+++ /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/.
- *)
-
-(* $Id$ *)
-
-exception TheTypeOfTheCurrentGoalIsAMetaICannotChooseTheRightElimiantionPrinciple
-exception NotAnInductiveTypeToEliminate
-exception WrongUriToVariable of string
-exception NotAnEliminator
-
-module PET = ProofEngineTypes
-
-(* lambda_abstract newmeta ty *)
-(* returns a triple [bo],[context],[ty'] where *)
-(* [ty] = Pi/LetIn [context].[ty'] ([context] is a vector!) *)
-(* and [bo] = Lambda/LetIn [context].(Meta [newmeta]) *)
-(* So, lambda_abstract is the core of the implementation of *)
-(* the Intros tactic. *)
-(* howmany = -1 means Intros, howmany > 0 means Intros n *)
-let lambda_abstract ?(howmany=(-1)) metasenv context newmeta ty mk_fresh_name =
- let module C = Cic in
- let rec collect_context context howmany do_whd ty =
- match howmany with
- | 0 ->
- let irl =
- CicMkImplicit.identity_relocation_list_for_metavariable context
- in
- context, ty, (C.Meta (newmeta,irl))
- | _ ->
- match ty with
- C.Cast (te,_) -> collect_context context howmany do_whd te
- | C.Prod (n,s,t) ->
- let n' = mk_fresh_name metasenv context n ~typ:s in
- let (context',ty,bo) =
- let entry = match n' with
- | C.Name _ -> Some (n',(C.Decl s))
- | C.Anonymous -> None
- in
- let ctx = entry :: context in
- collect_context ctx (howmany - 1) do_whd t
- in
- (context',ty,C.Lambda(n',s,bo))
- | C.LetIn (n,s,sty,t) ->
- let (context',ty,bo) =
- collect_context ((Some (n,(C.Def (s,sty))))::context) (howmany - 1) do_whd t
- in
- (context',ty,C.LetIn(n,s,sty,bo))
- | _ as t ->
- if howmany <= 0 then
- let irl =
- CicMkImplicit.identity_relocation_list_for_metavariable context
- in
- context, t, (C.Meta (newmeta,irl))
- else if do_whd then
- let t = CicReduction.whd ~delta:true context t in
- collect_context context howmany false t
- else
- raise (PET.Fail (lazy "intro(s): not enough products or let-ins"))
- in
- collect_context context howmany true ty
-
-let eta_expand metasenv context t arg =
- let module T = CicTypeChecker in
- let module S = CicSubstitution in
- let module C = Cic in
- let rec aux n =
- function
- t' when t' = S.lift n arg -> C.Rel (1 + n)
- | C.Rel m -> if m <= n then C.Rel m else C.Rel (m+1)
- | C.Var (uri,exp_named_subst) ->
- let exp_named_subst' = aux_exp_named_subst n exp_named_subst in
- C.Var (uri,exp_named_subst')
- | C.Meta (i,l) ->
- let l' =
- List.map (function None -> None | Some t -> Some (aux n t)) l
- in
- C.Meta (i, l')
- | C.Sort _
- | C.Implicit _ as t -> t
- | C.Cast (te,ty) -> C.Cast (aux n te, aux n ty)
- | C.Prod (nn,s,t) -> C.Prod (nn, aux n s, aux (n+1) t)
- | C.Lambda (nn,s,t) -> C.Lambda (nn, aux n s, aux (n+1) t)
- | C.LetIn (nn,s,ty,t) -> C.LetIn (nn, aux n s, aux n ty, aux (n+1) t)
- | C.Appl l -> C.Appl (List.map (aux n) l)
- | C.Const (uri,exp_named_subst) ->
- let exp_named_subst' = aux_exp_named_subst n exp_named_subst in
- C.Const (uri,exp_named_subst')
- | C.MutInd (uri,i,exp_named_subst) ->
- let exp_named_subst' = aux_exp_named_subst n exp_named_subst in
- C.MutInd (uri,i,exp_named_subst')
- | C.MutConstruct (uri,i,j,exp_named_subst) ->
- let exp_named_subst' = aux_exp_named_subst n exp_named_subst in
- C.MutConstruct (uri,i,j,exp_named_subst')
- | C.MutCase (sp,i,outt,t,pl) ->
- C.MutCase (sp,i,aux n outt, aux n t,
- List.map (aux n) pl)
- | C.Fix (i,fl) ->
- let tylen = List.length fl in
- let substitutedfl =
- List.map
- (fun (name,i,ty,bo) -> (name, i, aux n ty, aux (n+tylen) bo))
- fl
- in
- C.Fix (i, substitutedfl)
- | C.CoFix (i,fl) ->
- let tylen = List.length fl in
- let substitutedfl =
- List.map
- (fun (name,ty,bo) -> (name, aux n ty, aux (n+tylen) bo))
- fl
- in
- C.CoFix (i, substitutedfl)
- and aux_exp_named_subst n =
- List.map (function uri,t -> uri,aux n t)
- in
- let argty,_ =
- T.type_of_aux' metasenv context arg CicUniv.oblivion_ugraph (* TASSI: FIXME *)
- in
- let fresh_name =
- FreshNamesGenerator.mk_fresh_name ~subst:[]
- metasenv context (Cic.Name "Heta") ~typ:argty
- in
- (C.Appl [C.Lambda (fresh_name,argty,aux 0 t) ; arg])
-
-(*CSC: ma serve solamente la prima delle new_uninst e l'unione delle due!!! *)
-let classify_metas newmeta in_subst_domain subst_in metasenv =
- List.fold_right
- (fun (i,canonical_context,ty) (old_uninst,new_uninst) ->
- if in_subst_domain i then
- old_uninst,new_uninst
- else
- let ty' = subst_in canonical_context ty in
- let canonical_context' =
- List.fold_right
- (fun entry canonical_context' ->
- let entry' =
- match entry with
- Some (n,Cic.Decl s) ->
- Some (n,Cic.Decl (subst_in canonical_context' s))
- | None -> None
- | Some (n,Cic.Def (bo,ty)) ->
- Some
- (n,
- Cic.Def
- (subst_in canonical_context' bo,
- subst_in canonical_context' ty))
- in
- entry'::canonical_context'
- ) canonical_context []
- in
- if i < newmeta then
- ((i,canonical_context',ty')::old_uninst),new_uninst
- else
- old_uninst,((i,canonical_context',ty')::new_uninst)
- ) metasenv ([],[])
-
-(* Useful only inside apply_tac *)
-let
- generalize_exp_named_subst_with_fresh_metas context newmeta uri exp_named_subst
-=
- let module C = Cic in
- let params =
- let o,_ = CicEnvironment.get_obj CicUniv.oblivion_ugraph uri in
- CicUtil.params_of_obj o
- in
- let exp_named_subst_diff,new_fresh_meta,newmetasenvfragment,exp_named_subst'=
- let next_fresh_meta = ref newmeta in
- let newmetasenvfragment = ref [] in
- let exp_named_subst_diff = ref [] in
- let rec aux =
- function
- [],[] -> []
- | uri::tl,[] ->
- let ty =
- let o,_ = CicEnvironment.get_obj CicUniv.oblivion_ugraph uri in
- match o with
- C.Variable (_,_,ty,_,_) ->
- CicSubstitution.subst_vars !exp_named_subst_diff ty
- | _ -> raise (WrongUriToVariable (UriManager.string_of_uri uri))
- in
-(* CSC: patch to generate ?1 : ?2 : Type in place of ?1 : Type to simulate ?1 :< Type
- (match ty with
- C.Sort (C.Type _) as s -> (* TASSI: ?? *)
- let fresh_meta = !next_fresh_meta in
- let fresh_meta' = fresh_meta + 1 in
- next_fresh_meta := !next_fresh_meta + 2 ;
- let subst_item = uri,C.Meta (fresh_meta',[]) in
- newmetasenvfragment :=
- (fresh_meta,[],C.Sort (C.Type (CicUniv.fresh()))) ::
- (* TASSI: ?? *)
- (fresh_meta',[],C.Meta (fresh_meta,[])) :: !newmetasenvfragment ;
- exp_named_subst_diff := !exp_named_subst_diff @ [subst_item] ;
- subst_item::(aux (tl,[]))
- | _ ->
-*)
- let irl =
- CicMkImplicit.identity_relocation_list_for_metavariable context
- in
- let subst_item = uri,C.Meta (!next_fresh_meta,irl) in
- newmetasenvfragment :=
- (!next_fresh_meta,context,ty)::!newmetasenvfragment ;
- exp_named_subst_diff := !exp_named_subst_diff @ [subst_item] ;
- incr next_fresh_meta ;
- subst_item::(aux (tl,[]))(*)*)
- | uri::tl1,((uri',_) as s)::tl2 ->
- assert (UriManager.eq uri uri') ;
- s::(aux (tl1,tl2))
- | [],_ -> assert false
- in
- let exp_named_subst' = aux (params,exp_named_subst) in
- !exp_named_subst_diff,!next_fresh_meta,
- List.rev !newmetasenvfragment, exp_named_subst'
- in
- new_fresh_meta,newmetasenvfragment,exp_named_subst',exp_named_subst_diff
-;;
-
-let new_metasenv_and_unify_and_t newmeta' metasenv' subst context term' ty termty goal_arity =
- let (consthead,newmetasenv,arguments,_) =
- TermUtil.saturate_term newmeta' metasenv' context termty
- goal_arity in
- let subst,newmetasenv',_ =
- CicUnification.fo_unif_subst
- subst context newmetasenv consthead ty CicUniv.oblivion_ugraph
- in
- let t =
- if List.length arguments = 0 then term' else Cic.Appl (term'::arguments)
- in
- subst,newmetasenv',t
-
-let rec count_prods subst context ty =
- match CicReduction.whd ~subst context ty with
- Cic.Prod (n,s,t) -> 1 + count_prods subst (Some (n,Cic.Decl s)::context) t
- | _ -> 0
-
-let apply_with_subst ~term ~maxmeta (proof, goal) =
- (* Assumption: The term "term" must be closed in the current context *)
- let module T = CicTypeChecker in
- let module R = CicReduction in
- let module C = Cic in
- let (_,metasenv,subst,_,_, _) = proof in
- let metano,context,ty = CicUtil.lookup_meta goal metasenv in
- let newmeta = max (CicMkImplicit.new_meta metasenv subst) maxmeta in
- let exp_named_subst_diff,newmeta',newmetasenvfragment,term' =
- match term with
- C.Var (uri,exp_named_subst) ->
- let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
- generalize_exp_named_subst_with_fresh_metas context newmeta uri
- exp_named_subst
- in
- exp_named_subst_diff,newmeta',newmetasenvfragment,
- C.Var (uri,exp_named_subst')
- | C.Const (uri,exp_named_subst) ->
- let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
- generalize_exp_named_subst_with_fresh_metas context newmeta uri
- exp_named_subst
- in
- exp_named_subst_diff,newmeta',newmetasenvfragment,
- C.Const (uri,exp_named_subst')
- | C.MutInd (uri,tyno,exp_named_subst) ->
- let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
- generalize_exp_named_subst_with_fresh_metas context newmeta uri
- exp_named_subst
- in
- exp_named_subst_diff,newmeta',newmetasenvfragment,
- C.MutInd (uri,tyno,exp_named_subst')
- | C.MutConstruct (uri,tyno,consno,exp_named_subst) ->
- let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
- generalize_exp_named_subst_with_fresh_metas context newmeta uri
- exp_named_subst
- in
- exp_named_subst_diff,newmeta',newmetasenvfragment,
- C.MutConstruct (uri,tyno,consno,exp_named_subst')
- | _ -> [],newmeta,[],term
- in
- let metasenv' = metasenv@newmetasenvfragment in
- let termty,_ =
- CicTypeChecker.type_of_aux'
- metasenv' ~subst context term' CicUniv.oblivion_ugraph
- in
- let termty =
- CicSubstitution.subst_vars exp_named_subst_diff termty in
- let goal_arity = count_prods subst context ty in
- let subst,newmetasenv',t =
- let rec add_one_argument n =
- try
- new_metasenv_and_unify_and_t newmeta' metasenv' subst context term' ty
- termty n
- with CicUnification.UnificationFailure _ when n > 0 ->
- add_one_argument (n - 1)
- in
- add_one_argument goal_arity
- in
- let in_subst_domain i = List.exists (function (j,_) -> i=j) subst in
- let apply_subst = CicMetaSubst.apply_subst subst in
- let old_uninstantiatedmetas,new_uninstantiatedmetas =
- (* subst_in doesn't need the context. Hence the underscore. *)
- let subst_in _ = CicMetaSubst.apply_subst subst in
- classify_metas newmeta in_subst_domain subst_in newmetasenv'
- in
- let bo' = apply_subst t in
- let newmetasenv'' = new_uninstantiatedmetas@old_uninstantiatedmetas in
- let subst_in =
- (* if we just apply the subtitution, the type is irrelevant:
- we may use Implicit, since it will be dropped *)
- ((metano,(context,bo',Cic.Implicit None))::subst)
- in
- let (newproof, newmetasenv''') =
- ProofEngineHelpers.subst_meta_and_metasenv_in_proof proof metano subst_in
- newmetasenv''
- in
- let subst = ((metano,(context,bo',ty))::subst) in
- let newproof =
- let u,m,_,p,t,l = newproof in
- u,m,subst,p,t,l
- in
- subst,
- (newproof, List.map (function (i,_,_) -> i) new_uninstantiatedmetas),
- max maxmeta (CicMkImplicit.new_meta newmetasenv''' subst)
-
-
-(* ALB *)
-let apply_with_subst ~term ?(subst=[]) ?(maxmeta=0) status =
- try
- let status =
- if subst <> [] then
- let (u,m,_,p,t,l), g = status in (u,m,subst,p,t,l), g
- else status
- in
- apply_with_subst ~term ~maxmeta status
- with
- | CicUnification.UnificationFailure msg
- | CicTypeChecker.TypeCheckerFailure msg -> raise (PET.Fail msg)
-
-(* ALB *)
-let apply_tac_verbose ~term status =
- let subst, status, _ = apply_with_subst ~term status in
- (CicMetaSubst.apply_subst subst), status
-
-let apply_tac ~term status = snd (apply_tac_verbose ~term status)
-
- (* TODO per implementare i tatticali e' necessario che tutte le tattiche
- sollevino _solamente_ Fail *)
-let apply_tac ~term =
- let apply_tac ~term status =
- try
- apply_tac ~term status
- (* TODO cacciare anche altre eccezioni? *)
- with
- | CicUnification.UnificationFailure msg
- | CicTypeChecker.TypeCheckerFailure msg ->
- raise (PET.Fail msg)
- in
- PET.mk_tactic (apply_tac ~term)
-
-let applyP_tac ~term =
- let applyP_tac status =
- let res = PET.apply_tactic (apply_tac ~term) status in res
- in
- PET.mk_tactic applyP_tac
-
-let intros_tac ?howmany ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) ()=
- let intros_tac (proof, goal)
- =
- let module C = Cic in
- let module R = CicReduction in
- let (_,metasenv,_subst,_,_, _) = proof in
- let metano,context,ty = CicUtil.lookup_meta goal metasenv in
- let newmeta = ProofEngineHelpers.new_meta_of_proof ~proof in
- let (context',ty',bo') =
- lambda_abstract ?howmany metasenv context newmeta ty mk_fresh_name_callback
- in
- let (newproof, _) =
- ProofEngineHelpers.subst_meta_in_proof proof metano bo'
- [newmeta,context',ty']
- in
- (newproof, [newmeta])
- in
- PET.mk_tactic intros_tac
-
-let cut_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) term =
- let cut_tac
- ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
- term (proof, goal)
- =
- let module C = Cic in
- let curi,metasenv,_subst,pbo,pty, attrs = proof in
- let metano,context,ty = CicUtil.lookup_meta goal metasenv in
- let newmeta1 = ProofEngineHelpers.new_meta_of_proof ~proof in
- let newmeta2 = newmeta1 + 1 in
- let fresh_name =
- mk_fresh_name_callback metasenv context (Cic.Name "Hcut") ~typ:term in
- let context_for_newmeta1 =
- (Some (fresh_name,C.Decl term))::context in
- let irl1 =
- CicMkImplicit.identity_relocation_list_for_metavariable
- context_for_newmeta1
- in
- let irl2 =
- CicMkImplicit.identity_relocation_list_for_metavariable context
- in
- let newmeta1ty = CicSubstitution.lift 1 ty in
- let bo' =
- Cic.LetIn (fresh_name, C.Meta (newmeta2,irl2), term, C.Meta (newmeta1,irl1))
- in
- let (newproof, _) =
- ProofEngineHelpers.subst_meta_in_proof proof metano bo'
- [newmeta2,context,term; newmeta1,context_for_newmeta1,newmeta1ty];
- in
- (newproof, [newmeta1 ; newmeta2])
- in
- PET.mk_tactic (cut_tac ~mk_fresh_name_callback term)
-
-let letin_tac ?(mk_fresh_name_callback=FreshNamesGenerator.mk_fresh_name ~subst:[]) term =
- let letin_tac
- ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
- term (proof, goal)
- =
- let module C = Cic in
- let curi,metasenv,_subst,pbo,pty, attrs = proof in
- (* occur check *)
- let occur i t =
- let m = CicUtil.metas_of_term t in
- List.exists (fun (j,_) -> i=j) m
- in
- let metano,context,ty = CicUtil.lookup_meta goal metasenv in
- if occur metano term then
- raise
- (ProofEngineTypes.Fail (lazy
- "You can't letin a term containing the current goal"));
- let tty,_ =
- CicTypeChecker.type_of_aux' metasenv context term CicUniv.oblivion_ugraph in
- let newmeta = ProofEngineHelpers.new_meta_of_proof ~proof in
- let fresh_name =
- mk_fresh_name_callback metasenv context (Cic.Name "Hletin") ~typ:term in
- let context_for_newmeta =
- (Some (fresh_name,C.Def (term,tty)))::context in
- let irl =
- CicMkImplicit.identity_relocation_list_for_metavariable
- context_for_newmeta
- in
- let newmetaty = CicSubstitution.lift 1 ty in
- let bo' = C.LetIn (fresh_name,term,tty,C.Meta (newmeta,irl)) in
- let (newproof, _) =
- ProofEngineHelpers.subst_meta_in_proof
- proof metano bo'[newmeta,context_for_newmeta,newmetaty]
- in
- (newproof, [newmeta])
- in
- PET.mk_tactic (letin_tac ~mk_fresh_name_callback term)
-
-(* FG: exact_tac := apply_tac as in NTactics *)
-let exact_tac ~term = apply_tac ~term
-
-(* not really "primitive" tactics .... *)
-
-module TC = CicTypeChecker
-module UM = UriManager
-module R = CicReduction
-module C = Cic
-module PEH = ProofEngineHelpers
-module PER = ProofEngineReduction
-module MS = CicMetaSubst
-module S = CicSubstitution
-module T = Tacticals
-module RT = ReductionTactics
-
-let rec args_init n f =
- if n <= 0 then [] else f n :: args_init (pred n) f
-
-let mk_predicate_for_elim
- ~context ~metasenv ~subst ~ugraph ~goal ~arg ~using ~cpattern ~args_no
-=
- let instantiated_eliminator =
- let f n = if n = 1 then arg else C.Implicit None in
- C.Appl (using :: args_init args_no f)
- in
- let _actual_arg, iety, _metasenv', _ugraph =
- CicRefine.type_of_aux' metasenv context instantiated_eliminator ugraph
- in
- let _actual_meta, actual_args = match iety with
- | C.Meta (i, _) -> i, []
- | C.Appl (C.Meta (i, _) :: args) -> i, args
- | _ -> assert false
- in
-(* let _, upto = PEH.split_with_whd (List.nth splits pred_pos) in *)
- let rec mk_pred metasenv subst context' pred arg' cpattern' = function
- | [] -> metasenv, subst, pred, arg'
- | arg :: tail ->
-(* FG: we find the predicate for the eliminator as in the rewrite tactic ****)
- let argty, _ = TC.type_of_aux' metasenv ~subst context arg ugraph in
- let argty = CicReduction.whd ~subst context argty in
- let fresh_name =
- FreshNamesGenerator.mk_fresh_name
- ~subst metasenv context' C.Anonymous ~typ:argty in
- let hyp = Some (fresh_name, C.Decl argty) in
- let lazy_term c m u =
- let distance = List.length c - List.length context in
- S.lift distance arg, m, u in
- let pattern = Some lazy_term, [], Some cpattern' in
- let subst, metasenv, _ugraph, _conjecture, selected_terms =
- ProofEngineHelpers.select ~subst ~metasenv ~ugraph
- ~conjecture:(0, context, pred) ~pattern in
- let metasenv = MS.apply_subst_metasenv subst metasenv in
- let map (_context_of_t, t) l = t :: l in
- let what = List.fold_right map selected_terms [] in
- let arg' = MS.apply_subst subst arg' in
- let pred = PER.replace_with_rel_1_from ~equality:(==) ~what 1 pred in
- let pred = MS.apply_subst subst pred in
- let pred = C.Lambda (fresh_name, C.Implicit None, pred) in
- let cpattern' = C.Lambda (C.Anonymous, C.Implicit None, cpattern') in
- mk_pred metasenv subst (hyp :: context') pred arg' cpattern' tail
- in
- let metasenv, subst, pred, arg =
- mk_pred metasenv subst context goal arg cpattern (List.rev actual_args)
- in
- HLog.debug ("PREDICATE CONTEXT:\n" ^ CicPp.ppcontext ~metasenv context);
- HLog.debug ("PREDICATE: " ^ CicPp.ppterm ~metasenv pred ^ " ARGS: " ^ String.concat " " (List.map (CicPp.ppterm ~metasenv) actual_args));
- metasenv, subst, pred, arg, actual_args
-
-let beta_after_elim_tac upto predicate =
- let beta_after_elim_tac status =
- let proof, goal = status in
- let _, metasenv, _subst, _, _, _ = proof in
- let _, _, ty = CicUtil.lookup_meta goal metasenv in
- let mk_pattern ~equality ~upto ~predicate ty =
- (* code adapted from ProceduralConversion.generalize *)
- let meta = C.Implicit None in
- let hole = C.Implicit (Some `Hole) in
- let anon = C.Anonymous in
- let is_meta =
- let map b = function
- | C.Implicit None when b -> b
- | _ -> false
- in
- List.fold_left map true
- in
- let rec gen_fix len k (name, i, ty, bo) =
- name, i, gen_term k ty, gen_term (k + len) bo
- and gen_cofix len k (name, ty, bo) =
- name, gen_term k ty, gen_term (k + len) bo
- and gen_term k = function
- | C.Sort _
- | C.Implicit _
- | C.Const (_, _)
- | C.Var (_, _)
- | C.MutInd (_, _, _)
- | C.MutConstruct (_, _, _, _)
- | C.Meta (_, _)
- | C.Rel _ -> meta
- | C.Appl (hd :: tl) when equality hd (S.lift k predicate) ->
- assert (List.length tl = upto);
- hole
- | C.Appl ts ->
- let ts = List.map (gen_term k) ts in
- if is_meta ts then meta else C.Appl ts
- | C.Cast (te, ty) ->
- let te, ty = gen_term k te, gen_term k ty in
- if is_meta [te; ty] then meta else C.Cast (te, ty)
- | C.MutCase (sp, i, outty, t, pl) ->
- let outty, t, pl = gen_term k outty, gen_term k t, List.map (gen_term k) pl in
- if is_meta (outty :: t :: pl) then meta else hole (* C.MutCase (sp, i, outty, t, pl) *)
- | C.Prod (_, s, t) ->
- let s, t = gen_term k s, gen_term (succ k) t in
- if is_meta [s; t] then meta else C.Prod (anon, s, t)
- | C.Lambda (_, s, t) ->
- let s, t = gen_term k s, gen_term (succ k) t in
- if is_meta [s; t] then meta else C.Lambda (anon, s, t)
- | C.LetIn (_, s, ty, t) ->
- let s,ty,t = gen_term k s, gen_term k ty, gen_term (succ k) t in
- if is_meta [s; t] then meta else C.LetIn (anon, s, ty, t)
- | C.Fix (i, fl) -> C.Fix (i, List.map (gen_fix (List.length fl) k) fl)
- | C.CoFix (i, fl) -> C.CoFix (i, List.map (gen_cofix (List.length fl) k) fl)
- in
- None, [], Some (gen_term 0 ty)
- in
- let equality = CicUtil.alpha_equivalence in
- let pattern = mk_pattern ~equality ~upto ~predicate ty in
- let tactic = RT.head_beta_reduce_tac ~delta:false ~upto ~pattern in
- PET.apply_tactic tactic status
- in
- PET.mk_tactic beta_after_elim_tac
-
-(* ANCORA DA DEBUGGARE *)
-
-exception UnableToDetectTheTermThatMustBeGeneralizedYouMustGiveItExplicitly;;
-exception TheSelectedTermsMustLiveInTheGoalContext
-exception AllSelectedTermsMustBeConvertible;;
-exception GeneralizationInHypothesesNotImplementedYet;;
-
-let generalize_tac
- ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
- pattern
- =
- let module PET = ProofEngineTypes in
- let generalize_tac mk_fresh_name_callback
- ~pattern:(term,hyps_pat,_) status
- =
- if hyps_pat <> [] then raise GeneralizationInHypothesesNotImplementedYet;
- let (proof, goal) = status in
- let module C = Cic in
- let module T = Tacticals in
- let uri,metasenv,subst,pbo,pty, attrs = proof in
- let (_,context,ty) as conjecture = CicUtil.lookup_meta goal metasenv in
- let subst,metasenv,u,selected_hyps,terms_with_context =
- ProofEngineHelpers.select ~metasenv ~subst ~ugraph:CicUniv.oblivion_ugraph
- ~conjecture ~pattern in
- let context = CicMetaSubst.apply_subst_context subst context in
- let metasenv = CicMetaSubst.apply_subst_metasenv subst metasenv in
- let pbo = lazy (CicMetaSubst.apply_subst subst (Lazy.force pbo)) in
- let pty = CicMetaSubst.apply_subst subst pty in
- let term =
- match term with
- None -> None
- | Some term ->
- Some (fun context metasenv ugraph ->
- let term, metasenv, ugraph = term context metasenv ugraph in
- CicMetaSubst.apply_subst subst term,
- CicMetaSubst.apply_subst_metasenv subst metasenv,
- ugraph)
- in
- let u,typ,term, metasenv' =
- let context_of_t, (t, metasenv, u) =
- match terms_with_context, term with
- [], None ->
- raise
- UnableToDetectTheTermThatMustBeGeneralizedYouMustGiveItExplicitly
- | [], Some t -> context, t context metasenv u
- | (context_of_t, _)::_, Some t ->
- context_of_t, t context_of_t metasenv u
- | (context_of_t, t)::_, None -> context_of_t, (t, metasenv, u)
- in
- let t,e_subst,metasenv' =
- try
- CicMetaSubst.delift_rels [] metasenv
- (List.length context_of_t - List.length context) t
- with
- CicMetaSubst.DeliftingARelWouldCaptureAFreeVariable ->
- raise TheSelectedTermsMustLiveInTheGoalContext
- in
- (*CSC: I am not sure about the following two assertions;
- maybe I need to propagate the new subst and metasenv *)
- assert (e_subst = []);
- assert (metasenv' = metasenv);
- let typ,u = CicTypeChecker.type_of_aux' ~subst metasenv context t u in
- u,typ,t,metasenv
- in
- (* We need to check:
- 1. whether they live in the context of the goal;
- if they do they are also well-typed since they are closed subterms
- of a well-typed term in the well-typed context of the well-typed
- term
- 2. whether they are convertible
- *)
- ignore (
- List.fold_left
- (fun u (context_of_t,t) ->
- (* 1 *)
- let t,subst,metasenv'' =
- try
- CicMetaSubst.delift_rels [] metasenv'
- (List.length context_of_t - List.length context) t
- with
- CicMetaSubst.DeliftingARelWouldCaptureAFreeVariable ->
- raise TheSelectedTermsMustLiveInTheGoalContext in
- (*CSC: I am not sure about the following two assertions;
- maybe I need to propagate the new subst and metasenv *)
- assert (subst = []);
- assert (metasenv'' = metasenv');
- (* 2 *)
- let b,u1 = CicReduction.are_convertible ~subst context term t u in
- if not b then
- raise AllSelectedTermsMustBeConvertible
- else
- u1
- ) u terms_with_context) ;
- let status = (uri,metasenv',subst,pbo,pty, attrs),goal in
- let proof,goals =
- PET.apply_tactic
- (T.thens
- ~start:
- (cut_tac
- (C.Prod(
- (mk_fresh_name_callback metasenv context C.Anonymous ~typ:typ),
- typ,
- (ProofEngineReduction.replace_lifting_csc 1
- ~equality:(==)
- ~what:(List.map snd terms_with_context)
- ~with_what:(List.map (function _ -> C.Rel 1) terms_with_context)
- ~where:ty)
- )))
- ~continuations:
- [(apply_tac ~term:(C.Appl [C.Rel 1; CicSubstitution.lift 1 term])) ;
- T.id_tac])
- status
- in
- let _,metasenv'',_,_,_, _ = proof in
- (* CSC: the following is just a bad approximation since a meta
- can be closed and then re-opened! *)
- (proof,
- goals @
- (List.filter
- (fun j -> List.exists (fun (i,_,_) -> i = j) metasenv'')
- (ProofEngineHelpers.compare_metasenvs ~oldmetasenv:metasenv
- ~newmetasenv:metasenv')))
- in
- PET.mk_tactic (generalize_tac mk_fresh_name_callback ~pattern)
-;;
-
-let generalize_pattern_tac pattern =
- let generalize_pattern_tac (proof,goal) =
- let _,metasenv,_,_,_,_ = proof in
- let conjecture = CicUtil.lookup_meta goal metasenv in
- let _,context,_ = conjecture in
- let generalize_hyps =
- let _,hpatterns,_ = ProofEngineHelpers.sort_pattern_hyps context pattern in
- List.map fst hpatterns in
- let ids_and_patterns =
- List.map
- (fun id ->
- let rel,_ = ProofEngineHelpers.find_hyp id context in
- id,(Some (fun ctx m u -> CicSubstitution.lift (List.length ctx - List.length context) rel,m,u), [], Some (ProofEngineTypes.hole))
- ) generalize_hyps in
- let tactics =
- List.map
- (function (id,pattern) ->
- Tacticals.then_ ~start:(generalize_tac pattern)
- ~continuation:(Tacticals.try_tactic
- (ProofEngineStructuralRules.clear [id]))
- ) ids_and_patterns
- in
- PET.apply_tactic (Tacticals.seq tactics) (proof,goal)
- in
- PET.mk_tactic (generalize_pattern_tac)
-;;
-
-let pattern_after_generalize_pattern_tac (tp, hpatterns, cpattern) =
- let cpattern =
- match cpattern with
- None -> ProofEngineTypes.hole
- | Some t -> t
- in
- let cpattern =
- List.fold_left
- (fun t (_,ty) -> Cic.Prod (Cic.Anonymous, ty, t)) cpattern hpatterns
- in
- tp, [], Some cpattern
-;;
-
-let elim_tac ?using ?(pattern = PET.conclusion_pattern None) term =
- let elim_tac pattern (proof, goal) =
- let ugraph = CicUniv.oblivion_ugraph in
- let curi, metasenv, subst, proofbo, proofty, attrs = proof in
- let conjecture = CicUtil.lookup_meta goal metasenv in
- let metano, context, ty = conjecture in
- let pattern = pattern_after_generalize_pattern_tac pattern in
- let cpattern =
- match pattern with
- | None, [], Some cpattern -> cpattern
- | _ -> raise (PET.Fail (lazy "not implemented")) in
- let termty,_ugraph = TC.type_of_aux' metasenv ~subst context term ugraph in
- let termty = CicReduction.whd ~subst context termty in
- let termty, metasenv', arguments, _fresh_meta =
- TermUtil.saturate_term
- (ProofEngineHelpers.new_meta_of_proof proof) metasenv context termty 0 in
- let term = if arguments = [] then term else Cic.Appl (term::arguments) in
- let uri, exp_named_subst, typeno, _args =
- match termty with
- C.MutInd (uri,typeno,exp_named_subst) -> (uri,exp_named_subst,typeno,[])
- | C.Appl ((C.MutInd (uri,typeno,exp_named_subst))::args) ->
- (uri,exp_named_subst,typeno,args)
- | _ -> raise NotAnInductiveTypeToEliminate
- in
- let eliminator_uri =
- let buri = UM.buri_of_uri uri in
- let name =
- let o,_ugraph = CicEnvironment.get_obj ugraph uri in
- match o with
- C.InductiveDefinition (tys,_,_,_) ->
- let (name,_,_,_) = List.nth tys typeno in
- name
- | _ -> assert false
- in
- let ty_ty,_ugraph = TC.type_of_aux' metasenv' ~subst context ty ugraph in
- let ext =
- match ty_ty with
- C.Sort C.Prop -> "_ind"
- | C.Sort C.Set -> "_rec"
- | C.Sort (C.CProp _) -> "_rect"
- | C.Sort (C.Type _)-> "_rect"
- | C.Meta (_,_) -> raise TheTypeOfTheCurrentGoalIsAMetaICannotChooseTheRightElimiantionPrinciple
- | _ -> assert false
- in
- UM.uri_of_string (buri ^ "/" ^ name ^ ext ^ ".con")
- in
- let eliminator_ref = match using with
- | None -> C.Const (eliminator_uri, exp_named_subst)
- | Some t -> t
- in
- let ety, _ugraph =
- TC.type_of_aux' metasenv' ~subst context eliminator_ref ugraph in
-(* FG: ADDED PART ***********************************************************)
-(* FG: we can not assume eliminator is the default eliminator ***************)
- let splits, args_no = PEH.split_with_whd (context, ety) in
- let pred_pos = match List.hd splits with
- | _, C.Rel i when i > 1 && i <= args_no -> i
- | _, C.Appl (C.Rel i :: _) when i > 1 && i <= args_no -> i
- | _ -> raise NotAnEliminator
- in
- let metasenv', subst, pred, term, actual_args = match pattern with
- | None, [], Some (C.Implicit (Some `Hole)) ->
- metasenv', subst, C.Implicit None, term, []
- | _ ->
- mk_predicate_for_elim
- ~args_no ~context ~ugraph ~cpattern
- ~metasenv:metasenv' ~subst ~arg:term ~using:eliminator_ref ~goal:ty
- in
-(* FG: END OF ADDED PART ****************************************************)
- let term_to_refine =
- let f n =
- if n = pred_pos then pred else
- if n = 1 then term else C.Implicit None
- in
- C.Appl (eliminator_ref :: args_init args_no f)
- in
- let refined_term,_refined_termty,metasenv'',subst,_ugraph =
- CicRefine.type_of metasenv' subst context term_to_refine ugraph
- in
- let ipred = match refined_term with
- | C.Appl ts -> List.nth ts (List.length ts - pred_pos)
- | _ -> assert false
- in
- let new_goals =
- ProofEngineHelpers.compare_metasenvs
- ~oldmetasenv:metasenv ~newmetasenv:metasenv''
- in
- let proof' = curi,metasenv'',subst,proofbo,proofty, attrs in
- let proof'', new_goals' =
- PET.apply_tactic (apply_tac ~term:refined_term) (proof',goal)
- in
- (* The apply_tactic can have closed some of the new_goals *)
- let patched_new_goals =
- let (_,metasenv''',_,_,_, _) = proof'' in
- List.filter
- (function i -> List.exists (function (j,_,_) -> j=i) metasenv''')
- new_goals @ new_goals'
- in
- let res = proof'', patched_new_goals in
- let upto = List.length actual_args in
- if upto = 0 then res else
-(* FG: we use ipred (instantiated pred) instead of pred (not instantiated) *)
- let continuation = beta_after_elim_tac upto ipred in
- let dummy_status = proof,goal in
- PET.apply_tactic
- (T.then_ ~start:(PET.mk_tactic (fun _ -> res)) ~continuation)
- dummy_status
- in
- let reorder_pattern ((proof, goal) as status) =
- let _,metasenv,_,_,_,_ = proof in
- let conjecture = CicUtil.lookup_meta goal metasenv in
- let _,context,_ = conjecture in
- let pattern = ProofEngineHelpers.sort_pattern_hyps context pattern in
- PET.apply_tactic
- (Tacticals.then_ ~start:(generalize_pattern_tac pattern)
- ~continuation:(PET.mk_tactic (elim_tac pattern))) status
- in
- PET.mk_tactic reorder_pattern
-;;
-
-let cases_intros_tac ?(howmany=(-1)) ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) ?(pattern = PET.conclusion_pattern None) term =
- let cases_tac pattern (proof, goal) =
- let module TC = CicTypeChecker in
- let module U = UriManager in
- let module R = CicReduction in
- let module C = Cic in
- let (curi,metasenv,_subst, proofbo,proofty, attrs) = proof in
- let metano,context,ty = CicUtil.lookup_meta goal metasenv in
- let pattern = pattern_after_generalize_pattern_tac pattern in
- let _cpattern =
- match pattern with
- | None, [], Some cpattern ->
- let rec is_hole =
- function
- Cic.Implicit (Some `Hole) -> true
- | Cic.Prod (Cic.Anonymous,so,tgt) -> is_hole so && is_hole tgt
- | _ -> false
- in
- if not (is_hole cpattern) then
- raise (PET.Fail (lazy "not implemented"))
- | _ -> raise (PET.Fail (lazy "not implemented")) in
- let termty,_ = TC.type_of_aux' metasenv context term CicUniv.oblivion_ugraph in
- let termty = CicReduction.whd context termty in
- let (termty,metasenv',arguments,fresh_meta) =
- TermUtil.saturate_term
- (ProofEngineHelpers.new_meta_of_proof proof) metasenv context termty 0 in
- let term = if arguments = [] then term else Cic.Appl (term::arguments) in
- let uri,exp_named_subst,typeno,args =
- match termty with
- | C.MutInd (uri,typeno,exp_named_subst) -> (uri,exp_named_subst,typeno,[])
- | C.Appl ((C.MutInd (uri,typeno,exp_named_subst))::args) ->
- (uri,exp_named_subst,typeno,args)
- | _ -> raise NotAnInductiveTypeToEliminate
- in
- let paramsno,itty,patterns,right_args =
- match CicEnvironment.get_obj CicUniv.oblivion_ugraph uri with
- | C.InductiveDefinition (tys,_,paramsno,_),_ ->
- let _,left_parameters,right_args =
- List.fold_right
- (fun x (n,acc1,acc2) ->
- if n > 0 then (n-1,acc1,x::acc2) else (n,x::acc1,acc2))
- args (List.length args - paramsno, [],[])
- in
- let _,_,itty,cl = List.nth tys typeno in
- let rec aux left_parameters context t =
- match left_parameters,CicReduction.whd context t with
- | [],C.Prod (name,source,target) ->
- let fresh_name =
- mk_fresh_name_callback metasenv' context name ~typ:source
- in
- C.Lambda (fresh_name,C.Implicit None,
- aux [] (Some (fresh_name,C.Decl source)::context) target)
- | hd::tl,C.Prod (name,source,target) ->
- (* left parameters instantiation *)
- aux tl context (CicSubstitution.subst hd target)
- | [],_ -> C.Implicit None
- | _ -> assert false
- in
- paramsno,itty,
- List.map (function (_,cty) -> aux left_parameters context cty) cl,
- right_args
- | _ -> assert false
- in
- let outtypes =
- let n_right_args = List.length right_args in
- let n_lambdas = n_right_args + 1 in
- let lifted_ty = CicSubstitution.lift n_lambdas ty in
- let captured_ty =
- let what =
- List.map (CicSubstitution.lift n_lambdas) (right_args)
- in
- let with_what meta =
- let rec mkargs = function
- | 0 -> assert false
- | 1 -> []
- | n ->
- (if meta then Cic.Implicit None else Cic.Rel n)::(mkargs (n-1))
- in
- mkargs n_lambdas
- in
- let replaced = ref false in
- let replace = ProofEngineReduction.replace_lifting
- ~equality:(fun _ a b -> let rc = CicUtil.alpha_equivalence a b in
- if rc then replaced := true; rc)
- ~context:[]
- in
- let captured =
- replace ~what:[CicSubstitution.lift n_lambdas term]
- ~with_what:[Cic.Rel 1] ~where:lifted_ty
- in
- if not !replaced then
- (* this means the matched term is not there,
- * but maybe right params are: we user rels (to right args lambdas) *)
- [replace ~what ~with_what:(with_what false) ~where:captured]
- else
- (* since the matched is there, rights should be inferrable *)
- [replace ~what ~with_what:(with_what false) ~where:captured;
- replace ~what ~with_what:(with_what true) ~where:captured]
- in
- let captured_term_ty =
- let term_ty = CicSubstitution.lift n_right_args termty in
- let rec mkrels = function 0 -> []|n -> (Cic.Rel n)::(mkrels (n-1)) in
- let rec fstn acc l n =
- if n = 0 then acc else fstn (acc@[List.hd l]) (List.tl l) (n-1)
- in
- match term_ty with
- | C.MutInd _ -> term_ty
- | C.Appl ((C.MutInd (a,b,c))::args) ->
- C.Appl ((C.MutInd (a,b,c))::
- fstn [] args paramsno @ mkrels n_right_args)
- | _ -> raise NotAnInductiveTypeToEliminate
- in
- let rec add_lambdas captured_ty = function
- | 0 -> captured_ty
- | 1 ->
- C.Lambda (C.Name "matched", captured_term_ty, (add_lambdas captured_ty 0))
- | n ->
- C.Lambda (C.Name ("right_"^(string_of_int (n-1))),
- C.Implicit None, (add_lambdas captured_ty (n-1)))
- in
- List.map (fun x -> add_lambdas x n_lambdas) captured_ty
- in
- let rec first = (* easier than using tacticals *)
- function
- | [] -> raise (PET.Fail (lazy ("unable to generate a working outtype")))
- | outtype::rest ->
- let term_to_refine = C.MutCase (uri,typeno,outtype,term,patterns) in
- try
- let refined_term,_,metasenv'',_ =
- CicRefine.type_of_aux' metasenv' context term_to_refine
- CicUniv.oblivion_ugraph
- in
- let new_goals =
- ProofEngineHelpers.compare_metasenvs
- ~oldmetasenv:metasenv ~newmetasenv:metasenv''
- in
- let proof' = curi,metasenv'',_subst,proofbo,proofty, attrs in
- let proof'', new_goals' =
- PET.apply_tactic (apply_tac ~term:refined_term) (proof',goal)
- in
- (* The apply_tactic can have closed some of the new_goals *)
- let patched_new_goals =
- let (_,metasenv''',_subst,_,_,_) = proof'' in
- List.filter
- (function i -> List.exists (function (j,_,_) -> j=i) metasenv''')
- new_goals @ new_goals'
- in
- proof'', patched_new_goals
- with PET.Fail _ | CicRefine.RefineFailure _ | CicRefine.Uncertain _ -> first rest
- in
- first outtypes
- in
- let reorder_pattern ((proof, goal) as status) =
- let _,metasenv,_,_,_,_ = proof in
- let conjecture = CicUtil.lookup_meta goal metasenv in
- let _,context,_ = conjecture in
- let pattern = ProofEngineHelpers.sort_pattern_hyps context pattern in
- PET.apply_tactic
- (Tacticals.then_ ~start:(generalize_pattern_tac pattern)
- ~continuation:(PET.mk_tactic (cases_tac pattern))) status
- in
- PET.mk_tactic reorder_pattern
-;;
-
-
-let elim_intros_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
- ?depth ?using ?pattern what =
- Tacticals.then_ ~start:(elim_tac ?using ?pattern what)
- ~continuation:(intros_tac ~mk_fresh_name_callback ?howmany:depth ())
-;;
-
-(* The simplification is performed only on the conclusion *)
-let elim_intros_simpl_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
- ?depth ?using ?pattern what =
- Tacticals.then_ ~start:(elim_tac ?using ?pattern what)
- ~continuation:
- (Tacticals.thens
- ~start:(intros_tac ~mk_fresh_name_callback ?howmany:depth ())
- ~continuations:
- [ReductionTactics.simpl_tac
- ~pattern:(ProofEngineTypes.conclusion_pattern None)])
-;;
projects / helm.git / blobdiff