type substitution = (int * Cic.term) list
+(*** Functions to apply a substitution ***)
+
+let apply_subst_gen ~appl_fun subst term =
+ let rec um_aux =
+ let module C = Cic in
+ let module S = CicSubstitution in
+ function
+ C.Rel _ as t -> t
+ | C.Var _ as t -> t
+ | C.Meta (i, l) ->
+ (try
+ let t = List.assoc i subst in
+ um_aux (S.lift_meta l t)
+ with Not_found -> (* not constrained variable, i.e. free in subst*)
+ let l' =
+ List.map (function None -> None | Some t -> Some (um_aux t)) l
+ in
+ C.Meta (i,l'))
+ | C.Sort _ as t -> t
+ | C.Implicit -> assert false
+ | C.Cast (te,ty) -> C.Cast (um_aux te, um_aux ty)
+ | C.Prod (n,s,t) -> C.Prod (n, um_aux s, um_aux t)
+ | C.Lambda (n,s,t) -> C.Lambda (n, um_aux s, um_aux t)
+ | C.LetIn (n,s,t) -> C.LetIn (n, um_aux s, um_aux t)
+ | C.Appl (hd :: tl) -> appl_fun um_aux hd tl
+ | C.Appl _ -> assert false
+ | C.Const (uri,exp_named_subst) ->
+ let exp_named_subst' =
+ List.map (fun (uri, t) -> (uri, um_aux t)) exp_named_subst
+ in
+ C.Const (uri, exp_named_subst')
+ | C.MutInd (uri,typeno,exp_named_subst) ->
+ let exp_named_subst' =
+ List.map (fun (uri, t) -> (uri, um_aux t)) exp_named_subst
+ in
+ C.MutInd (uri,typeno,exp_named_subst')
+ | C.MutConstruct (uri,typeno,consno,exp_named_subst) ->
+ let exp_named_subst' =
+ List.map (fun (uri, t) -> (uri, um_aux t)) exp_named_subst
+ in
+ C.MutConstruct (uri,typeno,consno,exp_named_subst')
+ | C.MutCase (sp,i,outty,t,pl) ->
+ let pl' = List.map um_aux pl in
+ C.MutCase (sp, i, um_aux outty, um_aux t, pl')
+ | C.Fix (i, fl) ->
+ let fl' =
+ List.map (fun (name, i, ty, bo) -> (name, i, um_aux ty, um_aux bo)) fl
+ in
+ C.Fix (i, fl')
+ | C.CoFix (i, fl) ->
+ let fl' =
+ List.map (fun (name, ty, bo) -> (name, um_aux ty, um_aux bo)) fl
+ in
+ C.CoFix (i, fl')
+ in
+ um_aux term
+;;
+
+let apply_subst =
+ let appl_fun um_aux he tl =
+ let tl' = List.map um_aux tl in
+ begin
+ match um_aux he with
+ Cic.Appl l -> Cic.Appl (l@tl')
+ | he' -> Cic.Appl (he'::tl')
+ end
+ in
+ apply_subst_gen ~appl_fun
+;;
+
+(* apply_subst_reducing subst (Some (mtr,reductions_no)) t *)
+(* performs as (apply_subst subst t) until it finds an application of *)
+(* (META [meta_to_reduce]) that, once unwinding is performed, creates *)
+(* a new beta-redex; in this case up to [reductions_no] consecutive *)
+(* beta-reductions are performed. *)
+(* Hint: this function is usually called when [reductions_no] *)
+(* eta-expansions have been performed and the head of the new *)
+(* application has been unified with (META [meta_to_reduce]): *)
+(* during the unwinding the eta-expansions are undone. *)
+
+let apply_subst_reducing meta_to_reduce =
+ let appl_fun um_aux he tl =
+ let tl' = List.map um_aux tl in
+ let t' =
+ match um_aux he with
+ Cic.Appl l -> Cic.Appl (l@tl')
+ | he' -> Cic.Appl (he'::tl')
+ in
+ begin
+ match meta_to_reduce, he with
+ Some (mtr,reductions_no), Cic.Meta (m,_) when m = mtr ->
+ let rec beta_reduce =
+ function
+ (n,(Cic.Appl (Cic.Lambda (_,_,t)::he'::tl'))) when n > 0 ->
+ let he'' = CicSubstitution.subst he' t in
+ if tl' = [] then
+ he''
+ else
+ beta_reduce (n-1,Cic.Appl(he''::tl'))
+ | (_,t) -> t
+ in
+ beta_reduce (reductions_no,t')
+ | _,_ -> t'
+ end
+ in
+ apply_subst_gen ~appl_fun
+
+let rec apply_subst_context subst context =
+ List.fold_right
+ (fun item context ->
+ match item with
+ | Some (n, Cic.Decl t) ->
+ let t' = apply_subst subst t in
+ Some (n, Cic.Decl t') :: context
+ | Some (n, Cic.Def (t, ty)) ->
+ let ty' =
+ match ty with
+ | None -> None
+ | Some ty -> Some (apply_subst subst ty)
+ in
+ let t' = apply_subst subst t in
+ Some (n, Cic.Def (t', ty')) :: context
+ | None -> None :: context)
+ context []
+
+let apply_subst_metasenv subst metasenv =
+ List.map
+ (fun (n, context, ty) ->
+ (n, apply_subst_context subst context, apply_subst subst ty))
+ (List.filter
+ (fun (i, _, _) -> not (List.exists (fun (j, _) -> (j = i)) subst))
+ metasenv)
+
+(***** Pretty printing functions ******)
+
let ppsubst subst =
String.concat "\n"
(List.map
(fun (idx, term) -> Printf.sprintf "?%d := %s" idx (CicPp.ppterm term))
subst)
+;;
+
+let ppterm subst term = CicPp.ppterm (apply_subst subst term)
+
+let ppterm_in_context subst term name_context =
+ CicPp.pp (apply_subst subst term) name_context
+
+let ppcontext' ?(sep = "\n") subst context =
+ let separate s = if s = "" then "" else s ^ sep in
+ List.fold_right
+ (fun context_entry (i,name_context) ->
+ match context_entry with
+ Some (n,Cic.Decl t) ->
+ sprintf "%s%s : %s" (separate i) (CicPp.ppname n)
+ (ppterm_in_context subst t name_context), (Some n)::name_context
+ | Some (n,Cic.Def (bo,ty)) ->
+ sprintf "%s%s : %s := %s" (separate i) (CicPp.ppname n)
+ (match ty with
+ None -> "_"
+ | Some ty -> ppterm_in_context subst ty name_context)
+ (ppterm_in_context subst bo name_context), (Some n)::name_context
+ | None ->
+ sprintf "%s_ :? _" (separate i), None::name_context
+ ) context ("",[])
+
+let ppcontext ?sep subst context = fst (ppcontext' ?sep subst context)
+
+let ppmetasenv ?(sep = "\n") metasenv subst =
+ String.concat sep
+ (List.map
+ (fun (i, c, t) ->
+ let context,name_context = ppcontext' ~sep:"; " subst c in
+ sprintf "%s |- ?%d: %s" context i
+ (ppterm_in_context subst t name_context))
+ (List.filter
+ (fun (i, _, _) -> not (List.exists (fun (j, _) -> (j = i)) subst))
+ metasenv))
+
+(* From now on we recreate a kernel abstraction where substitutions are part of
+ * the calculus *)
+
+let lift subst n term =
+ let term = apply_subst subst term in
+ try
+ CicSubstitution.lift n term
+ with e ->
+ raise (MetaSubstFailure ("Lift failure: " ^ Printexc.to_string e))
+
+let subst subst t1 t2 =
+ let t1 = apply_subst subst t1 in
+ let t2 = apply_subst subst t2 in
+ try
+ CicSubstitution.subst t1 t2
+ with e ->
+ raise (MetaSubstFailure ("Subst failure: " ^ Printexc.to_string e))
+
+let whd subst context term =
+ let term = apply_subst subst term in
+ let context = apply_subst_context subst context in
+ try
+ CicReduction.whd context term
+ with e ->
+ raise (MetaSubstFailure ("Weak head reduction failure: " ^
+ Printexc.to_string e))
+
+let are_convertible subst context t1 t2 =
+ let context = apply_subst_context subst context in
+ let t1 = apply_subst subst t1 in
+ let t2 = apply_subst subst t2 in
+ CicReduction.are_convertible context t1 t2
+
+let tempi_type_of_aux_subst = ref 0.0;;
+let tempi_type_of_aux = ref 0.0;;
+
+let type_of_aux' metasenv subst context term =
+let time1 = Unix.gettimeofday () in
+ let term = apply_subst subst term in
+ let context = apply_subst_context subst context in
+ let metasenv =
+ List.map
+ (fun (i, c, t) -> (i, apply_subst_context subst c, apply_subst subst t))
+ (List.filter
+ (fun (i, _, _) -> not (List.exists (fun (j, _) -> (j = i)) subst))
+ metasenv)
+ in
+let time2 = Unix.gettimeofday () in
+let res =
+ try
+ CicTypeChecker.type_of_aux' metasenv context term
+ with CicTypeChecker.TypeCheckerFailure msg ->
+ raise (MetaSubstFailure ("Type checker failure: " ^ msg))
+in
+let time3 = Unix.gettimeofday () in
+ tempi_type_of_aux_subst := !tempi_type_of_aux_subst +. time3 -. time1 ;
+ tempi_type_of_aux := !tempi_type_of_aux +. time2 -. time1 ;
+ res
(**** DELIFT ****)
(* the delift function takes in input a metavariable index, an ordered list of
raise (MetaSubstFailure (sprintf
"Cannot restrict the context of the metavariable ?%d over the hypotheses %s since ?%d is already instantiated with %s and at least one of the hypotheses occurs in the substituted term"
n (names_of_context_indexes context to_be_restricted) n
- (CicPp.ppterm s)))
+ (ppterm subst s)))
with Not_found -> (more @ more_to_be_restricted @ more_to_be_restricted', metasenv', subst))
with Occur ->
raise (MetaSubstFailure (sprintf
if i = n then
raise (MetaSubstFailure (sprintf
"Cannot unify the metavariable ?%d with a term that has as subterm %s in which the same metavariable occurs (occur check)"
- i (CicPp.ppterm t)))
+ i (ppterm subst t)))
else
(* I do not consider the term associated to ?i in subst since *)
(* in this way I can restrict if something goes wrong. *)
debug_print "!!!!!!!!!!! First Order UnificationFailure, but maybe it could have been successful even in a first order setting (no conversion, only alpha convertibility)! Please, implement a better delift function !!!!!!!!!!!!!!!!" ;
raise (MetaSubstFailure (sprintf
"Error trying to abstract %s over [%s]: the algorithm only tried to abstract over bound variables"
- (CicPp.ppterm t)
+ (ppterm subst t)
(String.concat "; "
(List.map
- (function Some t -> CicPp.ppterm t | None -> "_")
+ (function Some t -> ppterm subst t | None -> "_")
l))))
in
let (metasenv, subst) = restrict subst !to_be_restricted metasenv in
(**** END OF DELIFT ****)
-let apply_subst_gen ~appl_fun subst term =
- let rec um_aux =
- let module C = Cic in
- let module S = CicSubstitution in
- function
- C.Rel _ as t -> t
- | C.Var _ as t -> t
- | C.Meta (i, l) ->
- (try
- let t = List.assoc i subst in
- um_aux (S.lift_meta l t)
- with Not_found -> (* not constrained variable, i.e. free in subst*)
- let l' =
- List.map (function None -> None | Some t -> Some (um_aux t)) l
- in
- C.Meta (i,l'))
- | C.Sort _ as t -> t
- | C.Implicit -> assert false
- | C.Cast (te,ty) -> C.Cast (um_aux te, um_aux ty)
- | C.Prod (n,s,t) -> C.Prod (n, um_aux s, um_aux t)
- | C.Lambda (n,s,t) -> C.Lambda (n, um_aux s, um_aux t)
- | C.LetIn (n,s,t) -> C.LetIn (n, um_aux s, um_aux t)
- | C.Appl (hd :: tl) -> appl_fun um_aux hd tl
- | C.Appl _ -> assert false
- | C.Const (uri,exp_named_subst) ->
- let exp_named_subst' =
- List.map (fun (uri, t) -> (uri, um_aux t)) exp_named_subst
- in
- C.Const (uri, exp_named_subst')
- | C.MutInd (uri,typeno,exp_named_subst) ->
- let exp_named_subst' =
- List.map (fun (uri, t) -> (uri, um_aux t)) exp_named_subst
- in
- C.MutInd (uri,typeno,exp_named_subst')
- | C.MutConstruct (uri,typeno,consno,exp_named_subst) ->
- let exp_named_subst' =
- List.map (fun (uri, t) -> (uri, um_aux t)) exp_named_subst
- in
- C.MutConstruct (uri,typeno,consno,exp_named_subst')
- | C.MutCase (sp,i,outty,t,pl) ->
- let pl' = List.map um_aux pl in
- C.MutCase (sp, i, um_aux outty, um_aux t, pl')
- | C.Fix (i, fl) ->
- let fl' =
- List.map (fun (name, i, ty, bo) -> (name, i, um_aux ty, um_aux bo)) fl
- in
- C.Fix (i, fl')
- | C.CoFix (i, fl) ->
- let fl' =
- List.map (fun (name, ty, bo) -> (name, um_aux ty, um_aux bo)) fl
- in
- C.CoFix (i, fl')
- in
- um_aux term
-
-let apply_subst =
- let appl_fun um_aux he tl =
- let tl' = List.map um_aux tl in
- begin
- match um_aux he with
- Cic.Appl l -> Cic.Appl (l@tl')
- | he' -> Cic.Appl (he'::tl')
- end
- in
- apply_subst_gen ~appl_fun
-
-let ppterm subst term = CicPp.ppterm (apply_subst subst term)
-
-(* apply_subst_reducing subst (Some (mtr,reductions_no)) t *)
-(* performs as (apply_subst subst t) until it finds an application of *)
-(* (META [meta_to_reduce]) that, once unwinding is performed, creates *)
-(* a new beta-redex; in this case up to [reductions_no] consecutive *)
-(* beta-reductions are performed. *)
-(* Hint: this function is usually called when [reductions_no] *)
-(* eta-expansions have been performed and the head of the new *)
-(* application has been unified with (META [meta_to_reduce]): *)
-(* during the unwinding the eta-expansions are undone. *)
-
-let apply_subst_reducing meta_to_reduce =
- let appl_fun um_aux he tl =
- let tl' = List.map um_aux tl in
- let t' =
- match um_aux he with
- Cic.Appl l -> Cic.Appl (l@tl')
- | he' -> Cic.Appl (he'::tl')
- in
- begin
- match meta_to_reduce, he with
- Some (mtr,reductions_no), Cic.Meta (m,_) when m = mtr ->
- let rec beta_reduce =
- function
- (n,(Cic.Appl (Cic.Lambda (_,_,t)::he'::tl'))) when n > 0 ->
- let he'' = CicSubstitution.subst he' t in
- if tl' = [] then
- he''
- else
- beta_reduce (n-1,Cic.Appl(he''::tl'))
- | (_,t) -> t
- in
- beta_reduce (reductions_no,t')
- | _,_ -> t'
- end
- in
- apply_subst_gen ~appl_fun
-
-let rec apply_subst_context subst context =
- List.fold_right
- (fun item context ->
- match item with
- | Some (n, Cic.Decl t) ->
- let t' = apply_subst subst t in
- Some (n, Cic.Decl t') :: context
- | Some (n, Cic.Def (t, ty)) ->
- let ty' =
- match ty with
- | None -> None
- | Some ty -> Some (apply_subst subst ty)
- in
- let t' = apply_subst subst t in
- Some (n, Cic.Def (t', ty')) :: context
- | None -> None :: context)
- context []
-
-let apply_subst_metasenv subst metasenv =
- List.map
- (fun (n, context, ty) ->
- (n, apply_subst_context subst context, apply_subst subst ty))
- (List.filter
- (fun (i, _, _) -> not (List.exists (fun (j, _) -> (j = i)) subst))
- metasenv)
-
-let ppterm subst term = CicPp.ppterm (apply_subst subst term)
-
-let ppterm_in_context subst term name_context =
- CicPp.pp (apply_subst subst term) name_context
-
-let ppcontext' ?(sep = "\n") subst context =
- let separate s = if s = "" then "" else s ^ sep in
- List.fold_right
- (fun context_entry (i,name_context) ->
- match context_entry with
- Some (n,Cic.Decl t) ->
- sprintf "%s%s : %s" (separate i) (CicPp.ppname n)
- (ppterm_in_context subst t name_context), (Some n)::name_context
- | Some (n,Cic.Def (bo,ty)) ->
- sprintf "%s%s : %s := %s" (separate i) (CicPp.ppname n)
- (match ty with
- None -> "_"
- | Some ty -> ppterm_in_context subst ty name_context)
- (ppterm_in_context subst bo name_context), (Some n)::name_context
- | None ->
- sprintf "%s_ :? _" (separate i), None::name_context
- ) context ("",[])
-
-let ppcontext ?sep subst context = fst (ppcontext' ?sep subst context)
-
-let ppmetasenv ?(sep = "\n") metasenv subst =
- String.concat sep
- (List.map
- (fun (i, c, t) ->
- let context,name_context = ppcontext' ~sep:"; " subst c in
- sprintf "%s |- ?%d: %s" context i
- (ppterm_in_context subst t name_context))
- (List.filter
- (fun (i, _, _) -> not (List.exists (fun (j, _) -> (j = i)) subst))
- metasenv))
-
-(* UNWIND THE MGU INSIDE THE MGU *)
-(*
-let unwind_subst metasenv subst =
- List.fold_left
- (fun (unwinded,metasenv) (i,_) ->
- let (_,canonical_context,_) = CicUtil.lookup_meta i metasenv in
- let identity_relocation_list =
- CicMkImplicit.identity_relocation_list_for_metavariable canonical_context
- in
- let (_,metasenv',subst') =
- unwind metasenv subst unwinded (Cic.Meta (i,identity_relocation_list))
- in
- subst',metasenv'
- ) ([],metasenv) subst
-*)
-
-(* From now on we recreate a kernel abstraction where substitutions are part of
- * the calculus *)
-
-let lift subst n term =
- let term = apply_subst subst term in
- try
- CicSubstitution.lift n term
- with e ->
- raise (MetaSubstFailure ("Lift failure: " ^ Printexc.to_string e))
-
-let subst subst t1 t2 =
- let t1 = apply_subst subst t1 in
- let t2 = apply_subst subst t2 in
- try
- CicSubstitution.subst t1 t2
- with e ->
- raise (MetaSubstFailure ("Subst failure: " ^ Printexc.to_string e))
-
-let whd subst context term =
- let term = apply_subst subst term in
- let context = apply_subst_context subst context in
- try
- CicReduction.whd context term
- with e ->
- raise (MetaSubstFailure ("Weak head reduction failure: " ^
- Printexc.to_string e))
-
-let are_convertible subst context t1 t2 =
- let context = apply_subst_context subst context in
- let t1 = apply_subst subst t1 in
- let t2 = apply_subst subst t2 in
- CicReduction.are_convertible context t1 t2
-
-let tempi_type_of_aux_subst = ref 0.0;;
-let tempi_type_of_aux = ref 0.0;;
-
-let type_of_aux' metasenv subst context term =
-let time1 = Unix.gettimeofday () in
- let term = apply_subst subst term in
- let context = apply_subst_context subst context in
- let metasenv =
- List.map
- (fun (i, c, t) -> (i, apply_subst_context subst c, apply_subst subst t))
- (List.filter
- (fun (i, _, _) -> not (List.exists (fun (j, _) -> (j = i)) subst))
- metasenv)
- in
-let time2 = Unix.gettimeofday () in
-let res =
- try
- CicTypeChecker.type_of_aux' metasenv context term
- with CicTypeChecker.TypeCheckerFailure msg ->
- raise (MetaSubstFailure ("Type checker failure: " ^ msg))
-in
-let time3 = Unix.gettimeofday () in
- tempi_type_of_aux_subst := !tempi_type_of_aux_subst +. time3 -. time1 ;
- tempi_type_of_aux := !tempi_type_of_aux +. time2 -. time1 ;
- res
(** {2 Format-like pretty printers} *)
projects / helm.git / commitdiff