+++ /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/.
- *)
-
-(* $Id$ *)
-
-open ProofEngineHelpers
-open ProofEngineTypes
-
-exception TheTypeOfTheCurrentGoalIsAMetaICannotChooseTheRightElimiantionPrinciple
-exception NotAnInductiveTypeToEliminate
-exception WrongUriToVariable of string
-
-(* 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 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 te
- | C.Prod (n,s,t) ->
- let n' = mk_fresh_name metasenv context n ~typ:s in
- let (context',ty,bo) =
- collect_context ((Some (n',(C.Decl s)))::context) (howmany - 1) t
- in
- (context',ty,C.Lambda(n',s,bo))
- | C.LetIn (n,s,t) ->
- let (context',ty,bo) =
- collect_context ((Some (n,(C.Def (s,None))))::context) (howmany - 1) t
- in
- (context',ty,C.LetIn(n,s,bo))
- | _ as t ->
- if howmany <= 0 then
- let irl =
- CicMkImplicit.identity_relocation_list_for_metavariable context
- in
- context, t, (C.Meta (newmeta,irl))
- else
- raise (Fail (lazy "intro(s): not enough products or let-ins"))
- in
- collect_context context howmany 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,t) -> C.LetIn (nn, aux n s, 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.empty_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))
- | Some (n,Cic.Def (s,None)) ->
- Some (n,Cic.Def ((subst_in canonical_context' s),None))
- | None -> None
- | Some (n,Cic.Def (bo,Some ty)) ->
- Some
- (n,
- Cic.Def
- (subst_in canonical_context' bo,
- Some (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.empty_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.empty_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' context term' ty termty goal_arity =
- let (consthead,newmetasenv,arguments,_) =
- saturate_term newmeta' metasenv' context termty goal_arity in
- let subst,newmetasenv',_ =
- CicUnification.fo_unif newmetasenv context consthead ty CicUniv.empty_ugraph
- in
- let t =
- if List.length arguments = 0 then term' else Cic.Appl (term'::arguments)
- in
- subst,newmetasenv',t
-
-let rec count_prods context ty =
- match CicReduction.whd context ty with
- Cic.Prod (n,s,t) -> 1 + count_prods (Some (n,Cic.Decl s)::context) t
- | _ -> 0
-
-let apply_tac_verbose_with_subst ~term (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,_,_) = proof in
- let metano,context,ty = CicUtil.lookup_meta goal metasenv in
- let newmeta = new_meta_of_proof ~proof 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' context term' CicUniv.empty_ugraph
- in
- let termty =
- CicSubstitution.subst_vars exp_named_subst_diff termty in
- let goal_arity = count_prods context ty in
- let subst,newmetasenv',t =
- let rec add_one_argument n =
- try
- new_metasenv_and_unify_and_t newmeta' metasenv' 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 *)
- CicMetaSubst.apply_subst ((metano,(context,bo',Cic.Implicit None))::subst)
- in
- let (newproof, newmetasenv''') =
- subst_meta_and_metasenv_in_proof proof metano subst_in newmetasenv''
- in
- (((metano,(context,bo',Cic.Implicit None))::subst)(* subst_in *), (* ALB *)
- (newproof,
- List.map (function (i,_,_) -> i) new_uninstantiatedmetas))
-
-
-(* ALB *)
-let apply_tac_verbose_with_subst ~term status =
- try
-(* apply_tac_verbose ~term status *)
- apply_tac_verbose_with_subst ~term status
- (* TODO cacciare anche altre eccezioni? *)
- with
- | CicUnification.UnificationFailure msg
- | CicTypeChecker.TypeCheckerFailure msg ->
- raise (Fail msg)
-
-(* ALB *)
-let apply_tac_verbose ~term status =
- let subst, status = apply_tac_verbose_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 (Fail msg)
- in
- mk_tactic (apply_tac ~term)
-
-let intros_tac ?howmany ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) ()=
- let intros_tac
- ?(mk_fresh_name_callback = (FreshNamesGenerator.mk_fresh_name ~subst:[])) ()
- (proof, goal)
- =
- let module C = Cic in
- let module R = CicReduction in
- let (_,metasenv,_,_) = proof in
- let metano,context,ty = CicUtil.lookup_meta goal metasenv in
- let newmeta = new_meta_of_proof ~proof in
- let (context',ty',bo') =
- lambda_abstract ?howmany metasenv context newmeta ty mk_fresh_name_callback
- in
- let (newproof, _) =
- subst_meta_in_proof proof metano bo' [newmeta,context',ty']
- in
- (newproof, [newmeta])
- in
- mk_tactic (intros_tac ~mk_fresh_name_callback ())
-
-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,pbo,pty = proof in
- let metano,context,ty = CicUtil.lookup_meta goal metasenv in
- let newmeta1 = 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' =
- C.Appl
- [C.Lambda (fresh_name,term,C.Meta (newmeta1,irl1)) ;
- C.Meta (newmeta2,irl2)]
- in
- let (newproof, _) =
- subst_meta_in_proof proof metano bo'
- [newmeta2,context,term; newmeta1,context_for_newmeta1,newmeta1ty];
- in
- (newproof, [newmeta1 ; newmeta2])
- in
- 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,pbo,pty = proof in
- let metano,context,ty = CicUtil.lookup_meta goal metasenv in
- let _,_ = (* TASSI: FIXME *)
- CicTypeChecker.type_of_aux' metasenv context term CicUniv.empty_ugraph in
- let newmeta = 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,None)))::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,C.Meta (newmeta,irl)) in
- let (newproof, _) =
- subst_meta_in_proof
- proof metano bo'[newmeta,context_for_newmeta,newmetaty]
- in
- (newproof, [newmeta])
- in
- mk_tactic (letin_tac ~mk_fresh_name_callback term)
-
- (** functional part of the "exact" tactic *)
-let exact_tac ~term =
- let exact_tac ~term (proof, goal) =
- (* Assumption: the term bo must be closed in the current context *)
- let (_,metasenv,_,_) = proof in
- let metano,context,ty = CicUtil.lookup_meta goal metasenv in
- let module T = CicTypeChecker in
- let module R = CicReduction in
- let ty_term,u = T.type_of_aux' metasenv context term CicUniv.empty_ugraph in
- let b,_ = R.are_convertible context ty_term ty u in (* TASSI: FIXME *)
- if b then
- begin
- let (newproof, metasenv') =
- subst_meta_in_proof proof metano term [] in
- (newproof, [])
- end
- else
- raise (Fail (lazy "The type of the provided term is not the one expected."))
- in
- mk_tactic (exact_tac ~term)
-
-(* not really "primitive" tactics .... *)
-let elim_tac ~term =
- let elim_tac ~term (proof, goal) =
- let module T = CicTypeChecker in
- let module U = UriManager in
- let module R = CicReduction in
- let module C = Cic in
- let (curi,metasenv,proofbo,proofty) = proof in
- let metano,context,ty = CicUtil.lookup_meta goal metasenv in
- let termty,_ = T.type_of_aux' metasenv context term CicUniv.empty_ugraph in
- let (termty,metasenv',arguments,fresh_meta) =
- ProofEngineHelpers.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 = U.buri_of_uri uri in
- let name =
- let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
- match o with
- C.InductiveDefinition (tys,_,_,_) ->
- let (name,_,_,_) = List.nth tys typeno in
- name
- | _ -> assert false
- in
- let ty_ty,_ = T.type_of_aux' metasenv' context ty CicUniv.empty_ugraph in
- let ext =
- match ty_ty with
- C.Sort C.Prop -> "_ind"
- | C.Sort C.Set -> "_rec"
- | C.Sort C.CProp -> "_rec"
- | C.Sort (C.Type _)-> "_rect"
- | C.Meta (_,_) -> raise TheTypeOfTheCurrentGoalIsAMetaICannotChooseTheRightElimiantionPrinciple
- | _ -> assert false
- in
- U.uri_of_string (buri ^ "/" ^ name ^ ext ^ ".con")
- in
- let eliminator_ref = C.Const (eliminator_uri,exp_named_subst) in
- let ety,_ =
- T.type_of_aux' metasenv' context eliminator_ref CicUniv.empty_ugraph in
- let rec find_args_no =
- function
- C.Prod (_,_,t) -> 1 + find_args_no t
- | C.Cast (s,_) -> find_args_no s
- | C.LetIn (_,_,t) -> 0 + find_args_no t
- | _ -> 0
- in
- let args_no = find_args_no ety in
- let term_to_refine =
- let rec make_tl base_case =
- function
- 0 -> [base_case]
- | n -> (C.Implicit None)::(make_tl base_case (n - 1))
- in
- C.Appl (eliminator_ref :: make_tl term (args_no - 1))
- in
- let refined_term,_,metasenv'',_ =
- CicRefine.type_of_aux' metasenv' context term_to_refine
- CicUniv.empty_ugraph
- in
- let new_goals =
- ProofEngineHelpers.compare_metasenvs
- ~oldmetasenv:metasenv ~newmetasenv:metasenv''
- in
- let proof' = curi,metasenv'',proofbo,proofty in
- let proof'', new_goals' =
- 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
- proof'', patched_new_goals
- in
- mk_tactic (elim_tac ~term)
-;;
-
-let elim_intros_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
- ?depth ?using what =
- Tacticals.then_ ~start:(elim_tac ~term: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 what =
- Tacticals.then_ ~start:(elim_tac ~term:what)
- ~continuation:
- (Tacticals.thens
- ~start:(intros_tac ~mk_fresh_name_callback ?howmany:depth ())
- ~continuations:
- [ReductionTactics.simpl_tac
- ~pattern:(ProofEngineTypes.conclusion_pattern None)])
-;;
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