wenzelm@2956
|
1 |
(* Title: Pure/sorts.ML
|
wenzelm@2956
|
2 |
Author: Markus Wenzel and Stefan Berghofer, TU Muenchen
|
wenzelm@2956
|
3 |
|
wenzelm@19514
|
4 |
The order-sorted algebra of type classes.
|
wenzelm@19529
|
5 |
|
wenzelm@19529
|
6 |
Classes denote (possibly empty) collections of types that are
|
wenzelm@19529
|
7 |
partially ordered by class inclusion. They are represented
|
wenzelm@19529
|
8 |
symbolically by strings.
|
wenzelm@19529
|
9 |
|
wenzelm@19529
|
10 |
Sorts are intersections of finitely many classes. They are represented
|
wenzelm@19529
|
11 |
by lists of classes. Normal forms of sorts are sorted lists of
|
wenzelm@19529
|
12 |
minimal classes (wrt. current class inclusion).
|
wenzelm@2956
|
13 |
*)
|
wenzelm@2956
|
14 |
|
wenzelm@2956
|
15 |
signature SORTS =
|
wenzelm@2956
|
16 |
sig
|
wenzelm@28623
|
17 |
val make: sort list -> sort OrdList.T
|
wenzelm@28374
|
18 |
val subset: sort OrdList.T * sort OrdList.T -> bool
|
wenzelm@28354
|
19 |
val union: sort OrdList.T -> sort OrdList.T -> sort OrdList.T
|
wenzelm@28354
|
20 |
val subtract: sort OrdList.T -> sort OrdList.T -> sort OrdList.T
|
wenzelm@28354
|
21 |
val remove_sort: sort -> sort OrdList.T -> sort OrdList.T
|
wenzelm@28354
|
22 |
val insert_sort: sort -> sort OrdList.T -> sort OrdList.T
|
wenzelm@28354
|
23 |
val insert_typ: typ -> sort OrdList.T -> sort OrdList.T
|
wenzelm@28354
|
24 |
val insert_typs: typ list -> sort OrdList.T -> sort OrdList.T
|
wenzelm@28354
|
25 |
val insert_term: term -> sort OrdList.T -> sort OrdList.T
|
wenzelm@28354
|
26 |
val insert_terms: term list -> sort OrdList.T -> sort OrdList.T
|
wenzelm@19645
|
27 |
type algebra
|
wenzelm@19645
|
28 |
val rep_algebra: algebra ->
|
wenzelm@20573
|
29 |
{classes: serial Graph.T,
|
wenzelm@19645
|
30 |
arities: (class * (class * sort list)) list Symtab.table}
|
wenzelm@21933
|
31 |
val all_classes: algebra -> class list
|
wenzelm@19645
|
32 |
val super_classes: algebra -> class -> class list
|
wenzelm@19645
|
33 |
val class_less: algebra -> class * class -> bool
|
wenzelm@19645
|
34 |
val class_le: algebra -> class * class -> bool
|
wenzelm@19645
|
35 |
val sort_eq: algebra -> sort * sort -> bool
|
wenzelm@19645
|
36 |
val sort_le: algebra -> sort * sort -> bool
|
wenzelm@19645
|
37 |
val sorts_le: algebra -> sort list * sort list -> bool
|
wenzelm@19645
|
38 |
val inter_sort: algebra -> sort * sort -> sort
|
wenzelm@24732
|
39 |
val minimize_sort: algebra -> sort -> sort
|
wenzelm@24732
|
40 |
val complete_sort: algebra -> sort -> sort
|
wenzelm@28623
|
41 |
val minimal_sorts: algebra -> sort list -> sort OrdList.T
|
wenzelm@19645
|
42 |
val certify_class: algebra -> class -> class (*exception TYPE*)
|
wenzelm@19645
|
43 |
val certify_sort: algebra -> sort -> sort (*exception TYPE*)
|
wenzelm@19645
|
44 |
val add_class: Pretty.pp -> class * class list -> algebra -> algebra
|
wenzelm@19645
|
45 |
val add_classrel: Pretty.pp -> class * class -> algebra -> algebra
|
wenzelm@19645
|
46 |
val add_arities: Pretty.pp -> string * (class * sort list) list -> algebra -> algebra
|
wenzelm@19645
|
47 |
val empty_algebra: algebra
|
wenzelm@19645
|
48 |
val merge_algebra: Pretty.pp -> algebra * algebra -> algebra
|
haftmann@28922
|
49 |
val classrels_of: algebra -> (class * class list) list
|
haftmann@28922
|
50 |
val instances_of: algebra -> (string * class) list
|
haftmann@22181
|
51 |
val subalgebra: Pretty.pp -> (class -> bool) -> (class * string -> sort list)
|
haftmann@22181
|
52 |
-> algebra -> (sort -> sort) * algebra
|
wenzelm@19578
|
53 |
type class_error
|
wenzelm@26639
|
54 |
val class_error: Pretty.pp -> class_error -> string
|
wenzelm@19578
|
55 |
exception CLASS_ERROR of class_error
|
wenzelm@19645
|
56 |
val mg_domain: algebra -> string -> sort -> sort list (*exception CLASS_ERROR*)
|
haftmann@28665
|
57 |
val meet_sort: algebra -> typ * sort
|
haftmann@28665
|
58 |
-> sort Vartab.table -> sort Vartab.table (*exception CLASS_ERROR*)
|
haftmann@28665
|
59 |
val meet_sort_typ: algebra -> typ * sort -> typ -> typ (*exception CLASS_ERROR*)
|
wenzelm@19645
|
60 |
val of_sort: algebra -> typ * sort -> bool
|
wenzelm@27555
|
61 |
val weaken: algebra -> ('a * class -> class -> 'a) -> 'a * class -> class -> 'a
|
wenzelm@19645
|
62 |
val of_sort_derivation: Pretty.pp -> algebra ->
|
wenzelm@22570
|
63 |
{class_relation: 'a * class -> class -> 'a,
|
wenzelm@22570
|
64 |
type_constructor: string -> ('a * class) list list -> class -> 'a,
|
wenzelm@22570
|
65 |
type_variable: typ -> ('a * class) list} ->
|
wenzelm@19584
|
66 |
typ * sort -> 'a list (*exception CLASS_ERROR*)
|
wenzelm@19645
|
67 |
val witness_sorts: algebra -> string list -> sort list -> sort list -> (typ * sort) list
|
wenzelm@2956
|
68 |
end;
|
wenzelm@2956
|
69 |
|
wenzelm@20573
|
70 |
structure Sorts: SORTS =
|
wenzelm@2956
|
71 |
struct
|
wenzelm@2956
|
72 |
|
wenzelm@19514
|
73 |
|
wenzelm@19529
|
74 |
(** ordered lists of sorts **)
|
wenzelm@14782
|
75 |
|
wenzelm@29269
|
76 |
val make = OrdList.make TermOrd.sort_ord;
|
wenzelm@29269
|
77 |
val op subset = OrdList.subset TermOrd.sort_ord;
|
wenzelm@29269
|
78 |
val op union = OrdList.union TermOrd.sort_ord;
|
wenzelm@29269
|
79 |
val subtract = OrdList.subtract TermOrd.sort_ord;
|
wenzelm@14782
|
80 |
|
wenzelm@29269
|
81 |
val remove_sort = OrdList.remove TermOrd.sort_ord;
|
wenzelm@29269
|
82 |
val insert_sort = OrdList.insert TermOrd.sort_ord;
|
wenzelm@14782
|
83 |
|
wenzelm@16598
|
84 |
fun insert_typ (TFree (_, S)) Ss = insert_sort S Ss
|
wenzelm@16598
|
85 |
| insert_typ (TVar (_, S)) Ss = insert_sort S Ss
|
wenzelm@16598
|
86 |
| insert_typ (Type (_, Ts)) Ss = insert_typs Ts Ss
|
wenzelm@16598
|
87 |
and insert_typs [] Ss = Ss
|
wenzelm@16598
|
88 |
| insert_typs (T :: Ts) Ss = insert_typs Ts (insert_typ T Ss);
|
wenzelm@14782
|
89 |
|
wenzelm@16598
|
90 |
fun insert_term (Const (_, T)) Ss = insert_typ T Ss
|
wenzelm@16598
|
91 |
| insert_term (Free (_, T)) Ss = insert_typ T Ss
|
wenzelm@16598
|
92 |
| insert_term (Var (_, T)) Ss = insert_typ T Ss
|
wenzelm@16598
|
93 |
| insert_term (Bound _) Ss = Ss
|
wenzelm@16598
|
94 |
| insert_term (Abs (_, T, t)) Ss = insert_term t (insert_typ T Ss)
|
wenzelm@16598
|
95 |
| insert_term (t $ u) Ss = insert_term t (insert_term u Ss);
|
wenzelm@14782
|
96 |
|
wenzelm@16598
|
97 |
fun insert_terms [] Ss = Ss
|
wenzelm@16598
|
98 |
| insert_terms (t :: ts) Ss = insert_terms ts (insert_term t Ss);
|
wenzelm@14782
|
99 |
|
wenzelm@14782
|
100 |
|
wenzelm@19529
|
101 |
|
wenzelm@19529
|
102 |
(** order-sorted algebra **)
|
wenzelm@2956
|
103 |
|
wenzelm@2956
|
104 |
(*
|
wenzelm@14782
|
105 |
classes: graph representing class declarations together with proper
|
wenzelm@14782
|
106 |
subclass relation, which needs to be transitive and acyclic.
|
wenzelm@2956
|
107 |
|
wenzelm@14782
|
108 |
arities: table of association lists of all type arities; (t, ars)
|
wenzelm@19531
|
109 |
means that type constructor t has the arities ars; an element
|
wenzelm@19531
|
110 |
(c, (c0, Ss)) of ars represents the arity t::(Ss)c being derived
|
wenzelm@19531
|
111 |
via c0 <= c. "Coregularity" of the arities structure requires
|
wenzelm@19531
|
112 |
that for any two declarations t::(Ss1)c1 and t::(Ss2)c2 such that
|
wenzelm@19531
|
113 |
c1 <= c2 holds Ss1 <= Ss2.
|
wenzelm@2956
|
114 |
*)
|
wenzelm@2956
|
115 |
|
wenzelm@19645
|
116 |
datatype algebra = Algebra of
|
wenzelm@20573
|
117 |
{classes: serial Graph.T,
|
wenzelm@19645
|
118 |
arities: (class * (class * sort list)) list Symtab.table};
|
wenzelm@19645
|
119 |
|
wenzelm@19645
|
120 |
fun rep_algebra (Algebra args) = args;
|
wenzelm@19645
|
121 |
|
wenzelm@19645
|
122 |
val classes_of = #classes o rep_algebra;
|
wenzelm@19645
|
123 |
val arities_of = #arities o rep_algebra;
|
wenzelm@19645
|
124 |
|
wenzelm@19645
|
125 |
fun make_algebra (classes, arities) =
|
wenzelm@19645
|
126 |
Algebra {classes = classes, arities = arities};
|
wenzelm@19645
|
127 |
|
wenzelm@19645
|
128 |
fun map_classes f (Algebra {classes, arities}) = make_algebra (f classes, arities);
|
wenzelm@19645
|
129 |
fun map_arities f (Algebra {classes, arities}) = make_algebra (classes, f arities);
|
wenzelm@19645
|
130 |
|
wenzelm@19645
|
131 |
|
wenzelm@19645
|
132 |
(* classes *)
|
wenzelm@19645
|
133 |
|
wenzelm@21933
|
134 |
fun all_classes (Algebra {classes, ...}) = Graph.all_preds classes (Graph.maximals classes);
|
wenzelm@21933
|
135 |
|
wenzelm@19645
|
136 |
val super_classes = Graph.imm_succs o classes_of;
|
wenzelm@2956
|
137 |
|
wenzelm@2956
|
138 |
|
wenzelm@19529
|
139 |
(* class relations *)
|
wenzelm@2956
|
140 |
|
wenzelm@19645
|
141 |
val class_less = Graph.is_edge o classes_of;
|
wenzelm@19645
|
142 |
fun class_le algebra (c1, c2) = c1 = c2 orelse class_less algebra (c1, c2);
|
wenzelm@2956
|
143 |
|
wenzelm@2956
|
144 |
|
wenzelm@19529
|
145 |
(* sort relations *)
|
wenzelm@2956
|
146 |
|
wenzelm@19645
|
147 |
fun sort_le algebra (S1, S2) =
|
wenzelm@23585
|
148 |
S1 = S2 orelse forall (fn c2 => exists (fn c1 => class_le algebra (c1, c2)) S1) S2;
|
wenzelm@2956
|
149 |
|
wenzelm@19645
|
150 |
fun sorts_le algebra (Ss1, Ss2) =
|
wenzelm@19645
|
151 |
ListPair.all (sort_le algebra) (Ss1, Ss2);
|
wenzelm@2956
|
152 |
|
wenzelm@19645
|
153 |
fun sort_eq algebra (S1, S2) =
|
wenzelm@19645
|
154 |
sort_le algebra (S1, S2) andalso sort_le algebra (S2, S1);
|
wenzelm@2956
|
155 |
|
wenzelm@2956
|
156 |
|
wenzelm@19529
|
157 |
(* intersection *)
|
wenzelm@14986
|
158 |
|
wenzelm@19645
|
159 |
fun inter_class algebra c S =
|
wenzelm@2956
|
160 |
let
|
wenzelm@2956
|
161 |
fun intr [] = [c]
|
wenzelm@2956
|
162 |
| intr (S' as c' :: c's) =
|
wenzelm@19645
|
163 |
if class_le algebra (c', c) then S'
|
wenzelm@19645
|
164 |
else if class_le algebra (c, c') then intr c's
|
wenzelm@2956
|
165 |
else c' :: intr c's
|
wenzelm@2956
|
166 |
in intr S end;
|
wenzelm@2956
|
167 |
|
wenzelm@19645
|
168 |
fun inter_sort algebra (S1, S2) =
|
wenzelm@19645
|
169 |
sort_strings (fold (inter_class algebra) S1 S2);
|
wenzelm@2956
|
170 |
|
wenzelm@2956
|
171 |
|
wenzelm@24732
|
172 |
(* normal forms *)
|
wenzelm@19529
|
173 |
|
wenzelm@24732
|
174 |
fun minimize_sort _ [] = []
|
wenzelm@24732
|
175 |
| minimize_sort _ (S as [_]) = S
|
wenzelm@24732
|
176 |
| minimize_sort algebra S =
|
wenzelm@19645
|
177 |
filter (fn c => not (exists (fn c' => class_less algebra (c', c)) S)) S
|
wenzelm@19529
|
178 |
|> sort_distinct string_ord;
|
wenzelm@19529
|
179 |
|
wenzelm@24732
|
180 |
fun complete_sort algebra =
|
wenzelm@24732
|
181 |
Graph.all_succs (classes_of algebra) o minimize_sort algebra;
|
wenzelm@24732
|
182 |
|
wenzelm@28623
|
183 |
fun minimal_sorts algebra raw_sorts =
|
wenzelm@28623
|
184 |
let
|
wenzelm@28623
|
185 |
fun le S1 S2 = sort_le algebra (S1, S2);
|
wenzelm@28623
|
186 |
val sorts = make (map (minimize_sort algebra) raw_sorts);
|
wenzelm@28623
|
187 |
in sorts |> filter_out (fn S => exists (fn S' => le S' S andalso not (le S S')) sorts) end;
|
wenzelm@28623
|
188 |
|
wenzelm@19529
|
189 |
|
wenzelm@19645
|
190 |
(* certify *)
|
wenzelm@19645
|
191 |
|
wenzelm@19645
|
192 |
fun certify_class algebra c =
|
wenzelm@19645
|
193 |
if can (Graph.get_node (classes_of algebra)) c then c
|
wenzelm@19645
|
194 |
else raise TYPE ("Undeclared class: " ^ quote c, [], []);
|
wenzelm@19645
|
195 |
|
wenzelm@24732
|
196 |
fun certify_sort classes = minimize_sort classes o map (certify_class classes);
|
wenzelm@19645
|
197 |
|
wenzelm@19645
|
198 |
|
wenzelm@19529
|
199 |
|
wenzelm@19529
|
200 |
(** build algebras **)
|
wenzelm@19529
|
201 |
|
wenzelm@19529
|
202 |
(* classes *)
|
wenzelm@19529
|
203 |
|
wenzelm@23655
|
204 |
fun err_dup_class c = error ("Duplicate declaration of class: " ^ quote c);
|
wenzelm@19529
|
205 |
|
wenzelm@19529
|
206 |
fun err_cyclic_classes pp css =
|
wenzelm@19529
|
207 |
error (cat_lines (map (fn cs =>
|
wenzelm@19529
|
208 |
"Cycle in class relation: " ^ Pretty.string_of_classrel pp cs) css));
|
wenzelm@19529
|
209 |
|
wenzelm@19645
|
210 |
fun add_class pp (c, cs) = map_classes (fn classes =>
|
wenzelm@19529
|
211 |
let
|
wenzelm@20573
|
212 |
val classes' = classes |> Graph.new_node (c, serial ())
|
wenzelm@23655
|
213 |
handle Graph.DUP dup => err_dup_class dup;
|
wenzelm@19529
|
214 |
val classes'' = classes' |> fold Graph.add_edge_trans_acyclic (map (pair c) cs)
|
wenzelm@19529
|
215 |
handle Graph.CYCLES css => err_cyclic_classes pp css;
|
wenzelm@19645
|
216 |
in classes'' end);
|
wenzelm@19529
|
217 |
|
wenzelm@19529
|
218 |
|
wenzelm@19529
|
219 |
(* arities *)
|
wenzelm@19529
|
220 |
|
wenzelm@19529
|
221 |
local
|
wenzelm@19529
|
222 |
|
wenzelm@19529
|
223 |
fun for_classes _ NONE = ""
|
wenzelm@19529
|
224 |
| for_classes pp (SOME (c1, c2)) =
|
wenzelm@19529
|
225 |
" for classes " ^ Pretty.string_of_classrel pp [c1, c2];
|
wenzelm@19529
|
226 |
|
wenzelm@19529
|
227 |
fun err_conflict pp t cc (c, Ss) (c', Ss') =
|
wenzelm@19529
|
228 |
error ("Conflict of type arities" ^ for_classes pp cc ^ ":\n " ^
|
wenzelm@19529
|
229 |
Pretty.string_of_arity pp (t, Ss, [c]) ^ " and\n " ^
|
wenzelm@19529
|
230 |
Pretty.string_of_arity pp (t, Ss', [c']));
|
wenzelm@19529
|
231 |
|
wenzelm@19645
|
232 |
fun coregular pp algebra t (c, (c0, Ss)) ars =
|
wenzelm@19529
|
233 |
let
|
wenzelm@19529
|
234 |
fun conflict (c', (_, Ss')) =
|
wenzelm@19645
|
235 |
if class_le algebra (c, c') andalso not (sorts_le algebra (Ss, Ss')) then
|
wenzelm@19529
|
236 |
SOME ((c, c'), (c', Ss'))
|
wenzelm@19645
|
237 |
else if class_le algebra (c', c) andalso not (sorts_le algebra (Ss', Ss)) then
|
wenzelm@19529
|
238 |
SOME ((c', c), (c', Ss'))
|
wenzelm@19529
|
239 |
else NONE;
|
wenzelm@19529
|
240 |
in
|
wenzelm@19529
|
241 |
(case get_first conflict ars of
|
wenzelm@19529
|
242 |
SOME ((c1, c2), (c', Ss')) => err_conflict pp t (SOME (c1, c2)) (c, Ss) (c', Ss')
|
wenzelm@19529
|
243 |
| NONE => (c, (c0, Ss)) :: ars)
|
wenzelm@19529
|
244 |
end;
|
wenzelm@19529
|
245 |
|
wenzelm@19645
|
246 |
fun complete algebra (c0, Ss) = map (rpair (c0, Ss)) (c0 :: super_classes algebra c0);
|
wenzelm@19645
|
247 |
|
wenzelm@19645
|
248 |
fun insert pp algebra t (c, (c0, Ss)) ars =
|
wenzelm@19529
|
249 |
(case AList.lookup (op =) ars c of
|
wenzelm@19645
|
250 |
NONE => coregular pp algebra t (c, (c0, Ss)) ars
|
wenzelm@19529
|
251 |
| SOME (_, Ss') =>
|
wenzelm@19645
|
252 |
if sorts_le algebra (Ss, Ss') then ars
|
wenzelm@19645
|
253 |
else if sorts_le algebra (Ss', Ss) then
|
wenzelm@19645
|
254 |
coregular pp algebra t (c, (c0, Ss))
|
wenzelm@19529
|
255 |
(filter_out (fn (c'', (_, Ss'')) => c = c'' andalso Ss'' = Ss') ars)
|
wenzelm@19529
|
256 |
else err_conflict pp t NONE (c, Ss) (c, Ss'));
|
wenzelm@19529
|
257 |
|
wenzelm@19645
|
258 |
fun insert_ars pp algebra (t, ars) arities =
|
wenzelm@19645
|
259 |
let val ars' =
|
wenzelm@19645
|
260 |
Symtab.lookup_list arities t
|
wenzelm@19645
|
261 |
|> fold_rev (fold_rev (insert pp algebra t)) (map (complete algebra) ars)
|
wenzelm@19645
|
262 |
in Symtab.update (t, ars') arities end;
|
wenzelm@19529
|
263 |
|
wenzelm@19529
|
264 |
in
|
wenzelm@19529
|
265 |
|
wenzelm@19645
|
266 |
fun add_arities pp arg algebra = algebra |> map_arities (insert_ars pp algebra arg);
|
wenzelm@19529
|
267 |
|
wenzelm@19645
|
268 |
fun add_arities_table pp algebra =
|
wenzelm@19645
|
269 |
Symtab.fold (fn (t, ars) => insert_ars pp algebra (t, map snd ars));
|
wenzelm@19529
|
270 |
|
wenzelm@19529
|
271 |
end;
|
wenzelm@19529
|
272 |
|
wenzelm@19529
|
273 |
|
wenzelm@19645
|
274 |
(* classrel *)
|
wenzelm@19645
|
275 |
|
wenzelm@19645
|
276 |
fun rebuild_arities pp algebra = algebra |> map_arities (fn arities =>
|
wenzelm@19645
|
277 |
Symtab.empty
|
wenzelm@19645
|
278 |
|> add_arities_table pp algebra arities);
|
wenzelm@19645
|
279 |
|
wenzelm@19645
|
280 |
fun add_classrel pp rel = rebuild_arities pp o map_classes (fn classes =>
|
wenzelm@19645
|
281 |
classes |> Graph.add_edge_trans_acyclic rel
|
wenzelm@19645
|
282 |
handle Graph.CYCLES css => err_cyclic_classes pp css);
|
wenzelm@19645
|
283 |
|
wenzelm@19645
|
284 |
|
wenzelm@19645
|
285 |
(* empty and merge *)
|
wenzelm@19645
|
286 |
|
wenzelm@19645
|
287 |
val empty_algebra = make_algebra (Graph.empty, Symtab.empty);
|
wenzelm@19645
|
288 |
|
wenzelm@19645
|
289 |
fun merge_algebra pp
|
wenzelm@19645
|
290 |
(Algebra {classes = classes1, arities = arities1},
|
wenzelm@19645
|
291 |
Algebra {classes = classes2, arities = arities2}) =
|
wenzelm@19645
|
292 |
let
|
wenzelm@19645
|
293 |
val classes' = Graph.merge_trans_acyclic (op =) (classes1, classes2)
|
wenzelm@23655
|
294 |
handle Graph.DUP c => err_dup_class c
|
wenzelm@19645
|
295 |
| Graph.CYCLES css => err_cyclic_classes pp css;
|
wenzelm@19645
|
296 |
val algebra0 = make_algebra (classes', Symtab.empty);
|
wenzelm@19645
|
297 |
val arities' = Symtab.empty
|
wenzelm@19645
|
298 |
|> add_arities_table pp algebra0 arities1
|
wenzelm@19645
|
299 |
|> add_arities_table pp algebra0 arities2;
|
wenzelm@19645
|
300 |
in make_algebra (classes', arities') end;
|
wenzelm@19645
|
301 |
|
wenzelm@21933
|
302 |
|
haftmann@28922
|
303 |
(* algebra projections *)
|
haftmann@28922
|
304 |
|
haftmann@28922
|
305 |
fun classrels_of (Algebra {classes, ...}) =
|
haftmann@28922
|
306 |
map (fn [c] => (c, Graph.imm_succs classes c)) (rev (Graph.strong_conn classes));
|
haftmann@28922
|
307 |
|
haftmann@28922
|
308 |
fun instances_of (Algebra {arities, ...}) =
|
haftmann@28922
|
309 |
Symtab.fold (fn (a, cs) => append (map (pair a o fst) cs)) arities [];
|
wenzelm@21933
|
310 |
|
haftmann@22181
|
311 |
fun subalgebra pp P sargs (algebra as Algebra {classes, arities}) =
|
haftmann@19952
|
312 |
let
|
wenzelm@24732
|
313 |
val restrict_sort = minimize_sort algebra o filter P o Graph.all_succs classes;
|
haftmann@22181
|
314 |
fun restrict_arity tyco (c, (_, Ss)) =
|
haftmann@22181
|
315 |
if P c then
|
haftmann@22181
|
316 |
SOME (c, (c, Ss |> map2 (curry (inter_sort algebra)) (sargs (c, tyco))
|
haftmann@22181
|
317 |
|> map restrict_sort))
|
haftmann@22181
|
318 |
else NONE;
|
wenzelm@21933
|
319 |
val classes' = classes |> Graph.subgraph P;
|
haftmann@22181
|
320 |
val arities' = arities |> Symtab.map' (map_filter o restrict_arity);
|
wenzelm@21933
|
321 |
in (restrict_sort, rebuild_arities pp (make_algebra (classes', arities'))) end;
|
haftmann@20465
|
322 |
|
wenzelm@19645
|
323 |
|
wenzelm@2956
|
324 |
|
wenzelm@2956
|
325 |
(** sorts of types **)
|
wenzelm@2956
|
326 |
|
wenzelm@26639
|
327 |
(* errors -- delayed message composition *)
|
wenzelm@19578
|
328 |
|
wenzelm@26639
|
329 |
datatype class_error =
|
wenzelm@26639
|
330 |
NoClassrel of class * class |
|
wenzelm@26639
|
331 |
NoArity of string * class |
|
wenzelm@26639
|
332 |
NoSubsort of sort * sort;
|
wenzelm@19578
|
333 |
|
wenzelm@26639
|
334 |
fun class_error pp (NoClassrel (c1, c2)) =
|
haftmann@22196
|
335 |
"No class relation " ^ Pretty.string_of_classrel pp [c1, c2]
|
wenzelm@26639
|
336 |
| class_error pp (NoArity (a, c)) =
|
haftmann@26326
|
337 |
"No type arity " ^ Pretty.string_of_arity pp (a, [], [c])
|
haftmann@26994
|
338 |
| class_error pp (NoSubsort (S1, S2)) =
|
haftmann@26994
|
339 |
"Cannot derive subsort relation " ^ Pretty.string_of_sort pp S1
|
haftmann@26994
|
340 |
^ " < " ^ Pretty.string_of_sort pp S2;
|
wenzelm@19578
|
341 |
|
wenzelm@19578
|
342 |
exception CLASS_ERROR of class_error;
|
wenzelm@19578
|
343 |
|
wenzelm@19578
|
344 |
|
wenzelm@7643
|
345 |
(* mg_domain *)
|
wenzelm@7643
|
346 |
|
wenzelm@19645
|
347 |
fun mg_domain algebra a S =
|
wenzelm@16881
|
348 |
let
|
wenzelm@19645
|
349 |
val arities = arities_of algebra;
|
wenzelm@16881
|
350 |
fun dom c =
|
wenzelm@18931
|
351 |
(case AList.lookup (op =) (Symtab.lookup_list arities a) c of
|
wenzelm@19578
|
352 |
NONE => raise CLASS_ERROR (NoArity (a, c))
|
wenzelm@19524
|
353 |
| SOME (_, Ss) => Ss);
|
wenzelm@19645
|
354 |
fun dom_inter c Ss = ListPair.map (inter_sort algebra) (dom c, Ss);
|
wenzelm@16881
|
355 |
in
|
wenzelm@16881
|
356 |
(case S of
|
wenzelm@19529
|
357 |
[] => raise Fail "Unknown domain of empty intersection"
|
wenzelm@16881
|
358 |
| c :: cs => fold dom_inter cs (dom c))
|
wenzelm@16881
|
359 |
end;
|
wenzelm@2956
|
360 |
|
wenzelm@2956
|
361 |
|
wenzelm@26639
|
362 |
(* meet_sort *)
|
wenzelm@26639
|
363 |
|
wenzelm@26639
|
364 |
fun meet_sort algebra =
|
wenzelm@26639
|
365 |
let
|
wenzelm@26639
|
366 |
fun inters S S' = inter_sort algebra (S, S');
|
wenzelm@26639
|
367 |
fun meet _ [] = I
|
wenzelm@26639
|
368 |
| meet (TFree (_, S)) S' =
|
wenzelm@26639
|
369 |
if sort_le algebra (S, S') then I
|
wenzelm@26639
|
370 |
else raise CLASS_ERROR (NoSubsort (S, S'))
|
wenzelm@26639
|
371 |
| meet (TVar (v, S)) S' =
|
wenzelm@26639
|
372 |
if sort_le algebra (S, S') then I
|
wenzelm@26639
|
373 |
else Vartab.map_default (v, S) (inters S')
|
wenzelm@26639
|
374 |
| meet (Type (a, Ts)) S = fold2 meet Ts (mg_domain algebra a S);
|
wenzelm@26639
|
375 |
in uncurry meet end;
|
wenzelm@26639
|
376 |
|
haftmann@28665
|
377 |
fun meet_sort_typ algebra (T, S) =
|
haftmann@28665
|
378 |
let
|
haftmann@28665
|
379 |
val tab = meet_sort algebra (T, S) Vartab.empty;
|
haftmann@28665
|
380 |
in Term.map_type_tvar (fn (v, _) =>
|
haftmann@28665
|
381 |
TVar (v, (the o Vartab.lookup tab) v))
|
haftmann@28665
|
382 |
end;
|
haftmann@28665
|
383 |
|
wenzelm@26639
|
384 |
|
wenzelm@2990
|
385 |
(* of_sort *)
|
wenzelm@2990
|
386 |
|
wenzelm@19645
|
387 |
fun of_sort algebra =
|
wenzelm@2990
|
388 |
let
|
wenzelm@2990
|
389 |
fun ofS (_, []) = true
|
wenzelm@19645
|
390 |
| ofS (TFree (_, S), S') = sort_le algebra (S, S')
|
wenzelm@19645
|
391 |
| ofS (TVar (_, S), S') = sort_le algebra (S, S')
|
wenzelm@2990
|
392 |
| ofS (Type (a, Ts), S) =
|
wenzelm@19645
|
393 |
let val Ss = mg_domain algebra a S in
|
wenzelm@2990
|
394 |
ListPair.all ofS (Ts, Ss)
|
wenzelm@19578
|
395 |
end handle CLASS_ERROR _ => false;
|
wenzelm@2990
|
396 |
in ofS end;
|
wenzelm@2990
|
397 |
|
wenzelm@2990
|
398 |
|
haftmann@27498
|
399 |
(* animating derivations *)
|
haftmann@27498
|
400 |
|
wenzelm@27555
|
401 |
fun weaken algebra class_relation =
|
wenzelm@27555
|
402 |
let
|
wenzelm@27555
|
403 |
fun path (x, c1 :: c2 :: cs) = path (class_relation (x, c1) c2, c2 :: cs)
|
wenzelm@27555
|
404 |
| path (x, _) = x;
|
wenzelm@27555
|
405 |
in fn (x, c1) => fn c2 =>
|
wenzelm@27555
|
406 |
(case Graph.irreducible_paths (classes_of algebra) (c1, c2) of
|
wenzelm@27555
|
407 |
[] => raise CLASS_ERROR (NoClassrel (c1, c2))
|
wenzelm@27555
|
408 |
| cs :: _ => path (x, cs))
|
wenzelm@27555
|
409 |
end;
|
wenzelm@2956
|
410 |
|
wenzelm@22570
|
411 |
fun of_sort_derivation pp algebra {class_relation, type_constructor, type_variable} =
|
wenzelm@19529
|
412 |
let
|
wenzelm@27555
|
413 |
val weaken = weaken algebra class_relation;
|
wenzelm@27555
|
414 |
val arities = arities_of algebra;
|
wenzelm@19578
|
415 |
|
wenzelm@19529
|
416 |
fun weakens S1 S2 = S2 |> map (fn c2 =>
|
wenzelm@19645
|
417 |
(case S1 |> find_first (fn (_, c1) => class_le algebra (c1, c2)) of
|
wenzelm@19529
|
418 |
SOME d1 => weaken d1 c2
|
haftmann@26994
|
419 |
| NONE => raise CLASS_ERROR (NoSubsort (map #2 S1, S2))));
|
wenzelm@19529
|
420 |
|
wenzelm@19529
|
421 |
fun derive _ [] = []
|
wenzelm@19529
|
422 |
| derive (Type (a, Ts)) S =
|
wenzelm@19529
|
423 |
let
|
wenzelm@19645
|
424 |
val Ss = mg_domain algebra a S;
|
wenzelm@19529
|
425 |
val dom = map2 (fn T => fn S => derive T S ~~ S) Ts Ss;
|
wenzelm@19529
|
426 |
in
|
wenzelm@19529
|
427 |
S |> map (fn c =>
|
wenzelm@19529
|
428 |
let
|
wenzelm@19529
|
429 |
val (c0, Ss') = the (AList.lookup (op =) (Symtab.lookup_list arities a) c);
|
wenzelm@19529
|
430 |
val dom' = map2 (fn d => fn S' => weakens d S' ~~ S') dom Ss';
|
wenzelm@22570
|
431 |
in weaken (type_constructor a dom' c0, c0) c end)
|
wenzelm@19529
|
432 |
end
|
wenzelm@22570
|
433 |
| derive T S = weakens (type_variable T) S;
|
wenzelm@19529
|
434 |
in uncurry derive end;
|
wenzelm@19529
|
435 |
|
wenzelm@19529
|
436 |
|
wenzelm@19529
|
437 |
(* witness_sorts *)
|
wenzelm@2956
|
438 |
|
wenzelm@19645
|
439 |
fun witness_sorts algebra types hyps sorts =
|
wenzelm@7643
|
440 |
let
|
wenzelm@19645
|
441 |
fun le S1 S2 = sort_le algebra (S1, S2);
|
skalberg@15531
|
442 |
fun get_solved S2 (T, S1) = if le S1 S2 then SOME (T, S2) else NONE;
|
skalberg@15531
|
443 |
fun get_hyp S2 S1 = if le S1 S2 then SOME (TFree ("'hyp", S1), S2) else NONE;
|
wenzelm@19645
|
444 |
fun mg_dom t S = SOME (mg_domain algebra t S) handle CLASS_ERROR _ => NONE;
|
wenzelm@7643
|
445 |
|
wenzelm@19578
|
446 |
fun witn_sort _ [] solved_failed = (SOME (propT, []), solved_failed)
|
wenzelm@19578
|
447 |
| witn_sort path S (solved, failed) =
|
wenzelm@19578
|
448 |
if exists (le S) failed then (NONE, (solved, failed))
|
wenzelm@7643
|
449 |
else
|
wenzelm@7643
|
450 |
(case get_first (get_solved S) solved of
|
wenzelm@19578
|
451 |
SOME w => (SOME w, (solved, failed))
|
skalberg@15531
|
452 |
| NONE =>
|
wenzelm@7643
|
453 |
(case get_first (get_hyp S) hyps of
|
wenzelm@19578
|
454 |
SOME w => (SOME w, (w :: solved, failed))
|
wenzelm@19584
|
455 |
| NONE => witn_types path types S (solved, failed)))
|
wenzelm@7643
|
456 |
|
wenzelm@19578
|
457 |
and witn_sorts path x = fold_map (witn_sort path) x
|
wenzelm@7643
|
458 |
|
wenzelm@19578
|
459 |
and witn_types _ [] S (solved, failed) = (NONE, (solved, S :: failed))
|
wenzelm@19578
|
460 |
| witn_types path (t :: ts) S solved_failed =
|
wenzelm@7643
|
461 |
(case mg_dom t S of
|
skalberg@15531
|
462 |
SOME SS =>
|
wenzelm@7643
|
463 |
(*do not descend into stronger args (achieving termination)*)
|
wenzelm@7643
|
464 |
if exists (fn D => le D S orelse exists (le D) path) SS then
|
wenzelm@19578
|
465 |
witn_types path ts S solved_failed
|
wenzelm@7643
|
466 |
else
|
wenzelm@19578
|
467 |
let val (ws, (solved', failed')) = witn_sorts (S :: path) SS solved_failed in
|
wenzelm@17756
|
468 |
if forall is_some ws then
|
wenzelm@18931
|
469 |
let val w = (Type (t, map (#1 o the) ws), S)
|
wenzelm@19578
|
470 |
in (SOME w, (w :: solved', failed')) end
|
wenzelm@19578
|
471 |
else witn_types path ts S (solved', failed')
|
wenzelm@7643
|
472 |
end
|
wenzelm@19578
|
473 |
| NONE => witn_types path ts S solved_failed);
|
wenzelm@7643
|
474 |
|
wenzelm@19584
|
475 |
in map_filter I (#1 (witn_sorts [] sorts ([], []))) end;
|
wenzelm@2956
|
476 |
|
wenzelm@2956
|
477 |
end;
|