1 (* Title: Pure/Isar/class.ML
2 Author: Florian Haftmann, TU Muenchen
4 Type classes derived from primitive axclasses and locales -- interfaces.
10 (*FIXME the split into class_target.ML, theory_target.ML and
11 class.ML is artificial*)
13 val class: binding -> class list -> Element.context_i list
14 -> theory -> string * local_theory
15 val class_cmd: binding -> xstring list -> Element.context list
16 -> theory -> string * local_theory
17 val prove_subclass: tactic -> class -> local_theory -> local_theory
18 val subclass: class -> local_theory -> Proof.state
19 val subclass_cmd: xstring -> local_theory -> Proof.state
22 structure Class : CLASS =
27 (** class definitions **)
31 (* calculating class-related rules including canonical interpretation *)
33 fun calculate thy class sups base_sort param_map assm_axiom =
35 val empty_ctxt = ProofContext.init_global thy;
37 (* instantiation of canonical interpretation *)
38 val aT = TFree (Name.aT, base_sort);
39 val param_map_const = (map o apsnd) Const param_map;
40 val param_map_inst = (map o apsnd)
41 (Const o apsnd (map_atyps (K aT))) param_map;
42 val const_morph = Element.inst_morphism thy
43 (Symtab.empty, Symtab.make param_map_inst);
44 val typ_morph = Element.inst_morphism thy
45 (Symtab.empty |> Symtab.update (Name.aT, TFree (Name.aT, [class])), Symtab.empty);
46 val (([raw_props], [(_, raw_inst_morph)], export_morph), _) = empty_ctxt
47 |> Expression.cert_goal_expression ([(class, (("", false),
48 Expression.Named param_map_const))], []);
49 val (props, inst_morph) = if null param_map
50 then (raw_props |> map (Morphism.term typ_morph),
51 raw_inst_morph $> typ_morph)
52 else (raw_props, raw_inst_morph); (*FIXME proper handling in
53 locale.ML / expression.ML would be desirable*)
55 (* witness for canonical interpretation *)
56 val prop = try the_single props;
57 val wit = Option.map (fn prop => let
58 val sup_axioms = map_filter (fst o rules thy) sups;
59 val loc_intro_tac = case Locale.intros_of thy class
60 of (_, NONE) => all_tac
61 | (_, SOME intro) => ALLGOALS (Tactic.rtac intro);
62 val tac = loc_intro_tac
63 THEN ALLGOALS (ProofContext.fact_tac (sup_axioms @ the_list assm_axiom))
64 in Element.prove_witness empty_ctxt prop tac end) prop;
65 val axiom = Option.map Element.conclude_witness wit;
67 (* canonical interpretation *)
68 val base_morph = inst_morph
69 $> Morphism.binding_morphism (Binding.prefix false (class_prefix class))
70 $> Element.satisfy_morphism (the_list wit);
71 val eq_morph = Element.eq_morphism thy (these_defs thy sups);
74 fun prove_assm_intro thm =
76 val ((_, [thm']), _) = Variable.import true [thm] empty_ctxt;
77 val const_eq_morph = case eq_morph
78 of SOME eq_morph => const_morph $> eq_morph
80 val thm'' = Morphism.thm const_eq_morph thm';
81 val tac = ALLGOALS (ProofContext.fact_tac [thm'']);
82 in Skip_Proof.prove_global thy [] [] (Thm.prop_of thm'') (K tac) end;
83 val assm_intro = Option.map prove_assm_intro
84 (fst (Locale.intros_of thy class));
87 val of_class_prop_concl = Logic.mk_of_class (aT, class);
88 val of_class_prop = case prop of NONE => of_class_prop_concl
89 | SOME prop => Logic.mk_implies (Morphism.term const_morph
90 ((map_types o map_atyps) (K aT) prop), of_class_prop_concl);
91 val sup_of_classes = map (snd o rules thy) sups;
92 val loc_axiom_intros = map Drule.export_without_context_open (Locale.axioms_of thy class);
93 val axclass_intro = #intro (AxClass.get_info thy class);
94 val base_sort_trivs = Thm.of_sort (Thm.ctyp_of thy aT, base_sort);
95 val tac = REPEAT (SOMEGOAL
96 (Tactic.match_tac (axclass_intro :: sup_of_classes
97 @ loc_axiom_intros @ base_sort_trivs)
98 ORELSE' Tactic.assume_tac));
99 val of_class = Skip_Proof.prove_global thy [] [] of_class_prop (K tac);
101 in (base_morph, eq_morph, export_morph, axiom, assm_intro, of_class) end;
104 (* reading and processing class specifications *)
106 fun prep_class_elems prep_decl thy sups raw_elems =
109 (* user space type system: only permits 'a type variable, improves towards 'a *)
110 val algebra = Sign.classes_of thy;
111 val inter_sort = curry (Sorts.inter_sort algebra);
112 val proto_base_sort = if null sups then Sign.defaultS thy
113 else fold inter_sort (map (base_sort thy) sups) [];
114 val base_constraints = (map o apsnd)
115 (map_type_tfree (K (TVar ((Name.aT, 0), proto_base_sort))) o fst o snd)
116 (these_operations thy sups);
117 val reject_bcd_etc = (map o map_atyps) (fn T as TFree (v, sort) =>
118 if v = Name.aT then T
119 else error ("No type variable other than " ^ Name.aT ^ " allowed in class specification")
121 fun singleton_fixate Ts =
123 fun extract f = (fold o fold_atyps) f Ts [];
125 (fn TFree (v, sort) => insert (op =) (v, sort) | _ => I);
126 val inferred_sort = extract
127 (fn TVar (_, sort) => inter_sort sort | _ => I);
128 val fixate_sort = if null tfrees then inferred_sort
130 of [(_, a_sort)] => if Sorts.sort_le algebra (a_sort, inferred_sort)
131 then inter_sort a_sort inferred_sort
132 else error ("Type inference imposes additional sort constraint "
133 ^ Syntax.string_of_sort_global thy inferred_sort
134 ^ " of type parameter " ^ Name.aT ^ " of sort "
135 ^ Syntax.string_of_sort_global thy a_sort ^ ".")
136 | _ => error "Multiple type variables in class specification.";
137 in (map o map_atyps) (K (TFree (Name.aT, fixate_sort))) Ts end;
138 fun add_typ_check level name f = Context.proof_map
139 (Syntax.add_typ_check level name (fn xs => fn ctxt =>
140 let val xs' = f xs in if eq_list (op =) (xs, xs') then NONE else SOME (xs', ctxt) end));
142 (* preprocessing elements, retrieving base sort from type-checked elements *)
143 val init_class_body = fold (ProofContext.add_const_constraint o apsnd SOME) base_constraints
144 #> redeclare_operations thy sups
145 #> add_typ_check 10 "reject_bcd_etc" reject_bcd_etc
146 #> add_typ_check ~10 "singleton_fixate" singleton_fixate;
147 val raw_supexpr = (map (fn sup => (sup, (("", false),
148 Expression.Positional []))) sups, []);
149 val ((raw_supparams, _, inferred_elems), _) = ProofContext.init_global thy
150 |> prep_decl raw_supexpr init_class_body raw_elems;
151 fun fold_element_types f (Element.Fixes fxs) = fold (fn (_, SOME T, _) => f T) fxs
152 | fold_element_types f (Element.Constrains cnstrs) = fold (f o snd) cnstrs
153 | fold_element_types f (Element.Assumes assms) = fold (fold (fn (t, ts) =>
154 fold_types f t #> (fold o fold_types) f ts) o snd) assms
155 | fold_element_types f (Element.Defines _) =
156 error ("\"defines\" element not allowed in class specification.")
157 | fold_element_types f (Element.Notes _) =
158 error ("\"notes\" element not allowed in class specification.");
159 val base_sort = if null inferred_elems then proto_base_sort else
160 case (fold o fold_element_types) Term.add_tfreesT inferred_elems []
161 of [] => error "No type variable in class specification"
162 | [(_, sort)] => sort
163 | _ => error "Multiple type variables in class specification";
164 val supparams = map (fn ((c, T), _) =>
165 (c, map_atyps (K (TFree (Name.aT, base_sort))) T)) raw_supparams;
166 val supparam_names = map fst supparams;
167 fun mk_param ((c, _), _) = Free (c, (the o AList.lookup (op =) supparams) c);
168 val supexpr = (map (fn sup => (sup, (("", false),
169 Expression.Positional (map (SOME o mk_param) (Locale.params_of thy sup))))) sups,
170 map (fn (c, T) => (Binding.name c, SOME T, NoSyn)) supparams);
172 in (base_sort, supparam_names, supexpr, inferred_elems) end;
174 val cert_class_elems = prep_class_elems Expression.cert_declaration;
175 val read_class_elems = prep_class_elems Expression.cert_read_declaration;
177 fun prep_class_spec prep_class prep_class_elems thy raw_supclasses raw_elems =
181 val inter_sort = curry (Sorts.inter_sort (Sign.classes_of thy));
182 val sups = map (prep_class thy) raw_supclasses
183 |> Sign.minimize_sort thy;
184 val _ = case filter_out (is_class thy) sups
186 | no_classes => error ("No (proper) classes: " ^ commas (map quote no_classes));
187 val raw_supparams = (map o apsnd) (snd o snd) (these_params thy sups);
188 val raw_supparam_names = map fst raw_supparams;
189 val _ = if has_duplicates (op =) raw_supparam_names
190 then error ("Duplicate parameter(s) in superclasses: "
191 ^ (commas o map quote o duplicates (op =)) raw_supparam_names)
194 (* infer types and base sort *)
195 val (base_sort, supparam_names, supexpr, inferred_elems) =
196 prep_class_elems thy sups raw_elems;
197 val sup_sort = inter_sort base_sort sups;
199 (* process elements as class specification *)
200 val class_ctxt = begin sups base_sort (ProofContext.init_global thy);
201 val ((_, _, syntax_elems), _) = class_ctxt
202 |> Expression.cert_declaration supexpr I inferred_elems;
203 fun check_vars e vs = if null vs
204 then error ("No type variable in part of specification element "
205 ^ (Pretty.string_of o Pretty.chunks) (Element.pretty_ctxt class_ctxt e))
207 fun check_element (e as Element.Fixes fxs) =
208 map (fn (_, SOME T, _) => check_vars e (Term.add_tfreesT T [])) fxs
209 | check_element (e as Element.Assumes assms) =
210 maps (fn (_, ts_pss) => map
211 (fn (t, _) => check_vars e (Term.add_tfrees t [])) ts_pss) assms
212 | check_element e = [()];
213 val _ = map check_element syntax_elems;
214 fun fork_syn (Element.Fixes xs) =
215 fold_map (fn (c, ty, syn) => cons (c, syn) #> pair (c, ty, NoSyn)) xs
217 | fork_syn x = pair x;
218 val (elems, global_syntax) = fold_map fork_syn syntax_elems [];
220 in (((sups, supparam_names), (sup_sort, base_sort, supexpr)), (elems, global_syntax)) end;
222 val cert_class_spec = prep_class_spec (K I) cert_class_elems;
223 val read_class_spec = prep_class_spec Sign.intern_class read_class_elems;
226 (* class establishment *)
228 fun add_consts class base_sort sups supparam_names global_syntax thy =
231 val supconsts = supparam_names
232 |> AList.make (snd o the o AList.lookup (op =) (these_params thy sups))
233 |> (map o apsnd o apsnd o map_atyps o K o TFree) (Name.aT, [class]);
234 val all_params = Locale.params_of thy class;
235 val raw_params = (snd o chop (length supparam_names)) all_params;
236 fun add_const ((raw_c, raw_ty), _) thy =
238 val b = Binding.name raw_c;
239 val c = Sign.full_name thy b;
240 val ty = map_atyps (K (TFree (Name.aT, base_sort))) raw_ty;
241 val ty0 = Type.strip_sorts ty;
242 val ty' = map_atyps (K (TFree (Name.aT, [class]))) ty0;
243 val syn = (the_default NoSyn o AList.lookup Binding.eq_name global_syntax) b;
246 |> Sign.declare_const ((b, ty0), syn)
248 |> pair ((Name.of_binding b, ty), (c, ty'))
252 |> Sign.add_path (class_prefix class)
253 |> fold_map add_const raw_params
254 ||> Sign.restore_naming thy
255 |-> (fn params => pair (supconsts @ (map o apfst) fst params, params))
258 fun adjungate_axclass bname class base_sort sups supsort supparam_names global_syntax thy =
261 fun globalize param_map = map_aterms
262 (fn Free (v, ty) => Const ((fst o the o AList.lookup (op =) param_map) v, ty)
264 val raw_pred = Locale.intros_of thy class
266 |> Option.map (Logic.unvarify_global o Logic.strip_imp_concl o Thm.prop_of);
267 fun get_axiom thy = case (#axioms o AxClass.get_info thy) class
272 |> add_consts class base_sort sups supparam_names global_syntax
273 |-> (fn (param_map, params) => AxClass.define_class (bname, supsort)
274 (map (fst o snd) params)
275 [(Thm.empty_binding, Option.map (globalize param_map) raw_pred |> the_list)]
278 #-> (fn assm_axiom => fold (Sign.add_const_constraint o apsnd SOME o snd) params
279 #> pair (param_map, params, assm_axiom)))
282 fun gen_class prep_class_spec b raw_supclasses raw_elems thy =
284 val class = Sign.full_name thy b;
285 val (((sups, supparam_names), (supsort, base_sort, supexpr)), (elems, global_syntax)) =
286 prep_class_spec thy raw_supclasses raw_elems;
289 |> Expression.add_locale b (Binding.qualify true "class" b) supexpr elems
290 |> snd |> Local_Theory.exit_global
291 |> adjungate_axclass b class base_sort sups supsort supparam_names global_syntax
292 ||> Theory.checkpoint
293 |-> (fn (param_map, params, assm_axiom) =>
294 `(fn thy => calculate thy class sups base_sort param_map assm_axiom)
295 #-> (fn (base_morph, eq_morph, export_morph, axiom, assm_intro, of_class) =>
296 Locale.add_registration (class, case eq_morph of SOME eq_morph => base_morph $> eq_morph | NONE => base_morph)
297 (*FIXME should avoid modification of base morphism, but then problem with sublocale linorder < distrib_lattice*)
298 (Option.map (rpair true) eq_morph) export_morph
299 #> register class sups params base_sort base_morph export_morph axiom assm_intro of_class))
300 |> Theory_Target.init (SOME class)
306 val class = gen_class cert_class_spec;
307 val class_cmd = gen_class read_class_spec;
312 (** subclass relations **)
316 fun gen_subclass prep_class do_proof raw_sup lthy =
318 val thy = ProofContext.theory_of lthy;
319 val proto_sup = prep_class thy raw_sup;
320 val proto_sub = case Theory_Target.peek lthy
321 of {is_class = false, ...} => error "Not in a class context"
322 | {target, ...} => target;
323 val (sub, sup) = AxClass.cert_classrel thy (proto_sub, proto_sup);
325 val expr = ([(sup, (("", false), Expression.Positional []))], []);
326 val (([props], deps, export), goal_ctxt) =
327 Expression.cert_goal_expression expr lthy;
328 val some_prop = try the_single props;
329 val some_dep_morph = try the_single (map snd deps);
330 fun after_qed some_wit =
331 ProofContext.theory (register_subclass (sub, sup)
332 some_dep_morph some_wit export)
333 #> ProofContext.theory_of #> Theory_Target.init (SOME sub);
334 in do_proof after_qed some_prop goal_ctxt end;
336 fun user_proof after_qed some_prop =
337 Element.witness_proof (after_qed o try the_single o the_single)
338 [the_list some_prop];
340 fun tactic_proof tac after_qed some_prop ctxt =
341 after_qed (Option.map
342 (fn prop => Element.prove_witness ctxt prop tac) some_prop) ctxt;
346 val subclass = gen_subclass (K I) user_proof;
347 fun prove_subclass tac = gen_subclass (K I) (tactic_proof tac);
348 val subclass_cmd = gen_subclass (ProofContext.read_class o ProofContext.init_global) user_proof;