author | wenzelm |
Wed, 29 Jun 2005 15:13:28 +0200 | |
changeset 16598 | 59381032be14 |
parent 16400 | f2ab5797bbd0 |
child 16881 | 570592642670 |
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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Type classes and sorts. |
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*) |
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signature SORTS = |
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sig |
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(*operations on ordered lists*) |
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val eq_set: sort list * sort list -> bool |
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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 insert_sort: sort -> sort list -> sort list |
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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 |
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val insert_terms: term list -> sort list -> sort list |
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(*signature information*) |
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type classes |
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type arities |
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val class_eq: classes -> class * class -> bool |
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val class_less: classes -> class * class -> bool |
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val class_le: classes -> class * class -> bool |
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val sort_eq: classes -> sort * sort -> bool |
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val sort_less: classes -> sort * sort -> bool |
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val sort_le: classes -> sort * sort -> bool |
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val sorts_le: classes -> sort list * sort list -> bool |
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val inter_class: classes -> class * sort -> sort |
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val inter_sort: classes -> sort * sort -> sort |
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val norm_sort: classes -> sort -> sort |
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val certify_class: classes -> class -> class |
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val certify_sort: classes -> sort -> sort |
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val of_sort: classes * arities -> typ * sort -> bool |
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exception DOMAIN of string * class |
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val mg_domain: classes * arities -> string -> sort -> sort list (*exception DOMAIN*) |
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val witness_sorts: classes * arities -> string list -> |
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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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(** 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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(types already defined in Pure/term.ML) |
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*) |
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(* ordered lists of sorts *) |
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val eq_set = OrdList.eq_set Term.sort_ord; |
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val op union = OrdList.union Term.sort_ord; |
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val subtract = OrdList.subtract Term.sort_ord; |
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val insert_sort = OrdList.insert Term.sort_ord; |
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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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fun insert_term (Const (_, T)) Ss = insert_typ T Ss |
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| insert_term (Free (_, T)) Ss = insert_typ T Ss |
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| insert_term (Var (_, T)) Ss = insert_typ T Ss |
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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) |
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| insert_term (t $ u) Ss = insert_term t (insert_term u Ss); |
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fun insert_terms [] Ss = Ss |
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| insert_terms (t :: ts) Ss = insert_terms ts (insert_term t Ss); |
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(* sort signature information *) |
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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 (c, |
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Ss) of ars represents the arity t::(Ss)c. "Coregularity" of the |
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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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type classes = stamp Graph.T; |
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type arities = (class * sort list) list Symtab.table; |
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(** equality and inclusion **) |
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(* classes *) |
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fun class_eq (_: classes) (c1, c2:class) = c1 = c2; |
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val class_less: classes -> class * class -> bool = Graph.is_edge; |
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fun class_le classes (c1, c2) = c1 = c2 orelse class_less classes (c1, c2); |
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(* sorts *) |
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fun sort_le classes (S1, S2) = |
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forall (fn c2 => exists (fn c1 => class_le classes (c1, c2)) S1) S2; |
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fun sorts_le classes (Ss1, Ss2) = |
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ListPair.all (sort_le classes) (Ss1, Ss2); |
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fun sort_eq classes (S1, S2) = |
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sort_le classes (S1, S2) andalso sort_le classes (S2, S1); |
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fun sort_less classes (S1, S2) = |
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sort_le classes (S1, S2) andalso not (sort_le classes (S2, S1)); |
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(* normal forms of sorts *) |
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local |
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fun minimal_class classes S c = |
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not (exists (fn c' => class_less classes (c', c)) S); |
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val distinct_class = gen_distinct (op = : class * class -> bool); |
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in |
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fun norm_sort _ [] = [] |
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| norm_sort _ (S as [_]) = S |
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| norm_sort classes S = |
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sort_strings (distinct_class (List.filter (minimal_class classes S) S)); |
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end; |
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(* certify *) |
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fun certify_class classes c = |
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if can (Graph.get_node classes) 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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(** intersection **) |
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(*intersect class with sort (preserves minimality)*) |
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fun inter_class classes (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 classes (c', c) then S' |
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else if class_le classes (c, c') then intr c's |
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else c' :: intr c's |
165 |
in intr S end; |
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(*instersect sorts (preserves minimality)*) |
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fun inter_sort classes = sort_strings o Library.foldr (inter_class classes); |
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(** sorts of types **) |
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(* mg_domain *) |
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exception DOMAIN of string * class; |
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fun mg_domain _ _ [] = sys_error "mg_domain" (*don't know number of args!*) |
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| mg_domain (classes, arities) a S = |
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let |
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fun mg_dom c = |
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(case Library.assoc_string (Symtab.lookup_multi (arities, a), c) of |
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NONE => raise DOMAIN (a, c) |
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| SOME Ss => Ss); |
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val doms = map mg_dom S; |
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in Library.foldl (ListPair.map (inter_sort classes)) (hd doms, tl doms) end; |
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(* of_sort *) |
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fun of_sort (classes, arities) = |
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let |
193 |
fun ofS (_, []) = true |
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| ofS (TFree (_, S), S') = sort_le classes (S, S') |
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| ofS (TVar (_, S), S') = sort_le classes (S, S') |
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| ofS (Type (a, Ts), S) = |
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diff
changeset
|
197 |
let val Ss = mg_domain (classes, arities) a S in |
2990 | 198 |
ListPair.all ofS (Ts, Ss) |
7643 | 199 |
end handle DOMAIN _ => false; |
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in ofS end; |
201 |
||
202 |
||
2956 | 203 |
|
7643 | 204 |
(** witness_sorts **) |
205 |
||
14828 | 206 |
local |
207 |
||
208 |
fun witness_aux (classes, arities) log_types hyps sorts = |
|
7643 | 209 |
let |
210 |
val top_witn = (propT, []); |
|
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parents:
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diff
changeset
|
211 |
fun le S1 S2 = sort_le classes (S1, S2); |
15531 | 212 |
fun get_solved S2 (T, S1) = if le S1 S2 then SOME (T, S2) else NONE; |
213 |
fun get_hyp S2 S1 = if le S1 S2 then SOME (TFree ("'hyp", S1), S2) else NONE; |
|
214 |
fun mg_dom t S = SOME (mg_domain (classes, arities) t S) handle DOMAIN _ => NONE; |
|
7643 | 215 |
|
15531 | 216 |
fun witn_sort _ (solved_failed, []) = (solved_failed, SOME top_witn) |
7643 | 217 |
| witn_sort path ((solved, failed), S) = |
15531 | 218 |
if exists (le S) failed then ((solved, failed), NONE) |
7643 | 219 |
else |
220 |
(case get_first (get_solved S) solved of |
|
15531 | 221 |
SOME w => ((solved, failed), SOME w) |
222 |
| NONE => |
|
7643 | 223 |
(case get_first (get_hyp S) hyps of |
15531 | 224 |
SOME w => ((w :: solved, failed), SOME w) |
225 |
| NONE => witn_types path log_types ((solved, failed), S))) |
|
7643 | 226 |
|
227 |
and witn_sorts path x = foldl_map (witn_sort path) x |
|
2956 | 228 |
|
15531 | 229 |
and witn_types _ [] ((solved, failed), S) = ((solved, S :: failed), NONE) |
7643 | 230 |
| witn_types path (t :: ts) (solved_failed, S) = |
231 |
(case mg_dom t S of |
|
15531 | 232 |
SOME SS => |
7643 | 233 |
(*do not descend into stronger args (achieving termination)*) |
234 |
if exists (fn D => le D S orelse exists (le D) path) SS then |
|
235 |
witn_types path ts (solved_failed, S) |
|
236 |
else |
|
237 |
let val ((solved', failed'), ws) = witn_sorts (S :: path) (solved_failed, SS) in |
|
15570 | 238 |
if forall isSome ws then |
239 |
let val w = (Type (t, map (#1 o valOf) ws), S) |
|
15531 | 240 |
in ((w :: solved', failed'), SOME w) end |
7643 | 241 |
else witn_types path ts ((solved', failed'), S) |
242 |
end |
|
15531 | 243 |
| NONE => witn_types path ts (solved_failed, S)); |
7643 | 244 |
|
245 |
in witn_sorts [] (([], []), sorts) end; |
|
246 |
||
14828 | 247 |
fun str_of_sort [c] = c |
248 |
| str_of_sort cs = enclose "{" "}" (commas cs); |
|
249 |
||
250 |
in |
|
7643 | 251 |
|
14782
d6ce35a1c386
incorporate sort ops from term.ML; use Graph.T; misc cleanup;
wenzelm
parents:
9281
diff
changeset
|
252 |
fun witness_sorts (classes, arities) log_types hyps sorts = |
7643 | 253 |
let |
14782
d6ce35a1c386
incorporate sort ops from term.ML; use Graph.T; misc cleanup;
wenzelm
parents:
9281
diff
changeset
|
254 |
(*double check result of witness search*) |
15531 | 255 |
fun check_result NONE = NONE |
256 |
| check_result (SOME (T, S)) = |
|
257 |
if of_sort (classes, arities) (T, S) then SOME (T, S) |
|
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incorporate sort ops from term.ML; use Graph.T; misc cleanup;
wenzelm
parents:
9281
diff
changeset
|
258 |
else sys_error ("Sorts.witness_sorts: bad witness for sort " ^ str_of_sort S); |
15570 | 259 |
in List.mapPartial check_result (#2 (witness_aux (classes, arities) log_types hyps sorts)) end; |
2956 | 260 |
|
261 |
end; |
|
14828 | 262 |
|
263 |
end; |