open Printf
+exception Elim_failure of string
+exception Can_t_eliminate
+
let fresh_binder =
let counter = ref ~-1 in
function
| true ->
incr counter;
- Cic.Name ("elim" ^ string_of_int !counter)
+ Cic.Name ("e" ^ string_of_int !counter)
| _ -> Cic.Anonymous
(** verifies if a given inductive type occurs in a term in target position *)
(* | Cic.Appl args -> List.exists (recursive uri typeno subst) args *)
| _ -> false
+ (** given a list of constructor types, return true if at least one of them is
+ * recursive, false otherwise *)
+let recursive_type uri typeno subst constructors =
+ let rec aux = function
+ | Cic.Prod (_, src, tgt) -> recursive uri typeno subst src || aux tgt
+ | _ -> false
+ in
+ List.exists (fun (_, ty) -> aux ty) constructors
+
let unfold_appl = function
| Cic.Appl ((Cic.Appl args) :: tl) -> Cic.Appl (args @ tl)
| t -> t
let t = strip_left_params consno paramsno t in
delta (ury, typeno, subst) dependent paramsno consno t p args
-let rec add_params indno ty eliminator =
+let rec add_params binder indno ty eliminator =
if indno = 0 then
eliminator
else
match ty with
- | Cic.Prod (binder, src, tgt) ->
- Cic.Prod (binder, src, add_params (indno - 1) tgt eliminator)
+ | Cic.Prod (name, src, tgt) ->
+ binder name src (add_params binder (indno - 1) tgt eliminator)
| _ -> assert false
let rec mk_rels consno = function
case tgt
| t ->
Cic.Lambda (fresh_binder true,
- CicSubstitution.lift_from (rightno + 1) liftno indty,
- case)
-
-exception Failure of string
+ CicSubstitution.lift_from (rightno + 1) liftno indty, case)
let string_of_sort = function
| Cic.Prop -> "Prop"
| Cic.Set -> "Set"
| Cic.Type _ -> "Type"
-let elim_of ?(sort = Cic.Type (CicUniv.fresh ())) uri typeno =
- let (obj, univ) = (CicEnvironment.get_obj uri CicUniv.empty_ugraph) in
- let subst = [] in
- match obj with
- | Cic.InductiveDefinition (indTypes, params, leftno) ->
- let (name, inductive, ty, constructors) =
- try
- List.nth indTypes typeno
- with Failure _ -> assert false
- in
- let paramsno = count_pi ty in (* number of (left or right) parameters *)
- let rightno = paramsno - leftno in
- let dependent = (strip_pi ty <> Cic.Sort Cic.Prop) in
- let conslen = List.length constructors in
- let consno = ref (conslen + 1) in
- if (not dependent) && (sort <> Cic.Prop) && (conslen > 1) then
- raise (Failure (sprintf "can't eliminate from Prop to %s"
- (string_of_sort sort)));
- let indty =
- let indty = Cic.MutInd (uri, typeno, subst) in
- if paramsno = 0 then
- indty
- else
- Cic.Appl (indty :: mk_rels 0 paramsno)
- in
- let mk_constructor consno =
- let constructor = Cic.MutConstruct (uri, typeno, consno, subst) in
- if leftno = 0 then
- constructor
- else
- Cic.Appl (constructor :: mk_rels consno leftno)
- in
- let eliminator =
- let p_ty = type_of_p sort dependent leftno indty ty in
- let final_ty =
- add_right_pi dependent leftno (conslen + 1) 1 rightno indty ty
- in
- Cic.Prod (Cic.Name "P", p_ty,
- (List.fold_right
- (fun (_, constructor) acc ->
- decr consno;
- let p = Cic.Rel !consno in
- Cic.Prod (Cic.Anonymous,
- (delta (uri, typeno, subst) dependent leftno !consno
- constructor p [mk_constructor !consno]),
- acc))
- constructors final_ty))
- in
- add_params leftno ty eliminator
- | _ -> assert false
-
let rec branch (uri, typeno, subst) insource paramsno t fix head args =
assert (subst = []);
match t with
| _ -> Cic.Appl (head :: args))
| Cic.Appl (Cic.MutInd (uri', typeno', subst') :: tl) when
UriManager.eq uri uri' && typeno = typeno' && subst = subst' ->
- let (lparams, rparams) = split tl paramsno in
- (match args with
- | [] when insource && rparams = [] -> fix
- | [] when insource -> Cic.Appl (fix :: rparams)
- | _ when insource -> Cic.Appl (fix :: rparams @ args)
- | _ -> Cic.Appl (head :: rparams @ args))
+ if insource then
+ let (lparams, rparams) = split tl paramsno in
+ Cic.Appl (fix :: rparams @ args)
+ else
+ (match args with
+ | [] -> head
+ | _ -> Cic.Appl (head :: args))
| Cic.Prod (binder, src, tgt) ->
if recursive uri typeno subst src then
let args = List.map (CicSubstitution.lift 1) args in
let phi =
let fix = CicSubstitution.lift 1 fix in
- branch (uri, typeno, subst) true paramsno src fix head
- (args @ [Cic.Rel 1])
+ let src = CicSubstitution.lift 1 src in
+ branch (uri, typeno, subst) true paramsno src fix head [Cic.Rel 1]
in
- let tgt = CicSubstitution.lift 1 tgt in
Cic.Lambda (fresh_binder true, src,
branch (uri, typeno, subst) insource paramsno tgt
(CicSubstitution.lift 1 fix) (CicSubstitution.lift 1 head)
let t = strip_left_params liftno paramsno t in
branch (uri, typeno, subst) insource paramsno t fix head args
-let body_of ?(sort = Cic.Type (CicUniv.fresh ())) uri typeno =
+let elim_of ?(sort = Cic.Type (CicUniv.fresh ())) uri typeno =
let (obj, univ) = (CicEnvironment.get_obj uri CicUniv.empty_ugraph) in
let subst = [] in
match obj with
let conslen = List.length constructors in
let consno = ref (conslen + 1) in
if (not dependent) && (sort <> Cic.Prop) && (conslen > 1) then
- raise (Failure (sprintf "can't eliminate from Prop to %s"
- (string_of_sort sort)));
+ raise Can_t_eliminate;
let indty =
let indty = Cic.MutInd (uri, typeno, subst) in
if paramsno = 0 then
else
Cic.Appl (constructor :: mk_rels consno leftno)
in
- let eliminator =
- let p_ty = type_of_p sort dependent leftno indty ty in
- let final_ty =
- add_right_pi dependent leftno (conslen + 1) 1 rightno indty ty
+ let p_ty = type_of_p sort dependent leftno indty ty in
+ let final_ty =
+ add_right_pi dependent leftno (conslen + 1) 1 rightno indty ty
+ in
+ let eliminator_type =
+ let cic =
+ Cic.Prod (Cic.Name "P", p_ty,
+ (List.fold_right
+ (fun (_, constructor) acc ->
+ decr consno;
+ let p = Cic.Rel !consno in
+ Cic.Prod (Cic.Anonymous,
+ (delta (uri, typeno, subst) dependent leftno !consno
+ constructor p [mk_constructor !consno]),
+ acc))
+ constructors final_ty))
in
+ add_params (fun b s t -> Cic.Prod (b, s, t)) leftno ty cic
+ in
+ let consno = ref (conslen + 1) in
+ let eliminator_body =
let fix = Cic.Rel (rightno + 2) in
+ let is_recursive = recursive_type uri typeno subst constructors in
+ let recshift = if is_recursive then 1 else 0 in
let (_, branches) =
List.fold_right
(fun (_, ty) (shift, branches) ->
- let head = Cic.Rel (rightno + shift + 2) in
+ let head = Cic.Rel (rightno + shift + 1 + recshift) in
let b =
- branch (uri, typeno, subst) false (rightno + conslen + 3) leftno
- ty fix head []
+ branch (uri, typeno, subst) false
+ (rightno + conslen + 2 + recshift) leftno ty fix head []
in
(shift + 1, b :: branches))
constructors (1, [])
in
- let case =
- Cic.MutCase (uri, typeno, Cic.Rel (conslen + rightno + 3), Cic.Rel 1,
- branches)
+ let mutcase =
+ Cic.MutCase (uri, typeno, Cic.Rel (conslen + rightno + 2 + recshift),
+ Cic.Rel 1, branches)
+ in
+ let body =
+ if is_recursive then
+ let fixfun =
+ add_right_lambda dependent leftno (conslen + 2) 2 rightno
+ indty mutcase ty
+ in
+ (* rightno is the decreasing argument, i.e. the argument of
+ * inductive type *)
+ Cic.Fix (0, ["f", rightno, final_ty, fixfun])
+ else
+ add_right_lambda dependent leftno (conslen + 1) 1 rightno indty
+ mutcase ty
in
- let fix_body =
- add_right_lambda dependent leftno (conslen + 1) 1 rightno
- indty case ty
+ let cic =
+ Cic.Lambda (Cic.Name "P", p_ty,
+ (List.fold_right
+ (fun (_, constructor) acc ->
+ decr consno;
+ let p = Cic.Rel !consno in
+ Cic.Lambda (fresh_binder true,
+ (delta (uri, typeno, subst) dependent leftno !consno
+ constructor p [mk_constructor !consno]),
+ acc))
+ constructors body))
in
- let fix = Cic.Fix (0, ["f", 0, final_ty, fix_body]) in
- Cic.Lambda (Cic.Name "P", p_ty,
- (List.fold_right
- (fun (_, constructor) acc ->
- decr consno;
- let p = Cic.Rel !consno in
- Cic.Lambda (fresh_binder true,
- (delta (uri, typeno, subst) dependent leftno !consno
- constructor p [mk_constructor !consno]),
- acc))
- constructors fix))
+ add_params (fun b s t -> Cic.Lambda (b, s, t)) leftno ty cic
+ in
+(*
+prerr_endline (CicPp.ppterm eliminator_type);
+prerr_endline (CicPp.ppterm eliminator_body);
+*)
+ let (computed_type, ugraph) =
+ try
+ CicTypeChecker.type_of_aux' [] [] eliminator_body CicUniv.empty_ugraph
+ with CicTypeChecker.TypeCheckerFailure msg ->
+ raise (Elim_failure (sprintf
+ "type checker failure while type checking:\n%s\nerror:\n%s"
+ (CicPp.ppterm eliminator_body) msg))
+ in
+ if not (fst (CicReduction.are_convertible []
+ eliminator_type computed_type ugraph))
+ then
+ raise (Failure (sprintf
+ "internal error: type mismatch on eliminator type\n%s\n%s"
+ (CicPp.ppterm eliminator_type) (CicPp.ppterm computed_type)));
+ let suffix =
+ match sort with
+ | Cic.Prop -> "_ind"
+ | Cic.Set -> "_rec"
+ | Cic.Type _ -> "_rect"
+ | _ -> assert false
in
- add_params leftno ty eliminator
+ let name = UriManager.name_of_uri uri ^ suffix in
+ Cic.Constant (name, Some eliminator_body, eliminator_type, [])
| _ -> assert false
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