author | wenzelm |
Thu, 05 Jul 2007 20:01:36 +0200 | |
changeset 23599 | d889725b0d8a |
parent 23585 | f07ef41ffb87 |
child 23655 | d2d1138e0ddc |
permissions | -rw-r--r-- |
2956 | 1 |
(* Title: Pure/sorts.ML |
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ID: $Id$ |
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Author: Markus Wenzel and Stefan Berghofer, TU Muenchen |
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The order-sorted algebra of type classes. |
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Classes denote (possibly empty) collections of types that are |
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partially ordered by class inclusion. They are represented |
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symbolically by strings. |
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Sorts are intersections of finitely many classes. They are represented |
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by lists of classes. Normal forms of sorts are sorted lists of |
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minimal classes (wrt. current class inclusion). |
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*) |
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||
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signature SORTS = |
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sig |
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val union: sort list -> sort list -> sort list |
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val subtract: sort list -> sort list -> sort list |
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val remove_sort: sort -> sort list -> sort list |
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59381032be14
removed obsolete eq_sort, mem_sort, subset_sort, eq_set_sort, ins_sort, union_sort, rems_sort;
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parents:
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val insert_sort: sort -> sort list -> sort list |
59381032be14
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val insert_typ: typ -> sort list -> sort list |
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val insert_typs: typ list -> sort list -> sort list |
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val insert_term: term -> sort list -> sort list |
59381032be14
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val insert_terms: term list -> sort list -> sort list |
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type algebra |
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val rep_algebra: algebra -> |
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{classes: serial Graph.T, |
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arities: (class * (class * sort list)) list Symtab.table} |
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classes: more direct way to achieve topological sorting;
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val all_classes: algebra -> class list |
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val minimal_classes: algebra -> class list |
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val super_classes: algebra -> class -> class list |
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val class_less: algebra -> class * class -> bool |
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val class_le: algebra -> class * class -> bool |
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val sort_eq: algebra -> sort * sort -> bool |
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val sort_le: algebra -> sort * sort -> bool |
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val sorts_le: algebra -> sort list * sort list -> bool |
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val inter_sort: algebra -> sort * sort -> sort |
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val certify_class: algebra -> class -> class (*exception TYPE*) |
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val certify_sort: algebra -> sort -> sort (*exception TYPE*) |
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val add_class: Pretty.pp -> class * class list -> algebra -> algebra |
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val add_classrel: Pretty.pp -> class * class -> algebra -> algebra |
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val add_arities: Pretty.pp -> string * (class * sort list) list -> algebra -> algebra |
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val empty_algebra: algebra |
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val merge_algebra: Pretty.pp -> algebra * algebra -> algebra |
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val subalgebra: Pretty.pp -> (class -> bool) -> (class * string -> sort list) |
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-> algebra -> (sort -> sort) * algebra |
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type class_error |
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val msg_class_error: Pretty.pp -> class_error -> string |
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val class_error: Pretty.pp -> class_error -> 'a |
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exception CLASS_ERROR of class_error |
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val mg_domain: algebra -> string -> sort -> sort list (*exception CLASS_ERROR*) |
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val of_sort: algebra -> typ * sort -> bool |
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val of_sort_derivation: Pretty.pp -> algebra -> |
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{class_relation: 'a * class -> class -> 'a, |
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type_constructor: string -> ('a * class) list list -> class -> 'a, |
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type_variable: typ -> ('a * class) list} -> |
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typ * sort -> 'a list (*exception CLASS_ERROR*) |
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val witness_sorts: algebra -> string list -> sort list -> sort list -> (typ * sort) list |
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end; |
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structure Sorts: SORTS = |
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struct |
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(** ordered lists of sorts **) |
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val op union = OrdList.union Term.sort_ord; |
59381032be14
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val subtract = OrdList.subtract Term.sort_ord; |
14782
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incorporate sort ops from term.ML; use Graph.T; misc cleanup;
wenzelm
parents:
9281
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val remove_sort = OrdList.remove Term.sort_ord; |
16598
59381032be14
removed obsolete eq_sort, mem_sort, subset_sort, eq_set_sort, ins_sort, union_sort, rems_sort;
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parents:
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val insert_sort = OrdList.insert Term.sort_ord; |
14782
d6ce35a1c386
incorporate sort ops from term.ML; use Graph.T; misc cleanup;
wenzelm
parents:
9281
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73 |
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16598
59381032be14
removed obsolete eq_sort, mem_sort, subset_sort, eq_set_sort, ins_sort, union_sort, rems_sort;
wenzelm
parents:
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fun insert_typ (TFree (_, S)) Ss = insert_sort S Ss |
59381032be14
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| insert_typ (TVar (_, S)) Ss = insert_sort S Ss |
59381032be14
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| insert_typ (Type (_, Ts)) Ss = insert_typs Ts Ss |
59381032be14
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parents:
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and insert_typs [] Ss = Ss |
59381032be14
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| insert_typs (T :: Ts) Ss = insert_typs Ts (insert_typ T Ss); |
14782
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incorporate sort ops from term.ML; use Graph.T; misc cleanup;
wenzelm
parents:
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79 |
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16598
59381032be14
removed obsolete eq_sort, mem_sort, subset_sort, eq_set_sort, ins_sort, union_sort, rems_sort;
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parents:
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fun insert_term (Const (_, T)) Ss = insert_typ T Ss |
59381032be14
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| insert_term (Free (_, T)) Ss = insert_typ T Ss |
59381032be14
removed obsolete eq_sort, mem_sort, subset_sort, eq_set_sort, ins_sort, union_sort, rems_sort;
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parents:
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| insert_term (Var (_, T)) Ss = insert_typ T Ss |
59381032be14
removed obsolete eq_sort, mem_sort, subset_sort, eq_set_sort, ins_sort, union_sort, rems_sort;
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parents:
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| insert_term (Bound _) Ss = Ss |
59381032be14
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| insert_term (Abs (_, T, t)) Ss = insert_term t (insert_typ T Ss) |
59381032be14
removed obsolete eq_sort, mem_sort, subset_sort, eq_set_sort, ins_sort, union_sort, rems_sort;
wenzelm
parents:
16400
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| insert_term (t $ u) Ss = insert_term t (insert_term u Ss); |
14782
d6ce35a1c386
incorporate sort ops from term.ML; use Graph.T; misc cleanup;
wenzelm
parents:
9281
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changeset
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86 |
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16598
59381032be14
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parents:
16400
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fun insert_terms [] Ss = Ss |
59381032be14
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wenzelm
parents:
16400
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changeset
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| insert_terms (t :: ts) Ss = insert_terms ts (insert_term t Ss); |
14782
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incorporate sort ops from term.ML; use Graph.T; misc cleanup;
wenzelm
parents:
9281
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|
d6ce35a1c386
incorporate sort ops from term.ML; use Graph.T; misc cleanup;
wenzelm
parents:
9281
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(** order-sorted algebra **) |
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(* |
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14782
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incorporate sort ops from term.ML; use Graph.T; misc cleanup;
wenzelm
parents:
9281
diff
changeset
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95 |
classes: graph representing class declarations together with proper |
d6ce35a1c386
incorporate sort ops from term.ML; use Graph.T; misc cleanup;
wenzelm
parents:
9281
diff
changeset
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subclass relation, which needs to be transitive and acyclic. |
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14782
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incorporate sort ops from term.ML; use Graph.T; misc cleanup;
wenzelm
parents:
9281
diff
changeset
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arities: table of association lists of all type arities; (t, ars) |
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means that type constructor t has the arities ars; an element |
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(c, (c0, Ss)) of ars represents the arity t::(Ss)c being derived |
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via c0 <= c. "Coregularity" of the arities structure requires |
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that for any two declarations t::(Ss1)c1 and t::(Ss2)c2 such that |
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c1 <= c2 holds Ss1 <= Ss2. |
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*) |
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datatype algebra = Algebra of |
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{classes: serial Graph.T, |
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arities: (class * (class * sort list)) list Symtab.table}; |
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fun rep_algebra (Algebra args) = args; |
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val classes_of = #classes o rep_algebra; |
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val arities_of = #arities o rep_algebra; |
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fun make_algebra (classes, arities) = |
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Algebra {classes = classes, arities = arities}; |
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fun map_classes f (Algebra {classes, arities}) = make_algebra (f classes, arities); |
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fun map_arities f (Algebra {classes, arities}) = make_algebra (classes, f arities); |
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(* classes *) |
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fun all_classes (Algebra {classes, ...}) = Graph.all_preds classes (Graph.maximals classes); |
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classes: more direct way to achieve topological sorting;
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val minimal_classes = Graph.minimals o classes_of; |
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val super_classes = Graph.imm_succs o classes_of; |
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(* class relations *) |
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val class_less = Graph.is_edge o classes_of; |
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fun class_le algebra (c1, c2) = c1 = c2 orelse class_less algebra (c1, c2); |
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(* sort relations *) |
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fun sort_le algebra (S1, S2) = |
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S1 = S2 orelse forall (fn c2 => exists (fn c1 => class_le algebra (c1, c2)) S1) S2; |
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fun sorts_le algebra (Ss1, Ss2) = |
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ListPair.all (sort_le algebra) (Ss1, Ss2); |
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fun sort_eq algebra (S1, S2) = |
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sort_le algebra (S1, S2) andalso sort_le algebra (S2, S1); |
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(* intersection *) |
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fun inter_class algebra c S = |
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let |
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fun intr [] = [c] |
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| intr (S' as c' :: c's) = |
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if class_le algebra (c', c) then S' |
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else if class_le algebra (c, c') then intr c's |
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else c' :: intr c's |
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in intr S end; |
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fun inter_sort algebra (S1, S2) = |
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sort_strings (fold (inter_class algebra) S1 S2); |
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(* normal form *) |
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fun norm_sort _ [] = [] |
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| norm_sort _ (S as [_]) = S |
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| norm_sort algebra S = |
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filter (fn c => not (exists (fn c' => class_less algebra (c', c)) S)) S |
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|> sort_distinct string_ord; |
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(* certify *) |
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fun certify_class algebra c = |
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if can (Graph.get_node (classes_of algebra)) c then c |
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else raise TYPE ("Undeclared class: " ^ quote c, [], []); |
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fun certify_sort classes = norm_sort classes o map (certify_class classes); |
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(** build algebras **) |
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(* classes *) |
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fun err_dup_classes cs = |
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error ("Duplicate declaration of class(es): " ^ commas_quote cs); |
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fun err_cyclic_classes pp css = |
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error (cat_lines (map (fn cs => |
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"Cycle in class relation: " ^ Pretty.string_of_classrel pp cs) css)); |
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fun add_class pp (c, cs) = map_classes (fn classes => |
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let |
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val classes' = classes |> Graph.new_node (c, serial ()) |
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handle Graph.DUP dup => err_dup_classes [dup]; |
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val classes'' = classes' |> fold Graph.add_edge_trans_acyclic (map (pair c) cs) |
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handle Graph.CYCLES css => err_cyclic_classes pp css; |
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in classes'' end); |
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(* arities *) |
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local |
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fun for_classes _ NONE = "" |
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| for_classes pp (SOME (c1, c2)) = |
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" for classes " ^ Pretty.string_of_classrel pp [c1, c2]; |
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fun err_conflict pp t cc (c, Ss) (c', Ss') = |
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error ("Conflict of type arities" ^ for_classes pp cc ^ ":\n " ^ |
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Pretty.string_of_arity pp (t, Ss, [c]) ^ " and\n " ^ |
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Pretty.string_of_arity pp (t, Ss', [c'])); |
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fun coregular pp algebra t (c, (c0, Ss)) ars = |
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let |
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fun conflict (c', (_, Ss')) = |
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if class_le algebra (c, c') andalso not (sorts_le algebra (Ss, Ss')) then |
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SOME ((c, c'), (c', Ss')) |
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else if class_le algebra (c', c) andalso not (sorts_le algebra (Ss', Ss)) then |
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SOME ((c', c), (c', Ss')) |
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else NONE; |
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in |
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(case get_first conflict ars of |
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SOME ((c1, c2), (c', Ss')) => err_conflict pp t (SOME (c1, c2)) (c, Ss) (c', Ss') |
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| NONE => (c, (c0, Ss)) :: ars) |
19514 | 227 |
end; |
228 |
||
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fun complete algebra (c0, Ss) = map (rpair (c0, Ss)) (c0 :: super_classes algebra c0); |
230 |
||
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fun insert pp algebra t (c, (c0, Ss)) ars = |
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19514 | 232 |
(case AList.lookup (op =) ars c of |
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NONE => coregular pp algebra t (c, (c0, Ss)) ars |
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| SOME (_, Ss') => |
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if sorts_le algebra (Ss, Ss') then ars |
236 |
else if sorts_le algebra (Ss', Ss) then |
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coregular pp algebra t (c, (c0, Ss)) |
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19524 | 238 |
(filter_out (fn (c'', (_, Ss'')) => c = c'' andalso Ss'' = Ss') ars) |
19514 | 239 |
else err_conflict pp t NONE (c, Ss) (c, Ss')); |
240 |
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fun insert_ars pp algebra (t, ars) arities = |
242 |
let val ars' = |
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Symtab.lookup_list arities t |
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|> fold_rev (fold_rev (insert pp algebra t)) (map (complete algebra) ars) |
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in Symtab.update (t, ars') arities end; |
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19514 | 246 |
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in |
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248 |
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fun add_arities pp arg algebra = algebra |> map_arities (insert_ars pp algebra arg); |
19514 | 250 |
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fun add_arities_table pp algebra = |
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Symtab.fold (fn (t, ars) => insert_ars pp algebra (t, map snd ars)); |
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19514 | 253 |
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end; |
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(* classrel *) |
258 |
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259 |
fun rebuild_arities pp algebra = algebra |> map_arities (fn arities => |
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Symtab.empty |
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|> add_arities_table pp algebra arities); |
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fun add_classrel pp rel = rebuild_arities pp o map_classes (fn classes => |
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classes |> Graph.add_edge_trans_acyclic rel |
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handle Graph.CYCLES css => err_cyclic_classes pp css); |
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268 |
(* empty and merge *) |
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val empty_algebra = make_algebra (Graph.empty, Symtab.empty); |
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fun merge_algebra pp |
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(Algebra {classes = classes1, arities = arities1}, |
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Algebra {classes = classes2, arities = arities2}) = |
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let |
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val classes' = Graph.merge_trans_acyclic (op =) (classes1, classes2) |
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handle Graph.DUPS cs => err_dup_classes cs |
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| Graph.CYCLES css => err_cyclic_classes pp css; |
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val algebra0 = make_algebra (classes', Symtab.empty); |
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val arities' = Symtab.empty |
|
281 |
|> add_arities_table pp algebra0 arities1 |
|
282 |
|> add_arities_table pp algebra0 arities2; |
|
283 |
in make_algebra (classes', arities') end; |
|
284 |
||
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285 |
|
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286 |
(* subalgebra *) |
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287 |
|
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288 |
fun subalgebra pp P sargs (algebra as Algebra {classes, arities}) = |
19952 | 289 |
let |
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290 |
val restrict_sort = norm_sort algebra o filter P o Graph.all_succs classes; |
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291 |
fun restrict_arity tyco (c, (_, Ss)) = |
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292 |
if P c then |
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293 |
SOME (c, (c, Ss |> map2 (curry (inter_sort algebra)) (sargs (c, tyco)) |
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294 |
|> map restrict_sort)) |
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295 |
else NONE; |
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296 |
val classes' = classes |> Graph.subgraph P; |
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297 |
val arities' = arities |> Symtab.map' (map_filter o restrict_arity); |
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298 |
in (restrict_sort, rebuild_arities pp (make_algebra (classes', arities'))) end; |
20465 | 299 |
|
19645 | 300 |
|
19529 | 301 |
|
302 |
(** sorts of types **) |
|
303 |
||
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|
304 |
(* errors *) |
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305 |
|
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306 |
datatype class_error = NoClassrel of class * class | NoArity of string * class; |
19529 | 307 |
|
22196 | 308 |
fun msg_class_error pp (NoClassrel (c1, c2)) = |
309 |
"No class relation " ^ Pretty.string_of_classrel pp [c1, c2] |
|
310 |
| msg_class_error pp (NoArity (a, c)) = |
|
311 |
"No type arity " ^ Pretty.string_of_arity pp (a, [], [c]); |
|
312 |
||
313 |
fun class_error pp = error o msg_class_error pp; |
|
19529 | 314 |
|
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315 |
exception CLASS_ERROR of class_error; |
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316 |
|
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|
317 |
|
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318 |
(* mg_domain *) |
19529 | 319 |
|
19645 | 320 |
fun mg_domain algebra a S = |
19529 | 321 |
let |
19645 | 322 |
val arities = arities_of algebra; |
19529 | 323 |
fun dom c = |
324 |
(case AList.lookup (op =) (Symtab.lookup_list arities a) c of |
|
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325 |
NONE => raise CLASS_ERROR (NoArity (a, c)) |
19529 | 326 |
| SOME (_, Ss) => Ss); |
19645 | 327 |
fun dom_inter c Ss = ListPair.map (inter_sort algebra) (dom c, Ss); |
19529 | 328 |
in |
329 |
(case S of |
|
330 |
[] => raise Fail "Unknown domain of empty intersection" |
|
331 |
| c :: cs => fold dom_inter cs (dom c)) |
|
332 |
end; |
|
333 |
||
334 |
||
335 |
(* of_sort *) |
|
336 |
||
19645 | 337 |
fun of_sort algebra = |
19529 | 338 |
let |
339 |
fun ofS (_, []) = true |
|
19645 | 340 |
| ofS (TFree (_, S), S') = sort_le algebra (S, S') |
341 |
| ofS (TVar (_, S), S') = sort_le algebra (S, S') |
|
19529 | 342 |
| ofS (Type (a, Ts), S) = |
19645 | 343 |
let val Ss = mg_domain algebra a S in |
19529 | 344 |
ListPair.all ofS (Ts, Ss) |
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345 |
end handle CLASS_ERROR _ => false; |
19529 | 346 |
in ofS end; |
347 |
||
348 |
||
349 |
(* of_sort_derivation *) |
|
350 |
||
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|
351 |
fun of_sort_derivation pp algebra {class_relation, type_constructor, type_variable} = |
19529 | 352 |
let |
19645 | 353 |
val {classes, arities} = rep_algebra algebra; |
19952 | 354 |
fun weaken_path (x, c1 :: c2 :: cs) = |
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changeset
|
355 |
weaken_path (class_relation (x, c1) c2, c2 :: cs) |
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|
356 |
| weaken_path (x, _) = x; |
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|
357 |
fun weaken (x, c1) c2 = |
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|
358 |
(case Graph.irreducible_paths classes (c1, c2) of |
f93b7637a5e6
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|
359 |
[] => raise CLASS_ERROR (NoClassrel (c1, c2)) |
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|
360 |
| cs :: _ => weaken_path (x, cs)); |
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diff
changeset
|
361 |
|
19529 | 362 |
fun weakens S1 S2 = S2 |> map (fn c2 => |
19645 | 363 |
(case S1 |> find_first (fn (_, c1) => class_le algebra (c1, c2)) of |
19529 | 364 |
SOME d1 => weaken d1 c2 |
365 |
| NONE => error ("Cannot derive subsort relation " ^ |
|
366 |
Pretty.string_of_sort pp (map #2 S1) ^ " < " ^ Pretty.string_of_sort pp S2))); |
|
367 |
||
368 |
fun derive _ [] = [] |
|
369 |
| derive (Type (a, Ts)) S = |
|
370 |
let |
|
19645 | 371 |
val Ss = mg_domain algebra a S; |
19529 | 372 |
val dom = map2 (fn T => fn S => derive T S ~~ S) Ts Ss; |
373 |
in |
|
374 |
S |> map (fn c => |
|
375 |
let |
|
376 |
val (c0, Ss') = the (AList.lookup (op =) (Symtab.lookup_list arities a) c); |
|
377 |
val dom' = map2 (fn d => fn S' => weakens d S' ~~ S') dom Ss'; |
|
22570
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parents:
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diff
changeset
|
378 |
in weaken (type_constructor a dom' c0, c0) c end) |
19529 | 379 |
end |
22570
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parents:
22364
diff
changeset
|
380 |
| derive T S = weakens (type_variable T) S; |
19529 | 381 |
in uncurry derive end; |
382 |
||
383 |
||
384 |
(* witness_sorts *) |
|
385 |
||
19645 | 386 |
fun witness_sorts algebra types hyps sorts = |
19529 | 387 |
let |
19645 | 388 |
fun le S1 S2 = sort_le algebra (S1, S2); |
19529 | 389 |
fun get_solved S2 (T, S1) = if le S1 S2 then SOME (T, S2) else NONE; |
390 |
fun get_hyp S2 S1 = if le S1 S2 then SOME (TFree ("'hyp", S1), S2) else NONE; |
|
19645 | 391 |
fun mg_dom t S = SOME (mg_domain algebra t S) handle CLASS_ERROR _ => NONE; |
19529 | 392 |
|
19578
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wenzelm
parents:
19531
diff
changeset
|
393 |
fun witn_sort _ [] solved_failed = (SOME (propT, []), solved_failed) |
f93b7637a5e6
added class_error and exception CLASS_ERROR (supercedes DOMAIN);
wenzelm
parents:
19531
diff
changeset
|
394 |
| witn_sort path S (solved, failed) = |
f93b7637a5e6
added class_error and exception CLASS_ERROR (supercedes DOMAIN);
wenzelm
parents:
19531
diff
changeset
|
395 |
if exists (le S) failed then (NONE, (solved, failed)) |
19529 | 396 |
else |
397 |
(case get_first (get_solved S) solved of |
|
19578
f93b7637a5e6
added class_error and exception CLASS_ERROR (supercedes DOMAIN);
wenzelm
parents:
19531
diff
changeset
|
398 |
SOME w => (SOME w, (solved, failed)) |
19529 | 399 |
| NONE => |
400 |
(case get_first (get_hyp S) hyps of |
|
19578
f93b7637a5e6
added class_error and exception CLASS_ERROR (supercedes DOMAIN);
wenzelm
parents:
19531
diff
changeset
|
401 |
SOME w => (SOME w, (w :: solved, failed)) |
19584 | 402 |
| NONE => witn_types path types S (solved, failed))) |
19529 | 403 |
|
19578
f93b7637a5e6
added class_error and exception CLASS_ERROR (supercedes DOMAIN);
wenzelm
parents:
19531
diff
changeset
|
404 |
and witn_sorts path x = fold_map (witn_sort path) x |
19529 | 405 |
|
19578
f93b7637a5e6
added class_error and exception CLASS_ERROR (supercedes DOMAIN);
wenzelm
parents:
19531
diff
changeset
|
406 |
and witn_types _ [] S (solved, failed) = (NONE, (solved, S :: failed)) |
f93b7637a5e6
added class_error and exception CLASS_ERROR (supercedes DOMAIN);
wenzelm
parents:
19531
diff
changeset
|
407 |
| witn_types path (t :: ts) S solved_failed = |
19529 | 408 |
(case mg_dom t S of |
409 |
SOME SS => |
|
410 |
(*do not descend into stronger args (achieving termination)*) |
|
411 |
if exists (fn D => le D S orelse exists (le D) path) SS then |
|
19578
f93b7637a5e6
added class_error and exception CLASS_ERROR (supercedes DOMAIN);
wenzelm
parents:
19531
diff
changeset
|
412 |
witn_types path ts S solved_failed |
19529 | 413 |
else |
19578
f93b7637a5e6
added class_error and exception CLASS_ERROR (supercedes DOMAIN);
wenzelm
parents:
19531
diff
changeset
|
414 |
let val (ws, (solved', failed')) = witn_sorts (S :: path) SS solved_failed in |
19529 | 415 |
if forall is_some ws then |
416 |
let val w = (Type (t, map (#1 o the) ws), S) |
|
19578
f93b7637a5e6
added class_error and exception CLASS_ERROR (supercedes DOMAIN);
wenzelm
parents:
19531
diff
changeset
|
417 |
in (SOME w, (w :: solved', failed')) end |
f93b7637a5e6
added class_error and exception CLASS_ERROR (supercedes DOMAIN);
wenzelm
parents:
19531
diff
changeset
|
418 |
else witn_types path ts S (solved', failed') |
19529 | 419 |
end |
19578
f93b7637a5e6
added class_error and exception CLASS_ERROR (supercedes DOMAIN);
wenzelm
parents:
19531
diff
changeset
|
420 |
| NONE => witn_types path ts S solved_failed); |
19529 | 421 |
|
19584 | 422 |
in map_filter I (#1 (witn_sorts [] sorts ([], []))) end; |
19529 | 423 |
|
19514 | 424 |
end; |