--- /dev/null
+(* Copyright (C) 2000, 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/.
+ *)
+
+exception CicReductionInternalError;;
+exception WrongUriToInductiveDefinition;;
+
+let fdebug = ref 1;;
+let debug t env s =
+ let rec debug_aux t i =
+ let module C = Cic in
+ let module U = UriManager in
+ CicPp.ppobj (C.Variable ("DEBUG", None, t)) ^ "\n" ^ i
+ in
+ if !fdebug = 0 then
+ begin
+ print_endline (s ^ "\n" ^ List.fold_right debug_aux (t::env) "") ;
+ flush stdout
+ end
+;;
+
+exception Impossible of int;;
+exception ReferenceToDefinition;;
+exception ReferenceToAxiom;;
+exception ReferenceToVariable;;
+exception ReferenceToCurrentProof;;
+exception ReferenceToInductiveDefinition;;
+
+type env = Cic.term list;;
+type stack = Cic.term list;;
+type config = int * env * Cic.term * stack;;
+
+(* k is the length of the environment e *)
+(* m is the current depth inside the term *)
+let unwind' m k e t =
+ let module C = Cic in
+ let module S = CicSubstitution in
+ if e = [] & k = 0 then t else
+ let rec unwind_aux m = function
+ C.Rel n as t -> if n <= m then t else
+ let d = try Some (List.nth e (n-m-1))
+ with _ -> None
+ in (match d with
+ Some t' -> if m = 0 then t'
+ else S.lift m t'
+ | None -> C.Rel (n-k))
+ | C.Var _ as t -> t
+ | C.Meta _ as t -> t
+ | C.Sort _ as t -> t
+ | C.Implicit as t -> t
+ | C.Cast (te,ty) -> C.Cast (unwind_aux m te, unwind_aux m ty) (*CSC ??? *)
+ | C.Prod (n,s,t) -> C.Prod (n, unwind_aux m s, unwind_aux (m + 1) t)
+ | C.Lambda (n,s,t) -> C.Lambda (n, unwind_aux m s, unwind_aux (m + 1) t)
+ | C.LetIn (n,s,t) -> C.LetIn (n, unwind_aux m s, unwind_aux (m + 1) t)
+ | C.Appl l -> C.Appl (List.map (unwind_aux m) l)
+ | C.Const _ as t -> t
+ | C.Abst _ as t -> t
+ | C.MutInd _ as t -> t
+ | C.MutConstruct _ as t -> t
+ | C.MutCase (sp,cookingsno,i,outt,t,pl) ->
+ C.MutCase (sp,cookingsno,i,unwind_aux m outt, unwind_aux m t,
+ List.map (unwind_aux m) pl)
+ | C.Fix (i,fl) ->
+ let len = List.length fl in
+ let substitutedfl =
+ List.map
+ (fun (name,i,ty,bo) -> (name, i, unwind_aux m ty, unwind_aux (m+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, unwind_aux m ty, unwind_aux (m+len) bo))
+ fl
+ in
+ C.CoFix (i, substitutedfl)
+ in
+ unwind_aux m t
+ ;;
+
+let unwind =
+ unwind' 0
+;;
+
+let rec reduce : config -> Cic.term =
+ let module C = Cic in
+ let module S = CicSubstitution in
+ function
+ (k, e, (C.Rel n as t), s) -> let d =
+(* prerr_string ("Rel " ^ string_of_int n) ; flush stderr ; *)
+ try Some (List.nth e (n-1))
+ with _ -> None
+ in (match d with
+ Some t' -> reduce (0, [],t',s)
+ | None -> if s = [] then C.Rel (n-k)
+ else C.Appl (C.Rel (n-k)::s))
+ | (k, e, (C.Var uri as t), s) ->
+ (match CicEnvironment.get_cooked_obj uri 0 with
+ C.Definition _ -> raise ReferenceToDefinition
+ | C.Axiom _ -> raise ReferenceToAxiom
+ | C.CurrentProof _ -> raise ReferenceToCurrentProof
+ | C.InductiveDefinition _ -> raise ReferenceToInductiveDefinition
+ | C.Variable (_,None,_) -> if s = [] then t else C.Appl (t::s)
+ | C.Variable (_,Some body,_) -> reduce (0, [], body, s)
+ )
+ | (k, e, (C.Meta _ as t), s) -> if s = [] then t
+ else C.Appl (t::s)
+ | (k, e, (C.Sort _ as t), s) -> t (* s should be empty *)
+ | (k, e, (C.Implicit as t), s) -> t (* s should be empty *)
+ | (k, e, (C.Cast (te,ty) as t), s) -> reduce (k, e,te,s) (* s should be empty *)
+ | (k, e, (C.Prod _ as t), s) -> unwind k e t (* s should be empty *)
+ | (k, e, (C.Lambda (_,_,t) as t'), []) -> unwind k e t'
+ | (k, e, C.Lambda (_,_,t), p::s) ->
+(* prerr_string ("Lambda body: " ^ CicPp.ppterm t) ; flush stderr ; *)
+ reduce (k+1, p::e,t,s)
+ | (k, e, (C.LetIn (_,m,t) as t'), s) -> let m' = reduce (k,e,m,[]) in
+ reduce (k+1, m'::e,t,s)
+ | (k, e, C.Appl [], s) -> raise (Impossible 1)
+ (* this is lazy
+ | (k, e, C.Appl (he::tl), s) -> let tl' = List.map (unwind k e) tl
+ in reduce (k, e, he, (List.append tl' s)) *)
+ (* this is strict *)
+ | (k, e, C.Appl (he::tl), s) ->
+ (* constants are NOT unfolded *)
+ let red = function
+ C.Const _ as t -> t
+ | t -> reduce (k, e,t,[]) in
+ let tl' = List.map red tl in
+ reduce (k, e, he , List.append tl' s)
+(*
+ | (k, e, C.Appl ((C.Lambda _ as he)::tl), s)
+ | (k, e, C.Appl ((C.Const _ as he)::tl), s)
+ | (k, e, C.Appl ((C.MutCase _ as he)::tl), s)
+ | (k, e, C.Appl ((C.Fix _ as he)::tl), s) ->
+(* strict evaluation, but constants are NOT
+ unfolded *)
+ let red = function
+ C.Const _ as t -> t
+ | t -> reduce (k, e,t,[]) in
+ let tl' = List.map red tl in
+ reduce (k, e, he , List.append tl' s)
+ | (k, e, C.Appl l, s) -> C.Appl (List.append (List.map (unwind k e) l) s) *)
+ | (k, e, (C.Const (uri,cookingsno) as t), s) ->
+ (match CicEnvironment.get_cooked_obj uri cookingsno with
+ C.Definition (_,body,_,_) -> reduce (0, [], body, s)
+ (* constants are closed *)
+ | C.Axiom _ -> if s = [] then t else C.Appl (t::s)
+ | C.Variable _ -> raise ReferenceToVariable
+ | C.CurrentProof (_,_,body,_) -> reduce (0, [], body, s)
+ | C.InductiveDefinition _ -> raise ReferenceToInductiveDefinition
+ )
+ | (k, e, (C.Abst _ as t), s) -> t (* s should be empty ????? *)
+ | (k, e, (C.MutInd (uri,_,_) as t),s) -> let t' = unwind k e t in
+ if s = [] then t' else C.Appl (t'::s)
+ | (k, e, (C.MutConstruct (uri,_,_,_) as t),s) ->
+ let t' = unwind k e t in
+ if s = [] then t' else C.Appl (t'::s)
+ | (k, e, (C.MutCase (mutind,cookingsno,i,_,term,pl) as t),s) ->
+ let decofix =
+ function
+ C.CoFix (i,fl) as t ->
+ 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
+ reduce (0,[],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
+ reduce (0,[], body', tl)
+ | t -> t
+ in
+ (match decofix (reduce (k, e,term,[])) with
+ C.MutConstruct (_,_,_,j) -> reduce (k, e, (List.nth pl (j-1)), s)
+ | C.Appl (C.MutConstruct (_,_,_,j) :: tl) ->
+ let (arity, r, num_ingredients) =
+ match CicEnvironment.get_obj mutind with
+ C.InductiveDefinition (tl,ingredients,r) ->
+ let (_,_,arity,_) = List.nth tl i
+ and num_ingredients =
+ List.fold_right
+ (fun (k,l) i ->
+ if k < cookingsno then i + List.length l else i
+ ) ingredients 0
+ in
+ (arity,r,num_ingredients)
+ | _ -> raise WrongUriToInductiveDefinition
+ in
+ let ts =
+ let num_to_eat = r + num_ingredients in
+ 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 (num_to_eat,tl)
+ in
+ reduce (k, e, (List.nth pl (j-1)),(ts@s))
+ | C.Abst _| C.Cast _ | C.Implicit ->
+ raise (Impossible 2) (* we don't trust our whd ;-) *)
+ | _ -> let t' = unwind k e t in
+ if s = [] then t' else C.Appl (t'::s)
+ )
+ | (k, e, (C.Fix (i,fl) as t), s) ->
+ let (_,recindex,_,body) = List.nth fl i in
+ let recparam =
+ try
+ Some (List.nth s recindex)
+ with
+ _ -> None
+ in
+ (match recparam with
+ Some recparam ->
+ (match reduce (0,[],recparam,[]) with
+ (* match recparam with *)
+ C.MutConstruct _
+ | C.Appl ((C.MutConstruct _)::_) ->
+ (* OLD
+ let body' =
+ let counter = ref (List.length fl) in
+ List.fold_right
+ (fun _ -> decr counter ; S.subst (C.Fix (!counter,fl)))
+ fl
+ body
+ in
+ reduce (k, e, body', s) *)
+ (* NEW *)
+ let leng = List.length fl in
+ let fl' =
+ let unwind_fl (name,recindex,typ,body) =
+ (name,recindex,unwind' leng k e typ, unwind' leng k e body) in
+ List.map unwind_fl fl in
+ let new_env =
+ let counter = ref leng in
+ let rec build_env e =
+ if !counter = 0 then e else (decr counter;
+ build_env ((C.Fix (!counter,fl'))::e)) in
+ build_env e in
+ reduce (k+leng, new_env, body,s)
+ | _ -> let t' = unwind k e t in
+ if s = [] then t' else C.Appl (t'::s)
+ )
+ | None -> let t' = unwind k e t in
+ if s = [] then t' else C.Appl (t'::s)
+ )
+ | (k, e,(C.CoFix (i,fl) as t),s) -> let t' = unwind k e t in
+ if s = [] then t' else C.Appl (t'::s);;
+
+let rec whd = let module C = Cic in
+ function
+ C.Rel _ as t -> t
+ | C.Var _ as t -> reduce (0, [], t, [])
+ | C.Meta _ as t -> t
+ | C.Sort _ as t -> t
+ | C.Implicit as t -> t
+ | C.Cast (te,ty) -> whd te
+ | C.Prod _ as t -> t
+ | C.Lambda _ as t -> t
+ | C.LetIn (n,s,t) -> reduce (1, [s], t, [])
+ | C.Appl [] -> raise (Impossible 1)
+ | C.Appl (he::tl) -> reduce (0, [], he, tl)
+ | C.Const _ as t -> reduce (0, [], t, [])
+ | C.Abst _ as t -> t
+ | C.MutInd _ as t -> t
+ | C.MutConstruct _ as t -> t
+ | C.MutCase _ as t -> reduce (0, [], t, [])
+ | C.Fix _ as t -> reduce (0, [], t, [])
+ | C.CoFix _ as t -> reduce (0, [], t, [])
+ ;;
+
+(* let whd t = reduce (0, [],t,[]);;
+ let res = reduce (0, [],t,[]) in
+ let rescsc = CicReductionNaif.whd t in
+ if not (CicReductionNaif.are_convertible res rescsc) then
+ begin
+ prerr_endline ("PRIMA: " ^ CicPp.ppterm t) ;
+ flush stderr ;
+ prerr_endline ("DOPO: " ^ CicPp.ppterm res) ;
+ flush stderr ;
+ prerr_endline ("CSC: " ^ CicPp.ppterm rescsc) ;
+ flush stderr ;
+ assert false ;
+ end
+ else
+ res ;; *)
+
+
+(* t1, t2 must be well-typed *)
+let are_convertible =
+ let rec aux t1 t2 =
+ if t1 = t2 then true
+ else
+ let aux2 t1 t2 =
+ let module U = UriManager in
+ let module C = Cic in
+ match (t1,t2) with
+ (C.Rel n1, C.Rel n2) -> n1 = n2
+ | (C.Var uri1, C.Var uri2) -> U.eq uri1 uri2
+ | (C.Meta n1, C.Meta n2) -> n1 = n2
+ | (C.Sort s1, C.Sort s2) -> true (*CSC da finire con gli universi *)
+ | (C.Prod (_,s1,t1), C.Prod(_,s2,t2)) ->
+ aux s1 s2 && aux t1 t2
+ | (C.Lambda (_,s1,t1), C.Lambda(_,s2,t2)) ->
+ aux s1 s2 && aux t1 t2
+ | (C.Appl l1, C.Appl l2) ->
+ (try
+ List.fold_right2 (fun x y b -> aux x y && b) l1 l2 true
+ with
+ Invalid_argument _ -> false
+ )
+ | (C.Const (uri1,_), C.Const (uri2,_)) ->
+ U.eq uri1 uri2
+ | (C.MutInd (uri1,k1,i1), C.MutInd (uri2,k2,i2)) ->
+ U.eq uri1 uri2 && i1 = i2
+ | (C.MutConstruct (uri1,_,i1,j1), C.MutConstruct (uri2,_,i2,j2)) ->
+ U.eq uri1 uri2 && i1 = i2 && j1 = j2
+ | (C.MutCase (uri1,_,i1,outtype1,term1,pl1),
+ C.MutCase (uri2,_,i2,outtype2,term2,pl2)) ->
+ (* aux outtype1 outtype2 should be true if aux pl1 pl2 *)
+ U.eq uri1 uri2 && i1 = i2 && aux outtype1 outtype2 &&
+ aux term1 term2 &&
+ List.fold_right2 (fun x y b -> b && aux x y) pl1 pl2 true
+ | (C.Fix (i1,fl1), C.Fix (i2,fl2)) ->
+ i1 = i2 &&
+ List.fold_right2
+ (fun (_,recindex1,ty1,bo1) (_,recindex2,ty2,bo2) b ->
+ b && recindex1 = recindex2 && aux ty1 ty2 && aux bo1 bo2)
+ fl1 fl2 true
+ | (C.CoFix (i1,fl1), C.CoFix (i2,fl2)) ->
+ i1 = i2 &&
+ List.fold_right2
+ (fun (_,ty1,bo1) (_,ty2,bo2) b ->
+ b && aux ty1 ty2 && aux bo1 bo2)
+ fl1 fl2 true
+ | (_,_) -> false
+ in
+ if aux2 t1 t2 then true
+ else aux2 (whd t1) (whd t2)
+in
+ aux
+;;
+
+
+
+
+
+
+
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