X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Focaml%2Ftactics%2FproofEngineReduction.ml;fp=helm%2Focaml%2Ftactics%2FproofEngineReduction.ml;h=755a098547eb4e6d13c75ed1c807c888727d5151;hb=792b5d29ebae8f917043d9dd226692919b5d6ca1;hp=0000000000000000000000000000000000000000;hpb=a14a8c7637fd0b95e9d4deccb20c6abc98e8f953;p=helm.git diff --git a/helm/ocaml/tactics/proofEngineReduction.ml b/helm/ocaml/tactics/proofEngineReduction.ml new file mode 100644 index 000000000..755a09854 --- /dev/null +++ b/helm/ocaml/tactics/proofEngineReduction.ml @@ -0,0 +1,973 @@ +(* 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 *) +(* 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 +;;