author | haftmann |
Wed, 28 Apr 2010 13:29:39 +0200 | |
changeset 36460 | c643b23e8592 |
parent 35845 | e5980f0ad025 |
child 36464 | b789c1731fb7 |
permissions | -rw-r--r-- |
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(* Title: Pure/Isar/class.ML |
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Author: Florian Haftmann, TU Muenchen |
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Type classes derived from primitive axclasses and locales - interfaces. |
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*) |
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signature CLASS = |
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sig |
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include CLASS_TARGET |
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(*FIXME the split into class_target.ML, theory_target.ML and |
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class.ML is artificial*) |
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val class: binding -> class list -> Element.context_i list |
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-> theory -> string * local_theory |
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val class_cmd: binding -> xstring list -> Element.context list |
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-> theory -> string * local_theory |
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val prove_subclass: tactic -> class -> local_theory -> local_theory |
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val subclass: class -> local_theory -> Proof.state |
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val subclass_cmd: xstring -> local_theory -> Proof.state |
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end; |
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structure Class : CLASS = |
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struct |
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open Class_Target; |
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(** class definitions **) |
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local |
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(* calculating class-related rules including canonical interpretation *) |
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fun calculate thy class sups base_sort param_map assm_axiom = |
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let |
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val empty_ctxt = ProofContext.init thy; |
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(* instantiation of canonical interpretation *) |
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val aT = TFree (Name.aT, base_sort); |
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val param_map_const = (map o apsnd) Const param_map; |
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val param_map_inst = (map o apsnd) |
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(Const o apsnd (map_atyps (K aT))) param_map; |
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val const_morph = Element.inst_morphism thy |
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(Symtab.empty, Symtab.make param_map_inst); |
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val typ_morph = Element.inst_morphism thy |
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(Symtab.empty |> Symtab.update (Name.aT, TFree (Name.aT, [class])), Symtab.empty); |
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val (([raw_props], [(_, raw_inst_morph)], export_morph), _) = empty_ctxt |
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|> Expression.cert_goal_expression ([(class, (("", false), |
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Expression.Named param_map_const))], []); |
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val (props, inst_morph) = if null param_map |
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then (raw_props |> map (Morphism.term typ_morph), |
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raw_inst_morph $> typ_morph) |
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else (raw_props, raw_inst_morph); (*FIXME proper handling in |
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locale.ML / expression.ML would be desirable*) |
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(* witness for canonical interpretation *) |
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val prop = try the_single props; |
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val wit = Option.map (fn prop => let |
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val sup_axioms = map_filter (fst o rules thy) sups; |
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val loc_intro_tac = case Locale.intros_of thy class |
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of (_, NONE) => all_tac |
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| (_, SOME intro) => ALLGOALS (Tactic.rtac intro); |
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val tac = loc_intro_tac |
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THEN ALLGOALS (ProofContext.fact_tac (sup_axioms @ the_list assm_axiom)) |
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in Element.prove_witness empty_ctxt prop tac end) prop; |
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val axiom = Option.map Element.conclude_witness wit; |
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(* canonical interpretation *) |
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val base_morph = inst_morph |
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$> Morphism.binding_morphism (Binding.prefix false (class_prefix class)) |
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$> Element.satisfy_morphism (the_list wit); |
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val eq_morph = Element.eq_morphism thy (these_defs thy sups); |
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(* assm_intro *) |
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fun prove_assm_intro thm = |
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let |
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val ((_, [thm']), _) = Variable.import true [thm] empty_ctxt; |
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val thm'' = Morphism.thm (const_morph $> eq_morph) thm'; |
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val tac = ALLGOALS (ProofContext.fact_tac [thm'']); |
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in Skip_Proof.prove_global thy [] [] (Thm.prop_of thm'') (K tac) end; |
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val assm_intro = Option.map prove_assm_intro |
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(fst (Locale.intros_of thy class)); |
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(* of_class *) |
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val of_class_prop_concl = Logic.mk_of_class (aT, class); |
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val of_class_prop = case prop of NONE => of_class_prop_concl |
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| SOME prop => Logic.mk_implies (Morphism.term const_morph |
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((map_types o map_atyps) (K aT) prop), of_class_prop_concl); |
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val sup_of_classes = map (snd o rules thy) sups; |
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val loc_axiom_intros = map Drule.export_without_context_open (Locale.axioms_of thy class); |
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val axclass_intro = #intro (AxClass.get_info thy class); |
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val base_sort_trivs = Thm.of_sort (Thm.ctyp_of thy aT, base_sort); |
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val tac = REPEAT (SOMEGOAL |
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(Tactic.match_tac (axclass_intro :: sup_of_classes |
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@ loc_axiom_intros @ base_sort_trivs) |
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ORELSE' Tactic.assume_tac)); |
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val of_class = Skip_Proof.prove_global thy [] [] of_class_prop (K tac); |
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in (base_morph, eq_morph, export_morph, axiom, assm_intro, of_class) end; |
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(* reading and processing class specifications *) |
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fun prep_class_elems prep_decl thy sups raw_elems = |
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let |
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(* user space type system: only permits 'a type variable, improves towards 'a *) |
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val algebra = Sign.classes_of thy; |
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val inter_sort = curry (Sorts.inter_sort algebra); |
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val proto_base_sort = if null sups then Sign.defaultS thy |
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else fold inter_sort (map (base_sort thy) sups) []; |
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val base_constraints = (map o apsnd) |
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(map_type_tfree (K (TVar ((Name.aT, 0), proto_base_sort))) o fst o snd) |
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(these_operations thy sups); |
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val reject_bcd_etc = (map o map_atyps) (fn T as TFree (v, sort) => |
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if v = Name.aT then T |
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else error ("No type variable other than " ^ Name.aT ^ " allowed in class specification") |
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| T => T); |
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fun singleton_fixate Ts = |
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let |
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fun extract f = (fold o fold_atyps) f Ts []; |
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val tfrees = extract |
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(fn TFree (v, sort) => insert (op =) (v, sort) | _ => I); |
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val inferred_sort = extract |
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(fn TVar (_, sort) => inter_sort sort | _ => I); |
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val fixate_sort = if null tfrees then inferred_sort |
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else case tfrees |
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of [(_, a_sort)] => if Sorts.sort_le algebra (a_sort, inferred_sort) |
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then inter_sort a_sort inferred_sort |
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else error ("Type inference imposes additional sort constraint " |
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^ Syntax.string_of_sort_global thy inferred_sort |
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^ " of type parameter " ^ Name.aT ^ " of sort " |
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^ Syntax.string_of_sort_global thy a_sort ^ ".") |
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| _ => error "Multiple type variables in class specification."; |
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in (map o map_atyps) (K (TFree (Name.aT, fixate_sort))) Ts end; |
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fun add_typ_check level name f = Context.proof_map |
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(Syntax.add_typ_check level name (fn xs => fn ctxt => |
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let val xs' = f xs in if eq_list (op =) (xs, xs') then NONE else SOME (xs', ctxt) end)); |
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(* preprocessing elements, retrieving base sort from type-checked elements *) |
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val init_class_body = fold (ProofContext.add_const_constraint o apsnd SOME) base_constraints |
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#> redeclare_operations thy sups |
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#> add_typ_check 10 "reject_bcd_etc" reject_bcd_etc |
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#> add_typ_check ~10 "singleton_fixate" singleton_fixate; |
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val raw_supexpr = (map (fn sup => (sup, (("", false), |
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Expression.Positional []))) sups, []); |
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val ((raw_supparams, _, inferred_elems), _) = ProofContext.init thy |
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|> prep_decl raw_supexpr init_class_body raw_elems; |
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fun fold_element_types f (Element.Fixes fxs) = fold (fn (_, SOME T, _) => f T) fxs |
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| fold_element_types f (Element.Constrains cnstrs) = fold (f o snd) cnstrs |
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| fold_element_types f (Element.Assumes assms) = fold (fold (fn (t, ts) => |
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fold_types f t #> (fold o fold_types) f ts) o snd) assms |
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| fold_element_types f (Element.Defines _) = |
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error ("\"defines\" element not allowed in class specification.") |
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| fold_element_types f (Element.Notes _) = |
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error ("\"notes\" element not allowed in class specification."); |
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val base_sort = if null inferred_elems then proto_base_sort else |
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case (fold o fold_element_types) Term.add_tfreesT inferred_elems [] |
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of [] => error "No type variable in class specification" |
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| [(_, sort)] => sort |
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| _ => error "Multiple type variables in class specification"; |
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val supparams = map (fn ((c, T), _) => |
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(c, map_atyps (K (TFree (Name.aT, base_sort))) T)) raw_supparams; |
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val supparam_names = map fst supparams; |
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fun mk_param ((c, _), _) = Free (c, (the o AList.lookup (op =) supparams) c); |
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val supexpr = (map (fn sup => (sup, (("", false), |
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Expression.Positional (map (SOME o mk_param) (Locale.params_of thy sup))))) sups, |
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map (fn (c, T) => (Binding.name c, SOME T, NoSyn)) supparams); |
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in (base_sort, supparam_names, supexpr, inferred_elems) end; |
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val cert_class_elems = prep_class_elems Expression.cert_declaration; |
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val read_class_elems = prep_class_elems Expression.cert_read_declaration; |
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fun prep_class_spec prep_class prep_class_elems thy raw_supclasses raw_elems = |
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let |
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(* prepare import *) |
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val inter_sort = curry (Sorts.inter_sort (Sign.classes_of thy)); |
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val sups = map (prep_class thy) raw_supclasses |
180 |
|> Sign.minimize_sort thy; |
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val _ = case filter_out (is_class thy) sups |
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of [] => () |
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| no_classes => error ("No (proper) classes: " ^ commas (map quote no_classes)); |
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val raw_supparams = (map o apsnd) (snd o snd) (these_params thy sups); |
185 |
val raw_supparam_names = map fst raw_supparams; |
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val _ = if has_duplicates (op =) raw_supparam_names |
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then error ("Duplicate parameter(s) in superclasses: " |
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^ (commas o map quote o duplicates (op =)) raw_supparam_names) |
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else (); |
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(* infer types and base sort *) |
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val (base_sort, supparam_names, supexpr, inferred_elems) = |
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prep_class_elems thy sups raw_elems; |
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val sup_sort = inter_sort base_sort sups; |
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(* process elements as class specification *) |
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val class_ctxt = begin sups base_sort (ProofContext.init thy); |
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val ((_, _, syntax_elems), _) = class_ctxt |
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|> Expression.cert_declaration supexpr I inferred_elems; |
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fun check_vars e vs = if null vs |
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then error ("No type variable in part of specification element " |
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^ (Pretty.output o Pretty.chunks) (Element.pretty_ctxt class_ctxt e)) |
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else (); |
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fun check_element (e as Element.Fixes fxs) = |
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map (fn (_, SOME T, _) => check_vars e (Term.add_tfreesT T [])) fxs |
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| check_element (e as Element.Assumes assms) = |
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maps (fn (_, ts_pss) => map |
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(fn (t, _) => check_vars e (Term.add_tfrees t [])) ts_pss) assms |
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| check_element e = [()]; |
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val _ = map check_element syntax_elems; |
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fun fork_syn (Element.Fixes xs) = |
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fold_map (fn (c, ty, syn) => cons (c, syn) #> pair (c, ty, NoSyn)) xs |
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#>> Element.Fixes |
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| fork_syn x = pair x; |
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val (elems, global_syntax) = fold_map fork_syn syntax_elems []; |
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216 |
|
32713 | 217 |
in (((sups, supparam_names), (sup_sort, base_sort, supexpr)), (elems, global_syntax)) end; |
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218 |
|
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val cert_class_spec = prep_class_spec (K I) cert_class_elems; |
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val read_class_spec = prep_class_spec Sign.intern_class read_class_elems; |
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221 |
|
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222 |
|
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223 |
(* class establishment *) |
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224 |
|
32206 | 225 |
fun add_consts class base_sort sups supparam_names global_syntax thy = |
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let |
29816 | 227 |
(*FIXME simplify*) |
32206 | 228 |
val supconsts = supparam_names |
26518 | 229 |
|> AList.make (snd o the o AList.lookup (op =) (these_params thy sups)) |
25683 | 230 |
|> (map o apsnd o apsnd o map_atyps o K o TFree) (Name.aT, [class]); |
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val all_params = Locale.params_of thy class; |
32206 | 232 |
val raw_params = (snd o chop (length supparam_names)) all_params; |
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fun add_const ((raw_c, raw_ty), _) thy = |
25683 | 234 |
let |
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val b = Binding.name raw_c; |
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val c = Sign.full_name thy b; |
25683 | 237 |
val ty = map_atyps (K (TFree (Name.aT, base_sort))) raw_ty; |
238 |
val ty0 = Type.strip_sorts ty; |
|
239 |
val ty' = map_atyps (K (TFree (Name.aT, [class]))) ty0; |
|
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val syn = (the_default NoSyn o AList.lookup Binding.eq_name global_syntax) b; |
25683 | 241 |
in |
242 |
thy |
|
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|> Sign.declare_const ((b, ty0), syn) |
25683 | 244 |
|> snd |
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|> pair ((Name.of_binding b, ty), (c, ty')) |
25683 | 246 |
end; |
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in |
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thy |
29547 | 249 |
|> Sign.add_path (class_prefix class) |
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|> fold_map add_const raw_params |
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||> Sign.restore_naming thy |
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|-> (fn params => pair (supconsts @ (map o apfst) fst params, params)) |
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253 |
end; |
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254 |
|
32206 | 255 |
fun adjungate_axclass bname class base_sort sups supsort supparam_names global_syntax thy = |
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256 |
let |
29816 | 257 |
(*FIXME simplify*) |
25683 | 258 |
fun globalize param_map = map_aterms |
259 |
(fn Free (v, ty) => Const ((fst o the o AList.lookup (op =) param_map) v, ty) |
|
260 |
| t => t); |
|
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val raw_pred = Locale.intros_of thy class |
25683 | 262 |
|> fst |
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|> Option.map (Logic.unvarify_global o Logic.strip_imp_concl o Thm.prop_of); |
25683 | 264 |
fun get_axiom thy = case (#axioms o AxClass.get_info thy) class |
265 |
of [] => NONE |
|
266 |
| [thm] => SOME thm; |
|
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in |
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268 |
thy |
32206 | 269 |
|> add_consts class base_sort sups supparam_names global_syntax |
25683 | 270 |
|-> (fn (param_map, params) => AxClass.define_class (bname, supsort) |
26518 | 271 |
(map (fst o snd) params) |
30211 | 272 |
[(Thm.empty_binding, Option.map (globalize param_map) raw_pred |> the_list)] |
25683 | 273 |
#> snd |
274 |
#> `get_axiom |
|
275 |
#-> (fn assm_axiom => fold (Sign.add_const_constraint o apsnd SOME o snd) params |
|
29526 | 276 |
#> pair (param_map, params, assm_axiom))) |
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277 |
end; |
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278 |
|
32206 | 279 |
fun gen_class prep_class_spec bname raw_supclasses raw_elems thy = |
24748 | 280 |
let |
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281 |
val class = Sign.full_name thy bname; |
32206 | 282 |
val (((sups, supparam_names), (supsort, base_sort, supexpr)), (elems, global_syntax)) = |
283 |
prep_class_spec thy raw_supclasses raw_elems; |
|
24218 | 284 |
in |
285 |
thy |
|
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286 |
|> Expression.add_locale bname Binding.empty supexpr elems |
33671 | 287 |
|> snd |> Local_Theory.exit_global |
32206 | 288 |
|> adjungate_axclass bname class base_sort sups supsort supparam_names global_syntax |
31696 | 289 |
||> Theory.checkpoint |
29526 | 290 |
|-> (fn (param_map, params, assm_axiom) => |
29547 | 291 |
`(fn thy => calculate thy class sups base_sort param_map assm_axiom) |
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292 |
#-> (fn (base_morph, eq_morph, export_morph, axiom, assm_intro, of_class) => |
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293 |
Locale.add_registration (class, base_morph $> eq_morph) NONE export_morph |
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294 |
(*FIXME should not modify base_morph, although admissible*) |
32850 | 295 |
#> register class sups params base_sort base_morph export_morph axiom assm_intro of_class)) |
33553 | 296 |
|> Theory_Target.init (SOME class) |
25038 | 297 |
|> pair class |
24218 | 298 |
end; |
299 |
||
300 |
in |
|
301 |
||
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302 |
val class = gen_class cert_class_spec; |
26518 | 303 |
val class_cmd = gen_class read_class_spec; |
24218 | 304 |
|
305 |
end; (*local*) |
|
306 |
||
307 |
||
29358 | 308 |
(** subclass relations **) |
25462 | 309 |
|
29358 | 310 |
local |
25462 | 311 |
|
29358 | 312 |
fun gen_subclass prep_class do_proof raw_sup lthy = |
25462 | 313 |
let |
29358 | 314 |
val thy = ProofContext.theory_of lthy; |
29558 | 315 |
val proto_sup = prep_class thy raw_sup; |
33553 | 316 |
val proto_sub = case Theory_Target.peek lthy |
29558 | 317 |
of {is_class = false, ...} => error "Not in a class context" |
29358 | 318 |
| {target, ...} => target; |
31987 | 319 |
val (sub, sup) = AxClass.cert_classrel thy (proto_sub, proto_sup); |
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320 |
|
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321 |
val expr = ([(sup, (("", false), Expression.Positional []))], []); |
29558 | 322 |
val (([props], deps, export), goal_ctxt) = |
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323 |
Expression.cert_goal_expression expr lthy; |
29526 | 324 |
val some_prop = try the_single props; |
29558 | 325 |
val some_dep_morph = try the_single (map snd deps); |
326 |
fun after_qed some_wit = |
|
327 |
ProofContext.theory (register_subclass (sub, sup) |
|
328 |
some_dep_morph some_wit export) |
|
33553 | 329 |
#> ProofContext.theory_of #> Theory_Target.init (SOME sub); |
29558 | 330 |
in do_proof after_qed some_prop goal_ctxt end; |
25485 | 331 |
|
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332 |
fun user_proof after_qed some_prop = |
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333 |
Element.witness_proof (after_qed o try the_single o the_single) |
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|
334 |
[the_list some_prop]; |
25485 | 335 |
|
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336 |
fun tactic_proof tac after_qed some_prop ctxt = |
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337 |
after_qed (Option.map |
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|
338 |
(fn prop => Element.prove_witness ctxt prop tac) some_prop) ctxt; |
28666 | 339 |
|
29358 | 340 |
in |
28666 | 341 |
|
29358 | 342 |
val subclass = gen_subclass (K I) user_proof; |
343 |
fun prove_subclass tac = gen_subclass (K I) (tactic_proof tac); |
|
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344 |
val subclass_cmd = gen_subclass (ProofContext.read_class o ProofContext.init) user_proof; |
25462 | 345 |
|
29358 | 346 |
end; (*local*) |
347 |
||
24218 | 348 |
end; |