-type binder_type =
- Declaration
- | Definition
-;;
-
-type metas_context = (int * Cic.term) list;;
-
-type context = (binder_type * Cic.name * Cic.term) list;;
+(* Copyright (C) 2000, 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/.
+ *)
-type sequent = context * Cic.term;;
-
-let proof = ref (None : (metas_context * Cic.term * Cic.term) option);;
-(*CSC: Quando facciamo Clear di una ipotesi, cosa succede? *)
-(* Note: the sequent is redundant: it can be computed from the type of the *)
-(* metavariable and its context in the proof. We keep it just for efficiency *)
-(* because computing the context of a term may be quite expensive. *)
-let goal = ref (None : (int * sequent) option);;
-
-exception NotImplemented
+let proof =
+ ref (None : (UriManager.uri * Cic.metasenv * Cic.term * Cic.term) option)
+;;
+let goal = ref (None : int option);;
-(*CSC: Funzione che deve sparire!!! *)
-let cic_context_of_context =
- List.map
- (function
- Declaration,_,t -> t
- | Definition,_,_ -> raise NotImplemented
- )
+(*CSC: commento vecchio *)
+(* refine_meta_with_brand_new_metasenv meta term subst_in newmetasenv *)
+(* This (heavy) function must be called when a tactic can instantiate old *)
+(* metavariables (i.e. existential variables). It substitues the metasenv *)
+(* of the proof with the result of removing [meta] from the domain of *)
+(* [newmetasenv]. Then it replaces Cic.Meta [meta] with [term] everywhere *)
+(* in the current proof. Finally it applies [apply_subst_replacing] to *)
+(* current proof. *)
+(*CSC: A questo punto perche' passare un bo' gia' istantiato, se tanto poi *)
+(*CSC: ci ripasso sopra apply_subst!!! *)
+(*CSC: Attenzione! Ora questa funzione applica anche [subst_in] a *)
+(*CSC: [newmetasenv]. *)
+let subst_meta_and_metasenv_in_current_proof meta subst_in newmetasenv =
+ let (uri,bo,ty) =
+ match !proof with
+ None -> assert false
+ | Some (uri,_,bo,ty) -> uri,bo,ty
+ in
+ let bo' = subst_in bo in
+ let metasenv' =
+ List.fold_right
+ (fun metasenv_entry i ->
+ match metasenv_entry with
+ (m,canonical_context,ty) when m <> meta ->
+ let canonical_context' =
+ List.map
+ (function
+ None -> None
+ | Some (i,Cic.Decl t) -> Some (i,Cic.Decl (subst_in t))
+ | Some (i,Cic.Def t) -> Some (i,Cic.Def (subst_in t))
+ ) canonical_context
+ in
+ (m,canonical_context',subst_in ty)::i
+ | _ -> i
+ ) newmetasenv []
+ in
+ proof := Some (uri,metasenv',bo',ty) ;
+ metasenv'
;;
-let refine_meta meta term newmetasenv =
- let (metasenv,bo,ty) =
+let subst_meta_in_current_proof meta term newmetasenv =
+ let (uri,metasenv,bo,ty) =
match !proof with
None -> assert false
- | Some (metasenv,bo,ty) -> metasenv,bo,ty
+ | Some (uri,metasenv,bo,ty) -> uri,metasenv,bo,ty
in
- let metasenv' = newmetasenv @ (List.remove_assoc meta metasenv) in
- let rec aux =
- let module C = Cic in
- function
- C.Rel _ as t -> t
- | C.Var _ as t -> t
- | C.Meta meta' when meta=meta' -> term
- | C.Meta _ as t -> t
- | C.Sort _ as t -> t
- | C.Implicit as t -> t
- | C.Cast (te,ty) -> C.Cast (aux te, aux ty)
- | C.Prod (n,s,t) -> C.Prod (n, aux s, aux t)
- | C.Lambda (n,s,t) -> C.Lambda (n, aux s, aux t)
- | C.LetIn (n,s,t) -> C.LetIn (n, aux s, aux t)
- | C.Appl l -> C.Appl (List.map aux l)
- | C.Const _ as t -> t
- | C.Abst _ as t -> t
- | C.MutInd _ as t -> t
- | C.MutConstruct _ as t -> t
- | C.MutCase (sp,cookingsno,i,outt,t,pl) ->
- C.MutCase (sp,cookingsno,i,aux outt, aux t,
- List.map aux pl)
- | C.Fix (i,fl) ->
- let substitutedfl =
+ let subst_in = CicUnification.apply_subst [meta,term] in
+ let metasenv' =
+ newmetasenv @ (List.filter (function (m,_,_) -> m <> meta) metasenv)
+ in
+ let metasenv'' =
+ List.map
+ (function i,canonical_context,ty ->
+ let canonical_context' =
List.map
- (fun (name,i,ty,bo) -> (name, i, aux ty, aux bo))
- fl
- in
- C.Fix (i, substitutedfl)
- | C.CoFix (i,fl) ->
- let substitutedfl =
- List.map
- (fun (name,ty,bo) -> (name, aux ty, aux bo))
- fl
+ (function
+ Some (n,Cic.Decl s) -> Some (n,Cic.Decl (subst_in s))
+ | Some (n,Cic.Def s) -> Some (n,Cic.Def (subst_in s))
+ | None -> None
+ ) canonical_context
in
- C.CoFix (i, substitutedfl)
- in
- let metasenv'' = List.map (function i,ty -> i,(aux ty)) metasenv' in
- let bo' = aux bo in
- proof := Some (metasenv'',bo',ty)
+ i,canonical_context',(subst_in ty)
+ ) metasenv'
+ in
+ let bo' = subst_in bo in
+ proof := Some (uri,metasenv'',bo',ty) ;
+ metasenv''
;;
-(* Returns the first meta whose number is above the number of the higher meta. *)
+(* Returns the first meta whose number is above the *)
+(* number of the higher meta. *)
let new_meta () =
let metasenv =
match !proof with
None -> assert false
- | Some (metasenv,_,_) -> metasenv
+ | Some (_,metasenv,_,_) -> metasenv
in
let rec aux =
function
None,[] -> 1
| Some n,[] -> n
- | None,(n,_)::tl -> aux (Some n,tl)
- | Some m,(n,_)::tl -> if n > m then aux (Some n,tl) else aux (Some m,tl)
+ | None,(n,_,_)::tl -> aux (Some n,tl)
+ | Some m,(n,_,_)::tl -> if n > m then aux (Some n,tl) else aux (Some m,tl)
in
1 + aux (None,metasenv)
;;
function
C.Rel _
| C.Var _ -> []
- | C.Meta n -> [n]
+ | C.Meta (n,_) -> [n]
| C.Sort _
| C.Implicit -> []
| C.Cast (te,ty) -> (aux te) @ (aux ty)
elim_duplicates metas
;;
+(* identity_relocation_list_for_metavariable i canonical_context *)
+(* returns the identity relocation list, which is the list [1 ; ... ; n] *)
+(* where n = List.length [canonical_context] *)
+(*CSC: ma mi basta la lunghezza del contesto canonico!!!*)
+let identity_relocation_list_for_metavariable canonical_context =
+ let canonical_context_length = List.length canonical_context in
+ let rec aux =
+ function
+ (_,[]) -> []
+ | (n,None::tl) -> None::(aux ((n+1),tl))
+ | (n,_::tl) -> (Some (Cic.Rel n))::(aux ((n+1),tl))
+ in
+ aux (1,canonical_context)
+;;
+
(* perforate context term ty *)
(* replaces the term [term] in the proof with a new metavariable whose type *)
(* is [ty]. [context] must be the context of [term] in the whole proof. This *)
let newmeta = new_meta () in
match !proof with
None -> assert false
- | Some (metasenv,bo,gty) ->
+ | Some (uri,metasenv,bo,gty) ->
(* We push the new meta at the end of the list for pretty-printing *)
(* purposes: in this way metas are ordered. *)
- let metasenv' = metasenv@[newmeta,ty] in
- let rec aux =
- function
- (* Is == strong enough? *)
- t when t == term -> C.Meta newmeta
- | C.Rel _ as t -> t
- | C.Var _ as t -> t
- | C.Meta _ as t -> t
- | C.Sort _ as t -> t
- | C.Implicit as t -> t
- | C.Cast (te,ty) -> C.Cast (aux te, aux ty)
- | C.Prod (n,s,t) -> C.Prod (n, aux s, aux t)
- | C.Lambda (n,s,t) -> C.Lambda (n, aux s, aux t)
- | C.LetIn (n,s,t) -> C.LetIn (n, aux s, aux t)
- | C.Appl l -> C.Appl (List.map aux l)
- | C.Const _ as t -> t
- | C.Abst _ as t -> t
- | C.MutInd _ as t -> t
- | C.MutConstruct _ as t -> t
- | C.MutCase (sp,cookingsno,i,outt,t,pl) ->
- C.MutCase (sp,cookingsno,i,aux outt, aux t,
- List.map aux pl)
- | C.Fix (i,fl) ->
- let substitutedfl =
- List.map
- (fun (name,i,ty,bo) -> (name, i, aux ty, aux bo))
- fl
- in
- C.Fix (i, substitutedfl)
- | C.CoFix (i,fl) ->
- let substitutedfl =
- List.map
- (fun (name,ty,bo) -> (name, aux ty, aux bo))
- fl
- in
- C.CoFix (i, substitutedfl)
- in
- let bo' = aux bo in
+ let metasenv' = metasenv@[newmeta,context,ty] in
+ let irl = identity_relocation_list_for_metavariable context in
+(*CSC: Bug: se ci sono due term uguali nella prova dovrei bucarne uno solo!!!*)
+ let bo' =
+ ProofEngineReduction.replace (==) term (C.Meta (newmeta,irl)) bo
+ in
(* It may be possible that some metavariables occurred only in *)
(* the term we are perforating and they now occurs no more. We *)
(* get rid of them, collecting the really useful metavariables *)
(* in metasenv''. *)
+(*CSC: Bug: una meta potrebbe non comparire in bo', ma comparire nel tipo *)
+(*CSC: di una metavariabile che compare in bo'!!!!!!! *)
let newmetas = metas_in_term bo' in
let metasenv'' =
- List.filter (function (n,_) -> List.mem n newmetas) metasenv'
+ List.filter (function (n,_,_) -> List.mem n newmetas) metasenv'
in
- proof := Some (metasenv'',bo',gty) ;
- goal := Some (newmeta,(context,ty)) ;
- newmeta
+ proof := Some (uri,metasenv'',bo',gty) ;
+ goal := Some newmeta
;;
(************************************************************)
exception Fail of string;;
+(*CSC: generatore di nomi? Chiedere il nome? *)
+let fresh_name =
+ let next_fresh_index = ref 0
+in
+ function () ->
+ incr next_fresh_index ;
+ "fresh_name" ^ string_of_int !next_fresh_index
+;;
+
+(* 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 =
+ 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' =
+ match n with
+ C.Name _ -> n
+(*CSC: generatore di nomi? Chiedere il nome? *)
+ | C.Anonimous -> C.Name (fresh_name ())
+ 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 intros () =
let module C = Cic in
let module R = CicReduction in
let metasenv =
match !proof with
None -> assert false
- | Some (metasenv,_,_) -> metasenv
+ | Some (_,metasenv,_,_) -> metasenv
in
- let (metano,context,ty) =
+ let metano,context,ty =
match !goal with
None -> assert false
- | Some (metano,(context,ty)) -> metano,context,ty
+ | Some metano -> List.find (function (m,_,_) -> m=metano) metasenv
in
let newmeta = new_meta () in
- let rec collect_context =
- function
- C.Cast (te,_) -> collect_context te
- | C.Prod (n,s,t) ->
- let (ctx,ty,bo) = collect_context t in
- ((Declaration,n,s)::ctx,ty,C.Lambda(n,s,bo))
- | C.LetIn (n,s,t) ->
- let (ctx,ty,bo) = collect_context t in
- ((Definition,n,s)::ctx,ty,C.LetIn(n,s,bo))
- | _ as t -> [], t, (C.Meta newmeta)
- in
- let revcontext',ty',bo' = collect_context ty in
- let context'' = (List.rev revcontext') @ context in
- refine_meta metano bo' [newmeta,ty'] ;
- goal := Some (newmeta,(context'',ty'))
+ let (context',ty',bo') = lambda_abstract context newmeta ty in
+ let _ = subst_meta_in_current_proof metano bo' [newmeta,context',ty'] in
+ goal := Some newmeta
;;
(* The term bo must be closed in the current context *)
let metasenv =
match !proof with
None -> assert false
- | Some (metasenv,_,_) -> metasenv
+ | Some (_,metasenv,_,_) -> metasenv
in
- let (metano,context,ty) =
+ let metano,context,ty =
match !goal with
None -> assert false
- | Some (metano,(context,ty)) ->
- assert (ty = List.assoc metano metasenv) ;
- (* Invariant: context is the actual context of the meta in the proof *)
- metano,context,ty
+ | Some metano -> List.find (function (m,_,_) -> m=metano) metasenv
in
- (*CSC: deve sparire! *)
- let context = cic_context_of_context context in
- if R.are_convertible (T.type_of_aux' metasenv context bo) ty then
- begin
- refine_meta metano bo [] ;
- goal := None
- end
+ if R.are_convertible context (T.type_of_aux' metasenv context bo) ty then
+ begin
+ let metasenv' = subst_meta_in_current_proof metano bo [] in
+ goal :=
+ match metasenv' with
+ [] -> None
+ | (n,_,_)::_ -> Some n
+ end
+ else
+ raise (Fail "The type of the provided term is not the one expected.")
+;;
+
+(*CSC: The call to the Intros tactic is embedded inside the code of the *)
+(*CSC: Elim tactic. Do we already need tacticals? *)
+(* 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 the nth new META lambda-abstracted as much as possible. Hence, this *)
+(* functions already provides the behaviour of Intros on the new goals. *)
+let new_metasenv_for_apply_intros 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 newcontext,ty',newargument = lambda_abstract context newmeta s in
+ let (res,newmetasenv,arguments,lastmeta) =
+ aux (newmeta + 1) (S.subst newargument t)
+ in
+ res,(newmeta,newcontext,ty')::newmetasenv,newargument::arguments,lastmeta
+ | t -> t,[],[],newmeta
+ in
+ let newmeta = new_meta () 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,newmeta,lastmeta
+;;
+
+(* 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 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
+ let newmeta = new_meta () 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,newmeta,lastmeta
+;;
+
+
+(*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
- raise (Fail "The type of the provided term is not the one expected.")
+ 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 ([],[])
;;
(* The term bo must be closed in the current context *)
let metasenv =
match !proof with
None -> assert false
- | Some (metasenv,_,_) -> metasenv
+ | Some (_,metasenv,_,_) -> metasenv
+ in
+ let metano,context,ty =
+ match !goal with
+ None -> assert false
+ | Some metano ->
+ List.find (function (m,_,_) -> m=metano) metasenv
+ in
+ let termty = CicTypeChecker.type_of_aux' metasenv context term in
+ (* newmeta is the lowest index of the new metas introduced *)
+ let (consthead,newmetas,arguments,newmeta,_) =
+ new_metasenv_for_apply context termty
+ in
+ let newmetasenv = newmetas@metasenv 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' =
+ if List.length newmetas = 0 then
+ term
+ else
+ let arguments' = List.map apply_subst arguments in
+ Cic.Appl (term::arguments')
+ in
+ let newmetasenv'' = new_uninstantiatedmetas@old_uninstantiatedmetas in
+ let newmetasenv''' =
+ let subst_in = CicUnification.apply_subst ((metano,bo')::subst) in
+ subst_meta_and_metasenv_in_current_proof metano subst_in
+ newmetasenv''
+ in
+ match newmetasenv''' with
+ [] -> goal := None
+ | (i,_,_)::_ -> goal := Some i
+;;
+
+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 _
+ | 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 _ as t -> t
+ | C.Abst _ -> assert false
+ | C.MutInd _
+ | C.MutConstruct _ as t -> t
+ | C.MutCase (sp,cookingsno,i,outt,t,pl) ->
+ C.MutCase (sp,cookingsno,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)
+ in
+ let argty =
+ T.type_of_aux' metasenv context arg
+ in
+ (C.Appl [C.Lambda ((C.Name "dummy"),argty,aux 0 t) ; arg])
+;;
+
+exception NotAnInductiveTypeToEliminate;;
+exception NotTheRightEliminatorShape;;
+exception NoHypothesesFound;;
+
+let elim_intros_simpl term =
+ let module T = CicTypeChecker in
+ let module U = UriManager in
+ let module R = CicReduction in
+ let module C = Cic in
+ let curi,metasenv =
+ match !proof with
+ None -> assert false
+ | Some (curi,metasenv,_,_) -> curi,metasenv
in
- let (metano,context,ty) =
+ let metano,context,ty =
match !goal with
None -> assert false
- | Some (metano,(context,ty)) ->
- assert (ty = List.assoc metano metasenv) ;
- (* Invariant: context is the actual context of the meta in the proof *)
- metano,context,ty
+ | Some metano ->
+ List.find (function (m,_,_) -> m=metano) metasenv
in
- (*CSC: deve sparire! *)
- let ciccontext = cic_context_of_context context in
- let mgu,mgut = CicUnification.apply metasenv ciccontext term ty in
- let mgul = Array.to_list mgu in
- let mgutl = Array.to_list mgut in
- let applymetas_to_metas =
- let newmeta = new_meta () in
- (* WARNING: here we are using the invariant that above the most *)
- (* recente new_meta() there are no used metas. *)
- Array.init (List.length mgul) (function i -> newmeta + i) in
- (* WARNING!!!!!!!!!!!!!!!!!!!!!!!!!!!!! *)
- (* Here we assume that either a META has been instantiated with *)
- (* a close term or with itself. *)
- let uninstantiatedmetas =
- List.fold_right2
- (fun bo ty newmetas ->
- match bo with
- Cic.Meta i ->
- let newmeta = applymetas_to_metas.(i) in
- (*CSC: se ty contiene metas, queste hanno il numero errato!!! *)
- let ty_with_newmetas =
- (* Substitues (META n) with (META (applymetas_to_metas.(n))) *)
- let rec aux =
- function
- C.Rel _
- | C.Var _ as t -> t
- | C.Meta n -> C.Meta (applymetas_to_metas.(n))
- | C.Sort _
- | C.Implicit as t -> t
- | C.Cast (te,ty) -> C.Cast (aux te, aux ty)
- | C.Prod (n,s,t) -> C.Prod (n, aux s, aux t)
- | C.Lambda (n,s,t) -> C.Lambda (n, aux s, aux t)
- | C.LetIn (n,s,t) -> C.LetIn (n, aux s, aux t)
- | C.Appl l -> C.Appl (List.map aux l)
- | C.Const _ as t -> t
- | C.Abst _ -> assert false
- | C.MutInd _
- | C.MutConstruct _ as t -> t
- | C.MutCase (sp,cookingsno,i,outt,t,pl) ->
- C.MutCase (sp,cookingsno,i,aux outt, aux t,
- List.map aux pl)
- | C.Fix (i,fl) ->
- let substitutedfl =
- List.map
- (fun (name,i,ty,bo) -> (name, i, aux ty, aux bo))
- fl
+ let termty = T.type_of_aux' metasenv context term in
+ let uri,cookingno,typeno,args =
+ match termty with
+ C.MutInd (uri,cookingno,typeno) -> (uri,cookingno,typeno,[])
+ | C.Appl ((C.MutInd (uri,cookingno,typeno))::args) ->
+ (uri,cookingno,typeno,args)
+ | _ -> raise NotAnInductiveTypeToEliminate
+ in
+ let eliminator_uri =
+ let buri = U.buri_of_uri uri in
+ let name =
+ match CicEnvironment.get_cooked_obj uri cookingno 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_cookingno =
+ UriManager.relative_depth curi eliminator_uri 0
+ in
+ let eliminator_ref = C.Const (eliminator_uri,eliminator_cookingno) in
+ let ety =
+ T.type_of_aux' [] [] eliminator_ref
+ in
+ let (econclusion,newmetas,arguments,newmeta,lastmeta) =
+(*
+ new_metasenv_for_apply context ety
+*)
+ new_metasenv_for_apply_intros 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
+(*CSC: Code to be used for Apply
+ C.Appl ((C.Meta (emeta,_))::fargs) -> emeta,fargs
+ | C.Meta (emeta,_) -> emeta,[]
+*)
+(*CSC: Code to be used for ApplyIntros *)
+ C.Appl (he::fargs) ->
+ let rec find_head =
+ function
+ C.Meta (emeta,_) -> emeta
+ | C.Lambda (_,_,t) -> find_head t
+ | C.LetIn (_,_,t) -> find_head t
+ | _ ->raise NotTheRightEliminatorShape
+ in
+ find_head he,fargs
+(* *)
+ | _ -> 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
+(*CSC: codice per l'elim
+ (* 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
+*)
+(*CSC: codice per l'elim_intros_simpl. Non effettua semplificazione. *)
+ let apply_subst context t =
+ let t' = CicUnification.apply_subst (subst1@subst2) t in
+ ProofEngineReduction.simpl context 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 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? *)
+(*CSC: codice per l'elim
+ 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
- C.Fix (i, substitutedfl)
- | C.CoFix (i,fl) ->
- let substitutedfl =
- List.map
- (fun (name,ty,bo) -> (name, aux ty, aux bo))
- fl
+*)
+(*CSC: codice per l'elim_intros_simpl *)
+ let apply_subst' t =
+ CicUnification.apply_subst
+ ((metano,bo')::(subst1@subst2)) t
in
- C.CoFix (i, substitutedfl)
+(* *)
+ subst_meta_and_metasenv_in_current_proof metano
+ apply_subst' newmetasenv'''
+ in
+ match newmetasenv'''' with
+ [] -> goal := None
+ | (i,_,_)::_ -> goal := Some i
+;;
+
+let reduction_tactic reduction_function term =
+ let curi,metasenv,pbo,pty =
+ match !proof with
+ None -> assert false
+ | Some (curi,metasenv,bo,ty) -> curi,metasenv,bo,ty
+ in
+ let metano,context,ty =
+ match !goal with
+ None -> assert false
+ | Some metano -> List.find (function (m,_,_) -> m=metano) metasenv
+ in
+ (* We don't know if [term] is a subterm of [ty] or a subterm of *)
+ (* the type of one metavariable. So we replace it everywhere. *)
+ (*CSC: Il vero problema e' che non sapendo dove sia il term non *)
+ (*CSC: sappiamo neppure quale sia il suo contesto!!!! Insomma, *)
+ (*CSC: e' meglio prima cercare il termine e scoprirne il *)
+ (*CSC: contesto, poi ridurre e infine rimpiazzare. *)
+ let replace context where=
+(*CSC: Per il momento se la riduzione fallisce significa solamente che *)
+(*CSC: siamo nel contesto errato. Metto il try, ma che schifo!!!! *)
+(*CSC: Anche perche' cosi' catturo anche quelle del replace che non dovrei *)
+ try
+ let term' = reduction_function context term in
+ ProofEngineReduction.replace ~equality:(==) ~what:term ~with_what:term'
+ ~where:where
+ with
+ _ -> where
+ in
+ let ty' = replace context ty in
+ let context' =
+ List.fold_right
+ (fun entry context ->
+ match entry with
+ Some (name,Cic.Def t) ->
+ (Some (name,Cic.Def (replace context t)))::context
+ | Some (name,Cic.Decl t) ->
+ (Some (name,Cic.Decl (replace context t)))::context
+ | None -> None::context
+ ) context []
+ in
+ let metasenv' =
+ List.map
+ (function
+ (n,_,_) when n = metano -> (metano,context',ty')
+ | _ as t -> t
+ ) metasenv
+ in
+ proof := Some (curi,metasenv',pbo,pty) ;
+ goal := Some metano
+;;
+
+(* Reduces [term] using [reduction_function] in the current scratch goal [ty] *)
+let reduction_tactic_in_scratch reduction_function term ty =
+ let metasenv =
+ match !proof with
+ None -> []
+ | Some (_,metasenv,_,_) -> metasenv
+ in
+ let metano,context,_ =
+ match !goal with
+ None -> assert false
+ | Some metano -> List.find (function (m,_,_) -> m=metano) metasenv
+ in
+ let term' = reduction_function context term in
+ ProofEngineReduction.replace
+ ~equality:(==) ~what:term ~with_what:term' ~where:ty
+;;
+
+let whd = reduction_tactic CicReduction.whd;;
+let reduce = reduction_tactic ProofEngineReduction.reduce;;
+let simpl = reduction_tactic ProofEngineReduction.simpl;;
+
+let whd_in_scratch = reduction_tactic_in_scratch CicReduction.whd;;
+let reduce_in_scratch =
+ reduction_tactic_in_scratch ProofEngineReduction.reduce;;
+let simpl_in_scratch =
+ reduction_tactic_in_scratch ProofEngineReduction.simpl;;
+
+(* It is just the opposite of whd. The code should probably be merged. *)
+let fold term =
+ let curi,metasenv,pbo,pty =
+ match !proof with
+ None -> assert false
+ | Some (curi,metasenv,bo,ty) -> curi,metasenv,bo,ty
+ in
+ let metano,context,ty =
+ match !goal with
+ None -> assert false
+ | Some metano -> List.find (function (m,_,_) -> m=metano) metasenv
+ in
+ let term' = CicReduction.whd context term in
+ (* We don't know if [term] is a subterm of [ty] or a subterm of *)
+ (* the type of one metavariable. So we replace it everywhere. *)
+ (*CSC: ma si potrebbe ovviare al problema. Ma non credo *)
+ (*CSC: che si guadagni nulla in fatto di efficienza. *)
+ let replace = ProofEngineReduction.replace
+ ~equality:(==) ~what:term' ~with_what:term
+ in
+ let ty' = replace ty in
+ let context' =
+ List.map
+ (function
+ Some (n,Cic.Decl t) -> Some (n,Cic.Decl (replace t))
+ | Some (n,Cic.Def t) -> Some (n,Cic.Def (replace t))
+ | None -> None
+ ) context
+ in
+ let metasenv' =
+ List.map
+ (function
+ (n,_,_) when n = metano -> (metano,context',ty')
+ | _ as t -> t
+ ) metasenv
+ in
+ proof := Some (curi,metasenv',pbo,pty) ;
+ goal := Some metano
+;;
+
+let cut term =
+ let module C = Cic in
+ let curi,metasenv,pbo,pty =
+ match !proof with
+ None -> assert false
+ | Some (curi,metasenv,bo,ty) -> curi,metasenv,bo,ty
+ in
+ let metano,context,ty =
+ match !goal with
+ None -> assert false
+ | Some metano -> List.find (function (m,_,_) -> m=metano) metasenv
+ in
+ let newmeta1 = new_meta () in
+ let newmeta2 = newmeta1 + 1 in
+ let context_for_newmeta1 =
+ (Some (C.Name "dummy_for_cut",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 (C.Name "dummy_for_cut",term,C.Meta (newmeta1,irl1)) ;
+ C.Meta (newmeta2,irl2)]
+ in
+ let _ =
+ subst_meta_in_current_proof metano bo'
+ [newmeta2,context,term; newmeta1,context_for_newmeta1,newmeta1ty];
+ in
+ goal := Some newmeta1
+;;
+
+let letin term =
+ let module C = Cic in
+ let curi,metasenv,pbo,pty =
+ match !proof with
+ None -> assert false
+ | Some (curi,metasenv,bo,ty) -> curi,metasenv,bo,ty
+ in
+ let metano,context,ty =
+ match !goal with
+ None -> assert false
+ | Some metano -> List.find (function (m,_,_) -> m=metano) metasenv
+ in
+ let _ = CicTypeChecker.type_of_aux' metasenv context term in
+ let newmeta = new_meta () in
+ let context_for_newmeta =
+ (Some (C.Name "dummy_for_letin",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 (C.Name "dummy_for_letin",term,C.Meta (newmeta,irl)) in
+ let _ = subst_meta_in_current_proof metano bo' [newmeta,context_for_newmeta,newmetaty] in
+ goal := Some newmeta
+;;
+
+exception NotConvertible;;
+
+(*CSC: Bug (or feature?). [input] is parsed in the context of the goal, *)
+(*CSC: while [goal_input] can have a richer context (because of binders) *)
+(*CSC: So it is _NOT_ possible to use those binders in the [input] term. *)
+(*CSC: Is that evident? Is that right? Or should it be changed? *)
+let change ~goal_input ~input =
+ let curi,metasenv,pbo,pty =
+ match !proof with
+ None -> assert false
+ | Some (curi,metasenv,bo,ty) -> curi,metasenv,bo,ty
+ in
+ let metano,context,ty =
+ match !goal with
+ None -> assert false
+ | Some metano -> List.find (function (m,_,_) -> m=metano) metasenv
+ in
+ (* are_convertible works only on well-typed terms *)
+ ignore (CicTypeChecker.type_of_aux' metasenv context input) ;
+ if CicReduction.are_convertible context goal_input input then
+ begin
+ let replace =
+ ProofEngineReduction.replace
+ ~equality:(==) ~what:goal_input ~with_what:input
+ 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
+ proof := Some (curi,metasenv',pbo,pty) ;
+ goal := Some metano
+ end
+ else
+ raise NotConvertible
+;;
+
+let clearbody =
+ let module C = Cic in
+ function
+ None -> assert false
+ | Some (_, C.Decl _) -> raise (Fail "No Body To Clear")
+ | Some (n_to_clear_body, C.Def term) as hyp_to_clear_body ->
+ let curi,metasenv,pbo,pty =
+ match !proof with
+ None -> assert false
+ | Some (curi,metasenv,bo,ty) -> curi,metasenv,bo,ty
+ in
+ let metano,_,_ =
+ match !goal with
+ None -> assert false
+ | Some metano -> List.find (function (m,_,_) -> m=metano) metasenv
+ in
+ let string_of_name =
+ function
+ C.Name n -> n
+ | C.Anonimous -> "_"
+ in
+ let metasenv' =
+ List.map
+ (function
+ (m,canonical_context,ty) when m = metano ->
+ let canonical_context' =
+ List.fold_right
+ (fun entry context ->
+ match entry with
+ t when t == hyp_to_clear_body ->
+ let cleared_entry =
+ let ty =
+ CicTypeChecker.type_of_aux' metasenv context term
+ in
+ Some (n_to_clear_body, Cic.Decl ty)
+ in
+ cleared_entry::context
+ | None -> None::context
+ | Some (n,C.Decl t)
+ | Some (n,C.Def t) ->
+ let _ =
+ try
+ CicTypeChecker.type_of_aux' metasenv context t
+ with
+ _ ->
+ raise
+ (Fail
+ ("The correctness of hypothesis " ^
+ string_of_name n ^
+ " relies on the body of " ^
+ string_of_name n_to_clear_body)
+ )
+ in
+ entry::context
+ ) canonical_context []
in
- aux ty
- in
- (newmeta,ty_with_newmetas)::newmetas
- | _ -> newmetas
- ) mgul mgutl []
+ let _ =
+ try
+ CicTypeChecker.type_of_aux' metasenv canonical_context' ty
+ with
+ _ ->
+ raise
+ (Fail
+ ("The correctness of the goal relies on the body of " ^
+ string_of_name n_to_clear_body))
+ in
+ m,canonical_context',ty
+ | t -> t
+ ) metasenv
+ in
+ proof := Some (curi,metasenv',pbo,pty)
+;;
+
+let clear hyp_to_clear =
+ let module C = Cic in
+ match hyp_to_clear with
+ None -> assert false
+ | Some (n_to_clear, _) ->
+ let curi,metasenv,pbo,pty =
+ match !proof with
+ None -> assert false
+ | Some (curi,metasenv,bo,ty) -> curi,metasenv,bo,ty
in
- let mgul' =
- List.map
- (function
- Cic.Meta i -> Cic.Meta (applymetas_to_metas.(i))
- | _ as t -> t
- ) mgul in
- let bo' =
- if List.length mgul' = 0 then
- term
- else
- Cic.Appl (term::mgul')
+ let metano,context,ty =
+ match !goal with
+ None -> assert false
+ | Some metano -> List.find (function (m,_,_) -> m=metano) metasenv
in
- refine_meta metano bo' uninstantiatedmetas ;
- match uninstantiatedmetas with
- (n,ty)::tl -> goal := Some (n,(context,ty))
- | [] -> goal := None
+ let string_of_name =
+ function
+ C.Name n -> n
+ | C.Anonimous -> "_"
+ in
+ let metasenv' =
+ List.map
+ (function
+ (m,canonical_context,ty) when m = metano ->
+ let canonical_context' =
+ List.fold_right
+ (fun entry context ->
+ match entry with
+ t when t == hyp_to_clear -> None::context
+ | None -> None::context
+ | Some (n,C.Decl t)
+ | Some (n,C.Def t) ->
+ let _ =
+ try
+ CicTypeChecker.type_of_aux' metasenv context t
+ with
+ _ ->
+ raise
+ (Fail
+ ("Hypothesis " ^
+ string_of_name n ^
+ " uses hypothesis " ^
+ string_of_name n_to_clear)
+ )
+ in
+ entry::context
+ ) canonical_context []
+ in
+ let _ =
+ try
+ CicTypeChecker.type_of_aux' metasenv canonical_context' ty
+ with
+ _ ->
+ raise
+ (Fail
+ ("Hypothesis " ^ string_of_name n_to_clear ^
+ " occurs in the goal"))
+ in
+ m,canonical_context',ty
+ | t -> t
+ ) metasenv
+ in
+ proof := Some (curi,metasenv',pbo,pty)
;;
projects / helm.git / blobdiff