From 89af6fc3f3940cb03553c403432dfff52e6d8d7a Mon Sep 17 00:00:00 2001 From: Pierre-Marie Pédrot Date: Wed, 26 Mar 2014 13:33:54 +0100 Subject: Adding an interface to Eqdecide and putting the grammar rules in a dedicated file. --- tactics/eqdecide.ml | 208 ++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 208 insertions(+) create mode 100644 tactics/eqdecide.ml (limited to 'tactics/eqdecide.ml') diff --git a/tactics/eqdecide.ml b/tactics/eqdecide.ml new file mode 100644 index 000000000..0effc3136 --- /dev/null +++ b/tactics/eqdecide.ml @@ -0,0 +1,208 @@ +(************************************************************************) +(* v * The Coq Proof Assistant / The Coq Development Team *) +(* (clear [destVar c]))) + +let choose_eq eqonleft = + if eqonleft then + left_with_bindings false Misctypes.NoBindings + else + right_with_bindings false Misctypes.NoBindings +let choose_noteq eqonleft = + if eqonleft then + right_with_bindings false Misctypes.NoBindings + else + left_with_bindings false Misctypes.NoBindings + +let mkBranches c1 c2 = + Tacticals.New.tclTHENLIST + [Proofview.V82.tactic (generalize [c2]); + Simple.elim c1; + intros; + Tacticals.New.onLastHyp Simple.case; + Proofview.V82.tactic clear_last; + intros] + +let solveNoteqBranch side = + Tacticals.New.tclTHEN (choose_noteq side) + (Tacticals.New.tclTHEN introf + (Tacticals.New.onLastHypId (fun id -> Extratactics.discrHyp id))) + +(* Constructs the type {c1=c2}+{~c1=c2} *) + +let mkDecideEqGoal eqonleft op rectype c1 c2 g = + let equality = mkApp(build_coq_eq(), [|rectype; c1; c2|]) in + let disequality = mkApp(build_coq_not (), [|equality|]) in + if eqonleft then mkApp(op, [|equality; disequality |]) + else mkApp(op, [|disequality; equality |]) + + +(* Constructs the type (x1,x2:R){x1=x2}+{~x1=x2} *) + +let mkGenDecideEqGoal rectype g = + let hypnames = pf_ids_of_hyps g in + let xname = next_ident_away (Id.of_string "x") hypnames + and yname = next_ident_away (Id.of_string "y") hypnames in + (mkNamedProd xname rectype + (mkNamedProd yname rectype + (mkDecideEqGoal true (build_coq_sumbool ()) + rectype (mkVar xname) (mkVar yname) g))) + +let eqCase tac = + (Tacticals.New.tclTHEN intro + (Tacticals.New.tclTHEN (Tacticals.New.onLastHyp Equality.rewriteLR) + (Tacticals.New.tclTHEN (Proofview.V82.tactic clear_last) + tac))) + +let diseqCase eqonleft = + let diseq = Id.of_string "diseq" in + let absurd = Id.of_string "absurd" in + (Tacticals.New.tclTHEN (intro_using diseq) + (Tacticals.New.tclTHEN (choose_noteq eqonleft) + (Tacticals.New.tclTHEN (Proofview.V82.tactic red_in_concl) + (Tacticals.New.tclTHEN (intro_using absurd) + (Tacticals.New.tclTHEN (Proofview.V82.tactic (Simple.apply (mkVar diseq))) + (Tacticals.New.tclTHEN (Extratactics.injHyp absurd) + (full_trivial []))))))) + +open Proofview.Notations + +(* spiwack: a small wrapper around [Hipattern]. *) + +let match_eqdec c = + try Proofview.tclUNIT (match_eqdec c) + with PatternMatchingFailure -> Proofview.tclZERO PatternMatchingFailure + +(* /spiwack *) + +let solveArg eqonleft op a1 a2 tac = + Proofview.Goal.enter begin fun gl -> + let rectype = Tacmach.New.of_old (fun g -> pf_type_of g a1) gl in + let decide = + Tacmach.New.of_old (fun g -> mkDecideEqGoal eqonleft op rectype a1 a2 g) gl + in + let subtacs = + if eqonleft then [eqCase tac;diseqCase eqonleft;default_auto] + else [diseqCase eqonleft;eqCase tac;default_auto] in + (Tacticals.New.tclTHENS (Proofview.V82.tactic (elim_type decide)) subtacs) + end + +let solveEqBranch rectype = + Proofview.tclORELSE + begin + Proofview.Goal.enter begin fun gl -> + let concl = Proofview.Goal.concl gl in + match_eqdec concl >>= fun (eqonleft,op,lhs,rhs,_) -> + let (mib,mip) = Global.lookup_inductive rectype in + let nparams = mib.mind_nparams in + let getargs l = List.skipn nparams (snd (decompose_app l)) in + let rargs = getargs rhs + and largs = getargs lhs in + List.fold_right2 + (solveArg eqonleft op) largs rargs + (Tacticals.New.tclTHEN (choose_eq eqonleft) intros_reflexivity) + end + end + begin function + | PatternMatchingFailure -> Proofview.tclZERO (UserError ("",Pp.str"Unexpected conclusion!")) + | e -> Proofview.tclZERO e + end + +(* The tactic Decide Equality *) + +let hd_app c = match kind_of_term c with + | App (h,_) -> h + | _ -> c + +let decideGralEquality = + Proofview.tclORELSE + begin + Proofview.Goal.enter begin fun gl -> + let concl = Proofview.Goal.concl gl in + match_eqdec concl >>= fun (eqonleft,_,c1,c2,typ) -> + let headtyp = Tacmach.New.of_old (fun g -> hd_app (pf_compute g typ)) gl in + begin match kind_of_term headtyp with + | Ind mi -> Proofview.tclUNIT mi + | _ -> Proofview.tclZERO (UserError ("",Pp.str"This decision procedure only works for inductive objects.")) + end >>= fun rectype -> + (Tacticals.New.tclTHEN + (mkBranches c1 c2) + (Tacticals.New.tclORELSE (solveNoteqBranch eqonleft) (solveEqBranch rectype))) + end + end + begin function + | PatternMatchingFailure -> + Proofview.tclZERO (UserError ("", Pp.str"The goal must be of the form {x<>y}+{x=y} or {x=y}+{x<>y}.")) + | e -> Proofview.tclZERO e + end + +let decideEqualityGoal = Tacticals.New.tclTHEN intros decideGralEquality + +let decideEquality rectype = + Proofview.Goal.enter begin fun gl -> + let decide = Tacmach.New.of_old (mkGenDecideEqGoal rectype) gl in + (Tacticals.New.tclTHENS (cut decide) [default_auto;decideEqualityGoal]) + end + + +(* The tactic Compare *) + +let compare c1 c2 = + Proofview.Goal.enter begin fun gl -> + let rectype = Tacmach.New.of_old (fun g -> pf_type_of g c1) gl in + let decide = Tacmach.New.of_old (fun g -> mkDecideEqGoal true (build_coq_sumbool ()) rectype c1 c2 g) gl in + (Tacticals.New.tclTHENS (cut decide) + [(Tacticals.New.tclTHEN intro + (Tacticals.New.tclTHEN (Tacticals.New.onLastHyp simplest_case) + (Proofview.V82.tactic clear_last))); + decideEquality rectype]) + end -- cgit v1.2.3