+++ /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/.
- *)
-
-open ProofEngineHelpers
-open ProofEngineTypes
-
-exception NotAnInductiveTypeToEliminate
-exception NotTheRightEliminatorShape
-exception NoHypothesesFound
-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. *)
-let lambda_abstract context newmeta ty mk_fresh_name =
- let module C = Cic in
- let rec collect_context context =
- function
- C.Cast (te,_) -> collect_context context te
- | C.Prod (n,s,t) ->
- let n' = mk_fresh_name context n ~typ:s in
- let (context',ty,bo) =
- collect_context ((Some (n',(C.Decl s)))::context) 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)))::context) t
- in
- (context',ty,C.LetIn(n,s,bo))
- | _ as t ->
- let irl = identity_relocation_list_for_metavariable context in
- context, t, (C.Meta (newmeta,irl))
- in
- collect_context context 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 _
- | 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
- in
- let fresh_name =
- ProofEngineHelpers.mk_fresh_name 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) ->
- Some (n,Cic.Def (subst_in canonical_context' s))
- | None -> None
- 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 ([],[])
-
-(* Auxiliary function for apply: given a type (a backbone), it returns its *)
-(* head, a META environment in which there is new a META for each hypothesis,*)
-(* a list of arguments for the new applications and the indexes of the first *)
-(* and last new METAs introduced. The nth argument in the list of arguments *)
-(* is just the nth new META. *)
-let new_metasenv_for_apply newmeta proof context ty =
- let module C = Cic in
- let module S = CicSubstitution in
- let rec aux newmeta =
- function
- C.Cast (he,_) -> aux newmeta he
- | C.Prod (name,s,t) ->
- let irl = identity_relocation_list_for_metavariable context in
- let newargument = C.Meta (newmeta,irl) in
- let (res,newmetasenv,arguments,lastmeta) =
- aux (newmeta + 1) (S.subst newargument t)
- in
- res,(newmeta,context,s)::newmetasenv,newargument::arguments,lastmeta
- | t -> t,[],[],newmeta
- in
- (* WARNING: here we are using the invariant that above the most *)
- (* recente new_meta() there are no used metas. *)
- let (res,newmetasenv,arguments,lastmeta) = aux newmeta ty in
- res,newmetasenv,arguments,lastmeta
-
-(* 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 =
- match CicEnvironment.get_obj uri with
- C.Constant (_,_,_,params)
- | C.CurrentProof (_,_,_,_,params)
- | C.Variable (_,_,_,params)
- | C.InductiveDefinition (_,params,_) -> params
- 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 =
- match CicEnvironment.get_obj uri with
- C.Variable (_,_,ty,_) ->
- CicSubstitution.subst_vars !exp_named_subst_diff ty
- | _ -> raise (WrongUriToVariable (UriManager.string_of_uri uri))
- in
- let irl = 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
-prerr_endline ("@@@ " ^ CicPp.ppterm (Cic.Var (uri,exp_named_subst)) ^ " |--> " ^ CicPp.ppterm (Cic.Var (uri,exp_named_subst'))) ;
- new_fresh_meta,newmetasenvfragment,exp_named_subst',exp_named_subst_diff
-;;
-
-let apply_tac ~term ~status:(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 = List.find (function (m,_,_) -> m=goal) metasenv in
- let newmeta = new_meta ~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
-prerr_endline ("^^^^^TERM': " ^ CicPp.ppterm term') ;
- let termty =
- CicSubstitution.subst_vars exp_named_subst_diff
- (CicTypeChecker.type_of_aux' metasenv' context term)
- in
-prerr_endline ("^^^^^TERMTY: " ^ CicPp.ppterm termty) ;
- (* newmeta is the lowest index of the new metas introduced *)
- let (consthead,newmetas,arguments,_) =
- new_metasenv_for_apply newmeta' proof context termty
- in
- let newmetasenv = metasenv'@newmetas in
- let subst,newmetasenv' =
- CicUnification.fo_unif newmetasenv context consthead ty
- in
- let in_subst_domain i = List.exists (function (j,_) -> i=j) subst in
- let apply_subst = CicUnification.apply_subst subst in
- let old_uninstantiatedmetas,new_uninstantiatedmetas =
- (* subst_in doesn't need the context. Hence the underscore. *)
- let subst_in _ = CicUnification.apply_subst subst in
- classify_metas newmeta in_subst_domain subst_in newmetasenv'
- in
- let bo' =
- apply_subst
- (if List.length newmetas = 0 then
- term'
- else
- Cic.Appl (term'::arguments)
- )
- in
-prerr_endline ("XXXX " ^ CicPp.ppterm (if List.length newmetas = 0 then term' else Cic.Appl (term'::arguments)) ^ " |>>> " ^ CicPp.ppterm bo') ;
- let newmetasenv'' = new_uninstantiatedmetas@old_uninstantiatedmetas in
- let (newproof, newmetasenv''') =
- let subst_in = CicUnification.apply_subst ((metano,bo')::subst) in
- subst_meta_and_metasenv_in_proof
- proof metano subst_in newmetasenv''
- in
- (newproof, List.map (function (i,_,_) -> i) new_uninstantiatedmetas)
-
- (* TODO per implementare i tatticali e' necessario che tutte le tattiche
- sollevino _solamente_ Fail *)
-let apply_tac ~term ~status =
- try
- apply_tac ~term ~status
- (* TODO cacciare anche altre eccezioni? *)
- with CicUnification.UnificationFailed as e ->
- raise (Fail (Printexc.to_string e))
-
-let intros_tac
- ?(mk_fresh_name_callback = ProofEngineHelpers.mk_fresh_name) ()
- ~status:(proof, goal)
-=
- let module C = Cic in
- let module R = CicReduction in
- let (_,metasenv,_,_) = proof in
- let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
- let newmeta = new_meta ~proof in
- let (context',ty',bo') =
- lambda_abstract context newmeta ty mk_fresh_name_callback
- in
- let (newproof, _) =
- subst_meta_in_proof proof metano bo' [newmeta,context',ty']
- in
- (newproof, [newmeta])
-
-let cut_tac
- ?(mk_fresh_name_callback = ProofEngineHelpers.mk_fresh_name)
- term ~status:(proof, goal)
-=
- let module C = Cic in
- let curi,metasenv,pbo,pty = proof in
- let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
- let newmeta1 = new_meta ~proof in
- let newmeta2 = newmeta1 + 1 in
- let fresh_name =
- mk_fresh_name_callback context (Cic.Name "Hcut") ~typ:term in
- let context_for_newmeta1 =
- (Some (fresh_name,C.Decl term))::context in
- let irl1 =
- identity_relocation_list_for_metavariable context_for_newmeta1 in
- let irl2 = 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])
-
-let letin_tac
- ?(mk_fresh_name_callback = ProofEngineHelpers.mk_fresh_name)
- term ~status:(proof, goal)
-=
- let module C = Cic in
- let curi,metasenv,pbo,pty = proof in
- let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
- let _ = CicTypeChecker.type_of_aux' metasenv context term in
- let newmeta = new_meta ~proof in
- let fresh_name =
- mk_fresh_name_callback context (Cic.Name "Hletin") ~typ:term in
- let context_for_newmeta =
- (Some (fresh_name,C.Def term))::context in
- let irl =
- 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])
-
- (** functional part of the "exact" tactic *)
-let exact_tac ~term ~status:(proof, goal) =
- (* Assumption: the term bo must be closed in the current context *)
- let (_,metasenv,_,_) = proof in
- let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
- let module T = CicTypeChecker in
- let module R = CicReduction in
- if R.are_convertible context (T.type_of_aux' metasenv context term) ty then
- begin
- let (newproof, metasenv') =
- subst_meta_in_proof proof metano term [] in
- (newproof, [])
- end
- else
- raise (Fail "The type of the provided term is not the one expected.")
-
-
-(* not really "primitive" tactics .... *)
-
-let elim_tac ~term ~status:(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,_,_) = proof in
- let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
- let termty = T.type_of_aux' metasenv context term 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 =
- match CicEnvironment.get_obj uri with
- C.InductiveDefinition (tys,_,_) ->
- let (name,_,_,_) = List.nth tys typeno in
- name
- | _ -> assert false
- in
- let ext =
- match T.type_of_aux' metasenv context ty with
- C.Sort C.Prop -> "_ind"
- | C.Sort C.Set -> "_rec"
- | C.Sort C.Type -> "_rect"
- | _ -> 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 in
- let newmeta = new_meta ~proof in
- let (econclusion,newmetas,arguments,lastmeta) =
- new_metasenv_for_apply newmeta proof context ety
- in
- (* Here we assume that we have only one inductive hypothesis to *)
- (* eliminate and that it is the last hypothesis of the theorem. *)
- (* A better approach would be fingering the hypotheses in some *)
- (* way. *)
- let meta_of_corpse =
- let (_,canonical_context,_) =
- List.find (function (m,_,_) -> m=(lastmeta - 1)) newmetas
- in
- let irl =
- identity_relocation_list_for_metavariable canonical_context
- in
- Cic.Meta (lastmeta - 1, irl)
- in
- let newmetasenv = newmetas @ metasenv in
- let subst1,newmetasenv' =
- CicUnification.fo_unif newmetasenv context term meta_of_corpse
- in
- let ueconclusion = CicUnification.apply_subst subst1 econclusion in
- (* The conclusion of our elimination principle is *)
- (* (?i farg1 ... fargn) *)
- (* The conclusion of our goal is ty. So, we can *)
- (* eta-expand ty w.r.t. farg1 .... fargn to get *)
- (* a new ty equal to (P farg1 ... fargn). Now *)
- (* ?i can be instantiated with P and we are ready *)
- (* to refine the term. *)
- let emeta, fargs =
- match ueconclusion with
- C.Appl ((C.Meta (emeta,_))::fargs) -> emeta,fargs
- | C.Meta (emeta,_) -> emeta,[]
- | _ -> raise NotTheRightEliminatorShape
- in
- let ty' = CicUnification.apply_subst subst1 ty in
- let eta_expanded_ty =
-(*CSC: newmetasenv' era metasenv ??????????? *)
- List.fold_left (eta_expand newmetasenv' context) ty' fargs
- in
- let subst2,newmetasenv'' =
-(*CSC: passo newmetasenv', ma alcune variabili sono gia' state sostituite
-da subst1!!!! Dovrei rimuoverle o sono innocue?*)
- CicUnification.fo_unif
- newmetasenv' context ueconclusion eta_expanded_ty
- in
- let in_subst_domain i =
- let eq_to_i = function (j,_) -> i=j in
- List.exists eq_to_i subst1 ||
- List.exists eq_to_i subst2
- in
- (* When unwinding the META that corresponds to the elimination *)
- (* predicate (which is emeta), we must also perform one-step *)
- (* beta-reduction. apply_subst doesn't need the context. Hence *)
- (* the underscore. *)
- let apply_subst _ t =
- let t' = CicUnification.apply_subst subst1 t in
- CicUnification.apply_subst_reducing
- subst2 (Some (emeta,List.length fargs)) t'
- in
- let old_uninstantiatedmetas,new_uninstantiatedmetas =
- classify_metas newmeta in_subst_domain apply_subst
- newmetasenv''
- in
- let arguments' = List.map (apply_subst context) arguments in
- let bo' = Cic.Appl (eliminator_ref::arguments') in
- let newmetasenv''' =
- new_uninstantiatedmetas@old_uninstantiatedmetas
- in
- let (newproof, newmetasenv'''') =
- (* When unwinding the META that corresponds to the *)
- (* elimination predicate (which is emeta), we must *)
- (* also perform one-step beta-reduction. *)
- (* The only difference w.r.t. apply_subst is that *)
- (* we also substitute metano with bo'. *)
- (*CSC: Nota: sostituire nuovamente subst1 e' superfluo, *)
- (*CSC: no? *)
- let apply_subst' t =
- let t' = CicUnification.apply_subst subst1 t in
- CicUnification.apply_subst_reducing
- ((metano,bo')::subst2)
- (Some (emeta,List.length fargs)) t'
- in
- subst_meta_and_metasenv_in_proof
- proof metano apply_subst' newmetasenv'''
- in
- (newproof,
- List.map (function (i,_,_) -> i) new_uninstantiatedmetas)
-;;
-
-(* The simplification is performed only on the conclusion *)
-let elim_intros_simpl_tac ~term =
- Tacticals.then_ ~start:(elim_tac ~term)
- ~continuation:
- (Tacticals.thens
- ~start:(intros_tac ())
- ~continuations:
- [ReductionTactics.simpl_tac ~also_in_hypotheses:false ~terms:None])
-;;
-
-exception NotConvertible
-
-(*CSC: Bug (or feature?). [with_what] is parsed in the context of the goal, *)
-(*CSC: while [what] can have a richer context (because of binders) *)
-(*CSC: So it is _NOT_ possible to use those binders in the [with_what] term. *)
-(*CSC: Is that evident? Is that right? Or should it be changed? *)
-let change_tac ~what ~with_what ~status:(proof, goal) =
- let curi,metasenv,pbo,pty = proof in
- let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
- (* are_convertible works only on well-typed terms *)
- ignore (CicTypeChecker.type_of_aux' metasenv context with_what) ;
- if CicReduction.are_convertible context what with_what then
- begin
- let replace =
- ProofEngineReduction.replace
- ~equality:(==) ~what:[what] ~with_what:[with_what]
- in
- let ty' = replace ty in
- let context' =
- List.map
- (function
- Some (name,Cic.Def t) -> Some (name,Cic.Def (replace t))
- | Some (name,Cic.Decl t) -> Some (name,Cic.Decl (replace t))
- | None -> None
- ) context
- in
- let metasenv' =
- List.map
- (function
- (n,_,_) when n = metano -> (metano,context',ty')
- | _ as t -> t
- ) metasenv
- in
- (curi,metasenv',pbo,pty), [metano]
- end
- else
- raise (ProofEngineTypes.Fail "Not convertible")
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