+++ /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/.
- *)
-
-(******************************************************************************)
-(* *)
-(* PROJECT HELM *)
-(* *)
-(* Claudio Sacerdoti Coen <sacerdot@cs.unibo.it> *)
-(* 12/04/2002 *)
-(* *)
-(* *)
-(******************************************************************************)
-
-(* $Id$ *)
-
-(* The code of this module is derived from the code of CicReduction *)
-
-exception Impossible of int;;
-exception ReferenceToConstant;;
-exception ReferenceToVariable;;
-exception ReferenceToCurrentProof;;
-exception ReferenceToInductiveDefinition;;
-exception WrongUriToInductiveDefinition;;
-exception WrongUriToConstant;;
-exception RelToHiddenHypothesis;;
-
-module C = Cic
-module S = CicSubstitution
-
-let debug = false
-let prerr_endline =
- if debug then prerr_endline else (fun x -> ())
-;;
-
-exception WhatAndWithWhatDoNotHaveTheSameLength;;
-
-(* Replaces "textually" in "where" every term in "what" with the corresponding
- term in "with_what". The terms in "what" ARE NOT lifted when binders are
- crossed. The terms in "with_what" ARE NOT lifted when binders are crossed.
- Every free variable in "where" IS NOT lifted by nnn.
-*)
-let replace ~equality ~what ~with_what ~where =
- let find_image t =
- let rec find_image_aux =
- function
- [],[] -> raise Not_found
- | what::tl1,with_what::tl2 ->
- if equality what t then with_what else find_image_aux (tl1,tl2)
- | _,_ -> raise WhatAndWithWhatDoNotHaveTheSameLength
- in
- find_image_aux (what,with_what)
- in
- let rec aux t =
- try
- find_image t
- with Not_found ->
- match t with
- C.Rel _ -> t
- | C.Var (uri,exp_named_subst) ->
- C.Var (uri,List.map (function (uri,t) -> uri, aux t) exp_named_subst)
- | C.Meta _ -> t
- | C.Sort _ -> 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,ty,t) -> C.LetIn (n, aux s, aux ty, aux t)
- | C.Appl l ->
- (* Invariant enforced: no application of an application *)
- (match List.map aux l with
- (C.Appl l')::tl -> C.Appl (l'@tl)
- | l' -> C.Appl l')
- | C.Const (uri,exp_named_subst) ->
- C.Const (uri,List.map (function (uri,t) -> uri, aux t) exp_named_subst)
- | C.MutInd (uri,i,exp_named_subst) ->
- C.MutInd
- (uri,i,List.map (function (uri,t) -> uri, aux t) exp_named_subst)
- | C.MutConstruct (uri,i,j,exp_named_subst) ->
- C.MutConstruct
- (uri,i,j,List.map (function (uri,t) -> uri, aux t) exp_named_subst)
- | C.MutCase (sp,i,outt,t,pl) ->
- C.MutCase (sp,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
- aux where
-;;
-
-(* Replaces in "where" every term in "what" with the corresponding
- term in "with_what". The terms in "what" ARE lifted when binders are
- crossed. The terms in "with_what" ARE lifted when binders are crossed.
- Every free variable in "where" IS NOT lifted by nnn.
- Thus "replace_lifting_csc 1 ~with_what:[Rel 1; ... ; Rel 1]" is the
- inverse of subst up to the fact that free variables in "where" are NOT
- lifted. *)
-let replace_lifting ~equality ~context ~what ~with_what ~where =
- let find_image ctx what t =
- let rec find_image_aux =
- function
- [],[] -> raise Not_found
- | what::tl1,with_what::tl2 ->
- if equality ctx what t then with_what else find_image_aux (tl1,tl2)
- | _,_ -> raise WhatAndWithWhatDoNotHaveTheSameLength
- in
- find_image_aux (what,with_what)
- in
- let add_ctx ctx n s = (Some (n, Cic.Decl s))::ctx in
- let add_ctx1 ctx n s ty = (Some (n, Cic.Def (s,ty)))::ctx in
- let rec substaux k ctx what t =
- try
- S.lift (k-1) (find_image ctx what t)
- with Not_found ->
- match t with
- C.Rel n as t -> t
- | C.Var (uri,exp_named_subst) ->
- let exp_named_subst' =
- List.map (function (uri,t) -> uri,substaux k ctx what t) exp_named_subst
- in
- C.Var (uri,exp_named_subst')
- | C.Meta (i, l) ->
- let l' =
- List.map
- (function
- None -> None
- | Some t -> Some (substaux k ctx what t)
- ) l
- in
- C.Meta(i,l')
- | C.Sort _ as t -> t
- | C.Implicit _ as t -> t
- | C.Cast (te,ty) -> C.Cast (substaux k ctx what te, substaux k ctx what ty)
- | C.Prod (n,s,t) ->
- C.Prod
- (n, substaux k ctx what s, substaux (k + 1) (add_ctx ctx n s) (List.map (S.lift 1) what) t)
- | C.Lambda (n,s,t) ->
- C.Lambda
- (n, substaux k ctx what s, substaux (k + 1) (add_ctx ctx n s) (List.map (S.lift 1) what) t)
- | C.LetIn (n,s,ty,t) ->
- C.LetIn
- (n, substaux k ctx what s, substaux k ctx what ty, substaux (k + 1) (add_ctx1 ctx n s ty) (List.map (S.lift 1) what) t)
- | C.Appl (he::tl) ->
- (* Invariant: no Appl applied to another Appl *)
- let tl' = List.map (substaux k ctx what) tl in
- begin
- match substaux k ctx what he with
- C.Appl l -> C.Appl (l@tl')
- | _ as he' -> C.Appl (he'::tl')
- end
- | C.Appl _ -> assert false
- | C.Const (uri,exp_named_subst) ->
- let exp_named_subst' =
- List.map (function (uri,t) -> uri,substaux k ctx what t) exp_named_subst
- in
- C.Const (uri,exp_named_subst')
- | C.MutInd (uri,i,exp_named_subst) ->
- let exp_named_subst' =
- List.map (function (uri,t) -> uri,substaux k ctx what t) exp_named_subst
- in
- C.MutInd (uri,i,exp_named_subst')
- | C.MutConstruct (uri,i,j,exp_named_subst) ->
- let exp_named_subst' =
- List.map (function (uri,t) -> uri,substaux k ctx what t) exp_named_subst
- in
- C.MutConstruct (uri,i,j,exp_named_subst')
- | C.MutCase (sp,i,outt,t,pl) ->
- C.MutCase (sp,i,substaux k ctx what outt, substaux k ctx what t,
- List.map (substaux k ctx what) pl)
- | C.Fix (i,fl) ->
- let len = List.length fl in
- let substitutedfl =
- List.map
- (fun (name,i,ty,bo) -> (* WRONG CTX *)
- (name, i, substaux k ctx what ty,
- substaux (k+len) ctx (List.map (S.lift len) what) bo)
- ) fl
- in
- C.Fix (i, substitutedfl)
- | C.CoFix (i,fl) ->
- let len = List.length fl in
- let substitutedfl =
- List.map
- (fun (name,ty,bo) -> (* WRONG CTX *)
- (name, substaux k ctx what ty,
- substaux (k+len) ctx (List.map (S.lift len) what) bo)
- ) fl
- in
- C.CoFix (i, substitutedfl)
- in
- substaux 1 context what where
-;;
-
-(* Replaces in "where" every term in "what" with the corresponding
- term in "with_what". The terms in "what" ARE NOT lifted when binders are
- crossed. The terms in "with_what" ARE lifted when binders are crossed.
- Every free variable in "where" IS lifted by nnn.
- Thus "replace_lifting_csc 1 ~with_what:[Rel 1; ... ; Rel 1]" is the
- inverse of subst up to the fact that "what" terms are NOT lifted. *)
-let replace_lifting_csc nnn ~equality ~what ~with_what ~where =
- let find_image t =
- let rec find_image_aux =
- function
- [],[] -> raise Not_found
- | what::tl1,with_what::tl2 ->
- if equality what t then with_what else find_image_aux (tl1,tl2)
- | _,_ -> raise WhatAndWithWhatDoNotHaveTheSameLength
- in
- find_image_aux (what,with_what)
- in
- let rec substaux k t =
- try
- S.lift (k-1) (find_image t)
- with Not_found ->
- match t with
- C.Rel n ->
- if n < k then C.Rel n else C.Rel (n + nnn)
- | C.Var (uri,exp_named_subst) ->
- let exp_named_subst' =
- List.map (function (uri,t) -> uri,substaux k t) exp_named_subst
- in
- C.Var (uri,exp_named_subst')
- | C.Meta (i, l) ->
- let l' =
- List.map
- (function
- None -> None
- | Some t -> Some (substaux k t)
- ) l
- in
- C.Meta(i,l')
- | C.Sort _ as t -> t
- | C.Implicit _ as t -> t
- | C.Cast (te,ty) -> C.Cast (substaux k te, substaux k ty)
- | C.Prod (n,s,t) ->
- C.Prod (n, substaux k s, substaux (k + 1) t)
- | C.Lambda (n,s,t) ->
- C.Lambda (n, substaux k s, substaux (k + 1) t)
- | C.LetIn (n,s,ty,t) ->
- C.LetIn (n, substaux k s, substaux k ty, substaux (k + 1) t)
- | C.Appl (he::tl) ->
- (* Invariant: no Appl applied to another Appl *)
- let tl' = List.map (substaux k) tl in
- begin
- match substaux k he with
- C.Appl l -> C.Appl (l@tl')
- | _ as he' -> C.Appl (he'::tl')
- end
- | C.Appl _ -> assert false
- | C.Const (uri,exp_named_subst) ->
- let exp_named_subst' =
- List.map (function (uri,t) -> uri,substaux k t) exp_named_subst
- in
- C.Const (uri,exp_named_subst')
- | C.MutInd (uri,i,exp_named_subst) ->
- let exp_named_subst' =
- List.map (function (uri,t) -> uri,substaux k t) exp_named_subst
- in
- C.MutInd (uri,i,exp_named_subst')
- | C.MutConstruct (uri,i,j,exp_named_subst) ->
- let exp_named_subst' =
- List.map (function (uri,t) -> uri,substaux k t) exp_named_subst
- in
- C.MutConstruct (uri,i,j,exp_named_subst')
- | C.MutCase (sp,i,outt,t,pl) ->
- C.MutCase (sp,i,substaux k outt, substaux k t,
- List.map (substaux k) pl)
- | C.Fix (i,fl) ->
- let len = List.length fl in
- let substitutedfl =
- List.map
- (fun (name,i,ty,bo) ->
- (name, i, substaux k ty, substaux (k+len) bo))
- fl
- in
- C.Fix (i, substitutedfl)
- | C.CoFix (i,fl) ->
- let len = List.length fl in
- let substitutedfl =
- List.map
- (fun (name,ty,bo) ->
- (name, substaux k ty, substaux (k+len) bo))
- fl
- in
- C.CoFix (i, substitutedfl)
- in
- substaux 1 where
-;;
-
-(* This is like "replace_lifting_csc 1 ~with_what:[Rel 1; ... ; Rel 1]"
- up to the fact that the index to start from can be specified *)
-let replace_with_rel_1_from ~equality ~what =
- let rec find_image t = function
- | [] -> false
- | hd :: tl -> equality t hd || find_image t tl
- in
- let rec subst_term k t =
- if find_image t what then C.Rel k else inspect_term k t
- and inspect_term k = function
- | C.Rel i -> if i < k then C.Rel i else C.Rel (succ i)
- | C.Sort _ as t -> t
- | C.Implicit _ as t -> t
- | C.Var (uri, enss) ->
- let enss = List.map (subst_ens k) enss in
- C.Var (uri, enss)
- | C.Const (uri ,enss) ->
- let enss = List.map (subst_ens k) enss in
- C.Const (uri, enss)
- | C.MutInd (uri, tyno, enss) ->
- let enss = List.map (subst_ens k) enss in
- C.MutInd (uri, tyno, enss)
- | C.MutConstruct (uri, tyno, consno, enss) ->
- let enss = List.map (subst_ens k) enss in
- C.MutConstruct (uri, tyno, consno, enss)
- | C.Meta (i, mss) ->
- let mss = List.map (subst_ms k) mss in
- C.Meta(i, mss)
- | C.Cast (t, v) -> C.Cast (subst_term k t, subst_term k v)
- | C.Appl ts ->
- let ts = List.map (subst_term k) ts in
- C.Appl ts
- | C.MutCase (uri, tyno, outty, t, cases) ->
- let cases = List.map (subst_term k) cases in
- C.MutCase (uri, tyno, subst_term k outty, subst_term k t, cases)
- | C.Prod (n, v, t) ->
- C.Prod (n, subst_term k v, subst_term (succ k) t)
- | C.Lambda (n, v, t) ->
- C.Lambda (n, subst_term k v, subst_term (succ k) t)
- | C.LetIn (n, v, ty, t) ->
- C.LetIn (n, subst_term k v, subst_term k ty, subst_term (succ k) t)
- | C.Fix (i, fixes) ->
- let fixesno = List.length fixes in
- let fixes = List.map (subst_fix fixesno k) fixes in
- C.Fix (i, fixes)
- | C.CoFix (i, cofixes) ->
- let cofixesno = List.length cofixes in
- let cofixes = List.map (subst_cofix cofixesno k) cofixes in
- C.CoFix (i, cofixes)
- and subst_ens k (uri, t) = uri, subst_term k t
- and subst_ms k = function
- | None -> None
- | Some t -> Some (subst_term k t)
- and subst_fix fixesno k (n, ind, ty, bo) =
- n, ind, subst_term k ty, subst_term (k + fixesno) bo
- and subst_cofix cofixesno k (n, ty, bo) =
- n, subst_term k ty, subst_term (k + cofixesno) bo
-in
-subst_term
-
-let unfold ?what context where =
- let contextlen = List.length context in
- let first_is_the_expandable_head_of_second context' t1 t2 =
- match t1,t2 with
- Cic.Const (uri,_), Cic.Const (uri',_)
- | Cic.Var (uri,_), Cic.Var (uri',_)
- | Cic.Const (uri,_), Cic.Appl (Cic.Const (uri',_)::_)
- | Cic.Var (uri,_), Cic.Appl (Cic.Var (uri',_)::_) -> UriManager.eq uri uri'
- | Cic.Const _, _
- | Cic.Var _, _ -> false
- | Cic.Rel n, Cic.Rel m
- | Cic.Rel n, Cic.Appl (Cic.Rel m::_) ->
- n + (List.length context' - contextlen) = m
- | Cic.Rel _, _ -> false
- | _,_ ->
- raise
- (ProofEngineTypes.Fail
- (lazy "The term to unfold is not a constant, a variable or a bound variable "))
- in
- let appl he tl =
- if tl = [] then he else Cic.Appl (he::tl) in
- let cannot_delta_expand t =
- raise
- (ProofEngineTypes.Fail
- (lazy ("The term " ^ CicPp.ppterm t ^ " cannot be delta-expanded"))) in
- let rec hd_delta_beta context tl =
- function
- Cic.Rel n as t ->
- (try
- match List.nth context (n-1) with
- Some (_,Cic.Decl _) -> cannot_delta_expand t
- | Some (_,Cic.Def (bo,_)) ->
- CicReduction.head_beta_reduce
- (appl (CicSubstitution.lift n bo) tl)
- | None -> raise RelToHiddenHypothesis
- with
- Failure _ -> assert false)
- | Cic.Const (uri,exp_named_subst) as t ->
- let o,_ = CicEnvironment.get_obj CicUniv.oblivion_ugraph uri in
- (match o with
- Cic.Constant (_,Some body,_,_,_) ->
- CicReduction.head_beta_reduce
- (appl (CicSubstitution.subst_vars exp_named_subst body) tl)
- | Cic.Constant (_,None,_,_,_) -> cannot_delta_expand t
- | Cic.Variable _ -> raise ReferenceToVariable
- | Cic.CurrentProof _ -> raise ReferenceToCurrentProof
- | Cic.InductiveDefinition _ -> raise ReferenceToInductiveDefinition
- )
- | Cic.Var (uri,exp_named_subst) as t ->
- let o,_ = CicEnvironment.get_obj CicUniv.oblivion_ugraph uri in
- (match o with
- Cic.Constant _ -> raise ReferenceToConstant
- | Cic.CurrentProof _ -> raise ReferenceToCurrentProof
- | Cic.InductiveDefinition _ -> raise ReferenceToInductiveDefinition
- | Cic.Variable (_,Some body,_,_,_) ->
- CicReduction.head_beta_reduce
- (appl (CicSubstitution.subst_vars exp_named_subst body) tl)
- | Cic.Variable (_,None,_,_,_) -> cannot_delta_expand t
- )
- | Cic.Appl [] -> assert false
- | Cic.Appl (he::tl) -> hd_delta_beta context tl he
- | t -> cannot_delta_expand t
- in
- let context_and_matched_term_list =
- match what with
- None -> [context, where]
- | Some what ->
- let res =
- ProofEngineHelpers.locate_in_term
- ~equality:first_is_the_expandable_head_of_second
- what ~where context
- in
- if res = [] then
- raise
- (ProofEngineTypes.Fail
- (lazy ("Term "^ CicPp.ppterm what ^ " not found in " ^ CicPp.ppterm where)))
- else
- res
- in
- let reduced_terms =
- List.map
- (function (context,where) -> hd_delta_beta context [] where)
- context_and_matched_term_list in
- let whats = List.map snd context_and_matched_term_list in
- replace ~equality:(==) ~what:whats ~with_what:reduced_terms ~where
-;;
-
-exception WrongShape;;
-exception AlreadySimplified;;
-
-(* Takes a well-typed term and *)
-(* 1) Performs beta-iota-zeta reduction until delta reduction is needed *)
-(* 2) Attempts delta-reduction. If the residual is a Fix lambda-abstracted *)
-(* w.r.t. zero or more variables and if the Fix can be reductaed, than it*)
-(* is reduced, the delta-reduction is succesfull and the whole algorithm *)
-(* is applied again to the new redex; Step 3.1) is applied to the result *)
-(* of the recursive simplification. Otherwise, if the Fix can not be *)
-(* reduced, than the delta-reductions fails and the delta-redex is *)
-(* not reduced. Otherwise, if the delta-residual is not the *)
-(* lambda-abstraction of a Fix, then it performs step 3.2). *)
-(* 3.1) Folds the application of the constant to the arguments that did not *)
-(* change in every iteration, i.e. to the actual arguments for the *)
-(* lambda-abstractions that precede the Fix. *)
-(* 3.2) Computes the head beta-zeta normal form of the term. Then it tries *)
-(* reductions. If the reduction cannot be performed, it returns the *)
-(* original term (not the head beta-zeta normal form of the definiendum) *)
-(*CSC: It does not perform simplification in a Case *)
-
-let simpl context =
- (* a simplified term is active if it can create a redex when used as an *)
- (* actual parameter *)
- let rec is_active =
- function
- C.Lambda _
- | C.MutConstruct _
- | C.Appl (C.MutConstruct _::_)
- | C.CoFix _ -> true
- | C.Cast (bo,_) -> is_active bo
- | C.LetIn _ -> assert false
- | _ -> false
- in
- (* reduceaux is equal to the reduceaux locally defined inside *)
- (* reduce, but for the const case. *)
- (**** Step 1 ****)
- let rec reduceaux context l =
- function
- C.Rel n as t ->
- (* we never perform delta expansion automatically *)
- if l = [] then t else C.Appl (t::l)
- | C.Var (uri,exp_named_subst) ->
- let exp_named_subst' =
- reduceaux_exp_named_subst context l exp_named_subst
- in
- (let o,_ = CicEnvironment.get_obj CicUniv.oblivion_ugraph uri in
- match o with
- C.Constant _ -> raise ReferenceToConstant
- | C.CurrentProof _ -> raise ReferenceToCurrentProof
- | C.InductiveDefinition _ -> raise ReferenceToInductiveDefinition
- | C.Variable (_,None,_,_,_) ->
- let t' = C.Var (uri,exp_named_subst') in
- if l = [] then t' else C.Appl (t'::l)
- | C.Variable (_,Some body,_,_,_) ->
- reduceaux context l
- (CicSubstitution.subst_vars exp_named_subst' body)
- )
- | C.Meta _ as t -> if l = [] then t else C.Appl (t::l)
- | C.Sort _ as t -> t (* l should be empty *)
- | C.Implicit _ as t -> t
- | C.Cast (te,ty) ->
- C.Cast (reduceaux context l te, reduceaux context [] ty)
- | C.Prod (name,s,t) ->
- assert (l = []) ;
- C.Prod (name,
- reduceaux context [] s,
- reduceaux ((Some (name,C.Decl s))::context) [] t)
- | C.Lambda (name,s,t) ->
- (match l with
- [] ->
- C.Lambda (name,
- reduceaux context [] s,
- reduceaux ((Some (name,C.Decl s))::context) [] t)
- | he::tl -> reduceaux context tl (S.subst he t)
- (* when name is Anonimous the substitution should be superfluous *)
- )
- | C.LetIn (n,s,ty,t) ->
- reduceaux context l (S.subst (reduceaux context [] s) t)
- | C.Appl (he::tl) ->
- let tl' = List.map (reduceaux context []) tl in
- reduceaux context (tl'@l) he
- | C.Appl [] -> raise (Impossible 1)
- | C.Const (uri,exp_named_subst) ->
- let exp_named_subst' =
- reduceaux_exp_named_subst context l exp_named_subst
- in
- (let o,_ = CicEnvironment.get_obj CicUniv.oblivion_ugraph uri in
- match o with
- C.Constant (_,Some body,_,_,_) ->
- if List.exists is_active l then
- try_delta_expansion context l
- (C.Const (uri,exp_named_subst'))
- (CicSubstitution.subst_vars exp_named_subst' body)
- else
- let t' = C.Const (uri,exp_named_subst') in
- if l = [] then t' else C.Appl (t'::l)
- | C.Constant (_,None,_,_,_) ->
- let t' = C.Const (uri,exp_named_subst') in
- if l = [] then t' else C.Appl (t'::l)
- | C.Variable _ -> raise ReferenceToVariable
- | C.CurrentProof (_,_,body,_,_,_) -> reduceaux context l body
- | C.InductiveDefinition _ -> raise ReferenceToInductiveDefinition
- )
- | C.MutInd (uri,i,exp_named_subst) ->
- let exp_named_subst' =
- reduceaux_exp_named_subst context l exp_named_subst
- in
- let t' = C.MutInd (uri,i,exp_named_subst') in
- if l = [] then t' else C.Appl (t'::l)
- | C.MutConstruct (uri,i,j,exp_named_subst) ->
- let exp_named_subst' =
- reduceaux_exp_named_subst context l exp_named_subst
- in
- let t' = C.MutConstruct(uri,i,j,exp_named_subst') in
- if l = [] then t' else C.Appl (t'::l)
- | C.MutCase (mutind,i,outtype,term,pl) ->
- let decofix =
- function
- C.CoFix (i,fl) ->
- let (_,_,body) = List.nth fl i in
- let body' =
- let counter = ref (List.length fl) in
- List.fold_right
- (fun _ -> decr counter ; S.subst (C.CoFix (!counter,fl)))
- fl
- body
- in
- reduceaux context [] body'
- | C.Appl (C.CoFix (i,fl) :: tl) ->
- let (_,_,body) = List.nth fl i in
- let body' =
- let counter = ref (List.length fl) in
- List.fold_right
- (fun _ -> decr counter ; S.subst (C.CoFix (!counter,fl)))
- fl
- body
- in
- let tl' = List.map (reduceaux context []) tl in
- reduceaux context tl' body'
- | t -> t
- in
- (match decofix (reduceaux context [] term) (*(CicReduction.whd context term)*) with
- C.MutConstruct (_,_,j,_) -> reduceaux context l (List.nth pl (j-1))
- | C.Appl (C.MutConstruct (_,_,j,_) :: tl) ->
- let (arity, r) =
- let o,_ = CicEnvironment.get_obj CicUniv.oblivion_ugraph mutind in
- match o with
- C.InductiveDefinition (tl,ingredients,r,_) ->
- let (_,_,arity,_) = List.nth tl i in
- (arity,r)
- | _ -> raise WrongUriToInductiveDefinition
- in
- let ts =
- let rec eat_first =
- function
- (0,l) -> l
- | (n,he::tl) when n > 0 -> eat_first (n - 1, tl)
- | _ -> raise (Impossible 5)
- in
- eat_first (r,tl)
- in
- reduceaux context (ts@l) (List.nth pl (j-1))
- | C.Cast _ | C.Implicit _ ->
- raise (Impossible 2) (* we don't trust our whd ;-) *)
- | _ ->
- let outtype' = reduceaux context [] outtype in
- let term' = reduceaux context [] term in
- let pl' = List.map (reduceaux context []) pl in
- let res =
- C.MutCase (mutind,i,outtype',term',pl')
- in
- if l = [] then res else C.Appl (res::l)
- )
- | C.Fix (i,fl) ->
- let tys,_ =
- List.fold_left
- (fun (types,len) (n,_,ty,_) ->
- (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
- len+1)
- ) ([],0) fl
- in
- let t' () =
- let fl' =
- List.map
- (function (n,recindex,ty,bo) ->
- (n,recindex,reduceaux context [] ty, reduceaux (tys@context) [] bo)
- ) fl
- in
- C.Fix (i, fl')
- in
- let (_,recindex,_,body) = List.nth fl i in
- let recparam =
- try
- Some (List.nth l recindex)
- with
- _ -> None
- in
- (match recparam with
- Some recparam ->
- (match reduceaux context [] recparam with
- C.MutConstruct _
- | C.Appl ((C.MutConstruct _)::_) ->
- let body' =
- let counter = ref (List.length fl) in
- List.fold_right
- (fun _ -> decr counter ; S.subst (C.Fix (!counter,fl)))
- fl
- body
- in
- (* Possible optimization: substituting whd recparam in l*)
- reduceaux context l body'
- | _ -> if l = [] then t' () else C.Appl ((t' ())::l)
- )
- | None -> if l = [] then t' () else C.Appl ((t' ())::l)
- )
- | C.CoFix (i,fl) ->
- let tys,_ =
- List.fold_left
- (fun (types,len) (n,ty,_) ->
- (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
- len+1)
- ) ([],0) fl
- in
- let t' =
- let fl' =
- List.map
- (function (n,ty,bo) ->
- (n,reduceaux context [] ty, reduceaux (tys@context) [] bo)
- ) fl
- in
- C.CoFix (i, fl')
- in
- if l = [] then t' else C.Appl (t'::l)
- and reduceaux_exp_named_subst context l =
- List.map (function uri,t -> uri,reduceaux context [] t)
- (**** Step 2 ****)
- and reduce_with_no_hope_to_fold_back t l =
- prerr_endline "reduce_with_no_hope_to_fold_back";
- let simplified = reduceaux context l t in
- let t' = if l = [] then t else C.Appl (t::l) in
- if t' = simplified then
- raise AlreadySimplified
- else
- simplified
-
- and try_delta_expansion context l term body =
- try
- let res,constant_args =
- let rec aux rev_constant_args l =
- function
- C.Lambda (name,s,t) ->
- begin
- match l with
- [] -> raise WrongShape
- | he::tl ->
- (* when name is Anonimous the substitution should *)
- (* be superfluous *)
- aux (he::rev_constant_args) tl (S.subst he t)
- end
- | C.LetIn (_,s,_,t) ->
- aux rev_constant_args l (S.subst s t)
- | C.Fix (i,fl) ->
- let (_,recindex,_,body) = List.nth fl i in
- let recparam =
- try
- List.nth l recindex
- with
- _ -> raise AlreadySimplified
- in
- (match reduceaux context [] recparam (*CicReduction.whd context recparam*) with
- C.MutConstruct _
- | C.Appl ((C.MutConstruct _)::_) ->
- let body' =
- let counter = ref (List.length fl) in
- List.fold_right
- (function _ ->
- decr counter ; S.subst (C.Fix (!counter,fl))
- ) fl body
- in
- (* Possible optimization: substituting whd *)
- (* recparam in l *)
- reduceaux context l body',
- List.rev rev_constant_args
- | _ -> raise AlreadySimplified
- )
- | _ -> raise WrongShape
- in
- aux [] l body
- in
- (**** Step 3.1 ****)
- let term_to_fold, delta_expanded_term_to_fold =
- match constant_args with
- [] -> term,body
- | _ -> C.Appl (term::constant_args), C.Appl (body::constant_args)
- in
- let simplified_term_to_fold =
- reduceaux context [] delta_expanded_term_to_fold
- in
- replace_lifting ~equality:(fun _ x y -> x = y) ~context
- ~what:[simplified_term_to_fold] ~with_what:[term_to_fold] ~where:res
- with
- WrongShape ->
- let rec skip_lambda n = function
- | Cic.Lambda (_,_,t) -> skip_lambda (n+1) t | t -> t, n
- in
- let is_fix uri =
- match fst(CicEnvironment.get_obj CicUniv.oblivion_ugraph uri) with
- | Cic.Constant (_,Some bo, _, _,_) ->
- (let t, _ = skip_lambda 0 bo in
- match t with | Cic.Fix _ -> true | _ -> false)
- | _ -> false
- in
- let guess_recno uri =
- prerr_endline ("GUESS: " ^ UriManager.string_of_uri uri);
- match fst(CicEnvironment.get_obj CicUniv.oblivion_ugraph uri) with
- | Cic.Constant (_,Some bo, _, _,_ ) ->
- let t, n = skip_lambda 0 bo in
- (match t with
- | Cic.Fix (i,fl) ->
- let _,recno,_,_ = List.nth fl i in
- prerr_endline ("GUESSED: " ^ string_of_int recno ^ " after " ^
- string_of_int n ^ " lambdas");
- recno + n
- | _ -> assert false)
- | _ -> assert false
- in
- let original_args = l in
- (**** Step 3.2 ****)
- let rec aux l =
- function
- | C.Lambda (name,s,t) ->
- (match l with
- | [] -> raise AlreadySimplified
- | he::tl ->
- (* when name is Anonimous the substitution should *)
- (* be superfluous *)
- aux tl (S.subst he t))
- | C.LetIn (_,s,_,t) -> aux l (S.subst s t)
- | Cic.Appl (Cic.Const (uri,_) :: args) as t when is_fix uri ->
- let recno =
- prerr_endline ("cerco : " ^ string_of_int (guess_recno uri)
- ^ " in: " ^ String.concat " "
- (List.map (fun x -> CicPp.ppterm x) args));
- prerr_endline ("e piglio il rispettivo in :"^String.concat " "
- (List.map (fun x -> CicPp.ppterm x) original_args));
- (* look for args[regno] in saved_args *)
- let wanted = List.nth (args@l) (guess_recno uri) in
- let rec aux n = function
- | [] -> n (* DA CAPIRE *)
- | t::_ when t = wanted -> n
- | _::tl -> aux (n+1) tl
- in
- aux 0 original_args
- in
- if recno = List.length original_args then
- reduce_with_no_hope_to_fold_back t l
- else
- let simplified = reduceaux context l t in
- let rec mk_implicits = function
- | n,_::tl when n = recno ->
- Cic.Implicit None :: (mk_implicits (n+1,tl))
- | n,arg::tl -> arg :: (mk_implicits (n+1,tl))
- | _,[] -> []
- in
- (* we try to fold back constant that do not expand to Fix *)
- let _ = prerr_endline
- ("INIZIO (" ^ string_of_int recno ^ ") : " ^ CicPp.ppterm
- simplified) in
- let term_to_fold =
- Cic.Appl (term:: mk_implicits (0,original_args))
- in
- (try
- let term_to_fold, _, metasenv, _ =
- CicRefine.type_of_aux' [] context term_to_fold
- CicUniv.oblivion_ugraph
- in
- let _ =
- prerr_endline ("RAFFINA: "^CicPp.ppterm term_to_fold) in
- let _ =
- prerr_endline
- ("RAFFINA: "^CicMetaSubst.ppmetasenv [] metasenv) in
- let simplified_term_to_fold = unfold context term_to_fold in
- let _ =
- prerr_endline ("SEMPLIFICA: " ^
- CicPp.ppterm simplified_term_to_fold)
- in
- let rec do_n f t =
- let t1 = f t in
- if t1 = t then t else do_n f t1
- in
- do_n
- (fun simplified ->
- let subst = ref [] in
- let myunif ctx t1 t2 =
- if !subst <> [] then false
- else
- try
- prerr_endline "MUNIF";
- prerr_endline (CicPp.ppterm t1);
- prerr_endline "VS";
- prerr_endline (CicPp.ppterm t2 ^ "\n");
- let subst1, _, _ =
- CicUnification.fo_unif metasenv ctx t1 t2
- CicUniv.oblivion_ugraph
- in
- prerr_endline "UNIFICANO\n\n\n";
- subst := subst1;
- true
- with
- | CicUnification.UnificationFailure s
- | CicUnification.Uncertain s
- | CicUnification.AssertFailure s ->
- prerr_endline (Lazy.force s); false
- | CicUtil.Meta_not_found _ -> false
- (*
- | _ as exn ->
- prerr_endline (Printexc.to_string exn);
- false*)
- in
- let t =
- replace_lifting myunif context
- [simplified_term_to_fold] [term_to_fold] simplified
- in
- let _ = prerr_endline "UNIFICA" in
- if List.length metasenv <> List.length !subst then
- let _ = prerr_endline ("SUBST CORTA " ^
- CicMetaSubst.ppsubst !subst ~metasenv)
- in
- simplified
- else
- if t = simplified then
- let _ = prerr_endline "NULLA DI FATTO" in
- simplified
- else
- let t = CicMetaSubst.apply_subst !subst t in
- prerr_endline ("ECCO: " ^ CicPp.ppterm t); t)
- simplified
- with
- | CicRefine.RefineFailure s
- | CicRefine.Uncertain s
- | CicRefine.AssertFailure s ->
- prerr_endline (Lazy.force s); simplified
- (*| exn -> prerr_endline (Printexc.to_string exn); simplified*))
- | t -> reduce_with_no_hope_to_fold_back t l
- in
- (try aux l body
- with
- AlreadySimplified ->
- if l = [] then term else C.Appl (term::l))
- | AlreadySimplified ->
- (* If we performed delta-reduction, we would find a Fix *)
- (* not applied to a constructor. So, we refuse to perform *)
- (* delta-reduction. *)
- if l = [] then term else C.Appl (term::l)
- in
- reduceaux context []
-;;
projects / helm.git / blobdiff