)
open Util
open Names
open Term
open Tacmach
open Tactics
open Tacticals
open Termops
open Reductionops
open Declarations
open Formula
open Sequent
open Unify
open Libnames
type seqtac= (Sequent.t -> tactic) -> Sequent.t -> tactic
type lseqtac= global_reference -> seqtac
let wrap n b tacrec seq gls=
let nc=pf_hyps gls in
let rec aux i nc=
if i<=0 then seq else
match nc with
[]->anomaly "Not the expected number of hyps"
| (id,_,typ)::q->
let gr=VarRef id in
(add_left (gr,typ) (aux (i-1) q) true gls) in
let seq1=
if b then
(change_right (pf_concl gls) (aux n nc) gls)
else
(aux n nc) in
tacrec seq1 gls
let id_of_global=function
VarRef id->id
| _->assert false
let clear_global=function
VarRef id->clear [id]
| _->tclIDTAC
let axiom_tac t seq=
try exact_no_check (constr_of_reference (find_left t seq))
with Not_found->tclFAIL 0 "No axiom link"
let evaluable_tac ec tacrec seq gl=
tclTHEN
(unfold_in_concl [[1],ec])
(wrap 0 true tacrec seq) gl
let left_evaluable_tac ec id tacrec seq gl=
tclTHENLIST
[generalize [constr_of_reference id];
clear_global id;
intro;
(fun gls->
let nid=(Tacmach.pf_nth_hyp_id gls 1) in
unfold_in_hyp [[1],ec] (Tacexpr.InHypType nid) gls);
wrap 1 false tacrec seq] gl
let and_tac tacrec seq=
tclTHEN simplest_split (wrap 0 true tacrec seq)
let left_and_tac ind id tacrec seq=
let n=(construct_nhyps ind).(0) in
tclTHENLIST
[simplest_elim (constr_of_reference id);
clear_global id;
tclDO n intro;
wrap n false tacrec seq]
let or_tac tacrec seq=
any_constructor (Some (tclSOLVE [wrap 0 true tacrec seq]))
let left_or_tac ind id tacrec seq=
let v=construct_nhyps ind in
let f n=
tclTHENLIST
[clear_global id;
tclDO n intro;
wrap n false tacrec seq] in
tclTHENSV
(simplest_elim (constr_of_reference id))
(Array.map f v)
let forall_tac tacrec seq=
tclTHEN intro (wrap 0 true tacrec seq)
let left_forall_tac i dom atoms internal id tacrec seq=
let insts=find_instances i atoms seq in
if insts=[] then
if internal && not (lookup id None seq) then
tclTHENS (cut dom)
[tclTHENLIST
[intro;
(fun gls->generalize
[mkApp(constr_of_reference id,
[|mkVar (Tacmach.pf_nth_hyp_id gls 1)|])] gls);
intro;
tclSOLVE [wrap 1 false tacrec
(deepen (record id None seq))]]
;tclTRY assumption]
else tclFAIL 0 "no phantom variable for external hyp"
else
let tac t=
if lookup id (Some t) seq then
tclFAIL 0 "already done"
else
tclTHENLIST
[generalize [mkApp(constr_of_reference id,[|t|])];
intro;
tclSOLVE
[wrap 1 false tacrec
(deepen (record id (Some t) seq))]] in
tclFIRST (List.map tac insts)
let arrow_tac tacrec seq=
tclTHEN intro (wrap 1 true tacrec seq)
let exists_tac i dom atoms tacrec seq=
let insts=find_instances i atoms seq in
if insts=[] then
tclTHENS (cut dom)
[tclTHENLIST
[intro;
(fun gls->
split (Rawterm.ImplicitBindings
[mkVar (Tacmach.pf_nth_hyp_id gls 1)]) gls);
tclSOLVE [wrap 0 false tacrec (deepen seq)]]
;tclTRY assumption]
else
let tac t=
tclTHEN (split (Rawterm.ImplicitBindings [t]))
(tclSOLVE [wrap 0 true tacrec (deepen seq)]) in
tclFIRST (List.map tac insts)
let left_exists_tac id tacrec seq=
tclTHENLIST
[simplest_elim (constr_of_reference id);
clear_global id;
tclDO 2 intro;
(wrap 1 false tacrec seq)]
let ll_arrow_tac a b c id tacrec seq=
let cc=mkProd(Anonymous,a,(lift 1 b)) in
let d=mkLambda (Anonymous,b,
mkApp ((constr_of_reference id),
[|mkLambda (Anonymous,(lift 1 a),(mkRel 2))|])) in
tclTHENS (cut c)
[tclTHENLIST
[intro;
clear_global id;
wrap 1 false tacrec seq];
tclTHENS (cut cc)
[exact_no_check (constr_of_reference id);
tclTHENLIST
[generalize [d];
intro;
clear_global id;
tclSOLVE [wrap 1 true tacrec seq]]]]
let ll_atom_tac a id tacrec seq=
try
tclTHENLIST
[generalize [mkApp(constr_of_reference id,
[|constr_of_reference (find_left a seq)|])];
clear_global id;
intro;
wrap 1 false tacrec seq]
with Not_found->tclFAIL 0 "No link"
let ll_false_tac id tacrec seq =
tclTHEN (clear_global id) (wrap 0 false tacrec seq)
let left_false_tac id=
simplest_elim (constr_of_reference id)
(*We use this function for and, or, exists*)
let ll_ind_tac ind largs id tacrec seq gl=
(try
let rcs=ind_hyps ind largs in
let vargs=Array.of_list largs in
(* construire le terme H->B, le generaliser etc *)
let myterm i=
let rc=rcs.(i) in
let p=List.length rc in
let cstr=mkApp ((mkConstruct (ind,(i+1))),vargs) in
let vars=Array.init p (fun j->mkRel (p-j)) in
let capply=mkApp ((lift p cstr),vars) in
let head=mkApp ((lift p (constr_of_reference id)),[|capply|]) in
Sign.it_mkLambda_or_LetIn head rc in
let lp=Array.length rcs in
let newhyps=List.map myterm (interval 0 (lp-1)) in
tclTHENLIST
[generalize newhyps;
clear_global id;
tclDO lp intro;
wrap lp false tacrec seq]
with Dependent_Inductive | Invalid_argument _ ->tclFAIL 0 "") gl
let ll_forall_tac prod id tacrec seq=
tclTHENS (cut prod)
[tclTHENLIST
[intro;
(fun gls->
let id0=pf_nth_hyp_id gls 1 in
let term=mkApp((constr_of_reference id),[|mkVar(id0)|]) in
tclTHEN (generalize [term]) (clear [id0]) gls);
clear_global id;
intro;
tclSOLVE [wrap 1 false tacrec (deepen seq)]];
tclSOLVE [wrap 0 true tacrec (deepen seq)]]
|
