src/Pure/sorts.ML
author paulson
Tue, 22 Jul 1997 11:14:18 +0200
changeset 3538 ed9de44032e0
parent 2990 271062b8c461
child 3633 1884b433c6a5
permissions -rw-r--r--
Removal of the tactical STATE
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(*  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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Type classes and sorts.
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*)
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signature SORTS =
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sig
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  type classrel
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  type arities
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  val str_of_sort: sort -> string
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  val str_of_arity: string * sort list * sort -> string
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  val class_eq: classrel -> class * class -> bool
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  val class_less: classrel -> class * class -> bool
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  val class_le: classrel -> class * class -> bool
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  val sort_eq: classrel -> sort * sort -> bool
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  val sort_less: classrel -> sort * sort -> bool
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  val sort_le: classrel -> sort * sort -> bool
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  val sorts_le: classrel -> sort list * sort list -> bool
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  val inter_class: classrel -> class * sort -> sort
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  val inter_sort: classrel -> sort * sort -> sort
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  val norm_sort: classrel -> sort -> sort
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  val of_sort: classrel -> arities -> typ * sort -> bool
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  val mg_domain: classrel -> arities -> string -> sort -> sort list
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  val nonempty_sort: classrel -> arities -> sort list -> sort -> bool
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end;
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structure Sorts: SORTS =
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struct
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(** type classes and sorts **)
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(*
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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
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  represented by lists of classes.  Normal forms of sorts are sorted
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  lists of minimal classes (wrt. current class inclusion).
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  (already defined in Pure/term.ML)
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*)
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(* sort signature information *)
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(*
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  classrel:
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    association list representing the proper subclass relation;
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    pairs (c, cs) represent the superclasses cs of c;
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  arities:
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    two-fold association list of all type arities; (t, ars) means
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    that type constructor t has the arities ars; an element (c, Ss) of
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    ars represents the arity t::(Ss)c.
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*)
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type classrel = (class * class list) list;
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type arities = (string * (class * sort list) list) list;
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(* print sorts and arities *)
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fun str_of_sort [c] = c
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  | str_of_sort cs = enclose "{" "}" (commas cs);
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fun str_of_dom Ss = enclose "(" ")" (commas (map str_of_sort Ss));
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fun str_of_arity (t, [], S) = t ^ " :: " ^ str_of_sort S
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  | str_of_arity (t, Ss, S) =
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      t ^ " :: " ^ str_of_dom Ss ^ " " ^ str_of_sort S;
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(** equality and inclusion **)
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(* classes *)
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fun class_eq _ (c1, c2:class) = c1 = c2;
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fun class_less classrel (c1, c2) =
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  (case assoc (classrel, c1) of
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     Some cs => c2 mem_string cs
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   | None => false);
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fun class_le classrel (c1, c2) =
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   c1 = c2 orelse class_less classrel (c1, c2);
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(* sorts *)
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fun sort_le classrel (S1, S2) =
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  forall (fn c2 => exists  (fn c1 => class_le classrel (c1, c2)) S1) S2;
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fun sorts_le classrel (Ss1, Ss2) =
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  ListPair.all (sort_le classrel) (Ss1, Ss2);
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fun sort_eq classrel (S1, S2) =
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  sort_le classrel (S1, S2) andalso sort_le classrel (S2, S1);
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fun sort_less classrel (S1, S2) =
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  sort_le classrel (S1, S2) andalso not (sort_le classrel (S2, S1));
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(* normal forms of sorts *)
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fun minimal_class classrel S c =
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  not (exists (fn c' => class_less classrel (c', c)) S);
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fun norm_sort classrel S =
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  sort_strings (distinct (filter (minimal_class classrel S) S));
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(** intersection **)
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(*intersect class with sort (preserves minimality)*)    (* FIXME tune? *)
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fun inter_class classrel (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 classrel (c', c) then S'
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          else if class_le classrel (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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(*instersect sorts (preserves minimality)*)
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fun inter_sort classrel = foldr (inter_class classrel);
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(** sorts of types **)
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(* mg_domain *)                 (*exception TYPE*)
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fun mg_dom arities a c =
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  (case assoc2 (arities, (a, c)) of
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    None => raise_type ("No way to get " ^ a ^ "::" ^ c ^ ".") [] []
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  | Some Ss => Ss);
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fun mg_domain _ _ _ [] = sys_error "mg_domain"  (*don't know number of args!*)
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  | mg_domain classrel arities a S =
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      let val doms = map (mg_dom arities a) S in
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        foldl (ListPair.map (inter_sort classrel)) (hd doms, tl doms)
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      end;
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(* of_sort *)
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fun of_sort classrel arities =
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  let
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    fun ofS (_, []) = true
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      | ofS (TFree (_, S), S') = sort_le classrel (S, S')
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      | ofS (TVar (_, S), S') = sort_le classrel (S, S')
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      | ofS (Type (a, Ts), S) =
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          let val Ss = mg_domain classrel arities a S in
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            ListPair.all ofS (Ts, Ss)
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          end handle TYPE _ => false;
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  in ofS end;
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(** nonempty_sort **)
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(* FIXME improve: proper sorts; non-base, non-ground types (vars from hyps) *)
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fun nonempty_sort classrel _ _ [] = true
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  | nonempty_sort classrel arities hyps S =
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      exists (exists (fn (c, Ss) => [c] = S andalso null Ss) o snd) arities
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        orelse exists (fn S' => sort_le classrel (S', S)) hyps;
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end;