--- /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 ->
+ (try
+ match List.nth context (n-1) with
+ Some (_,C.Decl _) -> if l = [] then t else C.Appl (t::l)
+ | Some (_,C.Def (bo,_)) ->
+ try_delta_expansion context l t (S.lift n bo)
+ | None -> raise RelToHiddenHypothesis
+ with
+ Failure _ -> assert false)
+ | 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,_,_,_) ->
+ 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 tys =
+ List.map (function (name,ty,_) -> Some (C.Name name, C.Decl ty)) fl in
+ 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