| Cut of loc * 'ident option * 'term
| Decompose of loc * 'ident option list
| Demodulate of loc
- | Destruct of loc * 'term
+ | Destruct of loc * 'term option
| Elim of loc * 'term * 'term option * ('term, 'lazy_term, 'ident) pattern *
'ident intros_spec
| ElimType of loc * 'term * 'term option * 'ident intros_spec
| Right of loc
| Ring of loc
| Split of loc
- | Subst of loc
| Symmetry of loc
| Transitivity of loc * 'term
(* Costruttori Aggiunti *)
Printf.sprintf "decompose%s"
(pp_intros_specs "names " (None, names))
| Demodulate _ -> "demodulate"
- | Destruct (_, term) -> "destruct " ^ term_pp term
+ | Destruct (_, None) -> "destruct"
+ | Destruct (_, Some term) -> "destruct " ^ term_pp term
| Elim (_, what, using, pattern, specs) ->
Printf.sprintf "elim %s%s %s%s"
(term_pp what)
| Right _ -> "right"
| Ring _ -> "ring"
| Split _ -> "split"
- | Subst _ -> "subst"
| Symmetry _ -> "symmetry"
| Transitivity (_, term) -> "transitivity " ^ term_pp term
(* Tattiche Aggiunte *)
| GrafiteAst.Demodulate _ ->
Tactics.demodulate
~dbd:(LibraryDb.instance ()) ~universe:status.GrafiteTypes.universe
- | GrafiteAst.Destruct (_,term) -> Tactics.destruct term
+ | GrafiteAst.Destruct (_,xterm) -> Tactics.destruct xterm
| GrafiteAst.Elim (_, what, using, pattern, (depth, names)) ->
Tactics.elim_intros ?using ?depth ~mk_fresh_name_callback:(PEH.namer_of names)
~pattern what
| GrafiteAst.Right _ -> Tactics.right
| GrafiteAst.Ring _ -> Tactics.ring
| GrafiteAst.Split _ -> Tactics.split
- | GrafiteAst.Subst _ -> Tactics.subst
| GrafiteAst.Symmetry _ -> Tactics.symmetry
| GrafiteAst.Transitivity (_, term) -> Tactics.transitivity term
(* Implementazioni Aggiunte *)
metasenv,GrafiteAst.Decompose (loc, names)
| GrafiteAst.Demodulate loc ->
metasenv,GrafiteAst.Demodulate loc
- | GrafiteAst.Destruct (loc,term) ->
+ | GrafiteAst.Destruct (loc, Some term) ->
let metasenv,term = disambiguate_term context metasenv term in
- metasenv,GrafiteAst.Destruct(loc,term)
+ metasenv,GrafiteAst.Destruct(loc, Some term)
+ | GrafiteAst.Destruct (loc, None) ->
+ metasenv,GrafiteAst.Destruct(loc,None)
| GrafiteAst.Exact (loc, term) ->
let metasenv,cic = disambiguate_term context metasenv term in
metasenv,GrafiteAst.Exact (loc, cic)
metasenv,GrafiteAst.Ring loc
| GrafiteAst.Split loc ->
metasenv,GrafiteAst.Split loc
- | GrafiteAst.Subst loc ->
- metasenv, GrafiteAst.Subst loc
| GrafiteAst.Symmetry loc ->
metasenv,GrafiteAst.Symmetry loc
| GrafiteAst.Transitivity (loc, term) ->
let idents = match idents with None -> [] | Some idents -> idents in
GrafiteAst.Decompose (loc, idents)
| IDENT "demodulate" -> GrafiteAst.Demodulate loc
- | IDENT "destruct"; t = tactic_term ->
- GrafiteAst.Destruct (loc, t)
+ | IDENT "destruct"; xt = OPT [ t = tactic_term -> t ] ->
+ GrafiteAst.Destruct (loc, xt)
| IDENT "elim"; what = tactic_term; using = using;
pattern = OPT pattern_spec;
(num, idents) = intros_spec ->
GrafiteAst.Ring loc
| IDENT "split" ->
GrafiteAst.Split loc
- | IDENT "subst" ->
- GrafiteAst.Subst loc
| IDENT "symmetry" ->
GrafiteAst.Symmetry loc
| IDENT "transitivity"; t = tactic_term ->
negationTactics.cmi: proofEngineTypes.cmi
equalityTactics.cmi: proofEngineTypes.cmi
auto.cmi: universe.cmi proofEngineTypes.cmi
-discriminationTactics.cmi: proofEngineTypes.cmi
-substTactic.cmi: proofEngineTypes.cmi
+destructTactic.cmi: proofEngineTypes.cmi
inversion.cmi: proofEngineTypes.cmi
ring.cmi: proofEngineTypes.cmi
setoids.cmi: proofEngineTypes.cmi
proofEngineReduction.cmx proofEngineHelpers.cmx primitiveTactics.cmx \
metadataQuery.cmx paramodulation/indexing.cmx equalityTactics.cmx \
paramodulation/equality.cmx autoTypes.cmx autoCache.cmx auto.cmi
-discriminationTactics.cmo: tacticals.cmi reductionTactics.cmi \
- proofEngineTypes.cmi proofEngineStructuralRules.cmi \
- proofEngineHelpers.cmi primitiveTactics.cmi introductionTactics.cmi \
- equalityTactics.cmi eliminationTactics.cmi discriminationTactics.cmi
-discriminationTactics.cmx: tacticals.cmx reductionTactics.cmx \
- proofEngineTypes.cmx proofEngineStructuralRules.cmx \
- proofEngineHelpers.cmx primitiveTactics.cmx introductionTactics.cmx \
- equalityTactics.cmx eliminationTactics.cmx discriminationTactics.cmi
-substTactic.cmo: tacticals.cmi reductionTactics.cmi proofEngineTypes.cmi \
- proofEngineStructuralRules.cmi proofEngineHelpers.cmi equalityTactics.cmi \
- discriminationTactics.cmi substTactic.cmi
-substTactic.cmx: tacticals.cmx reductionTactics.cmx proofEngineTypes.cmx \
- proofEngineStructuralRules.cmx proofEngineHelpers.cmx equalityTactics.cmx \
- discriminationTactics.cmx substTactic.cmi
+destructTactic.cmo: tacticals.cmi reductionTactics.cmi proofEngineTypes.cmi \
+ proofEngineStructuralRules.cmi proofEngineHelpers.cmi \
+ primitiveTactics.cmi introductionTactics.cmi equalityTactics.cmi \
+ eliminationTactics.cmi destructTactic.cmi
+destructTactic.cmx: tacticals.cmx reductionTactics.cmx proofEngineTypes.cmx \
+ proofEngineStructuralRules.cmx proofEngineHelpers.cmx \
+ primitiveTactics.cmx introductionTactics.cmx equalityTactics.cmx \
+ eliminationTactics.cmx destructTactic.cmi
inversion.cmo: tacticals.cmi reductionTactics.cmi proofEngineTypes.cmi \
proofEngineReduction.cmi proofEngineHelpers.cmi primitiveTactics.cmi \
equalityTactics.cmi inversion.cmi
statefulProofEngine.cmi
statefulProofEngine.cmx: proofEngineTypes.cmx history.cmx \
statefulProofEngine.cmi
-tactics.cmo: variousTactics.cmi tacticals.cmi substTactic.cmi setoids.cmi \
- ring.cmi reductionTactics.cmi proofEngineStructuralRules.cmi \
- primitiveTactics.cmi negationTactics.cmi inversion.cmi \
- introductionTactics.cmi fwdSimplTactic.cmi fourierR.cmi \
- equalityTactics.cmi eliminationTactics.cmi discriminationTactics.cmi \
- compose.cmi closeCoercionGraph.cmi auto.cmi tactics.cmi
-tactics.cmx: variousTactics.cmx tacticals.cmx substTactic.cmx setoids.cmx \
- ring.cmx reductionTactics.cmx proofEngineStructuralRules.cmx \
- primitiveTactics.cmx negationTactics.cmx inversion.cmx \
- introductionTactics.cmx fwdSimplTactic.cmx fourierR.cmx \
- equalityTactics.cmx eliminationTactics.cmx discriminationTactics.cmx \
- compose.cmx closeCoercionGraph.cmx auto.cmx tactics.cmi
+tactics.cmo: variousTactics.cmi tacticals.cmi setoids.cmi ring.cmi \
+ reductionTactics.cmi proofEngineStructuralRules.cmi primitiveTactics.cmi \
+ negationTactics.cmi inversion.cmi introductionTactics.cmi \
+ fwdSimplTactic.cmi fourierR.cmi equalityTactics.cmi \
+ eliminationTactics.cmi destructTactic.cmi compose.cmi \
+ closeCoercionGraph.cmi auto.cmi tactics.cmi
+tactics.cmx: variousTactics.cmx tacticals.cmx setoids.cmx ring.cmx \
+ reductionTactics.cmx proofEngineStructuralRules.cmx primitiveTactics.cmx \
+ negationTactics.cmx inversion.cmx introductionTactics.cmx \
+ fwdSimplTactic.cmx fourierR.cmx equalityTactics.cmx \
+ eliminationTactics.cmx destructTactic.cmx compose.cmx \
+ closeCoercionGraph.cmx auto.cmx tactics.cmi
declarative.cmo: universe.cmi tactics.cmi tacticals.cmi proofEngineTypes.cmi \
declarative.cmi
declarative.cmx: universe.cmx tactics.cmx tacticals.cmx proofEngineTypes.cmx \
negationTactics.cmi: proofEngineTypes.cmi
equalityTactics.cmi: proofEngineTypes.cmi
auto.cmi: universe.cmi proofEngineTypes.cmi
-discriminationTactics.cmi: proofEngineTypes.cmi
-substTactic.cmi: proofEngineTypes.cmi
+destructTactic.cmi: proofEngineTypes.cmi
inversion.cmi: proofEngineTypes.cmi
ring.cmi: proofEngineTypes.cmi
setoids.cmi: proofEngineTypes.cmi
proofEngineReduction.cmx proofEngineHelpers.cmx primitiveTactics.cmx \
metadataQuery.cmx paramodulation/indexing.cmx equalityTactics.cmx \
paramodulation/equality.cmx autoTypes.cmx autoCache.cmx auto.cmi
-discriminationTactics.cmo: tacticals.cmi reductionTactics.cmi \
- proofEngineTypes.cmi proofEngineStructuralRules.cmi \
- proofEngineHelpers.cmi primitiveTactics.cmi introductionTactics.cmi \
- equalityTactics.cmi eliminationTactics.cmi discriminationTactics.cmi
-discriminationTactics.cmx: tacticals.cmx reductionTactics.cmx \
- proofEngineTypes.cmx proofEngineStructuralRules.cmx \
- proofEngineHelpers.cmx primitiveTactics.cmx introductionTactics.cmx \
- equalityTactics.cmx eliminationTactics.cmx discriminationTactics.cmi
-substTactic.cmo: tacticals.cmi reductionTactics.cmi proofEngineTypes.cmi \
- proofEngineStructuralRules.cmi proofEngineHelpers.cmi equalityTactics.cmi \
- discriminationTactics.cmi substTactic.cmi
-substTactic.cmx: tacticals.cmx reductionTactics.cmx proofEngineTypes.cmx \
- proofEngineStructuralRules.cmx proofEngineHelpers.cmx equalityTactics.cmx \
- discriminationTactics.cmx substTactic.cmi
+destructTactic.cmo: tacticals.cmi reductionTactics.cmi proofEngineTypes.cmi \
+ proofEngineStructuralRules.cmi proofEngineHelpers.cmi \
+ primitiveTactics.cmi introductionTactics.cmi equalityTactics.cmi \
+ eliminationTactics.cmi destructTactic.cmi
+destructTactic.cmx: tacticals.cmx reductionTactics.cmx proofEngineTypes.cmx \
+ proofEngineStructuralRules.cmx proofEngineHelpers.cmx \
+ primitiveTactics.cmx introductionTactics.cmx equalityTactics.cmx \
+ eliminationTactics.cmx destructTactic.cmi
inversion.cmo: tacticals.cmi reductionTactics.cmi proofEngineTypes.cmi \
proofEngineReduction.cmi proofEngineHelpers.cmi primitiveTactics.cmi \
equalityTactics.cmi inversion.cmi
statefulProofEngine.cmi
statefulProofEngine.cmx: proofEngineTypes.cmx history.cmx \
statefulProofEngine.cmi
-tactics.cmo: variousTactics.cmi tacticals.cmi substTactic.cmi setoids.cmi \
- ring.cmi reductionTactics.cmi proofEngineStructuralRules.cmi \
- primitiveTactics.cmi negationTactics.cmi inversion.cmi \
- introductionTactics.cmi fwdSimplTactic.cmi fourierR.cmi \
- equalityTactics.cmi eliminationTactics.cmi discriminationTactics.cmi \
- compose.cmi closeCoercionGraph.cmi auto.cmi tactics.cmi
-tactics.cmx: variousTactics.cmx tacticals.cmx substTactic.cmx setoids.cmx \
- ring.cmx reductionTactics.cmx proofEngineStructuralRules.cmx \
- primitiveTactics.cmx negationTactics.cmx inversion.cmx \
- introductionTactics.cmx fwdSimplTactic.cmx fourierR.cmx \
- equalityTactics.cmx eliminationTactics.cmx discriminationTactics.cmx \
- compose.cmx closeCoercionGraph.cmx auto.cmx tactics.cmi
+tactics.cmo: variousTactics.cmi tacticals.cmi setoids.cmi ring.cmi \
+ reductionTactics.cmi proofEngineStructuralRules.cmi primitiveTactics.cmi \
+ negationTactics.cmi inversion.cmi introductionTactics.cmi \
+ fwdSimplTactic.cmi fourierR.cmi equalityTactics.cmi \
+ eliminationTactics.cmi destructTactic.cmi compose.cmi \
+ closeCoercionGraph.cmi auto.cmi tactics.cmi
+tactics.cmx: variousTactics.cmx tacticals.cmx setoids.cmx ring.cmx \
+ reductionTactics.cmx proofEngineStructuralRules.cmx primitiveTactics.cmx \
+ negationTactics.cmx inversion.cmx introductionTactics.cmx \
+ fwdSimplTactic.cmx fourierR.cmx equalityTactics.cmx \
+ eliminationTactics.cmx destructTactic.cmx compose.cmx \
+ closeCoercionGraph.cmx auto.cmx tactics.cmi
declarative.cmo: universe.cmi tactics.cmi tacticals.cmi proofEngineTypes.cmi \
declarative.cmi
declarative.cmx: universe.cmx tactics.cmx tacticals.cmx proofEngineTypes.cmx \
introductionTactics.mli eliminationTactics.mli negationTactics.mli \
equalityTactics.mli \
auto.mli \
- discriminationTactics.mli substTactic.mli \
+ destructTactic.mli \
inversion.mli inversion_principle.mli ring.mli setoids.mli \
fourier.mli fourierR.mli fwdSimplTactic.mli history.mli \
statefulProofEngine.mli tactics.mli declarative.mli
--- /dev/null
+(* Copyright (C) 2002, HELM Team.
+ *
+ * This file is part of HELM, an Hypertextual, Electronic
+ * Library of Mathematics, developed at the Computer Science
+ * Department, University of Bologna, Italy.
+ *
+ * HELM is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU General Public License
+ * as published by the Free Software Foundation; either version 2
+ * of the License, or (at your option) any later version.
+ *
+ * HELM is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with HELM; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+ * MA 02111-1307, USA.
+ *
+ * For details, see the HELM World-Wide-Web page,
+ * http://cs.unibo.it/helm/.
+ *)
+
+(* $Id$ *)
+
+module C = Cic
+module U = UriManager
+module P = PrimitiveTactics
+module T = Tacticals
+module CR = CicReduction
+module PST = ProofEngineStructuralRules
+module PET = ProofEngineTypes
+module CTC = CicTypeChecker
+module CU = CicUniv
+module S = CicSubstitution
+module RT = ReductionTactics
+module PEH = ProofEngineHelpers
+module ET = EqualityTactics
+module DTI = DoubleTypeInference
+module FNG = FreshNamesGenerator
+
+let debug = true
+let debug_print =
+ if debug then (fun x -> prerr_endline (Lazy.force x)) else (fun _ -> ())
+
+(* funzione generale di rilocazione dei riferimenti locali *)
+
+let relocate_term map t =
+ let rec map_xnss k xnss =
+ let imap (uri, t) = uri, map_term k t in
+ List.map imap xnss
+ and map_mss k mss =
+ let imap = function
+ | None -> None
+ | Some t -> Some (map_term k t)
+ in
+ List.map imap mss
+ and map_fs len k fs =
+ let imap (name, i, ty, bo) = name, i, map_term k ty, map_term (k + len) bo in
+ List.map imap fs
+ and map_cfs len k cfs =
+ let imap (name, ty, bo) = name, map_term k ty, map_term (k + len) bo in
+ List.map imap cfs
+ and map_term k = function
+ | C.Rel m -> if m < k then C.Rel m else C.Rel (map (m - k))
+ | C.Sort _ as t -> t
+ | C.Implicit _ as t -> t
+ | C.Var (uri, xnss) -> C.Var (uri, map_xnss k xnss)
+ | C.Const (uri, xnss) -> C.Const (uri, map_xnss k xnss)
+ | C.MutInd (uri, tyno, xnss) -> C.MutInd (uri, tyno, map_xnss k xnss)
+ | C.MutConstruct (uri, tyno, consno, xnss) ->
+ C.MutConstruct (uri, tyno, consno, map_xnss k xnss)
+ | C.Meta (i, mss) -> C.Meta(i, map_mss k mss)
+ | C.Cast (te, ty) -> C.Cast (map_term k te, map_term k ty)
+ | C.Appl ts -> C.Appl (List.map (map_term k) ts)
+ | C.MutCase (sp, i, outty, t, pl) ->
+ C.MutCase (sp, i, map_term k outty, map_term k t, List.map (map_term k) pl)
+ | C.Prod (n, s, t) -> C.Prod (n, map_term k s, map_term (succ k) t)
+ | C.Lambda (n, s, t) -> C.Lambda (n, map_term k s, map_term (succ k) t)
+ | C.LetIn (n, s, t) -> C.LetIn (n, map_term k s, map_term (succ k) t)
+ | C.Fix (i, fs) -> C.Fix (i, map_fs (List.length fs) k fs)
+ | C.CoFix (i, cfs) -> C.CoFix (i, map_cfs (List.length cfs) k cfs)
+ in
+ map_term 0 t
+
+let id n = n
+
+let after continuation aftermap beforemap =
+ continuation ~map:(fun n -> aftermap (beforemap n))
+
+let after2 continuation aftermap beforemap ~map =
+ continuation ~map:(fun n -> map (aftermap (beforemap n)))
+
+(* term ha tipo t1=t2; funziona solo se t1 e t2 hanno in testa costruttori
+diversi *)
+
+let discriminate_tac ~term =
+ let true_URI =
+ match LibraryObjects.true_URI () with
+ Some uri -> uri
+ | None -> raise (PET.Fail (lazy "You need to register the default \"true\" definition first. Please use the \"default\" command")) in
+ let false_URI =
+ match LibraryObjects.false_URI () with
+ Some uri -> uri
+ | None -> raise (PET.Fail (lazy "You need to register the default \"false\" definition first. Please use the \"default\" command")) in
+ let fail msg = raise (PET.Fail (lazy ("Discriminate: " ^ msg))) in
+ let find_discriminating_consno t1 t2 =
+ let rec aux t1 t2 =
+ match t1, t2 with
+ | C.MutConstruct _, C.MutConstruct _ when t1 = t2 -> None
+ | C.Appl ((C.MutConstruct _ as constr1) :: args1),
+ C.Appl ((C.MutConstruct _ as constr2) :: args2)
+ when constr1 = constr2 ->
+ let rec aux_list l1 l2 =
+ match l1, l2 with
+ | [], [] -> None
+ | hd1 :: tl1, hd2 :: tl2 ->
+ (match aux hd1 hd2 with
+ | None -> aux_list tl1 tl2
+ | Some _ as res -> res)
+ | _ -> (* same constructor applied to a different number of args *)
+ assert false
+ in
+ aux_list args1 args2
+ | ((C.MutConstruct (_,_,consno1,subst1)),
+ (C.MutConstruct (_,_,consno2,subst2)))
+ | ((C.MutConstruct (_,_,consno1,subst1)),
+ (C.Appl ((C.MutConstruct (_,_,consno2,subst2)) :: _)))
+ | ((C.Appl ((C.MutConstruct (_,_,consno1,subst1)) :: _)),
+ (C.MutConstruct (_,_,consno2,subst2)))
+ | ((C.Appl ((C.MutConstruct (_,_,consno1,subst1)) :: _)),
+ (C.Appl ((C.MutConstruct (_,_,consno2,subst2)) :: _)))
+ when (consno1 <> consno2) || (subst1 <> subst2) ->
+ Some consno2
+ | _ -> fail "not a discriminable equality"
+ in
+ aux t1 t2
+ in
+ let mk_branches_and_outtype turi typeno consno context args =
+ (* a list of "True" except for the element in position consno which
+ * is "False" *)
+ match fst (CicEnvironment.get_obj CU.empty_ugraph turi) with
+ | C.InductiveDefinition (ind_type_list,_,paramsno,_) ->
+ let _,_,rty,constructor_list = List.nth ind_type_list typeno in
+ let false_constr_id,_ = List.nth constructor_list (consno - 1) in
+ let branches =
+ List.map
+ (fun (id,cty) ->
+ (* dubbio: e' corretto ridurre in questo context ??? *)
+ let red_ty = CR.whd context cty in
+ let rec aux t k =
+ match t with
+ | C.Prod (_,_,target) when (k <= paramsno) ->
+ S.subst (List.nth args (k-1))
+ (aux target (k+1))
+ | C.Prod (binder,source,target) when (k > paramsno) ->
+ C.Lambda (binder, source, (aux target (k+1)))
+ | _ ->
+ if (id = false_constr_id)
+ then (C.MutInd(false_URI,0,[]))
+ else (C.MutInd(true_URI,0,[]))
+ in
+ (S.lift 1 (aux red_ty 1)))
+ constructor_list in
+ let outtype =
+ let seed = ref 0 in
+ let rec mk_lambdas rev_left_args =
+ function
+ 0, args, C.Prod (_,so,ta) ->
+ C.Lambda
+ (C.Name (incr seed; "x" ^ string_of_int !seed),
+ so,
+ mk_lambdas rev_left_args (0,args,ta))
+ | 0, args, C.Sort _ ->
+ let rec mk_rels =
+ function
+ 0 -> []
+ | n -> C.Rel n :: mk_rels (n - 1) in
+ let argsno = List.length args in
+ C.Lambda
+ (C.Name "x",
+ (if argsno + List.length rev_left_args > 0 then
+ C.Appl
+ (C.MutInd (turi, typeno, []) ::
+ (List.map
+ (S.lift (argsno + 1))
+ (List.rev rev_left_args)) @
+ mk_rels argsno)
+ else
+ C.MutInd (turi,typeno,[])),
+ C.Sort C.Prop)
+ | 0, _, _ -> assert false (* seriously screwed up *)
+ | n, he::tl, C.Prod (_,_,ta) ->
+ mk_lambdas (he::rev_left_args)(n-1,tl,S.subst he ta)
+ | n,_,_ ->
+ assert false (* we should probably reduce in some context *)
+ in
+ mk_lambdas [] (paramsno, args, rty)
+ in
+ branches, outtype
+ | _ -> assert false
+ in
+ let discriminate'_tac ~term status =
+ let (proof, goal) = status in
+ let _,metasenv,_subst,_,_, _ = proof in
+ let _,context,_ = CicUtil.lookup_meta goal metasenv in
+ let termty,_ =
+ CTC.type_of_aux' metasenv context term CU.empty_ugraph
+ in
+ match termty with
+ | C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2]
+ when LibraryObjects.is_eq_URI equri ->
+ let turi,typeno,exp_named_subst,args =
+ match tty with
+ | (C.MutInd (turi,typeno,exp_named_subst)) ->
+ turi,typeno,exp_named_subst,[]
+ | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::args)) ->
+ turi,typeno,exp_named_subst,args
+ | _ -> fail "not a discriminable equality"
+ in
+ let consno =
+ match find_discriminating_consno t1 t2 with
+ | Some consno -> consno
+ | None -> fail "discriminating terms are structurally equal"
+ in
+ let branches,outtype =
+ mk_branches_and_outtype turi typeno consno context args
+ in
+ PET.apply_tactic
+ (T.then_
+ ~start:(EliminationTactics.elim_type_tac (C.MutInd (false_URI, 0, [])))
+ ~continuation:
+ (T.then_
+ ~start:
+ (RT.change_tac
+ ~pattern:(PET.conclusion_pattern None)
+ (fun _ m u ->
+ C.Appl [
+ C.Lambda ( C.Name "x", tty,
+ C.MutCase (turi, typeno, outtype, (C.Rel 1), branches));
+ t2 ],
+ m, u))
+ ~continuation:
+ (T.then_
+ ~start:
+ (ET.rewrite_simpl_tac
+ ~direction:`RightToLeft
+ ~pattern:(PET.conclusion_pattern None)
+ term [])
+ ~continuation:
+ (IntroductionTactics.constructor_tac ~n:1)))) status
+ | _ -> fail "not an equality"
+ in
+ PET.mk_tactic (discriminate'_tac ~term)
+
+let exn_noneq =
+ PET.Fail (lazy "Injection: not an equality")
+let exn_nothingtodo =
+ PET.Fail (lazy "Nothing to do")
+let exn_discrnonind =
+ PET.Fail (lazy "Discriminate: object is not an Inductive Definition: it's imposible")
+let exn_injwronggoal =
+ PET.Fail (lazy "Injection: goal after cut is not correct")
+let exn_noneqind =
+ PET.Fail (lazy "Injection: not an equality over elements of an inductive type")
+
+let pp ctx t =
+ let names = List.map (function Some (n,_) -> Some n | None -> None) ctx in
+ CicPp.pp t names
+
+let clear_term first_time lterm =
+ let clear_term status =
+ let (proof, goal) = status in
+ let _,metasenv,_subst,_,_, _ = proof in
+ let _,context,_ = CicUtil.lookup_meta goal metasenv in
+ let term, metasenv, _ugraph = lterm context metasenv CU.empty_ugraph in
+ debug_print (lazy ("\nclear di: " ^ pp context term));
+ debug_print (lazy ("nel contesto:\n" ^ CicPp.ppcontext context));
+ let g () = if first_time then raise exn_nothingtodo else T.id_tac in
+ let tactic = match term with
+ | C.Rel n ->
+ begin match List.nth context (pred n) with
+ | Some (C.Name id, _) ->
+ T.if_ ~fail:(g ()) ~start:(PST.clear ~hyps:[id]) ~continuation:T.id_tac
+ | _ -> assert false
+ end
+ | _ -> g ()
+ in
+ PET.apply_tactic tactic status
+ in
+ PET.mk_tactic clear_term
+
+let simpl_in_term context = function
+ | Cic.Rel i ->
+ let name = match List.nth context (pred i) with
+ | Some (Cic.Name s, Cic.Def _) -> s
+ | Some (Cic.Name s, Cic.Decl _) -> s
+ | _ -> assert false
+ in
+ RT.simpl_tac ~pattern:(None,[name,Cic.Implicit (Some `Hole)],None)
+ | _ -> T.id_tac
+
+let mk_fresh_name metasenv context name typ =
+ let name = C.Name name in
+ match FNG.mk_fresh_name ~subst:[] metasenv context name ~typ with
+ | C.Name s -> s
+ | C.Anonymous -> assert false
+
+let exists context = function
+ | C.Rel i -> List.nth context (pred i) <> None
+ | _ -> true
+
+let rec recur_on_child_tac name =
+ let recur_on_child status =
+ let (proof, goal) = status in
+ let _, metasenv, _subst, _, _, _ = proof in
+ let _, context, _ = CicUtil.lookup_meta goal metasenv in
+ debug_print (lazy ("\nrecur_on_child su: " ^ name));
+ debug_print (lazy ("nel contesto:\n" ^ CicPp.ppcontext context));
+ let rec search_name i = function
+ | [] -> T.id_tac
+ | Some (Cic.Name n, _) :: _ when n = name ->
+ destruct ~first_time:false ~term:(Cic.Rel i)
+ | _ :: tl -> search_name (succ i) tl
+ in
+ PET.apply_tactic (search_name 1 context) status
+ in
+ PET.mk_tactic recur_on_child
+
+and injection_tac ~lterm ~i ~continuation =
+ let give_name seed = function
+ | C.Name _ as name -> name
+ | C.Anonymous -> C.Name (incr seed; "y" ^ string_of_int !seed)
+ in
+ let rec mk_rels = function | 0 -> [] | n -> C.Rel n :: (mk_rels (n - 1)) in
+ let injection_tac status =
+ let (proof, goal) = status in
+ (* precondizione: t1 e t2 hanno in testa lo stesso costruttore ma
+ * differiscono (o potrebbero differire?) nell'i-esimo parametro
+ * del costruttore *)
+ let _,metasenv,_subst,_,_, _ = proof in
+ let _,context,_ = CicUtil.lookup_meta goal metasenv in
+ let term, metasenv, _ugraph = lterm context metasenv CU.empty_ugraph in
+ let termty,_ =
+ CTC.type_of_aux' metasenv context term CU.empty_ugraph
+ in
+ debug_print (lazy ("\ninjection su : " ^ pp context termty));
+ match termty with (* an equality *)
+ | C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2]
+ when LibraryObjects.is_eq_URI equri ->
+ let turi,typeno,ens,params =
+ match tty with (* some inductive type *)
+ | C.MutInd (turi,typeno,ens) -> turi,typeno,ens,[]
+ | C.Appl (C.MutInd (turi,typeno,ens)::params) -> turi,typeno,ens,params
+ | _ -> raise exn_noneqind
+ in
+ let t1',t2',consno = (* sono i due sottotermini che differiscono *)
+ match t1,t2 with
+ | C.Appl ((C.MutConstruct (uri1,typeno1,consno1,ens1))::applist1),
+ C.Appl ((C.MutConstruct (uri2,typeno2,consno2,ens2))::applist2)
+ when (uri1 = uri2) && (typeno1 = typeno2) &&
+ (consno1 = consno2) && (ens1 = ens2) ->
+ (* controllo ridondante *)
+ List.nth applist1 (pred i),List.nth applist2 (pred i),consno2
+ | _ -> assert false
+ in
+ let tty',_ = CTC.type_of_aux' metasenv context t1' CU.empty_ugraph in
+ let patterns,outtype =
+ match fst (CicEnvironment.get_obj CU.empty_ugraph turi) with
+ | C.InductiveDefinition (ind_type_list,_,paramsno,_)->
+ let left_params, right_params = HExtlib.split_nth paramsno params in
+ let _,_,_,constructor_list = List.nth ind_type_list typeno in
+ let i_constr_id,_ = List.nth constructor_list (consno - 1) in
+ let patterns =
+ let seed = ref 0 in
+ List.map
+ (function (id,cty) ->
+ let reduced_cty = CR.whd context cty in
+ let rec aux k = function
+ | C.Prod (_,_,tgt) when k <= paramsno ->
+ let left = List.nth left_params (k-1) in
+ aux (k+1) (S.subst left tgt)
+ | C.Prod (binder,source,target) when k > paramsno ->
+ let binder' = give_name seed binder in
+ C.Lambda (binder',source,(aux (k+1) target))
+ | _ ->
+ let nr_param_constr = k - paramsno - 1 in
+ if id = i_constr_id then C.Rel (k - i)
+ else S.lift nr_param_constr t1'
+ (* + 1 per liftare anche il lambda aggiunto
+ * esternamente al case *)
+ in S.lift 1 (aux 1 reduced_cty))
+ constructor_list
+ in
+ (* this code should be taken from cases_tac *)
+ let outtype =
+ let seed = ref 0 in
+ let rec to_lambdas te head =
+ match CR.whd context te with
+ | C.Prod (binder,so,ta) ->
+ let binder' = give_name seed binder in
+ C.Lambda (binder',so,to_lambdas ta head)
+ | _ -> head
+ in
+ let rec skip_prods params te =
+ match params, CR.whd context te with
+ | [], _ -> te
+ | left::tl, C.Prod (_,_,ta) ->
+ skip_prods tl (S.subst left ta)
+ | _, _ -> assert false
+ in
+ let abstracted_tty =
+ let tty =
+ List.fold_left (fun x y -> S.subst y x) tty left_params
+ in
+ (* non lift, ma subst coi left! *)
+ match S.lift 1 tty with
+ | C.MutInd _ as tty' -> tty'
+ | C.Appl l ->
+ let keep,abstract = HExtlib.split_nth (paramsno +1) l in
+ let keep = List.map (S.lift paramsno) keep in
+ C.Appl (keep@mk_rels (List.length abstract))
+ | _ -> assert false
+ in
+ match ind_type_list with
+ | [] -> assert false
+ | (_,_,ty,_)::_ ->
+ (* this is in general wrong, do as in cases_tac *)
+ to_lambdas (skip_prods left_params ty)
+ (C.Lambda
+ (C.Name "cased", abstracted_tty,
+ (* here we should capture right parameters *)
+ (* 1 for his Lambda, one for the Lambda outside the match
+ * and then one for each to_lambda *)
+ S.lift (2+List.length right_params) tty'))
+ in
+ patterns,outtype
+ | _ -> raise exn_discrnonind
+ in
+ let cutted = C.Appl [C.MutInd (equri,0,[]) ; tty' ; t1' ; t2'] in
+ let changed =
+ C.Appl [ C.Lambda (C.Name "x", tty,
+ C.MutCase (turi,typeno,outtype,C.Rel 1,patterns)) ; t1]
+ in
+ (* check if cutted and changed are well typed and if t1' ~ changed *)
+ let go_on =
+ try
+ let _,g = CTC.type_of_aux' metasenv context cutted
+ CU.empty_ugraph
+ in
+ let _,g = CTC.type_of_aux' metasenv context changed g in
+ fst (CR.are_convertible ~metasenv context t1' changed g)
+ with
+ | CTC.TypeCheckerFailure _ -> false
+ in
+ if not go_on then begin
+ HLog.warn "destruct: injection failed";
+ PET.apply_tactic continuation status
+ end else
+ let fill_cut_tac term =
+ let fill_cut status =
+ debug_print (lazy "riempio il cut");
+ let (proof, goal) = status in
+ let _,metasenv,_subst,_,_, _ = proof in
+ let _,context,gty = CicUtil.lookup_meta goal metasenv in
+ let gty = Unshare.unshare gty in
+ let new_t1' = match gty with
+ | (C.Appl (C.MutInd (_,_,_)::_::t::_)) -> t
+ | _ -> raise exn_injwronggoal
+ in
+ debug_print (lazy ("metto: " ^ pp context changed));
+ debug_print (lazy ("al posto di: " ^ pp context new_t1'));
+ debug_print (lazy ("nel goal: " ^ pp context gty));
+ debug_print (lazy ("nel contesto:\n" ^ CicPp.ppcontext context));
+ debug_print (lazy ("e poi rewrite con: "^pp context term));
+ let tac = T.seq ~tactics:[
+ RT.change_tac
+ ~pattern:(None, [], Some (PEH.pattern_of ~term:gty [new_t1']))
+ (fun _ m u -> changed,m,u);
+ ET.rewrite_simpl_tac
+ ~direction:`LeftToRight
+ ~pattern:(PET.conclusion_pattern None)
+ term [];
+ ET.reflexivity_tac
+ ] in
+ PET.apply_tactic tac status
+ in
+ PET.mk_tactic fill_cut
+ in
+ debug_print (lazy ("CUT: " ^ pp context cutted));
+ let name = mk_fresh_name metasenv context "Hcut" cutted in
+ let mk_fresh_name_callback = PEH.namer_of [Some name] in
+ debug_print (lazy ("figlio: " ^ name));
+ let tactic =
+ T.thens ~start: (P.cut_tac ~mk_fresh_name_callback cutted)
+ ~continuations:[
+ T.seq ~tactics:[continuation; recur_on_child_tac name];
+ fill_cut_tac term
+ ]
+ in
+ PET.apply_tactic tactic status
+ | _ -> raise exn_noneq
+ in
+ PET.mk_tactic injection_tac
+
+and subst_tac ~lterm ~direction ~where ~continuation =
+ let subst_tac status =
+ let (proof, goal) = status in
+ let _,metasenv,_subst,_,_, _ = proof in
+ let _,context,_ = CicUtil.lookup_meta goal metasenv in
+ let term, metasenv, _ugraph = lterm context metasenv CU.empty_ugraph in
+ debug_print (lazy ("\nsubst " ^ (match direction with `LeftToRight -> "->" | `RightToLeft -> "<-") ^ " di: " ^ pp context term));
+ let tactic = match where with
+ | None ->
+ debug_print (lazy ("nella conclusione"));
+ let pattern = PET.conclusion_pattern None in
+ let tactic = ET.rewrite_tac ~direction ~pattern term [] in
+ T.then_ ~start:(T.try_tactic ~tactic) ~continuation
+ | Some name ->
+ debug_print (lazy ("nella premessa: " ^ name));
+ let pattern = None, [name, PET.hole], None in
+ let start = ET.rewrite_tac ~direction ~pattern term [] in
+ let ok_tactic =
+ T.seq ~tactics:[continuation; recur_on_child_tac name]
+ in
+ debug_print (lazy ("figlio: " ^ name));
+ T.if_ ~start ~continuation:ok_tactic ~fail:continuation
+ in
+ PET.apply_tactic tactic status
+ in
+ PET.mk_tactic subst_tac
+
+(* ~term vive nel contesto della tattica una volta ~mappato
+ * ~continuation riceve la mappa assoluta
+ *)
+and destruct ~first_time ~term =
+ let are_convertible hd1 hd2 metasenv context =
+ fst (CR.are_convertible ~metasenv context hd1 hd2 CU.empty_ugraph)
+ in
+ let destruct status =
+ let (proof, goal) = status in
+ let _,metasenv,_subst, _,_, _ = proof in
+ let _,context,_ = CicUtil.lookup_meta goal metasenv in
+ debug_print (lazy ("\ndestruct di: " ^ pp context term));
+ debug_print (lazy ("nel contesto:\n" ^ CicPp.ppcontext context));
+ let termty,_ =
+ CTC.type_of_aux' metasenv context term CU.empty_ugraph
+ in
+ debug_print (lazy ("\ndestruct su: " ^ pp context termty));
+ let mk_lterm term c m ug =
+ let distance = List.length c - List.length context in
+ S.lift distance term, m, ug
+ in
+ let lterm = mk_lterm term in
+ let mk_subst_chain direction index with_what what =
+ let k = match term with C.Rel i -> i | _ -> -1 in
+ let rec traverse_context first_time j = function
+ | [] ->
+ let continuation =
+ T.seq ~tactics:[
+ clear_term first_time lterm;
+ clear_term false (mk_lterm what);
+ clear_term false (mk_lterm with_what)
+ ]
+ in
+ subst_tac ~direction ~lterm ~where:None ~continuation
+ | Some (C.Name name, _) :: tl when j < index && j <> k ->
+ debug_print (lazy ("\nsubst programmata: cosa: " ^ string_of_int index ^ ", dove: " ^ string_of_int j));
+ subst_tac ~direction ~lterm ~where:(Some name)
+ ~continuation:(traverse_context false (succ j) tl)
+ | _ :: tl -> traverse_context first_time (succ j) tl
+ in
+ traverse_context first_time 1 context
+ in
+ let tac = match termty with
+ | C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2]
+ when LibraryObjects.is_eq_URI equri ->
+ begin match t1,t2 with
+(* injection part *)
+ | C.MutConstruct _,
+ C.MutConstruct _
+ when t1 = t2 -> clear_term first_time lterm
+ | C.Appl (C.MutConstruct _ as mc1 :: applist1),
+ C.Appl (C.MutConstruct _ as mc2 :: applist2)
+ when mc1 = mc2 ->
+ let rec traverse_list first_time i l1 l2 =
+ match l1, l2 with
+ | [], [] -> clear_term first_time lterm
+ | hd1 :: tl1, hd2 :: tl2 ->
+ if are_convertible hd1 hd2 metasenv context then
+ traverse_list first_time (succ i) tl1 tl2
+ else
+ injection_tac ~i ~lterm ~continuation:
+ (traverse_list false (succ i) tl1 tl2)
+ | _ -> assert false
+ (* i 2 termini hanno in testa lo stesso costruttore,
+ * ma applicato a un numero diverso di termini *)
+ in
+ traverse_list first_time 1 applist1 applist2
+(* discriminate part *)
+ | C.MutConstruct (_,_,consno1,ens1),
+ C.MutConstruct (_,_,consno2,ens2)
+ | C.MutConstruct (_,_,consno1,ens1),
+ C.Appl ((C.MutConstruct (_,_,consno2,ens2))::_)
+ | C.Appl ((C.MutConstruct (_,_,consno1,ens1))::_),
+ C.MutConstruct (_,_,consno2,ens2)
+ | C.Appl ((C.MutConstruct (_,_,consno1,ens1))::_),
+ C.Appl ((C.MutConstruct (_,_,consno2,ens2))::_)
+ when (consno1 <> consno2) || (ens1 <> ens2) ->
+ discriminate_tac ~term
+(* subst part *)
+ | C.Rel _, C.Rel _ when t1 = t2 ->
+ T.seq ~tactics:[
+ clear_term first_time lterm;
+ clear_term false (mk_lterm t1)
+ ]
+ | C.Rel i1, C.Rel i2 when i1 < i2 ->
+ mk_subst_chain `LeftToRight i1 t2 t1
+ | C.Rel i1, C.Rel i2 when i1 > i2 ->
+ mk_subst_chain `RightToLeft i2 t1 t2
+ | C.Rel i1, _ when DTI.does_not_occur i1 t2 ->
+ mk_subst_chain `LeftToRight i1 t2 t1
+ | _, C.Rel i2 when DTI.does_not_occur i2 t1 ->
+ mk_subst_chain `RightToLeft i2 t1 t2
+(* else part *)
+ | _ when not first_time -> T.id_tac
+ | _ (* when first_time *) ->
+ T.then_ ~start:(simpl_in_term context term)
+ ~continuation:(destruct ~first_time:false ~term)
+ end
+ | _ when not first_time -> T.id_tac
+ | _ (* when first_time *) -> raise exn_nothingtodo
+ in
+ PET.apply_tactic tac status
+ in
+ PET.mk_tactic destruct
+
+let lazy_destruct_tac ~first_time ~lterm =
+ let lazy_destruct status =
+ let (proof, goal) = status in
+ let _,metasenv,_subst,_,_, _ = proof in
+ let _,context,_ = CicUtil.lookup_meta goal metasenv in
+ let term, _, _ = lterm context metasenv CU.empty_ugraph in
+ let tactic =
+ if exists context term then destruct ~first_time ~term else T.id_tac
+ in
+ PET.apply_tactic tactic status
+ in
+ PET.mk_tactic lazy_destruct
+
+(* destruct performs either injection or discriminate *)
+(* equivalent to Coq's "analyze equality" *)
+let destruct_tac = function
+ | Some term -> destruct ~first_time:true ~term
+ | None ->
+ let destruct_all status =
+ let (proof, goal) = status in
+ let _,metasenv,_subst,_,_, _ = proof in
+ let _,context,_ = CicUtil.lookup_meta goal metasenv in
+ let mk_lterm term c m ug =
+ let distance = List.length c - List.length context in
+ S.lift distance term, m, ug
+ in
+ let rec mk_tactics first_time i tacs = function
+ | [] -> List.rev tacs
+ | Some _ :: tl ->
+ let lterm = mk_lterm (C.Rel i) in
+ let tacs = lazy_destruct_tac ~first_time ~lterm :: tacs in
+ mk_tactics false (succ i) tacs tl
+ | _ :: tl -> mk_tactics first_time (succ i) tacs tl
+ in
+ let tactics = mk_tactics false 1 [] context in
+ PET.apply_tactic (T.seq ~tactics) status
+ in
+ PET.mk_tactic destruct_all
--- /dev/null
+(* Copyright (C) 2002, HELM Team.
+ *
+ * This file is part of HELM, an Hypertextual, Electronic
+ * Library of Mathematics, developed at the Computer Science
+ * Department, University of Bologna, Italy.
+ *
+ * HELM is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU General Public License
+ * as published by the Free Software Foundation; either version 2
+ * of the License, or (at your option) any later version.
+ *
+ * HELM is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with HELM; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+ * MA 02111-1307, USA.
+ *
+ * For details, see the HELM World-Wide-Web page,
+ * http://cs.unibo.it/helm/.
+ *)
+
+(* Performs a recursive comparisons of the two sides of an equation
+ looking for constructors. If the two sides differ on two constructors,
+ it closes the current goal. If they differ by other two terms it introduces
+ an equality. *)
+val destruct_tac: Cic.term option -> ProofEngineTypes.tactic
+++ /dev/null
-(* Copyright (C) 2002, HELM Team.
- *
- * This file is part of HELM, an Hypertextual, Electronic
- * Library of Mathematics, developed at the Computer Science
- * Department, University of Bologna, Italy.
- *
- * HELM is free software; you can redistribute it and/or
- * modify it under the terms of the GNU General Public License
- * as published by the Free Software Foundation; either version 2
- * of the License, or (at your option) any later version.
- *
- * HELM is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with HELM; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
- * MA 02111-1307, USA.
- *
- * For details, see the HELM World-Wide-Web page,
- * http://cs.unibo.it/helm/.
- *)
-
-(* $Id$ *)
-
-module C = Cic
-module U = UriManager
-module P = PrimitiveTactics
-module T = Tacticals
-module CR = CicReduction
-module PST = ProofEngineStructuralRules
-module PET = ProofEngineTypes
-module CTC = CicTypeChecker
-module CU = CicUniv
-module S = CicSubstitution
-module RT = ReductionTactics
-module PEH = ProofEngineHelpers
-module ET = EqualityTactics
-
-let debug = false
-let debug_print =
- if debug then (fun x -> prerr_endline (Lazy.force x)) else (fun _ -> ())
-
-(* funzione generale di rilocazione dei riferimenti locali *)
-
-let relocate_term map t =
- let rec map_xnss k xnss =
- let imap (uri, t) = uri, map_term k t in
- List.map imap xnss
- and map_mss k mss =
- let imap = function
- | None -> None
- | Some t -> Some (map_term k t)
- in
- List.map imap mss
- and map_fs len k fs =
- let imap (name, i, ty, bo) = name, i, map_term k ty, map_term (k + len) bo in
- List.map imap fs
- and map_cfs len k cfs =
- let imap (name, ty, bo) = name, map_term k ty, map_term (k + len) bo in
- List.map imap cfs
- and map_term k = function
- | C.Rel m -> if m < k then C.Rel m else C.Rel (map (m - k))
- | C.Sort _ as t -> t
- | C.Implicit _ as t -> t
- | C.Var (uri, xnss) -> C.Var (uri, map_xnss k xnss)
- | C.Const (uri, xnss) -> C.Const (uri, map_xnss k xnss)
- | C.MutInd (uri, tyno, xnss) -> C.MutInd (uri, tyno, map_xnss k xnss)
- | C.MutConstruct (uri, tyno, consno, xnss) ->
- C.MutConstruct (uri, tyno, consno, map_xnss k xnss)
- | C.Meta (i, mss) -> C.Meta(i, map_mss k mss)
- | C.Cast (te, ty) -> C.Cast (map_term k te, map_term k ty)
- | C.Appl ts -> C.Appl (List.map (map_term k) ts)
- | C.MutCase (sp, i, outty, t, pl) ->
- C.MutCase (sp, i, map_term k outty, map_term k t, List.map (map_term k) pl)
- | C.Prod (n, s, t) -> C.Prod (n, map_term k s, map_term (succ k) t)
- | C.Lambda (n, s, t) -> C.Lambda (n, map_term k s, map_term (succ k) t)
- | C.LetIn (n, s, t) -> C.LetIn (n, map_term k s, map_term (succ k) t)
- | C.Fix (i, fs) -> C.Fix (i, map_fs (List.length fs) k fs)
- | C.CoFix (i, cfs) -> C.CoFix (i, map_cfs (List.length cfs) k cfs)
- in
- map_term 0 t
-
-let id n = n
-
-let after continuation aftermap beforemap =
- continuation ~map:(fun n -> aftermap (beforemap n))
-
-let after2 continuation aftermap beforemap ~map =
- continuation ~map:(fun n -> map (aftermap (beforemap n)))
-
-(* term ha tipo t1=t2; funziona solo se t1 e t2 hanno in testa costruttori
-diversi *)
-
-let discriminate_tac ~term =
- let true_URI =
- match LibraryObjects.true_URI () with
- Some uri -> uri
- | None -> raise (PET.Fail (lazy "You need to register the default \"true\" definition first. Please use the \"default\" command")) in
- let false_URI =
- match LibraryObjects.false_URI () with
- Some uri -> uri
- | None -> raise (PET.Fail (lazy "You need to register the default \"false\" definition first. Please use the \"default\" command")) in
- let fail msg = raise (PET.Fail (lazy ("Discriminate: " ^ msg))) in
- let find_discriminating_consno t1 t2 =
- let rec aux t1 t2 =
- match t1, t2 with
- | C.MutConstruct _, C.MutConstruct _ when t1 = t2 -> None
- | C.Appl ((C.MutConstruct _ as constr1) :: args1),
- C.Appl ((C.MutConstruct _ as constr2) :: args2)
- when constr1 = constr2 ->
- let rec aux_list l1 l2 =
- match l1, l2 with
- | [], [] -> None
- | hd1 :: tl1, hd2 :: tl2 ->
- (match aux hd1 hd2 with
- | None -> aux_list tl1 tl2
- | Some _ as res -> res)
- | _ -> (* same constructor applied to a different number of args *)
- assert false
- in
- aux_list args1 args2
- | ((C.MutConstruct (_,_,consno1,subst1)),
- (C.MutConstruct (_,_,consno2,subst2)))
- | ((C.MutConstruct (_,_,consno1,subst1)),
- (C.Appl ((C.MutConstruct (_,_,consno2,subst2)) :: _)))
- | ((C.Appl ((C.MutConstruct (_,_,consno1,subst1)) :: _)),
- (C.MutConstruct (_,_,consno2,subst2)))
- | ((C.Appl ((C.MutConstruct (_,_,consno1,subst1)) :: _)),
- (C.Appl ((C.MutConstruct (_,_,consno2,subst2)) :: _)))
- when (consno1 <> consno2) || (subst1 <> subst2) ->
- Some consno2
- | _ -> fail "not a discriminable equality"
- in
- aux t1 t2
- in
- let mk_branches_and_outtype turi typeno consno context args =
- (* a list of "True" except for the element in position consno which
- * is "False" *)
- match fst (CicEnvironment.get_obj CicUniv.empty_ugraph turi) with
- | C.InductiveDefinition (ind_type_list,_,paramsno,_) ->
- let _,_,rty,constructor_list = List.nth ind_type_list typeno in
- let false_constr_id,_ = List.nth constructor_list (consno - 1) in
- let branches =
- List.map
- (fun (id,cty) ->
- (* dubbio: e' corretto ridurre in questo context ??? *)
- let red_ty = CR.whd context cty in
- let rec aux t k =
- match t with
- | C.Prod (_,_,target) when (k <= paramsno) ->
- S.subst (List.nth args (k-1))
- (aux target (k+1))
- | C.Prod (binder,source,target) when (k > paramsno) ->
- C.Lambda (binder, source, (aux target (k+1)))
- | _ ->
- if (id = false_constr_id)
- then (C.MutInd(false_URI,0,[]))
- else (C.MutInd(true_URI,0,[]))
- in
- (S.lift 1 (aux red_ty 1)))
- constructor_list in
- let outtype =
- let seed = ref 0 in
- let rec mk_lambdas rev_left_args =
- function
- 0, args, C.Prod (_,so,ta) ->
- C.Lambda
- (C.Name (incr seed; "x" ^ string_of_int !seed),
- so,
- mk_lambdas rev_left_args (0,args,ta))
- | 0, args, C.Sort _ ->
- let rec mk_rels =
- function
- 0 -> []
- | n -> C.Rel n :: mk_rels (n - 1) in
- let argsno = List.length args in
- C.Lambda
- (C.Name "x",
- (if argsno + List.length rev_left_args > 0 then
- C.Appl
- (C.MutInd (turi, typeno, []) ::
- (List.map
- (S.lift (argsno + 1))
- (List.rev rev_left_args)) @
- mk_rels argsno)
- else
- C.MutInd (turi,typeno,[])),
- C.Sort C.Prop)
- | 0, _, _ -> assert false (* seriously screwed up *)
- | n, he::tl, C.Prod (_,_,ta) ->
- mk_lambdas (he::rev_left_args)(n-1,tl,S.subst he ta)
- | n,_,_ ->
- assert false (* we should probably reduce in some context *)
- in
- mk_lambdas [] (paramsno, args, rty)
- in
- branches, outtype
- | _ -> assert false
- in
- let discriminate'_tac ~term status =
- let (proof, goal) = status in
- let _,metasenv,_subst,_,_, _ = proof in
- let _,context,_ = CicUtil.lookup_meta goal metasenv in
- let termty,_ =
- CTC.type_of_aux' metasenv context term CicUniv.empty_ugraph
- in
- match termty with
- | C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2]
- when LibraryObjects.is_eq_URI equri ->
- let turi,typeno,exp_named_subst,args =
- match tty with
- | (C.MutInd (turi,typeno,exp_named_subst)) ->
- turi,typeno,exp_named_subst,[]
- | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::args)) ->
- turi,typeno,exp_named_subst,args
- | _ -> fail "not a discriminable equality"
- in
- let consno =
- match find_discriminating_consno t1 t2 with
- | Some consno -> consno
- | None -> fail "discriminating terms are structurally equal"
- in
- let branches,outtype =
- mk_branches_and_outtype turi typeno consno context args
- in
- PET.apply_tactic
- (T.then_
- ~start:(EliminationTactics.elim_type_tac (C.MutInd (false_URI, 0, [])))
- ~continuation:
- (T.then_
- ~start:
- (RT.change_tac
- ~pattern:(PET.conclusion_pattern None)
- (fun _ m u ->
- C.Appl [
- C.Lambda ( C.Name "x", tty,
- C.MutCase (turi, typeno, outtype, (C.Rel 1), branches));
- t2 ],
- m, u))
- ~continuation:
- (T.then_
- ~start:
- (ET.rewrite_simpl_tac
- ~direction:`RightToLeft
- ~pattern:(PET.conclusion_pattern None)
- term [])
- ~continuation:
- (IntroductionTactics.constructor_tac ~n:1)))) status
- | _ -> fail "not an equality"
- in
- PET.mk_tactic (discriminate'_tac ~term)
-
-let exn_nonproj =
- PET.Fail (lazy "Injection: not a projectable equality")
-let exn_noneq =
- PET.Fail (lazy "Injection: not an equality")
-let exn_nothingtodo =
- PET.Fail (lazy "Nothing to do")
-let exn_discrnonind =
- PET.Fail (lazy "Discriminate: object is not an Inductive Definition: it's imposible")
-let exn_injwronggoal =
- PET.Fail (lazy "Injection: goal after cut is not correct")
-let exn_noneqind =
- PET.Fail (lazy "Injection: not an equality over elements of an inductive type")
-
-let pp ctx t =
- let names = List.map (function Some (n,_) -> Some n | None -> None) ctx in
- CicPp.pp t names
-
-let clear_term first_time context term =
- let g () = if first_time then raise exn_nothingtodo else T.id_tac in
- match term with
- | C.Rel n ->
- begin match List.nth context (pred n) with
- | Some (C.Name id, _) -> PST.clear ~hyps:[id]
- | _ -> assert false
- end
- | _ -> g ()
-
-let simpl_in_term context = function
- | Cic.Rel i ->
- let name = match List.nth context (pred i) with
- | Some (Cic.Name s, Cic.Def _) -> s
- | Some (Cic.Name s, Cic.Decl _) -> s
- | _ -> assert false
- in
- RT.simpl_tac ~pattern:(None,[name,Cic.Implicit (Some `Hole)],None)
- | _ -> raise exn_nonproj
-
-(* ~term vive nel contesto della tattica una volta ~mappato
- * ~continuation riceve la mappa assoluta
- *)
-let rec injection_tac ~map ~term ~i ~continuation =
- let give_name seed = function
- | C.Name _ as name -> name
- | C.Anonymous -> C.Name (incr seed; "y" ^ string_of_int !seed)
- in
- let rec mk_rels = function | 0 -> [] | n -> C.Rel n :: (mk_rels (n - 1)) in
- let injection_tac status =
- let (proof, goal) = status in
- (* precondizione: t1 e t2 hanno in testa lo stesso costruttore ma
- * differiscono (o potrebbero differire?) nell'i-esimo parametro
- * del costruttore *)
- let _,metasenv,_subst,_,_, _ = proof in
- let _,context,_ = CicUtil.lookup_meta goal metasenv in
- let term = relocate_term map term in
- let termty,_ =
- CTC.type_of_aux' metasenv context term CicUniv.empty_ugraph
- in
- debug_print (lazy ("\ninjection su : " ^ pp context termty));
- match termty with (* an equality *)
- | C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2]
- when LibraryObjects.is_eq_URI equri ->
- let turi,typeno,ens,params =
- match tty with (* some inductive type *)
- | C.MutInd (turi,typeno,ens) -> turi,typeno,ens,[]
- | C.Appl (C.MutInd (turi,typeno,ens)::params) -> turi,typeno,ens,params
- | _ -> raise exn_noneqind
- in
- let t1',t2',consno = (* sono i due sottotermini che differiscono *)
- match t1,t2 with
- | C.Appl ((C.MutConstruct (uri1,typeno1,consno1,ens1))::applist1),
- C.Appl ((C.MutConstruct (uri2,typeno2,consno2,ens2))::applist2)
- when (uri1 = uri2) && (typeno1 = typeno2) &&
- (consno1 = consno2) && (ens1 = ens2) ->
- (* controllo ridondante *)
- List.nth applist1 (pred i),List.nth applist2 (pred i),consno2
- | _ -> assert false
- in
- let tty',_ = CTC.type_of_aux' metasenv context t1' CU.empty_ugraph in
- let patterns,outtype =
- match fst (CicEnvironment.get_obj CicUniv.empty_ugraph turi) with
- | C.InductiveDefinition (ind_type_list,_,paramsno,_)->
- let left_params, right_params = HExtlib.split_nth paramsno params in
- let _,_,_,constructor_list = List.nth ind_type_list typeno in
- let i_constr_id,_ = List.nth constructor_list (consno - 1) in
- let patterns =
- let seed = ref 0 in
- List.map
- (function (id,cty) ->
- let reduced_cty = CR.whd context cty in
- let rec aux k = function
- | C.Prod (_,_,tgt) when k <= paramsno ->
- let left = List.nth left_params (k-1) in
- aux (k+1) (S.subst left tgt)
- | C.Prod (binder,source,target) when k > paramsno ->
- let binder' = give_name seed binder in
- C.Lambda (binder',source,(aux (k+1) target))
- | _ ->
- let nr_param_constr = k - paramsno - 1 in
- if id = i_constr_id then C.Rel (k - i)
- else S.lift nr_param_constr t1'
- (* + 1 per liftare anche il lambda aggiunto
- * esternamente al case *)
- in S.lift 1 (aux 1 reduced_cty))
- constructor_list
- in
- (* this code should be taken from cases_tac *)
- let outtype =
- let seed = ref 0 in
- let rec to_lambdas te head =
- match CR.whd context te with
- | C.Prod (binder,so,ta) ->
- let binder' = give_name seed binder in
- C.Lambda (binder',so,to_lambdas ta head)
- | _ -> head
- in
- let rec skip_prods params te =
- match params, CR.whd context te with
- | [], _ -> te
- | left::tl, C.Prod (_,_,ta) ->
- skip_prods tl (S.subst left ta)
- | _, _ -> assert false
- in
- let abstracted_tty =
- let tty =
- List.fold_left (fun x y -> S.subst y x) tty left_params
- in
- (* non lift, ma subst coi left! *)
- match S.lift 1 tty with
- | C.MutInd _ as tty' -> tty'
- | C.Appl l ->
- let keep,abstract = HExtlib.split_nth (paramsno +1) l in
- let keep = List.map (S.lift paramsno) keep in
- C.Appl (keep@mk_rels (List.length abstract))
- | _ -> assert false
- in
- match ind_type_list with
- | [] -> assert false
- | (_,_,ty,_)::_ ->
- (* this is in general wrong, do as in cases_tac *)
- to_lambdas (skip_prods left_params ty)
- (C.Lambda
- (C.Name "cased", abstracted_tty,
- (* here we should capture right parameters *)
- (* 1 for his Lambda, one for the Lambda outside the match
- * and then one for each to_lambda *)
- S.lift (2+List.length right_params) tty'))
- in
- patterns,outtype
- | _ -> raise exn_discrnonind
- in
- let cutted = C.Appl [C.MutInd (equri,0,[]) ; tty' ; t1' ; t2'] in
- let changed =
- C.Appl [ C.Lambda (C.Name "x", tty,
- C.MutCase (turi,typeno,outtype,C.Rel 1,patterns)) ; t1]
- in
- (* check if cutted and changed are well typed and if t1' ~ changed *)
- let go_on =
- try
- let _,g = CTC.type_of_aux' metasenv context cutted
- CicUniv.empty_ugraph
- in
- let _,g = CTC.type_of_aux' metasenv context changed g in
- fst (CR.are_convertible ~metasenv context t1' changed g)
- with
- | CTC.TypeCheckerFailure _ -> false
- in
- if not go_on then
- PET.apply_tactic (continuation ~map) status
- else
- let tac term =
- let tac status =
- debug_print (lazy "riempio il cut");
- let (proof, goal) = status in
- let _,metasenv,_subst,_,_, _ = proof in
- let _,context,gty = CicUtil.lookup_meta goal metasenv in
- let gty = Unshare.unshare gty in
- let new_t1' = match gty with
- | (C.Appl (C.MutInd (_,_,_)::_::t::_)) -> t
- | _ -> raise exn_injwronggoal
- in
- debug_print (lazy ("metto: " ^ pp context changed));
- debug_print (lazy ("al posto di: " ^ pp context new_t1'));
- debug_print (lazy ("nel goal: " ^ pp context gty));
- debug_print (lazy ("nel contesto:\n" ^ CicPp.ppcontext context));
- debug_print (lazy ("e poi rewrite con: "^pp context term));
- let tac = T.seq ~tactics:[
- RT.change_tac
- ~pattern:(None, [], Some (PEH.pattern_of ~term:gty [new_t1']))
- (fun _ m u -> changed,m,u);
- ET.rewrite_simpl_tac
- ~direction:`LeftToRight
- ~pattern:(PET.conclusion_pattern None)
- term [];
- ET.reflexivity_tac
- ] in
- PET.apply_tactic tac status
- in
- PET.mk_tactic tac
- in
- debug_print (lazy ("CUT: " ^ pp context cutted));
- PET.apply_tactic
- (T.thens ~start: (P.cut_tac cutted)
- ~continuations:[
- (destruct ~first_time:false ~term:(C.Rel 1) ~map:id
- ~continuation:(after2 continuation succ map)
- );
- tac term]
- ) status
- | _ -> raise exn_noneq
- in
- PET.mk_tactic injection_tac
-
-(* ~term vive nel contesto della tattica una volta ~mappato
- * ~continuation riceve la mappa assoluta
- *)
-and subst_tac ~map ~term ~direction ~where ~continuation =
- let fail_tactic = continuation ~map in
- let subst_tac status =
- let term = relocate_term map term in
- let tactic = match where with
- | None ->
- let pattern = PET.conclusion_pattern None in
- let tactic = ET.rewrite_tac ~direction ~pattern term [] in
- T.then_ ~start:(T.try_tactic ~tactic)
- ~continuation:fail_tactic
- | Some name ->
- let pattern = None, [name, PET.hole], None in
- let start = ET.rewrite_tac ~direction ~pattern term [] in
- let continuation =
- destruct ~first_time:false ~term:(C.Rel 1) ~map:id
- ~continuation:(after2 continuation succ map)
- in
- T.if_ ~start ~continuation ~fail:fail_tactic
- in
- PET.apply_tactic tactic status
- in
- PET.mk_tactic subst_tac
-
-(* ~term vive nel contesto della tattica una volta ~mappato
- * ~continuation riceve la mappa assoluta
- *)
-and destruct ~first_time ~map ~term ~continuation =
- let are_convertible hd1 hd2 metasenv context =
- fst (CR.are_convertible ~metasenv context hd1 hd2 CicUniv.empty_ugraph)
- in
- let destruct status =
- let (proof, goal) = status in
- let _,metasenv,_subst, _,_, _ = proof in
- let _,context,_ = CicUtil.lookup_meta goal metasenv in
- let term = relocate_term map term in
- debug_print (lazy ("\nqnify di: " ^ pp context term));
- debug_print (lazy ("nel contesto:\n" ^ CicPp.ppcontext context));
- let termty,_ =
- CTC.type_of_aux' metasenv context term CicUniv.empty_ugraph
- in
- debug_print (lazy ("\nqnify su: " ^ pp context termty));
- let tac = match termty with
- | C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2]
- when LibraryObjects.is_eq_URI equri -> begin
- match (CR.whd ~delta:true context tty) with
- | C.MutInd _
- | C.Appl (C.MutInd _ :: _) ->
- begin match t1,t2 with
- | C.MutConstruct _,
- C.MutConstruct _
- when t1 = t2 ->
- T.then_ ~start:(clear_term first_time context term)
- ~continuation:(continuation ~map)
- | C.Appl (C.MutConstruct _ as mc1 :: applist1),
- C.Appl (C.MutConstruct _ as mc2 :: applist2)
- when mc1 = mc2 ->
- let rec traverse_list first_time i l1 l2 =
- match l1, l2 with
- | [], [] ->
- fun ~map:aftermap ->
- T.then_ ~start:(clear_term first_time context term)
- ~continuation:(after continuation aftermap map)
- | hd1 :: tl1, hd2 :: tl2 ->
- if are_convertible hd1 hd2 metasenv context then
- traverse_list first_time (succ i) tl1 tl2
- else
- injection_tac ~i ~term ~continuation:
- (traverse_list false (succ i) tl1 tl2)
- | _ -> assert false
- (* i 2 termini hanno in testa lo stesso costruttore,
- * ma applicato a un numero diverso di termini *)
- in
- traverse_list first_time 1 applist1 applist2 ~map:id
- | C.MutConstruct (_,_,consno1,ens1),
- C.MutConstruct (_,_,consno2,ens2)
- | C.MutConstruct (_,_,consno1,ens1),
- C.Appl ((C.MutConstruct (_,_,consno2,ens2))::_)
- | C.Appl ((C.MutConstruct (_,_,consno1,ens1))::_),
- C.MutConstruct (_,_,consno2,ens2)
- | C.Appl ((C.MutConstruct (_,_,consno1,ens1))::_),
- C.Appl ((C.MutConstruct (_,_,consno2,ens2))::_)
- when (consno1 <> consno2) || (ens1 <> ens2) ->
- discriminate_tac ~term
- | _ when not first_time -> continuation ~map
- | _ (* when first_time *) ->
- T.then_ ~start:(simpl_in_term context term)
- ~continuation:(destruct ~first_time:false ~term ~map ~continuation)
- end
- | _ when not first_time -> continuation ~map
- | _ (* when first_time *) -> raise exn_nonproj
- end
- | _ -> raise exn_nonproj
- in
- PET.apply_tactic tac status
- in
- PET.mk_tactic destruct
-
-(* destruct performs either injection or discriminate *)
-(* equivalent to Coq's "analyze equality" *)
-let destruct_tac =
- destruct
- ~first_time:true ~map:id ~continuation:(fun ~map -> T.id_tac)
+++ /dev/null
-(* Copyright (C) 2002, HELM Team.
- *
- * This file is part of HELM, an Hypertextual, Electronic
- * Library of Mathematics, developed at the Computer Science
- * Department, University of Bologna, Italy.
- *
- * HELM is free software; you can redistribute it and/or
- * modify it under the terms of the GNU General Public License
- * as published by the Free Software Foundation; either version 2
- * of the License, or (at your option) any later version.
- *
- * HELM is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with HELM; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
- * MA 02111-1307, USA.
- *
- * For details, see the HELM World-Wide-Web page,
- * http://cs.unibo.it/helm/.
- *)
-
-(* Performs a recursive comparisons of the two sides of an equation
- looking for constructors. If the two sides differ on two constructors,
- it closes the current goal. If they differ by other two terms it introduces
- an equality. *)
-val destruct_tac: term:Cic.term -> ProofEngineTypes.tactic
+++ /dev/null
-(* Copyright (C) 2002, HELM Team.
- *
- * This file is part of HELM, an Hypertextual, Electronic
- * Library of Mathematics, developed at the Computer Science
- * Department, University of Bologna, Italy.
- *
- * HELM is free software; you can redistribute it and/or
- * modify it under the terms of the GNU General Public License
- * as published by the Free Software Foundation; either version 2
- * of the License, or (at your option) any later version.
- *
- * HELM is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with HELM; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
- * MA 02111-1307, USA.
- *
- * For details, see the HELM World-Wide-Web page,
- * http://cs.unibo.it/helm/.
- *)
-
-module C = Cic
-module DT = DiscriminationTactics
-module DTI = DoubleTypeInference
-module ET = EqualityTactics
-module HEL = HExtlib
-module LO = LibraryObjects
-module PEH = ProofEngineHelpers
-module PESR = ProofEngineStructuralRules
-module PET = ProofEngineTypes
-module RT = ReductionTactics
-module S = CicSubstitution
-module T = Tacticals
-module TC = CicTypeChecker
-
-let lift_rewrite_tac ~context ~direction ~pattern equality =
- let lift_rewrite_tac status =
- let (proof, goal) = status in
- let (_, metasenv, _subst, _, _, _) = proof in
- let _, new_context, _ = CicUtil.lookup_meta goal metasenv in
- let n = List.length new_context - List.length context in
- let equality = S.lift n equality in
- PET.apply_tactic (ET.rewrite_tac ~direction ~pattern equality []) status
- in
- PET.mk_tactic lift_rewrite_tac
-
-let lift_destruct_tac ~context ~what =
- let lift_destruct_tac status =
- let (proof, goal) = status in
- let (_, metasenv, _subst, _, _, _) = proof in
- let _, new_context, _ = CicUtil.lookup_meta goal metasenv in
- let n = List.length new_context - List.length context in
- let what = S.lift n what in
- PET.apply_tactic (DT.destruct_tac ~term:what) status
- in
- PET.mk_tactic lift_destruct_tac
-
-let msg0 = lazy "Subst: not found in context"
-let msg1 = lazy "Subst: not an erasable equation"
-let msg2 = lazy "Subst: recursive equation"
-let msg3 = lazy "Subst: no progress"
-
-let rec subst_tac ~try_tactic ~hyp =
- let hole = C.Implicit (Some `Hole) in
- let meta = C.Implicit None in
- let rec ind = function
- | C.MutInd _ -> true
- | C.Appl (t :: tl) -> ind t
- | _ -> false
- in
- let rec constr = function
- | C.MutConstruct _ -> true
- | C.Appl (t :: tl) -> constr t
- | _ -> false
- in
- let subst_tac status =
- let (proof, goal) = status in
- let (_, metasenv, _subst, _, _, _) = proof in
- let _, context, _ = CicUtil.lookup_meta goal metasenv in
- let what = match PEH.get_rel context hyp with
- | Some t -> t
- | None -> raise (PET.Fail msg0)
- in
- let ty, _ = TC.type_of_aux' metasenv context what CicUniv.empty_ugraph in
- let subst_g direction i t =
- let rewrite pattern =
- let tactic = lift_rewrite_tac ~context ~direction ~pattern what in
- try_tactic ~tactic
- in
- let var = match PEH.get_name context i with
- | Some name -> name
- | None -> raise (PET.Fail msg0)
- in
- if DTI.does_not_occur i t then () else raise (PET.Fail msg2);
- let map self = function
- | Some (C.Name s, _) when s <> self ->
- Some (rewrite (None, [(s, hole)], None))
- | _ -> None
- in
- let rew_hips = HEL.list_rev_map_filter (map hyp) context in
- let rew_concl = rewrite (None, [], Some hole) in
- let clear = PESR.clear ~hyps:[hyp; var] in
- List.rev_append (rew_concl :: rew_hips) [clear]
- in
- let destruct_g () =
- [lift_destruct_tac ~context ~what; PESR.clear ~hyps:[hyp]]
- in
- let whd_g () =
- let whd_pattern = C.Appl [meta; hole; hole; hole] in
- let pattern = None, [hyp, whd_pattern], None in
- [RT.whd_tac ~pattern; subst_tac ~try_tactic ~hyp]
- in
- let tactics = match ty with
- | (C.Appl [(C.MutInd (uri, 0, [])); _; C.Rel i; t])
- when LO.is_eq_URI uri -> subst_g `LeftToRight i t
- | (C.Appl [(C.MutInd (uri, 0, [])); _; t; C.Rel i])
- when LO.is_eq_URI uri -> subst_g `RightToLeft i t
- | (C.Appl [(C.MutInd (uri, 0, [])); t; t1; t2])
- when LO.is_eq_URI uri && ind t && constr t1 && constr t2 -> destruct_g ()
- | (C.Appl [(C.MutInd (uri, 0, [])); _; t1; t2])
- when LO.is_eq_URI uri -> whd_g ()
- | _ -> raise (PET.Fail msg1)
- in
- PET.apply_tactic (T.seq ~tactics) status
- in
- PET.mk_tactic subst_tac
-
-let subst_tac =
- let subst_tac status =
- let progress = ref false in
- let try_tactic ~tactic =
- let try_tactic status =
- try
- let result = PET.apply_tactic tactic status in
- progress := true; result
- with
- | PET.Fail _ -> PET.apply_tactic T.id_tac status
- in
- PET.mk_tactic try_tactic
- in
- let subst hyp = try_tactic ~tactic:(subst_tac ~try_tactic ~hyp) in
- let map = function
- | Some (C.Name s, _) -> Some (subst s)
- | _ -> None
- in
- let (proof, goal) = status in
- let (_, metasenv, _subst, _, _, _) = proof in
- let _, context, _ = CicUtil.lookup_meta goal metasenv in
- let tactics = HEL.list_rev_map_filter map context in
- let result = PET.apply_tactic (T.seq ~tactics) status in
- if !progress then result else raise (PET.Fail msg3)
- in
- PET.mk_tactic subst_tac
-
- let try_tac tactic = T.try_tactic ~tactic
- let then_tac start continuation = T.then_ ~start ~continuation
-
-let subst_tac =
- let tactic = T.repeat_tactic ~tactic:subst_tac in
- T.try_tactic ~tactic
+++ /dev/null
-(* Copyright (C) 2002, HELM Team.
- *
- * This file is part of HELM, an Hypertextual, Electronic
- * Library of Mathematics, developed at the Computer Science
- * Department, University of Bologna, Italy.
- *
- * HELM is free software; you can redistribute it and/or
- * modify it under the terms of the GNU General Public License
- * as published by the Free Software Foundation; either version 2
- * of the License, or (at your option) any later version.
- *
- * HELM is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with HELM; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
- * MA 02111-1307, USA.
- *
- * For details, see the HELM World-Wide-Web page,
- * http://cs.unibo.it/helm/.
- *)
-
-(* rewrites and clears all simple equalities in the context *)
-val subst_tac: ProofEngineTypes.tactic
let cut = PrimitiveTactics.cut_tac
let decompose = EliminationTactics.decompose_tac
let demodulate = Auto.demodulate_tac
-let destruct = DiscriminationTactics.destruct_tac
+let destruct = DestructTactic.destruct_tac
let elim_intros = PrimitiveTactics.elim_intros_tac
let elim_intros_simpl = PrimitiveTactics.elim_intros_simpl_tac
let elim_type = EliminationTactics.elim_type_tac
let simpl = ReductionTactics.simpl_tac
let solve_rewrite = Auto.solve_rewrite_tac
let split = IntroductionTactics.split_tac
-let subst = SubstTactic.subst_tac
let symmetry = EqualityTactics.symmetry_tac
let transitivity = EqualityTactics.transitivity_tac
let unfold = ReductionTactics.unfold_tac
-(* GENERATED FILE, DO NOT EDIT. STAMP:Fri Jul 6 11:03:35 CEST 2007 *)
+(* GENERATED FILE, DO NOT EDIT. STAMP:Tue Nov 6 16:23:06 CET 2007 *)
val absurd : term:Cic.term -> ProofEngineTypes.tactic
val apply : term:Cic.term -> ProofEngineTypes.tactic
val applyS :
unit -> ProofEngineTypes.tactic
val demodulate :
dbd:HSql.dbd -> universe:Universe.universe -> ProofEngineTypes.tactic
-val destruct : term:Cic.term -> ProofEngineTypes.tactic
+val destruct : Cic.term option -> ProofEngineTypes.tactic
val elim_intros :
?mk_fresh_name_callback:ProofEngineTypes.mk_fresh_name_type ->
?depth:int ->
val solve_rewrite :
universe:Universe.universe -> ?steps:int -> unit -> ProofEngineTypes.tactic
val split : ProofEngineTypes.tactic
-val subst : ProofEngineTypes.tactic
val symmetry : ProofEngineTypes.tactic
val transitivity : term:Cic.term -> ProofEngineTypes.tactic
val unfold :
(in_list ? (mk_bound D y V) (H @ ((mk_bound B x T) :: G))).
intros 10;elim H
[simplify in H1;elim (in_cons_case ? ? ? ? H1)
- [destruct H3;elim (H2 Hcut1)
+ [destruct H3;elim (H2);reflexivity
|simplify;apply (in_Skip ? ? ? ? H3);]
|simplify in H2;simplify;elim (in_cons_case ? ? ? ? H2)
[rewrite > H4;apply in_Base
intros 7;elim H 0
[simplify;intros;(*FIXME*)generalize in match H1;intro;inversion H1;intros
[lapply (nil_cons ? G (mk_bound B x T));elim (Hletin H4)
- |destruct H8;rewrite < Hcut2 in H6;rewrite < Hcut in H4;
- rewrite < Hcut in H6;apply (WFE_cons ? ? ? ? H4 H6 H2)]
+ |destruct H8;apply (WFE_cons ? ? ? ? H4 H6 H2)]
|intros;simplify;generalize in match H2;elim t;simplify in H4;
inversion H4;intros
[destruct H5
|destruct H9;apply WFE_cons
- [rewrite < Hcut in H5;apply (H1 H5 H3)
- |rewrite < (fv_env_extends ? x B C T U);rewrite > Hcut;rewrite > Hcut2;
- assumption
- |rewrite < Hcut3 in H8;rewrite > Hcut1;apply (WFT_env_incl ? ? H8);
+ [apply (H1 H5 H3)
+ |rewrite < (fv_env_extends ? x B C T U); assumption
+ |apply (WFT_env_incl ? ? H8);
rewrite < (fv_env_extends ? x B C T U);unfold;intros;
- rewrite > Hcut;assumption]]]
+ assumption]]]
qed.
lemma WFE_bound_bound : \forall B,x,T,U,G. (WFEnv G) \to
intros 6;elim H
[lapply (in_list_nil ? ? H1);elim Hletin
|elim (in_cons_case ? ? ? ? H6)
- [destruct H7;subst;elim (in_cons_case ? ? ? ? H5)
- [destruct H7;assumption
- |elim H7;elim H3;apply boundinenv_natinfv;apply (ex_intro ? ? b);
+ [destruct H7;destruct;elim (in_cons_case ? ? ? ? H5)
+ [destruct H7;reflexivity
+ |elim H7;elim H3;apply boundinenv_natinfv;apply (ex_intro ? ? B);
apply (ex_intro ? ? T);assumption]
|elim (in_cons_case ? ? ? ? H5)
[destruct H8;elim H3;apply boundinenv_natinfv;apply (ex_intro ? ? B);
- apply (ex_intro ? ? U);rewrite < Hcut1;assumption
+ apply (ex_intro ? ? U);assumption
|apply (H2 H8 H7)]]]
qed.
intros.elim (fresh_name ((fv_type U)@(fv_env G))).lapply(H a)
[unfold;intros;lapply (fv_WFT ? x ? Hletin)
[simplify in Hletin1;inversion Hletin1;intros
- [destruct H4;elim H1;rewrite > Hcut;rewrite < H3.autobatch
- |destruct H6;rewrite > Hcut1;assumption]
+ [destruct H4;elim H1;autobatch
+ |destruct H6;assumption]
|apply in_FV_subst;assumption]
|*:intro;apply H1;autobatch]
qed.
[unfold;intro;apply H8;apply (incl_bound_fv ? ? H7 ? H9)
|apply (WFE_cons ? ? ? ? H6 H8);autobatch
|unfold;intros;inversion H9;intros
- [destruct H11;rewrite > Hcut;apply in_Base
- |destruct H13;rewrite < Hcut1 in H10;apply in_Skip;apply (H7 ? H10)]]]
+ [destruct H11;apply in_Base
+ |destruct H13;apply in_Skip;apply (H7 ? H10)]]]
qed.
theorem narrowing:∀X,G,G1,U,P,M,N.
|generalize in match H7;generalize in match H4;generalize in match H2;
generalize in match H5;clear H7 H4 H2 H5;
generalize in match (refl_eq ? (Arrow t t1));
- elim H6 in ⊢ (? ? ? %→%); clear H6; intros; subst;
+ elim H6 in ⊢ (? ? ? %→%); clear H6; intros; destruct;
[apply (SA_Trans_TVar ? ? ? ? H);apply (H4 ? ? H8 H9);autobatch
- |inversion H11;intros; subst; autobatch depth=4 width=4 size=9;
+ |inversion H11;intros; destruct; autobatch depth=4 width=4 size=9;
]
|generalize in match H7;generalize in match H4;generalize in match H2;
generalize in match H5;clear H7 H4 H2 H5;
- generalize in match (refl_eq ? (Forall t t1));elim H6 in ⊢ (? ? ? %→%);subst
+ generalize in match (refl_eq ? (Forall t t1));elim H6 in ⊢ (? ? ? %→%);destruct;
[apply (SA_Trans_TVar ? ? ? ? H);apply (H4 ? H7 H8 H9 H10);reflexivity
- |inversion H11;intros;subst
+ |inversion H11;intros;destruct;
[apply SA_Top
[autobatch
|apply WFT_Forall
|intro;apply H15;apply H8;apply (WFT_to_incl ? ? ? H3);
assumption
|simplify;autobatch
- |apply (narrowing X (mk_bound true X t::l2)
+ |apply (narrowing X (mk_bound true X t::l1)
? ? ? ? ? H7 ? ? [])
[intros;apply H9
[unfold;intros;lapply (H8 ? H17);rewrite > fv_append;
[unfold;intro;apply H8;apply (incl_bound_fv ? ? H7 ? H9)
|apply (WFE_cons ? ? ? ? H6 H8);autobatch
|unfold;intros;inversion H9;intros
- [destruct H11;rewrite > Hcut;apply in_Base
- |destruct H13;rewrite < Hcut1 in H10;apply in_Skip;apply (H7 ? H10)]]]
+ [destruct H11;apply in_Base
+ |destruct H13;apply in_Skip;apply (H7 ? H10)]]]
qed.
theorem narrowing:∀X,G,G1,U,P,M,N.
elim H2 in ⊢ (? ? ? % → ? ? ? % → %);
[1,2: destruct H6
|5: destruct H8
- | lapply (H5 H6 H7); subst; clear H5;
+ | lapply (H5 H6 H7); destruct; clear H5;
apply H;
assumption
- | subst;
+ | destruct;
clear H4 H6;
apply H1;
assumption
[rewrite > (JSubtype_Top ? ? H3);autobatch
|apply (JSubtype_Arrow_inv ? ? ? ? ? ? ? H6); intros;
[ autobatch
- | inversion H7;intros; subst; autobatch depth=4 width=4 size=9
+ | inversion H7;intros; destruct; autobatch depth=4 width=4 size=9
]
|generalize in match H7;generalize in match H4;generalize in match H2;
generalize in match H5;clear H7 H4 H2 H5;
- generalize in match (refl_eq ? (Forall t t1));elim H6 in ⊢ (? ? ? %→%);subst
+ generalize in match (refl_eq ? (Forall t t1));elim H6 in ⊢ (? ? ? %→%);destruct;
[apply (SA_Trans_TVar ? ? ? ? H);apply (H4 ? H7 H8 H9 H10);reflexivity
- |inversion H11;intros;subst
+ |inversion H11;intros;destruct;
[apply SA_Top
[autobatch
|apply WFT_Forall
|intro;apply H15;apply H8;apply (WFT_to_incl ? ? ? H3);
assumption
|simplify;autobatch
- |apply (narrowing X (mk_bound true X t::l2)
+ |apply (narrowing X (mk_bound true X t::l1)
? ? ? ? ? H7 ? ? [])
[intros;apply H9
[unfold;intros;lapply (H8 ? H17);rewrite > fv_append;
lemma in_cons_case : ∀A.∀x,h:A.∀t:list A.x ∈ h::t → x = h ∨ (x ∈ t).
intros;inversion H;intros
- [destruct H2;left;symmetry;assumption
+ [destruct H2;left;symmetry;reflexivity
|destruct H4;right;applyS H1]
qed.
intros 3.
elim l
[right.apply H
- |simplify in H1.inversion H1;intros
- [destruct H3.left.rewrite < Hcut.
- apply in_Base
- |destruct H5.
- elim (H l2)
- [left.apply in_Skip.
- rewrite < H4.assumption
- |right.rewrite < H4.assumption
- |rewrite > Hcut1.rewrite > H4.assumption
+ |simplify in H1.inversion H1;intros; destruct;
+ [left.apply in_Base
+ | elim (H l2)
+ [left.apply in_Skip. assumption
+ |right.assumption
+ |assumption
]
]
]
(* goal: x=pos y=pos *)
elim (decidable_eq_nat n n1:((n=n1) \lor ((n=n1) \to False))).
left.apply eq_f.assumption.
- right.unfold Not.intros (H_inj).apply H. destruct H_inj. assumption.
+ right.unfold Not.intros (H_inj).apply H. destruct H_inj. reflexivity.
(* goal: x=pos y=neg *)
right.unfold Not.intro.apply (not_eq_pos_neg n n1). assumption.
(* goal: x=neg *)
[1: generalize in match H; rewrite > (b2pT ? ? (eqP (list_eqType d2) ? ?) H2);
intros; clear H H2; rewrite < (pirrel ? ? ? H1 H3 (eqType_decidable nat_eqType));
reflexivity
- |2: unfold Not; intros (H3); destruct H3; rewrite > Hcut in H2;
+ |2: unfold Not; intros (H3); destruct H3;
rewrite > (cmp_refl (list_eqType d2)) in H2; destruct H2;]
qed.
[ intros; lapply (b2pF ? ? (eqP d ? ?) H1) as H'; clear H1;
destruct H; rewrite > Hcut in H'; apply H'; reflexivity;
| intros; lapply (IH ? H1) as H'; destruct H;
- rewrite > Hcut1 in H'; apply H'; reflexivity;]]]]
+ apply H'; reflexivity;]]]]
qed.
definition list_eqType : eqType → eqType ≝ λd:eqType.mk_eqType ? ? (lcmpP d).
| C1 : ∀x:nat.∀a:A.∀b:B. complex A B b a
| C2 : ∀a,a1:A.∀b,b1:B.∀x:nat. complex A B b1 a1 → complex A B b a.
-
theorem recursive1: ∀ x,y : nat.
(C1 ? ? O (Some ? x) y) =
(C1 ? ? (S O) (Some ? x) y) → False.
-intros; destruct H;
+intros; destruct H.
qed.
theorem recursive2: ∀ x,y,z,t : nat.
(C1 ? ? t (Some ? x) y) =
(C1 ? ? z (Some ? x) y) → t=z.
-intros; destruct H;assumption.
+intros; destruct H; reflexivity.
qed.
theorem recursive3: ∀ x,y,z,t : nat.
C2 ? ? (None ?) ? (S O) ? z (C1 ? ? (S O) (Some ? x) y) =
C2 ? ? (None ?) ? (S O) ? t (C1 ? ? (S O) (Some ? x) y) → z=t.
-intros; destruct H;assumption.
+intros; destruct H; reflexivity.
qed.
theorem recursive4: ∀ x,y,z,t : nat.
C2 ? ? (None ?) ? (S O) ? z (C1 ? ? (S O) (Some ? z) y) =
C2 ? ? (None ?) ? (S O) ? t (C1 ? ? (S O) (Some ? x) y) → z=t.
-intros; destruct H;assumption.
+intros; destruct H; reflexivity.
qed.
theorem recursive2: ∀ x,y : nat.
projects / helm.git / commitdiff