--- /dev/null
+(* Copyright (C) 2004, 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://helm.cs.unibo.it/
+ *)
+
+(* $Id$ *)
+
+module C = Cic
+
+exception Meta_not_found of int
+exception Subst_not_found of int
+
+let lookup_meta index metasenv =
+ try
+ List.find (fun (index', _, _) -> index = index') metasenv
+ with Not_found -> raise (Meta_not_found index)
+
+let lookup_subst n subst =
+ try
+ List.assoc n subst
+ with Not_found -> raise (Subst_not_found n)
+
+let exists_meta index = List.exists (fun (index', _, _) -> (index = index'))
+
+(* clean_up_meta take a substitution, a metasenv a meta_inex and a local
+context l and clean up l with respect to the hidden hipothesis in the
+canonical context *)
+
+let clean_up_local_context subst metasenv n l =
+ let cc =
+ (try
+ let (cc,_,_) = lookup_subst n subst in cc
+ with Subst_not_found _ ->
+ try
+ let (_,cc,_) = lookup_meta n metasenv in cc
+ with Meta_not_found _ -> assert false) in
+ (try
+ List.map2
+ (fun t1 t2 ->
+ match t1,t2 with
+ None , _ -> None
+ | _ , t -> t) cc l
+ with
+ Invalid_argument _ ->
+ assert false)
+
+let is_closed =
+ let module C = Cic in
+ let rec is_closed k =
+ function
+ C.Rel m when m > k -> false
+ | C.Rel m -> true
+ | C.Meta (_,l) ->
+ List.fold_left
+ (fun i t -> i && (match t with None -> true | Some t -> is_closed k t)
+ ) true l
+ | C.Sort _ -> true
+ | C.Implicit _ -> assert false
+ | C.Cast (te,ty) -> is_closed k te && is_closed k ty
+ | C.Prod (name,so,dest) -> is_closed k so && is_closed (k+1) dest
+ | C.Lambda (_,so,dest) -> is_closed k so && is_closed (k+1) dest
+ | C.LetIn (_,so,ty,dest) ->
+ is_closed k so && is_closed k ty && is_closed (k+1) dest
+ | C.Appl l ->
+ List.fold_right (fun x i -> i && is_closed k x) l true
+ | C.Var (_,exp_named_subst)
+ | C.Const (_,exp_named_subst)
+ | C.MutInd (_,_,exp_named_subst)
+ | C.MutConstruct (_,_,_,exp_named_subst) ->
+ List.fold_right (fun (_,x) i -> i && is_closed k x)
+ exp_named_subst true
+ | C.MutCase (_,_,out,te,pl) ->
+ is_closed k out && is_closed k te &&
+ List.fold_right (fun x i -> i && is_closed k x) pl true
+ | C.Fix (_,fl) ->
+ let len = List.length fl in
+ let k_plus_len = k + len in
+ List.fold_right
+ (fun (_,_,ty,bo) i -> i && is_closed k ty && is_closed k_plus_len bo
+ ) fl true
+ | C.CoFix (_,fl) ->
+ let len = List.length fl in
+ let k_plus_len = k + len in
+ List.fold_right
+ (fun (_,ty,bo) i -> i && is_closed k ty && is_closed k_plus_len bo
+ ) fl true
+in
+ is_closed 0
+;;
+
+let rec is_meta_closed =
+ function
+ C.Rel _ -> true
+ | C.Meta _ -> false
+ | C.Sort _ -> true
+ | C.Implicit _ -> assert false
+ | C.Cast (te,ty) -> is_meta_closed te && is_meta_closed ty
+ | C.Prod (name,so,dest) -> is_meta_closed so && is_meta_closed dest
+ | C.Lambda (_,so,dest) -> is_meta_closed so && is_meta_closed dest
+ | C.LetIn (_,so,ty,dest) ->
+ is_meta_closed so &&
+ is_meta_closed ty &&
+ is_meta_closed dest
+ | C.Appl l ->
+ not (List.exists (fun x -> not (is_meta_closed x)) l)
+ | C.Var (_,exp_named_subst)
+ | C.Const (_,exp_named_subst)
+ | C.MutInd (_,_,exp_named_subst)
+ | C.MutConstruct (_,_,_,exp_named_subst) ->
+ not (List.exists (fun (_,x) -> not (is_meta_closed x)) exp_named_subst)
+ | C.MutCase (_,_,out,te,pl) ->
+ is_meta_closed out && is_meta_closed te &&
+ not (List.exists (fun x -> not (is_meta_closed x)) pl)
+ | C.Fix (_,fl) ->
+ not (List.exists
+ (fun (_,_,ty,bo) ->
+ not (is_meta_closed ty) || not (is_meta_closed bo))
+ fl)
+ | C.CoFix (_,fl) ->
+ not (List.exists
+ (fun (_,ty,bo) ->
+ not (is_meta_closed ty) || not (is_meta_closed bo))
+ fl)
+;;
+
+let xpointer_RE = Str.regexp "\\([^#]+\\)#xpointer(\\(.*\\))"
+let slash_RE = Str.regexp "/"
+
+let term_of_uri uri =
+ let s = UriManager.string_of_uri uri in
+ try
+ (if UriManager.uri_is_con uri then
+ C.Const (uri, [])
+ else if UriManager.uri_is_var uri then
+ C.Var (uri, [])
+ else if not (Str.string_match xpointer_RE s 0) then
+ raise (UriManager.IllFormedUri s)
+ else
+ let (baseuri,xpointer) = (Str.matched_group 1 s, Str.matched_group 2 s) in
+ let baseuri = UriManager.uri_of_string baseuri in
+ (match Str.split slash_RE xpointer with
+ | [_; tyno] -> C.MutInd (baseuri, int_of_string tyno - 1, [])
+ | [_; tyno; consno] ->
+ C.MutConstruct
+ (baseuri, int_of_string tyno - 1, int_of_string consno, [])
+ | _ -> raise Exit))
+ with
+ | Exit
+ | Failure _
+ | Not_found -> raise (UriManager.IllFormedUri s)
+
+let uri_of_term = function
+ | C.Const (uri, _)
+ | C.Var (uri, _) -> uri
+ | C.MutInd (baseuri, tyno, _) ->
+ UriManager.uri_of_string
+ (Printf.sprintf "%s#xpointer(1/%d)" (UriManager.string_of_uri baseuri) (tyno+1))
+ | C.MutConstruct (baseuri, tyno, consno, _) ->
+ UriManager.uri_of_string
+ (Printf.sprintf "%s#xpointer(1/%d/%d)" (UriManager.string_of_uri baseuri)
+ (tyno + 1) consno)
+ | _ -> raise (Invalid_argument "uri_of_term")
+
+
+(*
+let pack terms =
+ List.fold_right
+ (fun term acc -> C.Prod (C.Anonymous, term, acc))
+ terms (C.Sort (C.Type (CicUniv.fresh ())))
+
+let rec unpack = function
+ | C.Prod (C.Anonymous, term, C.Sort (C.Type _)) -> [term]
+ | C.Prod (C.Anonymous, term, tgt) -> term :: unpack tgt
+ | _ -> assert false
+*)
+
+let rec strip_prods n = function
+ | t when n = 0 -> t
+ | C.Prod (_, _, tgt) when n > 0 -> strip_prods (n-1) tgt
+ | _ -> failwith "not enough prods"
+
+let params_of_obj = function
+ | C.Constant (_, _, _, params, _)
+ | C.Variable (_, _, _, params, _)
+ | C.CurrentProof (_, _, _, _, params, _)
+ | C.InductiveDefinition (_, params, _, _) ->
+ params
+
+let attributes_of_obj = function
+ | C.Constant (_, _, _, _, attributes)
+ | C.Variable (_, _, _, _, attributes)
+ | C.CurrentProof (_, _, _, _, _, attributes)
+ | C.InductiveDefinition (_, _, _, attributes) ->
+ attributes
+
+let is_generated obj = List.exists ((=) `Generated) (attributes_of_obj obj)
+
+let arity_of_composed_coercion obj =
+ let attrs = attributes_of_obj obj in
+ try
+ let tag=List.find (function `Class (`Coercion _) -> true|_->false) attrs in
+ match tag with
+ | `Class (`Coercion n) -> n
+ | _-> assert false
+ with Not_found -> 0
+;;
+
+let projections_of_record obj uri =
+ let attrs = attributes_of_obj obj in
+ try
+ let tag=List.find (function `Class (`Record _) -> true|_->false) attrs in
+ match tag with
+ | `Class (`Record l) ->
+ List.map (fun (name,_,_) ->
+ let buri = UriManager.buri_of_uri uri in
+ let puri = UriManager.uri_of_string (buri ^ "/" ^ name ^ ".con") in
+ puri) l
+ | _-> assert false
+ with Not_found -> []
+;;
+
+let rec mk_rels howmany from =
+ match howmany with
+ | 0 -> []
+ | _ -> (C.Rel (howmany + from)) :: (mk_rels (howmany-1) from)
+
+let id_of_annterm =
+ function
+ | C.ARel (id,_,_,_)
+ | C.AVar (id,_,_)
+ | C.AMeta (id,_,_)
+ | C.ASort (id,_)
+ | C.AImplicit (id,_)
+ | C.ACast (id,_,_)
+ | C.AProd (id,_,_,_)
+ | C.ALambda (id,_,_,_)
+ | C.ALetIn (id,_,_,_,_)
+ | C.AAppl (id,_)
+ | C.AConst (id,_,_)
+ | C.AMutInd (id,_,_,_)
+ | C.AMutConstruct (id,_,_,_,_)
+ | C.AMutCase (id,_,_,_,_,_)
+ | C.AFix (id,_,_)
+ | C.ACoFix (id,_,_) -> id
+
+
+let rec rehash_term =
+ let module C = Cic in
+ let recons uri = UriManager.uri_of_string (UriManager.string_of_uri uri) in
+ function
+ | (C.Rel _) as t -> t
+ | C.Var (uri,exp_named_subst) ->
+ let uri' = recons uri in
+ let exp_named_subst' =
+ List.map
+ (function (uri,t) ->(recons uri,rehash_term 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 (rehash_term t)
+ ) l
+ in
+ C.Meta(i,l')
+ | C.Sort (C.Type u) ->
+ CicUniv.assert_univ u;
+ C.Sort (C.Type (CicUniv.recons_univ u))
+ | C.Sort _ as t -> t
+ | C.Implicit _ as t -> t
+ | C.Cast (te,ty) -> C.Cast (rehash_term te, rehash_term ty)
+ | C.Prod (n,s,t) -> C.Prod (n, rehash_term s, rehash_term t)
+ | C.Lambda (n,s,t) -> C.Lambda (n, rehash_term s, rehash_term t)
+ | C.LetIn (n,s,ty,t) ->
+ C.LetIn (n, rehash_term s, rehash_term ty, rehash_term t)
+ | C.Appl l -> C.Appl (List.map rehash_term l)
+ | C.Const (uri,exp_named_subst) ->
+ let uri' = recons uri in
+ let exp_named_subst' =
+ List.map
+ (function (uri,t) -> (recons uri,rehash_term t)) exp_named_subst
+ in
+ C.Const (uri',exp_named_subst')
+ | C.MutInd (uri,tyno,exp_named_subst) ->
+ let uri' = recons uri in
+ let exp_named_subst' =
+ List.map
+ (function (uri,t) -> (recons uri,rehash_term t)) exp_named_subst
+ in
+ C.MutInd (uri',tyno,exp_named_subst')
+ | C.MutConstruct (uri,tyno,consno,exp_named_subst) ->
+ let uri' = recons uri in
+ let exp_named_subst' =
+ List.map
+ (function (uri,t) -> (recons uri,rehash_term t)) exp_named_subst
+ in
+ C.MutConstruct (uri',tyno,consno,exp_named_subst')
+ | C.MutCase (uri,i,outty,t,pl) ->
+ C.MutCase (recons uri, i, rehash_term outty, rehash_term t,
+ List.map rehash_term pl)
+ | C.Fix (i, fl) ->
+ let liftedfl =
+ List.map
+ (fun (name, i, ty, bo) ->
+ (name, i, rehash_term ty, rehash_term bo))
+ fl
+ in
+ C.Fix (i, liftedfl)
+ | C.CoFix (i, fl) ->
+ let liftedfl =
+ List.map
+ (fun (name, ty, bo) -> (name, rehash_term ty, rehash_term bo))
+ fl
+ in
+ C.CoFix (i, liftedfl)
+
+let rehash_obj =
+ let module C = Cic in
+ let recons uri = UriManager.uri_of_string (UriManager.string_of_uri uri) in
+ function
+ C.Constant (name,bo,ty,params,attrs) ->
+ let bo' =
+ match bo with
+ None -> None
+ | Some bo -> Some (rehash_term bo)
+ in
+ let ty' = rehash_term ty in
+ let params' = List.map recons params in
+ C.Constant (name, bo', ty', params',attrs)
+ | C.CurrentProof (name,conjs,bo,ty,params,attrs) ->
+ let conjs' =
+ List.map
+ (function (i,hyps,ty) ->
+ (i,
+ List.map (function
+ None -> None
+ | Some (name,C.Decl t) ->
+ Some (name,C.Decl (rehash_term t))
+ | Some (name,C.Def (bo,ty)) ->
+ Some (name,C.Def (rehash_term bo, rehash_term ty))) hyps,
+ rehash_term ty))
+ conjs
+ in
+ let bo' = rehash_term bo in
+ let ty' = rehash_term ty in
+ let params' = List.map recons params in
+ C.CurrentProof (name, conjs', bo', ty', params',attrs)
+ | C.Variable (name,bo,ty,params,attrs) ->
+ let bo' =
+ match bo with
+ None -> None
+ | Some bo -> Some (rehash_term bo)
+ in
+ let ty' = rehash_term ty in
+ let params' = List.map recons params in
+ C.Variable (name, bo', ty', params',attrs)
+ | C.InductiveDefinition (tl,params,paramsno,attrs) ->
+ let params' = List.map recons params in
+ let tl' =
+ List.map (function (name, inductive, ty, constructors) ->
+ name,
+ inductive,
+ rehash_term ty,
+ (List.map
+ (function (name, ty) -> name, rehash_term ty)
+ constructors))
+ tl
+ in
+ C.InductiveDefinition (tl', params', paramsno, attrs)
+
+let rec metas_of_term = function
+ | C.Meta (i, c) -> [i,c]
+ | C.Var (_, ens)
+ | C.Const (_, ens)
+ | C.MutInd (_, _, ens)
+ | C.MutConstruct (_, _, _, ens) ->
+ List.flatten (List.map (fun (u, t) -> metas_of_term t) ens)
+ | C.Cast (s, t)
+ | C.Prod (_, s, t)
+ | C.Lambda (_, s, t) -> (metas_of_term s) @ (metas_of_term t)
+ | C.LetIn (_, s, ty, t) ->
+ (metas_of_term s) @ (metas_of_term ty) @ (metas_of_term t)
+ | C.Appl l -> List.flatten (List.map metas_of_term l)
+ | C.MutCase (uri, i, s, t, l) ->
+ (metas_of_term s) @ (metas_of_term t) @
+ (List.flatten (List.map metas_of_term l))
+ | C.Fix (i, il) ->
+ List.flatten
+ (List.map (fun (s, i, t1, t2) ->
+ (metas_of_term t1) @ (metas_of_term t2)) il)
+ | C.CoFix (i, il) ->
+ List.flatten
+ (List.map (fun (s, t1, t2) ->
+ (metas_of_term t1) @ (metas_of_term t2)) il)
+ | _ -> []
+;;
+
+module MetaOT = struct
+ type t = int * C.term option list
+ let compare = Pervasives.compare
+end
+
+module S = Set.Make(MetaOT)
+
+let rec metas_of_term_set = function
+ | C.Meta (i, c) -> S.singleton (i,c)
+ | C.Var (_, ens)
+ | C.Const (_, ens)
+ | C.MutInd (_, _, ens)
+ | C.MutConstruct (_, _, _, ens) ->
+ List.fold_left
+ (fun s (_,t) -> S.union s (metas_of_term_set t))
+ S.empty ens
+ | C.Cast (s, t)
+ | C.Prod (_, s, t)
+ | C.Lambda (_, s, t) -> S.union (metas_of_term_set s) (metas_of_term_set t)
+ | C.LetIn (_, s, ty, t) ->
+ S.union (metas_of_term_set s)
+ (S.union (metas_of_term_set ty) (metas_of_term_set t))
+ | C.Appl l ->
+ List.fold_left
+ (fun s t -> S.union s (metas_of_term_set t))
+ S.empty l
+ | C.MutCase (uri, i, s, t, l) ->
+ S.union
+ (S.union (metas_of_term_set s) (metas_of_term_set t))
+ (List.fold_left
+ (fun s t -> S.union s (metas_of_term_set t))
+ S.empty l)
+ | C.Fix (_, il) ->
+ (List.fold_left
+ (fun s (_,_,t1,t2) ->
+ S.union s (S.union (metas_of_term_set t1) (metas_of_term_set t2))))
+ S.empty il
+ | C.CoFix (i, il) ->
+ (List.fold_left
+ (fun s (_,t1,t2) ->
+ S.union s (S.union (metas_of_term_set t1) (metas_of_term_set t2))))
+ S.empty il
+ | _ -> S.empty
+;;
+
+let metas_of_term_set t =
+ let s = metas_of_term_set t in
+ S.elements s
+;;
+
+(* syntactic_equality up to the *)
+(* distinction between fake dependent products *)
+(* and non-dependent products, alfa-conversion *)
+let alpha_equivalence =
+ 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,ty,t), C.LetIn(_,s',ty',t') ->
+ aux s s' && aux ty ty' && aux t t'
+ | C.Appl l, C.Appl l' when List.length l = List.length 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)
+ | C.Meta (i, subst), C.Meta (i', subst') ->
+ i = i' &&
+ (try
+ List.fold_left2
+ (fun b xt xt' -> match xt,xt' with
+ | Some t, Some t' -> b && aux t t'
+ | _ -> b
+ ) true subst subst'
+ with
+ Invalid_argument _ -> false)
+ | C.Appl [t], t' | t, C.Appl [t'] -> assert false
+(* FG: are we _really_ sure of these?
+ | C.Sort (C.Type u), C.Sort (C.Type u') -> u = u'
+ | C.Implicit a, C.Implicit a' -> a = a'
+ we insert an unused variable below to genarate a warning at compile time
+*)
+ | _,_ -> 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
+
+let is_sober t =
+ let rec sober_term g = function
+ | C.Rel _
+ | C.Sort _
+ | C.Implicit _ -> g
+ | C.Const (_, xnss)
+ | C.Var (_, xnss)
+ | C.MutConstruct (_, _, _, xnss)
+ | C.MutInd (_, _, xnss) -> sober_xnss g xnss
+ | C.Meta (_, xss) -> sober_xss g xss
+ | C.Lambda (_, v, t)
+ | C.Prod (_, v, t)
+ | C.Cast (t, v) -> sober_term (sober_term g t) v
+ | C.LetIn (_, v, ty, t) -> sober_term
+ (sober_term (sober_term g t) ty) v
+ | C.Appl []
+ | C.Appl [_] -> fun b -> false
+ | C.Appl ts -> sober_terms g ts
+ | C.MutCase (_, _, t, v, ts) ->
+ sober_terms (sober_term (sober_term g t) v) ts
+ | C.Fix (_, ifs) -> sober_ifs g ifs
+ | C.CoFix (_, cifs) -> sober_cifs g cifs
+ and sober_terms g = List.fold_left sober_term g
+ and sober_xnss g =
+ let map g (_, t) = sober_term g t in
+ List.fold_left map g
+ and sober_xss g =
+ let map g = function
+ | None -> g
+ | Some t -> sober_term g t
+ in
+ List.fold_left map g
+ and sober_ifs g =
+ let map g (_, _, t, v) = sober_term (sober_term g t) v in
+ List.fold_left map g
+ and sober_cifs g =
+ let map g (_, t, v) = sober_term (sober_term g t) v in
+ List.fold_left map g
+ in
+ sober_term (fun b -> b) t true
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