From f4b01f86f36f3b1ee11f383e3c056a458a76cb96 Mon Sep 17 00:00:00 2001 From: Enrico Tassi Date: Tue, 25 Mar 2008 17:56:20 +0000 Subject: [PATCH] new are_convertible and head_beta_reduce --- .../components/ng_kernel/nCicReduction.ml | 467 ++++-------------- .../components/ng_kernel/nCicReduction.mli | 12 +- 2 files changed, 95 insertions(+), 384 deletions(-) diff --git a/helm/software/components/ng_kernel/nCicReduction.ml b/helm/software/components/ng_kernel/nCicReduction.ml index 5bb6260ca..64133384d 100644 --- a/helm/software/components/ng_kernel/nCicReduction.ml +++ b/helm/software/components/ng_kernel/nCicReduction.ml @@ -1,4 +1,5 @@ -(* ||M|| This file is part of HELM, an Hypertextual, Electronic +(* + ||M|| This file is part of HELM, an Hypertextual, Electronic ||A|| Library of Mathematics, developed at the Computer Science ||T|| Department, University of Bologna, Italy. ||I|| @@ -497,27 +498,21 @@ let whd = profiler_whd.HExtlib.profile (whd ~delta ~subst context) t *) -(* - - (* mimic ocaml (<< 3.08) "=" behaviour. Tests physical equality first then - * fallbacks to structural equality *) +(* mimic ocaml (<< 3.08) "=" behaviour. Tests physical equality first then + * fallbacks to structural equality *) let (===) x y = Pervasives.compare x y = 0 ;; module C = NCic (* t1, t2 must be well-typed *) let are_convertible whd ?(subst=[]) ?(metasenv=[]) = - let heuristic = ref true in let rec aux test_equality_only context t1 t2 = let rec aux2 test_equality_only t1 t2 = if t1 === t2 then true else match (t1,t2) with - | (C.Rel n1, C.Rel n2) -> n1 = n2 - | (C.Sort (C.Type a), C.Sort (C.Type b)) -> a <= b - | (C.Sort (C.Type a), C.Sort (C.Type b)) when test_equality_only -> a=b | (C.Sort s1,C.Sort (C.Type _)) -> (not test_equality_only) | (C.Sort s1, C.Sort s2) -> s1 = s2 @@ -525,379 +520,99 @@ let are_convertible whd ?(subst=[]) ?(metasenv=[]) = aux true context s1 s2 && aux test_equality_only ((name1, C.Decl s1)::context) t1 t2 | (C.Lambda (name1,s1,t1), C.Lambda(_,s2,t2)) -> - aux test_equality_only context s1 s2 && (* sure?! *) - aux test_equality_only ((name1, C.Decl s1)::context) t1 t2 - - | (C.Meta (n1,l1), C.Meta (n2,l2)) -> - if n1 = n2 then - let b2, ugraph1 = - let l1 = CicUtil.clean_up_local_context subst metasenv n1 l1 in - let l2 = CicUtil.clean_up_local_context subst metasenv n2 l2 in - List.fold_left2 - (fun (b,ugraph) t1 t2 -> - if b then - match t1,t2 with - None,_ - | _,None -> true,ugraph - | Some t1',Some t2' -> - aux test_equality_only context t1' t2' ugraph - else - false,ugraph - ) (true,ugraph) l1 l2 - in - if b2 then true,ugraph1 else false,ugraph - else - false,ugraph - | C.Meta (n1,l1), _ -> - (try - let _,term,_ = NCicUtils.lookup_subst n1 subst in - let term' = CicSubstitution.subst_meta l1 term in - aux test_equality_only context term' t2 ugraph - with CicUtil.Subst_not_found _ -> false,ugraph) - | _, C.Meta (n2,l2) -> - (try - let _,term,_ = CicUtil.lookup_subst n2 subst in - let term' = CicSubstitution.subst_meta l2 term in - aux test_equality_only context t1 term' ugraph - with CicUtil.Subst_not_found _ -> false,ugraph) - | (C.LetIn (name1,s1,t1), C.LetIn(_,s2,t2)) -> - let b',ugraph' = aux test_equality_only context s1 s2 ugraph in - if b' then - aux test_equality_only - ((Some (name1, (C.Def (s1,None))))::context) t1 t2 ugraph' - else - false,ugraph - | (C.Appl l1, C.Appl l2) -> - (try - List.fold_right2 - (fun x y (b,ugraph) -> - if b then - aux test_equality_only context x y ugraph - else - false,ugraph) l1 l2 (true,ugraph) - with - Invalid_argument _ -> false,ugraph - ) - | (C.Const (uri1,exp_named_subst1), C.Const (uri2,exp_named_subst2)) -> - let b' = U.eq uri1 uri2 in - if b' then - (try - List.fold_right2 - (fun (uri1,x) (uri2,y) (b,ugraph) -> - if b && U.eq uri1 uri2 then - aux test_equality_only context x y ugraph - else - false,ugraph - ) exp_named_subst1 exp_named_subst2 (true,ugraph) - with - Invalid_argument _ -> false,ugraph - ) - else - false,ugraph - | (C.MutInd (uri1,i1,exp_named_subst1), - C.MutInd (uri2,i2,exp_named_subst2) - ) -> - let b' = U.eq uri1 uri2 && i1 = i2 in - if b' then - (try - List.fold_right2 - (fun (uri1,x) (uri2,y) (b,ugraph) -> - if b && U.eq uri1 uri2 then - aux test_equality_only context x y ugraph - else - false,ugraph - ) exp_named_subst1 exp_named_subst2 (true,ugraph) - with - Invalid_argument _ -> false,ugraph - ) - else - false,ugraph - | (C.MutConstruct (uri1,i1,j1,exp_named_subst1), - C.MutConstruct (uri2,i2,j2,exp_named_subst2) - ) -> - let b' = U.eq uri1 uri2 && i1 = i2 && j1 = j2 in - if b' then - (try - List.fold_right2 - (fun (uri1,x) (uri2,y) (b,ugraph) -> - if b && U.eq uri1 uri2 then - aux test_equality_only context x y ugraph - else - false,ugraph - ) exp_named_subst1 exp_named_subst2 (true,ugraph) - with - Invalid_argument _ -> false,ugraph - ) - else - false,ugraph - | (C.MutCase (uri1,i1,outtype1,term1,pl1), - C.MutCase (uri2,i2,outtype2,term2,pl2)) -> - let b' = U.eq uri1 uri2 && i1 = i2 in - if b' then - let b'',ugraph''=aux test_equality_only context - outtype1 outtype2 ugraph in - if b'' then - let b''',ugraph'''= aux test_equality_only context - term1 term2 ugraph'' in - List.fold_right2 - (fun x y (b,ugraph) -> - if b then - aux test_equality_only context x y ugraph - else - false,ugraph) - pl1 pl2 (b''',ugraph''') - else - false,ugraph - else - false,ugraph - | (C.Fix (i1,fl1), C.Fix (i2,fl2)) -> - let tys,_ = - List.fold_left - (fun (types,len) (n,_,ty,_) -> - (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types, - len+1) - ) ([],0) fl1 - in - if i1 = i2 then - List.fold_right2 - (fun (_,recindex1,ty1,bo1) (_,recindex2,ty2,bo2) (b,ugraph) -> - if b && recindex1 = recindex2 then - let b',ugraph' = aux test_equality_only context ty1 ty2 - ugraph in - if b' then - aux test_equality_only (tys@context) bo1 bo2 ugraph' - else - false,ugraph - else - false,ugraph) - fl1 fl2 (true,ugraph) - else - false,ugraph - | (C.CoFix (i1,fl1), C.CoFix (i2,fl2)) -> - let tys,_ = - List.fold_left - (fun (types,len) (n,ty,_) -> - (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types, - len+1) - ) ([],0) fl1 - in - if i1 = i2 then - List.fold_right2 - (fun (_,ty1,bo1) (_,ty2,bo2) (b,ugraph) -> - if b then - let b',ugraph' = aux test_equality_only context ty1 ty2 - ugraph in - if b' then - aux test_equality_only (tys@context) bo1 bo2 ugraph' - else - false,ugraph - else - false,ugraph) - fl1 fl2 (true,ugraph) - else - false,ugraph - | C.Cast (bo,_),t -> aux2 test_equality_only bo t ugraph - | t,C.Cast (bo,_) -> aux2 test_equality_only t bo ugraph - | (C.Implicit _, _) | (_, C.Implicit _) -> assert false - | (_,_) -> false,ugraph + aux true context s1 s2 && + aux true ((name1, C.Decl s1)::context) t1 t2 + | (C.LetIn (name1,ty1,s1,t1), C.LetIn(_,ty2,s2,t2)) -> + aux test_equality_only context ty1 ty2 && + aux test_equality_only context s1 s2 && + aux test_equality_only ((name1, C.Def (s1,ty1))::context) t1 t2 + + | (C.Meta (n1,(s1, C.Irl i1)), C.Meta (n2,(s2, C.Irl i2))) + when n1 = n2 && s1 = s2 -> true + | (C.Meta (n1,(s1, l1)), C.Meta (n2,(s2, l2))) when n1 = n2 -> + let l1 = NCicUtils.expand_local_context l1 in + let l2 = NCicUtils.expand_local_context l2 in + (try List.for_all2 + (fun t1 t2 -> aux test_equality_only context + (NCicSubstitution.lift s1 t1) + (NCicSubstitution.lift s2 t2)) + l1 l2 + with Invalid_argument _ -> false) + + | C.Meta (n1,l1), _ -> + (try + let _,_,term,_ = NCicUtils.lookup_subst n1 subst in + let term = NCicSubstitution.subst_meta l1 term in + aux test_equality_only context term t2 + with NCicUtils.Subst_not_found _ -> false) + | _, C.Meta (n2,l2) -> + (try + let _,_,term,_ = NCicUtils.lookup_subst n2 subst in + let term = NCicSubstitution.subst_meta l2 term in + aux test_equality_only context t1 term + with NCicUtils.Subst_not_found _ -> false) + + | (C.Appl l1, C.Appl l2) -> + (try List.for_all2 (aux test_equality_only context) l1 l2 + with Invalid_argument _ -> false) + + | (C.Match (ref1,outtype1,term1,pl1), + C.Match (ref2,outtype2,term2,pl2)) -> + NReference.eq ref1 ref2 && + aux test_equality_only context outtype1 outtype2 && + aux test_equality_only context term1 term2 && + (try List.for_all2 (aux test_equality_only context) pl1 pl2 + with Invalid_argument _ -> false) + + | (C.Implicit _, _) | (_, C.Implicit _) -> assert false + | (_,_) -> false in - let res = - if !heuristic then - aux2 test_equality_only t1 t2 ugraph - else - false,ugraph - in - if fst res = true then - res - else -begin -(*if !heuristic then prerr_endline ("NON FACILE: " ^ CicPp.ppterm t1 ^ " <===> " ^ CicPp.ppterm t2);*) - (* heuristic := false; *) - debug t1 [t2] "PREWHD"; -(*prerr_endline ("PREWHD: " ^ CicPp.ppterm t1 ^ " <===> " ^ CicPp.ppterm t2);*) -(* -prerr_endline ("PREWHD: " ^ CicPp.ppterm t1 ^ " <===> " ^ CicPp.ppterm t2); - let t1' = whd ?delta:(Some true) ?subst:(Some subst) context t1 in - let t2' = whd ?delta:(Some true) ?subst:(Some subst) context t2 in - debug t1' [t2'] "POSTWHD"; -*) -let rec convert_machines ugraph = - function - [] -> true,ugraph - | ((k1,env1,ens1,h1,s1),(k2,env2,ens2,h2,s2))::tl -> - let (b,ugraph) as res = - aux2 test_equality_only - (R.unwind (k1,env1,ens1,h1,[])) (R.unwind (k2,env2,ens2,h2,[])) ugraph + if aux2 test_equality_only t1 t2 then + true + else + let rec convert_machines = function + | [] -> true + | ((k1,env1,h1,s1),(k2,env2,h2,s2))::tl -> + aux2 test_equality_only + (R.unwind (k1,env1,h1,[])) (R.unwind (k2,env2,h2,[])) && + let problems = + let red_stack = + List.map + (fun si-> R.reduce ~delta:0 ~subst context(RS.from_stack si)) + in + try Some (List.combine (red_stack s1) (red_stack s2) @ tl) + with Invalid_argument _ -> None + in + match problems with + | None -> false + | Some problems -> convert_machines problems in - if b then - let problems = - try - Some - (List.combine - (List.map - (fun si-> R.reduce ~delta:false ~subst context(RS.from_stack si)) - s1) - (List.map - (fun si-> R.reduce ~delta:false ~subst context(RS.from_stack si)) - s2) - @ tl) - with - Invalid_argument _ -> None - in - match problems with - None -> false,ugraph - | Some problems -> convert_machines ugraph problems - else - res -in - convert_machines ugraph - [R.reduce ~delta:true ~subst context (0,[],[],t1,[]), - R.reduce ~delta:true ~subst context (0,[],[],t2,[])] -(*prerr_endline ("POSTWH: " ^ CicPp.ppterm t1' ^ " <===> " ^ CicPp.ppterm t2');*) -(* - aux2 test_equality_only t1' t2' ugraph -*) -end + convert_machines + [R.reduce ~delta:0 ~subst context (0,[],t1,[]), + R.reduce ~delta:0 ~subst context (0,[],t2,[])] in - aux false (*c t1 t2 ugraph *) + aux false ;; -*) -(* {{{ DEBUGGING ONLY -let whd ?(delta=true) ?(subst=[]) context t = - let res = whd ~delta ~subst context t in - let rescsc = CicReductionNaif.whd ~delta ~subst context t in - if not (fst (are_convertible CicReductionNaif.whd ~subst context res rescsc CicUniv.empty_ugraph)) then - begin - debug_print (lazy ("PRIMA: " ^ CicPp.ppterm t)) ; - flush stderr ; - debug_print (lazy ("DOPO: " ^ CicPp.ppterm res)) ; - flush stderr ; - debug_print (lazy ("CSC: " ^ CicPp.ppterm rescsc)) ; - flush stderr ; -fdebug := 0 ; -let _ = are_convertible CicReductionNaif.whd ~subst context res rescsc CicUniv.empty_ugraph in - assert false ; - end - else - res +let are_convertible = are_convertible whd + +let rec head_beta_reduce ?(delta=max_int) ?(upto=(-1)) t l = + match upto, t, l with + | 0, C.Appl l1, _ -> C.Appl (l1 @ l) + | 0, t, [] -> t + | 0, t, _ -> C.Appl (t::l) + | _, C.Appl (hd::tl), _ -> head_beta_reduce ~delta ~upto hd (tl @ l) + | _, C.Lambda(_,_,bo), arg::tl -> + let bo = NCicSubstitution.subst arg bo in + head_beta_reduce ~delta ~upto:(upto - 1) bo tl + | _, C.Const (NReference.Ref (height, _, NReference.Def) as re), _ + when delta <= height -> + let _, _, bo, _, _, _ = NCicEnvironment.get_checked_def re in + head_beta_reduce ~upto ~delta bo l + | _, t, [] -> t + | _, t, _ -> C.Appl (t::l) ;; - }}} *) - -(*let are_convertible = are_convertible whd*) -(* {{{ let profiler_other_whd = HExtlib.profile ~enable:profile "~are_convertible.whd" -let whd ?(delta=true) ?(subst=[]) context t = - let foo () = - whd ~delta ~subst context t - in - profiler_other_whd.HExtlib.profile foo () - }}} *) - -(* {{{ let rec normalize ?(delta=true) ?(subst=[]) ctx term = - let module C = Cic in - let t = whd ~delta ~subst ctx term in - let aux = normalize ~delta ~subst in - let decl name t = Some (name, C.Decl t) in - match t with - | C.Rel n -> t - | C.Var (uri,exp_named_subst) -> - C.Var (uri, List.map (fun (n,t) -> n,aux ctx t) exp_named_subst) - | C.Meta (i,l) -> - C.Meta (i,List.map (function Some t -> Some (aux ctx t) | None -> None) l) - | C.Sort _ -> t - | C.Implicit _ -> t - | C.Cast (te,ty) -> C.Cast (aux ctx te, aux ctx ty) - | C.Prod (n,s,t) -> - let s' = aux ctx s in - C.Prod (n, s', aux ((decl n s')::ctx) t) - | C.Lambda (n,s,t) -> - let s' = aux ctx s in - C.Lambda (n, s', aux ((decl n s')::ctx) t) - | C.LetIn (n,s,t) -> - (* the term is already in weak head normal form *) - assert false - | C.Appl (h::l) -> C.Appl (h::(List.map (aux ctx) l)) - | C.Appl [] -> assert false - | C.Const (uri,exp_named_subst) -> - C.Const (uri, List.map (fun (n,t) -> n,aux ctx t) exp_named_subst) - | C.MutInd (uri,typeno,exp_named_subst) -> - C.MutInd (uri,typeno, List.map (fun (n,t) -> n,aux ctx t) exp_named_subst) - | C.MutConstruct (uri,typeno,consno,exp_named_subst) -> - C.MutConstruct (uri, typeno, consno, - List.map (fun (n,t) -> n,aux ctx t) exp_named_subst) - | C.MutCase (sp,i,outt,t,pl) -> - C.MutCase (sp,i, aux ctx outt, aux ctx t, List.map (aux ctx) pl) -(*CSC: to be completed, I suppose *) - | C.Fix _ -> t - | C.CoFix _ -> t - -let normalize ?delta ?subst ctx term = -(* prerr_endline ("NORMALIZE:" ^ CicPp.ppterm term); *) - let t = normalize ?delta ?subst ctx term in -(* prerr_endline ("NORMALIZED:" ^ CicPp.ppterm t); *) - t - }}} *) - -(* {{{ performs an head beta/cast reduction -let rec head_beta_reduce ?(delta=false) ?(upto=(-1)) t = - match upto with - 0 -> t - | n -> - match t with - (Cic.Appl (Cic.Lambda (_,_,t)::he'::tl')) -> - let he'' = CicSubstitution.subst he' t in - if tl' = [] then - he'' - else - let he''' = - match he'' with - Cic.Appl l -> Cic.Appl (l@tl') - | _ -> Cic.Appl (he''::tl') - in - head_beta_reduce ~delta ~upto:(upto - 1) he''' - | Cic.Cast (te,_) -> head_beta_reduce ~delta ~upto te - | Cic.Appl (Cic.Const (uri,ens)::tl) as t when delta=true -> - let bo = - match fst (CicEnvironment.get_cooked_obj CicUniv.empty_ugraph uri) with - Cic.Constant (_,bo,_,_,_) -> bo - | Cic.Variable _ -> raise ReferenceToVariable - | Cic.CurrentProof (_,_,bo,_,_,_) -> Some bo - | Cic.InductiveDefinition _ -> raise ReferenceToInductiveDefinition - in - (match bo with - None -> t - | Some bo -> - head_beta_reduce ~upto - ~delta (Cic.Appl ((CicSubstitution.subst_vars ens bo)::tl))) - | Cic.Const (uri,ens) as t when delta=true -> - let bo = - match fst (CicEnvironment.get_cooked_obj CicUniv.empty_ugraph uri) with - Cic.Constant (_,bo,_,_,_) -> bo - | Cic.Variable _ -> raise ReferenceToVariable - | Cic.CurrentProof (_,_,bo,_,_,_) -> Some bo - | Cic.InductiveDefinition _ -> raise ReferenceToInductiveDefinition - in - (match bo with - None -> t - | Some bo -> - head_beta_reduce ~delta ~upto (CicSubstitution.subst_vars ens bo)) - | t -> t - }}} *) - -(* {{{ -let are_convertible ?subst ?metasenv context t1 t2 ugraph = - let before = Unix.gettimeofday () in - let res = are_convertible ?subst ?metasenv context t1 t2 ugraph in - let after = Unix.gettimeofday () in - let diff = after -. before in - if diff > 0.1 then - begin - let nc = List.map (function None -> None | Some (n,_) -> Some n) context in - prerr_endline - ("\n#(" ^ string_of_float diff ^ "):\n" ^ CicPp.pp t1 nc ^ "\n<=>\n" ^ CicPp.pp t2 nc); - end; - res - }}} *) +let head_beta_reduce ?delta ?upto t = head_beta_reduce ?delta ?upto t [];; (* vim:set foldmethod=marker: *) diff --git a/helm/software/components/ng_kernel/nCicReduction.mli b/helm/software/components/ng_kernel/nCicReduction.mli index 3677944bd..a45d8422f 100644 --- a/helm/software/components/ng_kernel/nCicReduction.mli +++ b/helm/software/components/ng_kernel/nCicReduction.mli @@ -28,10 +28,9 @@ exception ReferenceToConstant exception ReferenceToVariable exception ReferenceToCurrentProof exception ReferenceToInductiveDefinition -(* -val fdebug : int ref + val whd : - ?delta:bool -> ?subst:NCic.substitution -> + ?delta:int -> ?subst:NCic.substitution -> NCic.context -> NCic.term -> NCic.term @@ -39,11 +38,8 @@ val are_convertible : ?subst:NCic.substitution -> ?metasenv:NCic.metasenv -> NCic.context -> NCic.term -> NCic.term -> bool -val normalize: - ?delta:bool -> ?subst:Cic.substitution -> Cic.context -> Cic.term -> Cic.term - + (* performs head beta/(delta)/cast reduction; the default is to not perform delta reduction; if provided, ~upto is the maximum number of beta redexes reduced *) -val head_beta_reduce: ?delta:bool -> ?upto:int -> Cic.term -> Cic.term -*) +val head_beta_reduce: ?delta:int -> ?upto:int -> NCic.term -> NCic.term -- 2.39.2