open Printf
-let fresh_binder =
- let counter = ref ~-1 in
- function
- | true ->
- incr counter;
- Cic.Name ("elim" ^ string_of_int !counter)
- | _ -> Cic.Anonymous
-
- (** verifies if a given uri occurs in a term in target position *)
-let rec recursive uri = function
- | Cic.Prod (_, _, target) -> recursive uri target
- | Cic.MutInd (uri', _, _) -> UriManager.eq uri uri'
- | Cic.Appl args -> List.exists (recursive uri) args
+exception Elim_failure of string Lazy.t
+exception Can_t_eliminate
+
+let debug_print = fun _ -> ()
+(*let debug_print s = prerr_endline (Lazy.force s) *)
+
+let counter = ref ~-1 ;;
+
+let fresh_binder () = Cic.Name "matita_dummy"
+(*
+ incr counter;
+ Cic.Name ("e" ^ string_of_int !counter) *)
+
+ (** verifies if a given inductive type occurs in a term in target position *)
+let rec recursive uri typeno = function
+ | Cic.Prod (_, _, target) -> recursive uri typeno target
+ | Cic.MutInd (uri', typeno', [])
+ | Cic.Appl (Cic.MutInd (uri', typeno', []) :: _) ->
+ UriManager.eq uri uri' && typeno = typeno'
| _ -> false
+ (** given a list of constructor types, return true if at least one of them is
+ * recursive, false otherwise *)
+let recursive_type uri typeno constructors =
+ let rec aux = function
+ | Cic.Prod (_, src, tgt) -> recursive uri typeno 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
* @param paramsno number of Prod to ignore in this constructor (i.e. number of
* inductive parameters)
* @param dependent true if we are in the dependent case (i.e. sort <> Prop) *)
-let rec delta (uri, typeno, subst) dependent paramsno consno t p args =
- assert (subst = []);
+let rec delta (uri, typeno) dependent paramsno consno t p args =
match t with
- | Cic.MutInd (uri', typeno', subst') ->
+ | Cic.MutInd (uri', typeno', []) when
+ UriManager.eq uri uri' && typeno = typeno' ->
if dependent then
(match args with
| [] -> assert false
| _ -> unfold_appl (Cic.Appl [p; unfold_appl (Cic.Appl args)]))
else
p
- | Cic.Appl (Cic.MutInd (uri', typeno', subst') :: tl) when
- UriManager.eq uri uri' && typeno = typeno' && subst = subst' ->
+ | Cic.Appl (Cic.MutInd (uri', typeno', []) :: tl) when
+ UriManager.eq uri uri' && typeno = typeno' ->
let (lparams, rparams) = split tl paramsno in
if dependent then
(match args with
| [] -> p
| _ -> Cic.Appl (p :: rparams))
| Cic.Prod (binder, src, tgt) ->
- if recursive uri src then
+ if recursive uri typeno src then
let args = List.map (CicSubstitution.lift 2) args in
let phi =
let src = CicSubstitution.lift 1 src in
- delta (uri, typeno, subst) dependent paramsno consno src
+ delta (uri, typeno) dependent paramsno consno src
(CicSubstitution.lift 1 p) [Cic.Rel 1]
in
let tgt = CicSubstitution.lift 1 tgt in
- Cic.Prod (fresh_binder dependent, src,
+ Cic.Prod (fresh_binder (), src,
Cic.Prod (Cic.Anonymous, phi,
- delta (uri, typeno, subst) dependent paramsno consno tgt
+ delta (uri, typeno) dependent paramsno consno tgt
(CicSubstitution.lift 2 p) (args @ [Cic.Rel 2])))
else (* non recursive *)
let args = List.map (CicSubstitution.lift 1) args in
- Cic.Prod (fresh_binder dependent, src,
- delta (uri, typeno, subst) dependent paramsno consno tgt
+ Cic.Prod (fresh_binder (), src,
+ delta (uri, typeno) dependent paramsno consno tgt
(CicSubstitution.lift 1 p) (args @ [Cic.Rel 1]))
| _ -> assert false
strip_left_params consno (leftno - 1) tgt
| _ -> assert false
-let delta (ury, typeno, subst) dependent paramsno consno t p args =
+let delta (ury, typeno) dependent paramsno consno t p args =
let t = strip_left_params consno paramsno t in
- delta (ury, typeno, subst) dependent paramsno consno t p args
+ delta (ury, typeno) 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) ->
+ let name =
+ match name with
+ Cic.Name _ -> name
+ | Cic.Anonymous -> fresh_binder ()
+ in
+ binder name src (add_params binder (indno - 1) tgt eliminator)
| _ -> assert false
let rec mk_rels consno = function
let rec type_of_p sort dependent leftno indty = function
| Cic.Prod (n, src, tgt) when leftno = 0 ->
- Cic.Prod (n, src, type_of_p sort dependent leftno indty tgt)
+ let n =
+ if dependent then
+ match n with
+ Cic.Name _ -> n
+ | Cic.Anonymous -> fresh_binder ()
+ else
+ n
+ in
+ Cic.Prod (n, src, type_of_p sort dependent leftno indty tgt)
| Cic.Prod (_, _, tgt) -> type_of_p sort dependent (leftno - 1) indty tgt
| t ->
if dependent then
let rec add_right_pi dependent strip liftno liftfrom rightno indty = function
| Cic.Prod (_, src, tgt) when strip = 0 ->
- Cic.Prod (fresh_binder true,
- CicSubstitution.lift_from (liftfrom + 1) liftno src,
+ Cic.Prod (fresh_binder (),
+ CicSubstitution.lift_from liftfrom liftno src,
add_right_pi dependent strip liftno (liftfrom + 1) rightno indty tgt)
| Cic.Prod (_, _, tgt) ->
add_right_pi dependent (strip - 1) liftno liftfrom rightno indty tgt
| t ->
if dependent then
- Cic.Prod (fresh_binder dependent,
+ Cic.Prod (fresh_binder (),
CicSubstitution.lift_from (rightno + 1) liftno indty,
Cic.Appl (Cic.Rel (1 + liftno + rightno) :: mk_rels 0 (rightno + 1)))
else
else
Cic.Appl (Cic.Rel (1 + liftno + rightno) :: mk_rels 1 rightno))
-exception Failure of string
+let rec add_right_lambda dependent strip liftno liftfrom rightno indty case =
+function
+ | Cic.Prod (_, src, tgt) when strip = 0 ->
+ Cic.Lambda (fresh_binder (),
+ CicSubstitution.lift_from liftfrom liftno src,
+ add_right_lambda dependent strip liftno (liftfrom + 1) rightno indty
+ case tgt)
+ | Cic.Prod (_, _, tgt) ->
+ add_right_lambda true (strip - 1) liftno liftfrom rightno indty
+ case tgt
+ | t ->
+ Cic.Lambda (fresh_binder (),
+ CicSubstitution.lift_from (rightno + 1) liftno indty, case)
-let string_of_sort = function
- | Cic.Prop -> "Prop"
- | Cic.CProp -> "CProp"
- | Cic.Set -> "Set"
- | Cic.Type _ -> "Type"
+let rec branch (uri, typeno) insource paramsno t fix head args =
+ match t with
+ | Cic.MutInd (uri', typeno', []) when
+ UriManager.eq uri uri' && typeno = typeno' ->
+ if insource then
+ (match args with
+ | [arg] -> Cic.Appl (fix :: args)
+ | _ -> Cic.Appl (head :: [Cic.Appl args]))
+ else
+ (match args with
+ | [] -> head
+ | _ -> Cic.Appl (head :: args))
+ | Cic.Appl (Cic.MutInd (uri', typeno', []) :: tl) when
+ UriManager.eq uri uri' && typeno = typeno' ->
+ if insource then
+ let (lparams, rparams) = split tl paramsno in
+ match args with
+ | [arg] -> Cic.Appl (fix :: rparams @ args)
+ | _ -> Cic.Appl (fix :: rparams @ [Cic.Appl args])
+ else
+ (match args with
+ | [] -> head
+ | _ -> Cic.Appl (head :: args))
+ | Cic.Prod (binder, src, tgt) ->
+ if recursive uri typeno src then
+ let args = List.map (CicSubstitution.lift 1) args in
+ let phi =
+ let fix = CicSubstitution.lift 1 fix in
+ let src = CicSubstitution.lift 1 src in
+ branch (uri, typeno) true paramsno src fix head [Cic.Rel 1]
+ in
+ Cic.Lambda (fresh_binder (), src,
+ branch (uri, typeno) insource paramsno tgt
+ (CicSubstitution.lift 1 fix) (CicSubstitution.lift 1 head)
+ (args @ [Cic.Rel 1; phi]))
+ else (* non recursive *)
+ let args = List.map (CicSubstitution.lift 1) args in
+ Cic.Lambda (fresh_binder (), src,
+ branch (uri, typeno) insource paramsno tgt
+ (CicSubstitution.lift 1 fix) (CicSubstitution.lift 1 head)
+ (args @ [Cic.Rel 1]))
+ | _ -> assert false
+
+let branch (uri, typeno) insource liftno paramsno t fix head args =
+ let t = strip_left_params liftno paramsno t in
+ branch (uri, typeno) insource paramsno t fix head args
-let elim_of ?(sort = Cic.Type (CicUniv.fresh ())) uri typeno =
- let (obj, univ) = (CicEnvironment.get_obj uri CicUniv.empty_ugraph) in
- let subst = [] in
+let elim_of ~sort uri typeno =
+ counter := ~-1;
+ let (obj, univ) = (CicEnvironment.get_obj CicUniv.empty_ugraph uri) in
match obj with
- | Cic.InductiveDefinition (indTypes, params, leftno) ->
+ | 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 head = match strip_pi ty with Cic.Sort s -> s 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)));
+ if
+ not
+ (CicTypeChecker.check_allowed_sort_elimination uri typeno head sort)
+ then
+ raise Can_t_eliminate;
let indty =
- let indty = Cic.MutInd (uri, typeno, subst) in
+ let indty = Cic.MutInd (uri, typeno, []) 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
+ let constructor = Cic.MutConstruct (uri, typeno, consno, []) 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 (paramsno - leftno)
- 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) dependent leftno !consno
+ constructor p [mk_constructor !consno]),
+ acc))
+ constructors final_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))
+ add_params (fun b s t -> Cic.Prod (b, s, t)) leftno ty cic
in
- add_params leftno ty eliminator
- | _ -> assert false
+ let consno = ref (conslen + 1) in
+ let eliminator_body =
+ let fix = Cic.Rel (rightno + 2) in
+ let is_recursive = recursive_type uri typeno 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 + 1 + recshift) in
+ let b =
+ branch (uri, typeno) false
+ (rightno + conslen + 2 + recshift) leftno ty fix head []
+ in
+ (shift + 1, b :: branches))
+ constructors (1, [])
+ in
+ let shiftno = conslen + rightno + 2 + recshift in
+ let outtype =
+ if dependent then
+ Cic.Rel shiftno
+ else
+ let head =
+ if rightno = 0 then
+ CicSubstitution.lift 1 (Cic.Rel shiftno)
+ else
+ Cic.Appl
+ ((CicSubstitution.lift (rightno + 1) (Cic.Rel shiftno)) ::
+ mk_rels 1 rightno)
+ in
+ add_right_lambda true leftno shiftno 1 rightno indty head ty
+ in
+ let mutcase =
+ Cic.MutCase (uri, typeno, outtype, Cic.Rel 1, branches)
+ in
+ let body =
+ if is_recursive then
+ let fixfun =
+ add_right_lambda dependent leftno (conslen + 2) 1 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 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 (),
+ (delta (uri, typeno) dependent leftno !consno
+ constructor p [mk_constructor !consno]),
+ acc))
+ constructors body))
+ in
+ add_params (fun b s t -> Cic.Lambda (b, s, t)) leftno ty cic
+ in
+(*
+debug_print (lazy (CicPp.ppterm eliminator_type));
+debug_print (lazy (CicPp.ppterm eliminator_body));
+*)
+ let eliminator_type =
+ FreshNamesGenerator.mk_fresh_names [] [] [] eliminator_type in
+ let eliminator_body =
+ FreshNamesGenerator.mk_fresh_names [] [] [] eliminator_body in
+(*
+debug_print (lazy (CicPp.ppterm eliminator_type));
+debug_print (lazy (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 (lazy (sprintf
+ "type checker failure while type checking:\n%s\nerror:\n%s"
+ (CicPp.ppterm eliminator_body) (Lazy.force 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
+ let name = UriManager.name_of_uri uri ^ suffix in
+ let buri = UriManager.buri_of_uri uri in
+ let uri = UriManager.uri_of_string (buri ^ "/" ^ name ^ ".con") in
+ let obj_attrs = [`Class (`Elim sort); `Generated] in
+ uri,
+ Cic.Constant (name, Some eliminator_body, eliminator_type, [], obj_attrs)
+ | _ ->
+ failwith (sprintf "not an inductive definition (%s)"
+ (UriManager.string_of_uri uri))
projects / helm.git / blobdiff