author  ballarin 
Sat, 31 Jul 2010 21:14:20 +0200  
changeset 38107  3a46cebd7983 
parent 37101  7099a9ed3be2 
child 38350  480b2de9927c 
permissions  rwrr 
35120  1 
(* Title: Pure/Isar/class.ML 
24218  2 
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 classrelated 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_global 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*) 

29547  54 

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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 const_eq_morph = case eq_morph 
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of SOME eq_morph => const_morph $> eq_morph 
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 NONE => const_morph 
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val thm'' = Morphism.thm const_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 typechecked 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_global 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)); 
29608  182 
val sups = map (prep_class thy) raw_supclasses 
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> 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); 
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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_global 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.string_of 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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32713  220 
in (((sups, supparam_names), (sup_sort, base_sort, supexpr)), (elems, global_syntax)) end; 
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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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(* class establishment *) 
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32206  228 
fun add_consts class base_sort sups supparam_names global_syntax thy = 
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let 
29816  230 
(*FIXME simplify*) 
32206  231 
val supconsts = supparam_names 
26518  232 
> AList.make (snd o the o AList.lookup (op =) (these_params thy sups)) 
25683  233 
> (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  235 
val raw_params = (snd o chop (length supparam_names)) all_params; 
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fun add_const ((raw_c, raw_ty), _) thy = 
25683  237 
let 
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val b = Binding.name raw_c; 
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val c = Sign.full_name thy b; 
25683  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; 

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val syn = (the_default NoSyn o AList.lookup Binding.eq_name global_syntax) b; 
25683  244 
in 
245 
thy 

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> Sign.declare_const ((b, ty0), syn) 
25683  247 
> snd 
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> pair ((Name.of_binding b, ty), (c, ty')) 
25683  249 
end; 
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in 
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thy 
29547  252 
> 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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end; 
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32206  258 
fun adjungate_axclass bname class base_sort sups supsort supparam_names global_syntax thy = 
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let 
29816  260 
(*FIXME simplify*) 
25683  261 
fun globalize param_map = map_aterms 
262 
(fn Free (v, ty) => Const ((fst o the o AList.lookup (op =) param_map) v, ty) 

263 
 t => t); 

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val raw_pred = Locale.intros_of thy class 
25683  265 
> fst 
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> Option.map (Logic.unvarify_global o Logic.strip_imp_concl o Thm.prop_of); 
25683  267 
fun get_axiom thy = case (#axioms o AxClass.get_info thy) class 
268 
of [] => NONE 

269 
 [thm] => SOME thm; 

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in 
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thy 
32206  272 
> add_consts class base_sort sups supparam_names global_syntax 
25683  273 
> (fn (param_map, params) => AxClass.define_class (bname, supsort) 
26518  274 
(map (fst o snd) params) 
30211  275 
[(Thm.empty_binding, Option.map (globalize param_map) raw_pred > the_list)] 
25683  276 
#> snd 
277 
#> `get_axiom 

278 
#> (fn assm_axiom => fold (Sign.add_const_constraint o apsnd SOME o snd) params 

29526  279 
#> pair (param_map, params, assm_axiom))) 
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end; 
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281 

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fun gen_class prep_class_spec b raw_supclasses raw_elems thy = 
24748  283 
let 
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val class = Sign.full_name thy b; 
32206  285 
val (((sups, supparam_names), (supsort, base_sort, supexpr)), (elems, global_syntax)) = 
286 
prep_class_spec thy raw_supclasses raw_elems; 

24218  287 
in 
288 
thy 

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> Expression.add_locale b (Binding.qualify true "class" b) supexpr elems 
33671  290 
> snd > Local_Theory.exit_global 
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> adjungate_axclass b class base_sort sups supsort supparam_names global_syntax 
31696  292 
> Theory.checkpoint 
29526  293 
> (fn (param_map, params, assm_axiom) => 
29547  294 
`(fn thy => calculate thy class sups base_sort param_map assm_axiom) 
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#> (fn (base_morph, eq_morph, export_morph, axiom, assm_intro, of_class) => 
38107  296 
Context.theory_map (Locale.add_registration (class, base_morph) 
297 
(Option.map (rpair true) eq_morph) export_morph) 

32850  298 
#> register class sups params base_sort base_morph export_morph axiom assm_intro of_class)) 
33553  299 
> Theory_Target.init (SOME class) 
25038  300 
> pair class 
24218  301 
end; 
302 

303 
in 

304 

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val class = gen_class cert_class_spec; 
26518  306 
val class_cmd = gen_class read_class_spec; 
24218  307 

308 
end; (*local*) 

309 

310 

29358  311 
(** subclass relations **) 
25462  312 

29358  313 
local 
25462  314 

29358  315 
fun gen_subclass prep_class do_proof raw_sup lthy = 
25462  316 
let 
29358  317 
val thy = ProofContext.theory_of lthy; 
29558  318 
val proto_sup = prep_class thy raw_sup; 
33553  319 
val proto_sub = case Theory_Target.peek lthy 
29558  320 
of {is_class = false, ...} => error "Not in a class context" 
29358  321 
 {target, ...} => target; 
31987  322 
val (sub, sup) = AxClass.cert_classrel thy (proto_sub, proto_sup); 
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val expr = ([(sup, (("", false), Expression.Positional []))], []); 
29558  325 
val (([props], deps, export), goal_ctxt) = 
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Expression.cert_goal_expression expr lthy; 
29526  327 
val some_prop = try the_single props; 
29558  328 
val some_dep_morph = try the_single (map snd deps); 
329 
fun after_qed some_wit = 

330 
ProofContext.theory (register_subclass (sub, sup) 

331 
some_dep_morph some_wit export) 

33553  332 
#> ProofContext.theory_of #> Theory_Target.init (SOME sub); 
29558  333 
in do_proof after_qed some_prop goal_ctxt end; 
25485  334 

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fun user_proof after_qed some_prop = 
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Element.witness_proof (after_qed o try the_single o the_single) 
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[the_list some_prop]; 
25485  338 

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fun tactic_proof tac after_qed some_prop ctxt = 
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after_qed (Option.map 
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(fn prop => Element.prove_witness ctxt prop tac) some_prop) ctxt; 
28666  342 

29358  343 
in 
28666  344 

29358  345 
val subclass = gen_subclass (K I) user_proof; 
346 
fun prove_subclass tac = gen_subclass (K I) (tactic_proof tac); 

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val subclass_cmd = gen_subclass (ProofContext.read_class o ProofContext.init_global) user_proof; 
25462  348 

29358  349 
end; (*local*) 
350 

24218  351 
end; 