author | blanchet |
Mon, 06 Dec 2010 13:29:23 +0100 | |
changeset 40996 | 63112be4a469 |
parent 39687 | 4e9b6ada3a21 |
child 42383 | 0ae4ad40d7b5 |
permissions | -rw-r--r-- |
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(* Title: Pure/sorts.ML |
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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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signature SORTS = |
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sig |
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val make: sort list -> sort Ord_List.T |
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val subset: sort Ord_List.T * sort Ord_List.T -> bool |
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val union: sort Ord_List.T -> sort Ord_List.T -> sort Ord_List.T |
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val subtract: sort Ord_List.T -> sort Ord_List.T -> sort Ord_List.T |
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val remove_sort: sort -> sort Ord_List.T -> sort Ord_List.T |
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val insert_sort: sort -> sort Ord_List.T -> sort Ord_List.T |
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val insert_typ: typ -> sort Ord_List.T -> sort Ord_List.T |
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val insert_typs: typ list -> sort Ord_List.T -> sort Ord_List.T |
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val insert_term: term -> sort Ord_List.T -> sort Ord_List.T |
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val insert_terms: term list -> sort Ord_List.T -> sort Ord_List.T |
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type algebra |
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replaced Sorts.rep_algebra by slightly more abstract selectors classes_of/arities_of;
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val classes_of: algebra -> serial Graph.T |
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arities: no need to maintain original codomain (cf. f795c1164708) -- completion happens in axclass.ML;
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val arities_of: algebra -> (class * sort list) list Symtab.table |
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val all_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 minimize_sort: algebra -> sort -> sort |
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val complete_sort: algebra -> sort -> sort |
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val minimal_sorts: algebra -> sort list -> sort Ord_List.T |
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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 option) |
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-> algebra -> (sort -> sort) * algebra |
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added class_error and exception CLASS_ERROR (supercedes DOMAIN);
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type class_error |
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val class_error: Pretty.pp -> class_error -> string |
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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 meet_sort: algebra -> typ * sort |
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-> sort Vartab.table -> sort Vartab.table (*exception CLASS_ERROR*) |
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val meet_sort_typ: algebra -> typ * sort -> typ -> typ (*exception CLASS_ERROR*) |
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val of_sort: algebra -> typ * sort -> bool |
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val of_sort_derivation: algebra -> |
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{class_relation: typ -> 'a * class -> class -> 'a, |
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type_constructor: string * typ list -> ('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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Sorts.of_sort_derivation: do not use slow Graph.irreducible_paths here, which not always needed (SUBTLE CHANGE IN SEMANTICS);
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val classrel_derivation: algebra -> |
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('a * class -> class -> 'a) -> 'a * class -> class -> 'a (*exception CLASS_ERROR*) |
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witness_sorts: proper type witnesses for hyps, not invented "'hyp" variables;
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val witness_sorts: algebra -> string list -> (typ * 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 make = Ord_List.make Term_Ord.sort_ord; |
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val subset = Ord_List.subset Term_Ord.sort_ord; |
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val union = Ord_List.union Term_Ord.sort_ord; |
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val subtract = Ord_List.subtract Term_Ord.sort_ord; |
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val remove_sort = Ord_List.remove Term_Ord.sort_ord; |
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val insert_sort = Ord_List.insert Term_Ord.sort_ord; |
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removed obsolete eq_sort, mem_sort, subset_sort, eq_set_sort, ins_sort, union_sort, rems_sort;
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fun insert_typ (TFree (_, S)) Ss = insert_sort S Ss |
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| insert_typ (TVar (_, S)) Ss = insert_sort S Ss |
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| insert_typ (Type (_, Ts)) Ss = insert_typs Ts Ss |
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and insert_typs [] Ss = Ss |
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| insert_typs (T :: Ts) Ss = insert_typs Ts (insert_typ T Ss); |
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incorporate sort ops from term.ML; use Graph.T; misc cleanup;
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removed obsolete eq_sort, mem_sort, subset_sort, eq_set_sort, ins_sort, union_sort, rems_sort;
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fun insert_term (Const (_, T)) Ss = insert_typ T Ss |
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removed obsolete eq_sort, mem_sort, subset_sort, eq_set_sort, ins_sort, union_sort, rems_sort;
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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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| 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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| insert_term (Bound _) Ss = Ss |
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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;
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| insert_term (t $ u) Ss = insert_term t (insert_term u Ss); |
14782
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16598
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removed obsolete eq_sort, mem_sort, subset_sort, eq_set_sort, ins_sort, union_sort, rems_sort;
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fun insert_terms [] Ss = Ss |
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removed obsolete eq_sort, mem_sort, subset_sort, eq_set_sort, ins_sort, union_sort, rems_sort;
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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;
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|
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incorporate sort ops from term.ML; use Graph.T; misc cleanup;
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(** order-sorted algebra **) |
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(* |
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classes: graph representing class declarations together with proper |
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subclass relation, which needs to be transitive and acyclic. |
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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, Ss) of ars represents the arity t::(Ss)c. "Coregularity" of |
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the arities structure requires that for any two declarations |
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t::(Ss1)c1 and t::(Ss2)c2 such that 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 * sort list) list Symtab.table}; |
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fun classes_of (Algebra {classes, ...}) = classes; |
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fun arities_of (Algebra {arities, ...}) = arities; |
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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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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 forms *) |
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fun minimize_sort _ [] = [] |
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| minimize_sort _ (S as [_]) = S |
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| minimize_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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fun complete_sort algebra = |
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Graph.all_succs (classes_of algebra) o minimize_sort algebra; |
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fun minimal_sorts algebra raw_sorts = |
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let |
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fun le S1 S2 = sort_le algebra (S1, S2); |
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val sorts = make (map (minimize_sort algebra) raw_sorts); |
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in sorts |> filter_out (fn S => exists (fn S' => le S' S andalso not (le S S')) sorts) end; |
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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 = map (certify_class classes); |
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(** build algebras **) |
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(* classes *) |
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fun err_dup_class c = error ("Duplicate declaration of class: " ^ quote c); |
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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_class dup; |
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val classes'' = classes' |> fold Graph.add_edge_trans_acyclic (map (pair c) cs) |
210 |
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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227 |
fun coregular pp algebra t (c, Ss) ars = |
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let |
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229 |
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, Ss) :: ars) |
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end; |
240 |
||
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fun complete algebra (c, Ss) = map (rpair Ss) (c :: super_classes algebra c); |
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243 |
fun insert pp algebra t (c, Ss) ars = |
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(case AList.lookup (op =) ars c of |
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|
245 |
NONE => coregular pp algebra t (c, Ss) ars |
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arities: no need to maintain original codomain (cf. f795c1164708) -- completion happens in axclass.ML;
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|
246 |
| SOME Ss' => |
19645 | 247 |
if sorts_le algebra (Ss, Ss') then ars |
37248
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arities: no need to maintain original codomain (cf. f795c1164708) -- completion happens in axclass.ML;
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|
248 |
else if sorts_le algebra (Ss', Ss) |
8e8e5f9d1441
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|
249 |
then coregular pp algebra t (c, Ss) (remove (op =) (c, Ss') ars) |
19514 | 250 |
else err_conflict pp t NONE (c, Ss) (c, Ss')); |
251 |
||
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|
252 |
in |
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|
253 |
|
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|
254 |
fun insert_ars pp algebra t = fold_rev (insert pp algebra t); |
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|
255 |
|
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|
256 |
fun insert_complete_ars pp algebra (t, ars) arities = |
19645 | 257 |
let val ars' = |
258 |
Symtab.lookup_list arities t |
|
35975
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|
259 |
|> fold_rev (insert_ars pp algebra t) (map (complete algebra) ars); |
19645 | 260 |
in Symtab.update (t, ars') arities end; |
19514 | 261 |
|
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|
262 |
fun add_arities pp arg algebra = |
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|
263 |
algebra |> map_arities (insert_complete_ars pp algebra arg); |
19514 | 264 |
|
19645 | 265 |
fun add_arities_table pp algebra = |
37248
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|
266 |
Symtab.fold (fn (t, ars) => insert_complete_ars pp algebra (t, ars)); |
19514 | 267 |
|
268 |
end; |
|
269 |
||
19529 | 270 |
|
19645 | 271 |
(* classrel *) |
272 |
||
273 |
fun rebuild_arities pp algebra = algebra |> map_arities (fn arities => |
|
274 |
Symtab.empty |
|
275 |
|> add_arities_table pp algebra arities); |
|
276 |
||
277 |
fun add_classrel pp rel = rebuild_arities pp o map_classes (fn classes => |
|
278 |
classes |> Graph.add_edge_trans_acyclic rel |
|
279 |
handle Graph.CYCLES css => err_cyclic_classes pp css); |
|
280 |
||
281 |
||
282 |
(* empty and merge *) |
|
283 |
||
284 |
val empty_algebra = make_algebra (Graph.empty, Symtab.empty); |
|
285 |
||
286 |
fun merge_algebra pp |
|
287 |
(Algebra {classes = classes1, arities = arities1}, |
|
288 |
Algebra {classes = classes2, arities = arities2}) = |
|
289 |
let |
|
290 |
val classes' = Graph.merge_trans_acyclic (op =) (classes1, classes2) |
|
23655
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|
291 |
handle Graph.DUP c => err_dup_class c |
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|
292 |
| Graph.CYCLES css => err_cyclic_classes pp css; |
19645 | 293 |
val algebra0 = make_algebra (classes', Symtab.empty); |
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|
294 |
val arities' = |
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|
295 |
(case (pointer_eq (classes1, classes2), pointer_eq (arities1, arities2)) of |
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|
296 |
(true, true) => arities1 |
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|
297 |
| (true, false) => (*no completion*) |
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|
298 |
(arities1, arities2) |> Symtab.join (fn t => fn (ars1, ars2) => |
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|
299 |
if pointer_eq (ars1, ars2) then raise Symtab.SAME |
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|
300 |
else insert_ars pp algebra0 t ars2 ars1) |
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|
301 |
| (false, true) => (*unary completion*) |
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|
302 |
Symtab.empty |
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|
303 |
|> add_arities_table pp algebra0 arities1 |
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|
304 |
| (false, false) => (*binary completion*) |
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|
305 |
Symtab.empty |
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|
306 |
|> add_arities_table pp algebra0 arities1 |
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|
307 |
|> add_arities_table pp algebra0 arities2); |
19645 | 308 |
in make_algebra (classes', arities') end; |
309 |
||
21933
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classes: more direct way to achieve topological sorting;
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changeset
|
310 |
|
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arities: no need to maintain original codomain (cf. f795c1164708) -- completion happens in axclass.ML;
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|
311 |
(* algebra projections *) (* FIXME potentially violates abstract type integrity *) |
28922 | 312 |
|
22181
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changeset
|
313 |
fun subalgebra pp P sargs (algebra as Algebra {classes, arities}) = |
19952 | 314 |
let |
24732 | 315 |
val restrict_sort = minimize_sort algebra o filter P o Graph.all_succs classes; |
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|
316 |
fun restrict_arity t (c, Ss) = |
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|
317 |
if P c then |
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parents:
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|
318 |
(case sargs (c, t) of |
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arities: no need to maintain original codomain (cf. f795c1164708) -- completion happens in axclass.ML;
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parents:
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|
319 |
SOME sorts => |
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|
320 |
SOME (c, Ss |> map2 (curry (inter_sort algebra)) sorts |> map restrict_sort) |
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arities: no need to maintain original codomain (cf. f795c1164708) -- completion happens in axclass.ML;
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parents:
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|
321 |
| NONE => NONE) |
22181
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added explicit query function for arities to subalgebra projection
haftmann
parents:
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diff
changeset
|
322 |
else NONE; |
21933
819ef284720b
classes: more direct way to achieve topological sorting;
wenzelm
parents:
21926
diff
changeset
|
323 |
val classes' = classes |> Graph.subgraph P; |
39020 | 324 |
val arities' = arities |> Symtab.map (map_filter o restrict_arity); |
21933
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classes: more direct way to achieve topological sorting;
wenzelm
parents:
21926
diff
changeset
|
325 |
in (restrict_sort, rebuild_arities pp (make_algebra (classes', arities'))) end; |
20465 | 326 |
|
19645 | 327 |
|
19529 | 328 |
|
329 |
(** sorts of types **) |
|
330 |
||
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00e48e1d9afd
Sorts.of_sort_derivation: do not use slow Graph.irreducible_paths here, which not always needed (SUBTLE CHANGE IN SEMANTICS);
wenzelm
parents:
35408
diff
changeset
|
331 |
(* errors -- performance tuning via delayed message composition *) |
19578
f93b7637a5e6
added class_error and exception CLASS_ERROR (supercedes DOMAIN);
wenzelm
parents:
19531
diff
changeset
|
332 |
|
26639 | 333 |
datatype class_error = |
36105 | 334 |
No_Classrel of class * class | |
335 |
No_Arity of string * class | |
|
336 |
No_Subsort of sort * sort; |
|
19529 | 337 |
|
36105 | 338 |
fun class_error pp (No_Classrel (c1, c2)) = |
22196 | 339 |
"No class relation " ^ Pretty.string_of_classrel pp [c1, c2] |
36105 | 340 |
| class_error pp (No_Arity (a, c)) = |
26326 | 341 |
"No type arity " ^ Pretty.string_of_arity pp (a, [], [c]) |
36105 | 342 |
| class_error pp (No_Subsort (S1, S2)) = |
26994 | 343 |
"Cannot derive subsort relation " ^ Pretty.string_of_sort pp S1 |
344 |
^ " < " ^ Pretty.string_of_sort pp S2; |
|
19529 | 345 |
|
19578
f93b7637a5e6
added class_error and exception CLASS_ERROR (supercedes DOMAIN);
wenzelm
parents:
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diff
changeset
|
346 |
exception CLASS_ERROR of class_error; |
f93b7637a5e6
added class_error and exception CLASS_ERROR (supercedes DOMAIN);
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parents:
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diff
changeset
|
347 |
|
f93b7637a5e6
added class_error and exception CLASS_ERROR (supercedes DOMAIN);
wenzelm
parents:
19531
diff
changeset
|
348 |
|
f93b7637a5e6
added class_error and exception CLASS_ERROR (supercedes DOMAIN);
wenzelm
parents:
19531
diff
changeset
|
349 |
(* mg_domain *) |
19529 | 350 |
|
19645 | 351 |
fun mg_domain algebra a S = |
19529 | 352 |
let |
19645 | 353 |
val arities = arities_of algebra; |
19529 | 354 |
fun dom c = |
355 |
(case AList.lookup (op =) (Symtab.lookup_list arities a) c of |
|
36105 | 356 |
NONE => raise CLASS_ERROR (No_Arity (a, c)) |
37248
8e8e5f9d1441
arities: no need to maintain original codomain (cf. f795c1164708) -- completion happens in axclass.ML;
wenzelm
parents:
36429
diff
changeset
|
357 |
| SOME Ss => Ss); |
19645 | 358 |
fun dom_inter c Ss = ListPair.map (inter_sort algebra) (dom c, Ss); |
19529 | 359 |
in |
360 |
(case S of |
|
361 |
[] => raise Fail "Unknown domain of empty intersection" |
|
362 |
| c :: cs => fold dom_inter cs (dom c)) |
|
363 |
end; |
|
364 |
||
365 |
||
26639 | 366 |
(* meet_sort *) |
367 |
||
368 |
fun meet_sort algebra = |
|
369 |
let |
|
370 |
fun inters S S' = inter_sort algebra (S, S'); |
|
371 |
fun meet _ [] = I |
|
372 |
| meet (TFree (_, S)) S' = |
|
373 |
if sort_le algebra (S, S') then I |
|
36105 | 374 |
else raise CLASS_ERROR (No_Subsort (S, S')) |
26639 | 375 |
| meet (TVar (v, S)) S' = |
376 |
if sort_le algebra (S, S') then I |
|
377 |
else Vartab.map_default (v, S) (inters S') |
|
378 |
| meet (Type (a, Ts)) S = fold2 meet Ts (mg_domain algebra a S); |
|
379 |
in uncurry meet end; |
|
380 |
||
28665 | 381 |
fun meet_sort_typ algebra (T, S) = |
37248
8e8e5f9d1441
arities: no need to maintain original codomain (cf. f795c1164708) -- completion happens in axclass.ML;
wenzelm
parents:
36429
diff
changeset
|
382 |
let val tab = meet_sort algebra (T, S) Vartab.empty; |
8e8e5f9d1441
arities: no need to maintain original codomain (cf. f795c1164708) -- completion happens in axclass.ML;
wenzelm
parents:
36429
diff
changeset
|
383 |
in Term.map_type_tvar (fn (v, _) => TVar (v, (the o Vartab.lookup tab) v)) end; |
28665 | 384 |
|
26639 | 385 |
|
19529 | 386 |
(* of_sort *) |
387 |
||
19645 | 388 |
fun of_sort algebra = |
19529 | 389 |
let |
390 |
fun ofS (_, []) = true |
|
19645 | 391 |
| ofS (TFree (_, S), S') = sort_le algebra (S, S') |
392 |
| ofS (TVar (_, S), S') = sort_le algebra (S, S') |
|
19529 | 393 |
| ofS (Type (a, Ts), S) = |
19645 | 394 |
let val Ss = mg_domain algebra a S in |
19529 | 395 |
ListPair.all ofS (Ts, Ss) |
19578
f93b7637a5e6
added class_error and exception CLASS_ERROR (supercedes DOMAIN);
wenzelm
parents:
19531
diff
changeset
|
396 |
end handle CLASS_ERROR _ => false; |
19529 | 397 |
in ofS end; |
398 |
||
399 |
||
27498 | 400 |
(* animating derivations *) |
401 |
||
32791 | 402 |
fun of_sort_derivation algebra {class_relation, type_constructor, type_variable} = |
19529 | 403 |
let |
27555 | 404 |
val arities = arities_of algebra; |
19578
f93b7637a5e6
added class_error and exception CLASS_ERROR (supercedes DOMAIN);
wenzelm
parents:
19531
diff
changeset
|
405 |
|
36104
fecb587a1d0e
of_sort_derivation: weaken bypasses derivation for identical sort -- accomodate proof terms by krauss/schropp, for example;
wenzelm
parents:
36103
diff
changeset
|
406 |
fun weaken T D1 S2 = |
fecb587a1d0e
of_sort_derivation: weaken bypasses derivation for identical sort -- accomodate proof terms by krauss/schropp, for example;
wenzelm
parents:
36103
diff
changeset
|
407 |
let val S1 = map snd D1 in |
fecb587a1d0e
of_sort_derivation: weaken bypasses derivation for identical sort -- accomodate proof terms by krauss/schropp, for example;
wenzelm
parents:
36103
diff
changeset
|
408 |
if S1 = S2 then map fst D1 |
fecb587a1d0e
of_sort_derivation: weaken bypasses derivation for identical sort -- accomodate proof terms by krauss/schropp, for example;
wenzelm
parents:
36103
diff
changeset
|
409 |
else |
fecb587a1d0e
of_sort_derivation: weaken bypasses derivation for identical sort -- accomodate proof terms by krauss/schropp, for example;
wenzelm
parents:
36103
diff
changeset
|
410 |
S2 |> map (fn c2 => |
fecb587a1d0e
of_sort_derivation: weaken bypasses derivation for identical sort -- accomodate proof terms by krauss/schropp, for example;
wenzelm
parents:
36103
diff
changeset
|
411 |
(case D1 |> find_first (fn (_, c1) => class_le algebra (c1, c2)) of |
fecb587a1d0e
of_sort_derivation: weaken bypasses derivation for identical sort -- accomodate proof terms by krauss/schropp, for example;
wenzelm
parents:
36103
diff
changeset
|
412 |
SOME d1 => class_relation T d1 c2 |
36105 | 413 |
| NONE => raise CLASS_ERROR (No_Subsort (S1, S2)))) |
36104
fecb587a1d0e
of_sort_derivation: weaken bypasses derivation for identical sort -- accomodate proof terms by krauss/schropp, for example;
wenzelm
parents:
36103
diff
changeset
|
414 |
end; |
19529 | 415 |
|
36103 | 416 |
fun derive (_, []) = [] |
417 |
| derive (T as Type (a, Us), S) = |
|
19529 | 418 |
let |
19645 | 419 |
val Ss = mg_domain algebra a S; |
36103 | 420 |
val dom = map2 (fn U => fn S => derive (U, S) ~~ S) Us Ss; |
19529 | 421 |
in |
422 |
S |> map (fn c => |
|
423 |
let |
|
37248
8e8e5f9d1441
arities: no need to maintain original codomain (cf. f795c1164708) -- completion happens in axclass.ML;
wenzelm
parents:
36429
diff
changeset
|
424 |
val Ss' = the (AList.lookup (op =) (Symtab.lookup_list arities a) c); |
36102
a51d1d154c71
of_sort_derivation: pass-through full type information -- following the version by krauss/schropp;
wenzelm
parents:
35975
diff
changeset
|
425 |
val dom' = map (fn ((U, d), S') => weaken U d S' ~~ S') ((Us ~~ dom) ~~ Ss'); |
37248
8e8e5f9d1441
arities: no need to maintain original codomain (cf. f795c1164708) -- completion happens in axclass.ML;
wenzelm
parents:
36429
diff
changeset
|
426 |
in type_constructor (a, Us) dom' c end) |
19529 | 427 |
end |
36103 | 428 |
| derive (T, S) = weaken T (type_variable T) S; |
429 |
in derive end; |
|
19529 | 430 |
|
35961
00e48e1d9afd
Sorts.of_sort_derivation: do not use slow Graph.irreducible_paths here, which not always needed (SUBTLE CHANGE IN SEMANTICS);
wenzelm
parents:
35408
diff
changeset
|
431 |
fun classrel_derivation algebra class_relation = |
00e48e1d9afd
Sorts.of_sort_derivation: do not use slow Graph.irreducible_paths here, which not always needed (SUBTLE CHANGE IN SEMANTICS);
wenzelm
parents:
35408
diff
changeset
|
432 |
let |
00e48e1d9afd
Sorts.of_sort_derivation: do not use slow Graph.irreducible_paths here, which not always needed (SUBTLE CHANGE IN SEMANTICS);
wenzelm
parents:
35408
diff
changeset
|
433 |
fun path (x, c1 :: c2 :: cs) = path (class_relation (x, c1) c2, c2 :: cs) |
00e48e1d9afd
Sorts.of_sort_derivation: do not use slow Graph.irreducible_paths here, which not always needed (SUBTLE CHANGE IN SEMANTICS);
wenzelm
parents:
35408
diff
changeset
|
434 |
| path (x, _) = x; |
00e48e1d9afd
Sorts.of_sort_derivation: do not use slow Graph.irreducible_paths here, which not always needed (SUBTLE CHANGE IN SEMANTICS);
wenzelm
parents:
35408
diff
changeset
|
435 |
in |
00e48e1d9afd
Sorts.of_sort_derivation: do not use slow Graph.irreducible_paths here, which not always needed (SUBTLE CHANGE IN SEMANTICS);
wenzelm
parents:
35408
diff
changeset
|
436 |
fn (x, c1) => fn c2 => |
00e48e1d9afd
Sorts.of_sort_derivation: do not use slow Graph.irreducible_paths here, which not always needed (SUBTLE CHANGE IN SEMANTICS);
wenzelm
parents:
35408
diff
changeset
|
437 |
(case Graph.irreducible_paths (classes_of algebra) (c1, c2) of |
36105 | 438 |
[] => raise CLASS_ERROR (No_Classrel (c1, c2)) |
35961
00e48e1d9afd
Sorts.of_sort_derivation: do not use slow Graph.irreducible_paths here, which not always needed (SUBTLE CHANGE IN SEMANTICS);
wenzelm
parents:
35408
diff
changeset
|
439 |
| cs :: _ => path (x, cs)) |
00e48e1d9afd
Sorts.of_sort_derivation: do not use slow Graph.irreducible_paths here, which not always needed (SUBTLE CHANGE IN SEMANTICS);
wenzelm
parents:
35408
diff
changeset
|
440 |
end; |
00e48e1d9afd
Sorts.of_sort_derivation: do not use slow Graph.irreducible_paths here, which not always needed (SUBTLE CHANGE IN SEMANTICS);
wenzelm
parents:
35408
diff
changeset
|
441 |
|
19529 | 442 |
|
443 |
(* witness_sorts *) |
|
444 |
||
19645 | 445 |
fun witness_sorts algebra types hyps sorts = |
19529 | 446 |
let |
19645 | 447 |
fun le S1 S2 = sort_le algebra (S1, S2); |
31946
99ac0321cd47
witness_sorts: proper type witnesses for hyps, not invented "'hyp" variables;
wenzelm
parents:
30242
diff
changeset
|
448 |
fun get S2 (T, S1) = if le S1 S2 then SOME (T, S2) else NONE; |
19645 | 449 |
fun mg_dom t S = SOME (mg_domain algebra t S) handle CLASS_ERROR _ => NONE; |
19529 | 450 |
|
19578
f93b7637a5e6
added class_error and exception CLASS_ERROR (supercedes DOMAIN);
wenzelm
parents:
19531
diff
changeset
|
451 |
fun witn_sort _ [] solved_failed = (SOME (propT, []), solved_failed) |
f93b7637a5e6
added class_error and exception CLASS_ERROR (supercedes DOMAIN);
wenzelm
parents:
19531
diff
changeset
|
452 |
| witn_sort path S (solved, failed) = |
f93b7637a5e6
added class_error and exception CLASS_ERROR (supercedes DOMAIN);
wenzelm
parents:
19531
diff
changeset
|
453 |
if exists (le S) failed then (NONE, (solved, failed)) |
19529 | 454 |
else |
31946
99ac0321cd47
witness_sorts: proper type witnesses for hyps, not invented "'hyp" variables;
wenzelm
parents:
30242
diff
changeset
|
455 |
(case get_first (get S) solved of |
19578
f93b7637a5e6
added class_error and exception CLASS_ERROR (supercedes DOMAIN);
wenzelm
parents:
19531
diff
changeset
|
456 |
SOME w => (SOME w, (solved, failed)) |
19529 | 457 |
| NONE => |
31946
99ac0321cd47
witness_sorts: proper type witnesses for hyps, not invented "'hyp" variables;
wenzelm
parents:
30242
diff
changeset
|
458 |
(case get_first (get S) hyps of |
19578
f93b7637a5e6
added class_error and exception CLASS_ERROR (supercedes DOMAIN);
wenzelm
parents:
19531
diff
changeset
|
459 |
SOME w => (SOME w, (w :: solved, failed)) |
19584 | 460 |
| NONE => witn_types path types S (solved, failed))) |
19529 | 461 |
|
19578
f93b7637a5e6
added class_error and exception CLASS_ERROR (supercedes DOMAIN);
wenzelm
parents:
19531
diff
changeset
|
462 |
and witn_sorts path x = fold_map (witn_sort path) x |
19529 | 463 |
|
19578
f93b7637a5e6
added class_error and exception CLASS_ERROR (supercedes DOMAIN);
wenzelm
parents:
19531
diff
changeset
|
464 |
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
|
465 |
| witn_types path (t :: ts) S solved_failed = |
19529 | 466 |
(case mg_dom t S of |
467 |
SOME SS => |
|
468 |
(*do not descend into stronger args (achieving termination)*) |
|
469 |
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
|
470 |
witn_types path ts S solved_failed |
19529 | 471 |
else |
19578
f93b7637a5e6
added class_error and exception CLASS_ERROR (supercedes DOMAIN);
wenzelm
parents:
19531
diff
changeset
|
472 |
let val (ws, (solved', failed')) = witn_sorts (S :: path) SS solved_failed in |
19529 | 473 |
if forall is_some ws then |
474 |
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
|
475 |
in (SOME w, (w :: solved', failed')) end |
f93b7637a5e6
added class_error and exception CLASS_ERROR (supercedes DOMAIN);
wenzelm
parents:
19531
diff
changeset
|
476 |
else witn_types path ts S (solved', failed') |
19529 | 477 |
end |
19578
f93b7637a5e6
added class_error and exception CLASS_ERROR (supercedes DOMAIN);
wenzelm
parents:
19531
diff
changeset
|
478 |
| NONE => witn_types path ts S solved_failed); |
19529 | 479 |
|
19584 | 480 |
in map_filter I (#1 (witn_sorts [] sorts ([], []))) end; |
19529 | 481 |
|
19514 | 482 |
end; |