+++ /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;;
-
-let alpha_equivalence =
- let module C = Cic in
- let rec aux t t' =
- if t = t' then true
- else
- match t,t' with
- C.Var (uri1,exp_named_subst1), C.Var (uri2,exp_named_subst2) ->
- UriManager.eq uri1 uri2 &&
- aux_exp_named_subst exp_named_subst1 exp_named_subst2
- | C.Cast (te,ty), C.Cast (te',ty') ->
- aux te te' && aux ty ty'
- | C.Prod (_,s,t), C.Prod (_,s',t') ->
- aux s s' && aux t t'
- | C.Lambda (_,s,t), C.Lambda (_,s',t') ->
- aux s s' && aux t t'
- | C.LetIn (_,s,t), C.LetIn(_,s',t') ->
- aux s s' && aux t t'
- | C.Appl l, C.Appl l' ->
- (try
- List.fold_left2
- (fun b t1 t2 -> b && aux t1 t2) true l l'
- with
- Invalid_argument _ -> false)
- | C.Const (uri,exp_named_subst1), C.Const (uri',exp_named_subst2) ->
- UriManager.eq uri uri' &&
- aux_exp_named_subst exp_named_subst1 exp_named_subst2
- | C.MutInd (uri,i,exp_named_subst1), C.MutInd (uri',i',exp_named_subst2) ->
- UriManager.eq uri uri' && i = i' &&
- aux_exp_named_subst exp_named_subst1 exp_named_subst2
- | C.MutConstruct (uri,i,j,exp_named_subst1),
- C.MutConstruct (uri',i',j',exp_named_subst2) ->
- UriManager.eq uri uri' && i = i' && j = j' &&
- aux_exp_named_subst exp_named_subst1 exp_named_subst2
- | C.MutCase (sp,i,outt,t,pl), C.MutCase (sp',i',outt',t',pl') ->
- UriManager.eq sp sp' && i = i' &&
- aux outt outt' && aux t t' &&
- (try
- List.fold_left2
- (fun b t1 t2 -> b && aux t1 t2) true pl pl'
- with
- Invalid_argument _ -> false)
- | C.Fix (i,fl), C.Fix (i',fl') ->
- i = i' &&
- (try
- List.fold_left2
- (fun b (_,i,ty,bo) (_,i',ty',bo') ->
- b && i = i' && aux ty ty' && aux bo bo'
- ) true fl fl'
- with
- Invalid_argument _ -> false)
- | C.CoFix (i,fl), C.CoFix (i',fl') ->
- i = i' &&
- (try
- List.fold_left2
- (fun b (_,ty,bo) (_,ty',bo') ->
- b && aux ty ty' && aux bo bo'
- ) true fl fl'
- with
- Invalid_argument _ -> false)
- | _,_ -> false (* we already know that t != t' *)
- and aux_exp_named_subst exp_named_subst1 exp_named_subst2 =
- try
- List.fold_left2
- (fun b (uri1,t1) (uri2,t2) ->
- b && UriManager.eq uri1 uri2 && aux t1 t2
- ) true exp_named_subst1 exp_named_subst2
- with
- Invalid_argument _ -> false
- in
- aux
-;;
-
-exception WhatAndWithWhatDoNotHaveTheSameLength;;
-
-(* "textual" replacement of several subterms with other ones *)
-let replace ~equality ~what ~with_what ~where =
- let module C = Cic in
- 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,t) -> C.LetIn (n, aux s, 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 a term a term with another one. *)
-(* Lifting are performed as usual. *)
-let replace_lifting ~equality ~what ~with_what ~where =
- let module C = Cic in
- let module S = CicSubstitution in
- let find_image what 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 what t =
- try
- S.lift (k-1) (find_image 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 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 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 what te, substaux k what ty)
- | C.Prod (n,s,t) ->
- C.Prod
- (n, substaux k what s, substaux (k + 1) (List.map (S.lift 1) what) t)
- | C.Lambda (n,s,t) ->
- C.Lambda
- (n, substaux k what s, substaux (k + 1) (List.map (S.lift 1) what) t)
- | C.LetIn (n,s,t) ->
- C.LetIn
- (n, substaux k what s, substaux (k + 1) (List.map (S.lift 1) what) t)
- | C.Appl (he::tl) ->
- (* Invariant: no Appl applied to another Appl *)
- let tl' = List.map (substaux k what) tl in
- begin
- match substaux k 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 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 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 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 what outt, substaux k what t,
- List.map (substaux k what) pl)
- | C.Fix (i,fl) ->
- let len = List.length fl in
- let substitutedfl =
- List.map
- (fun (name,i,ty,bo) ->
- (name, i, substaux k what ty,
- substaux (k+len) (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) ->
- (name, substaux k what ty,
- substaux (k+len) (List.map (S.lift len) what) bo)
- ) fl
- in
- C.CoFix (i, substitutedfl)
- in
- substaux 1 what where
-;;
-
-(* replaces in a term a list of terms with other ones. *)
-(* Lifting are performed as usual. *)
-let replace_lifting_csc nnn ~equality ~what ~with_what ~where =
- let module C = Cic in
- let module S = CicSubstitution in
- 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,t) ->
- C.LetIn (n, substaux k s, 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
-;;
-
-(* Takes a well-typed term and fully reduces it. *)
-(*CSC: It does not perform reduction in a Case *)
-let reduce context =
- let rec reduceaux context l =
- let module C = Cic in
- let module S = CicSubstitution in
- function
- C.Rel n as t ->
- (match List.nth context (n-1) with
- Some (_,C.Decl _) -> if l = [] then t else C.Appl (t::l)
- | Some (_,C.Def (bo,_)) -> reduceaux context l (S.lift n bo)
- | None -> raise RelToHiddenHypothesis
- )
- | 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.empty_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 l 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,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.empty_ugraph uri in
- match o with
- C.Constant (_,Some body,_,_,_) ->
- (reduceaux context l
- (CicSubstitution.subst_vars exp_named_subst' body))
- | 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
- (CicSubstitution.subst_vars exp_named_subst' 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) 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.empty_ugraph mutind in
- match o with
- C.InductiveDefinition (tl,_,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.map (function (name,_,ty,_) -> Some (C.Name name, C.Decl ty)) 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.map (function (name,ty,_) -> Some (C.Name name, C.Decl ty)) 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)
- in
- reduceaux context []
-;;
-
-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 =
- (* reduceaux is equal to the reduceaux locally defined inside *)
- (* reduce, but for the const case. *)
- (**** Step 1 ****)
- let rec reduceaux context l =
- let module C = Cic in
- let module S = CicSubstitution in
- 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.empty_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,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.empty_ugraph uri in
- match o with
- C.Constant (_,Some body,_,_,_) ->
- try_delta_expansion context l
- (C.Const (uri,exp_named_subst'))
- (CicSubstitution.subst_vars exp_named_subst' body)
- | 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 (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.empty_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.map (function (name,_,ty,_) -> Some (C.Name name, C.Decl ty)) 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.map (function (name,ty,_) -> Some (C.Name name, C.Decl ty)) 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 try_delta_expansion context l term body =
- let module C = Cic in
- let module S = CicSubstitution in
- 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 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 (=) [simplified_term_to_fold] [term_to_fold] res
- with
- WrongShape ->
- (**** 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)
- | t ->
- let simplified = reduceaux context l t in
- if t = simplified then
- raise AlreadySimplified
- else
- simplified
- 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 []
-;;
-
-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.empty_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.empty_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
-;;
projects / helm.git / blobdiff