author  haftmann 
Wed, 21 Jan 2009 23:40:23 +0100  
changeset 29608  564ea783ace8 
parent 29575  41d604e59e93 
child 29624  e61ba06cddcd 
permissions  rwrr 
29358  1 
(* Title: Pure/Isar/ML 
24218  2 
Author: Florian Haftmann, TU Muenchen 
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Type classes derived from primitive axclasses and locales  interfaces. 
24218  5 
*) 
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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*) 

29358  12 

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val class: bstring > class list > Element.context_i list 
29378  14 
> theory > string * local_theory 
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val class_cmd: bstring > xstring list > Element.context list 
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> theory > string * local_theory 
29358  17 
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 

24218  20 
end; 
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structure Class : CLASS = 

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struct 

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open Class_Target; 
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(** define classes **) 
24218  28 

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local 

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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; 

34 

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(* instantiation of canonical interpretation *) 

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(*FIXME inst_morph should be calculated manually and not instantiate constraint*) 

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val aT = TFree (Name.aT, base_sort); 
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val (([props], [(_, inst_morph)], export_morph), _) = empty_ctxt 
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> Expression.cert_goal_expression ([(class, (("", false), 

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Expression.Named ((map o apsnd) Const param_map)))], []); 

41 

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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 

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(Binding.add_prefix false (class_prefix class)) 

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$> Element.satisfy_morphism (the_list wit); 

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val defs = these_defs thy sups; 

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val eq_morph = Element.eq_morphism thy defs; 

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val morph = base_morph $> eq_morph; 

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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 prop = thm > Thm.prop_of > Logic.unvarify 

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> Morphism.term (inst_morph $> eq_morph) 

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> (map_types o map_atyps) (K aT); 

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fun tac ctxt = LocalDefs.unfold_tac ctxt (map Thm.symmetric defs) (*FIXME*) 

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THEN ALLGOALS (ProofContext.fact_tac [thm]); 

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in Goal.prove_global thy [] [] prop (tac o #context) 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_inclass (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 inst_morph prop, 

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of_class_prop_concl) > (map_types o map_atyps) (K aT) 

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val sup_of_classes = map (snd o rules thy) sups; 

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val loc_axiom_intros = map Drule.standard' (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 = Drule.sort_triv 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 = Goal.prove_global thy [] [] of_class_prop (K tac); 

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in (base_morph, morph, export_morph, axiom, assm_intro, of_class) end; 

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fun add_typ_check level name f = Context.proof_map (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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val singleton_infer_param = (map o map_atyps) (fn T as TVar (vi as (_, i), sort) => 
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if TypeInfer.is_param vi then TypeInfer.param i (Name.aT, sort) 

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else error ("Illegal schematic type variable in class specification: " ^ Term.string_of_vname vi) 
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(*FIXME does not occur*) 
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 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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val singleton_fixate = (map o map_atyps) (fn TVar (vi, sort) 
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=> TFree (Name.aT, sort)  T => T); 
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fun add_tfrees_of_element (Element.Fixes fxs) = fold (fn (_, SOME T, _) => Term.add_tfreesT T 
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 _ => I) fxs 
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 add_tfrees_of_element (Element.Constrains cnstrs) = fold (Term.add_tfreesT o snd) cnstrs 
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 add_tfrees_of_element (Element.Assumes assms) = fold (fold (fn (t, ts) => 
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Term.add_tfrees t #> fold Term.add_tfrees ts) o snd) assms 
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 add_tfrees_of_element _ = I; 
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fun fork_syn (Element.Fixes xs) = 
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fold_map (fn (c, ty, syn) => cons (Binding.base_name 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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fun prep_class_spec prep_class prep_decl 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 
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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 ("These are not classes: " ^ commas (map quote no_classes)); 

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val supparams = (map o apsnd) (snd o snd) (these_params thy sups); 

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val supparam_names = map fst supparams; 
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val _ = if has_duplicates (op =) supparam_names 
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then error ("Duplicate parameter(s) in superclasses: " 
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^ (commas o map quote o duplicates (op =)) supparam_names) 
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else (); 
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val supexpr = (map (fn sup => (sup, (("", false), Expression.Positional []))) 
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sups, []); 
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val given_basesort = fold inter_sort (map (base_sort thy) sups) []; 
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(* infer types and base sort *) 
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val base_constraints = (map o apsnd) 
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(map_type_tfree (K (TVar ((Name.aT, 0), given_basesort))) o fst o snd) 
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(these_operations thy sups); 
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val ((_, _, inferred_elems), _) = ProofContext.init thy 
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> fold (ProofContext.add_const_constraint o apsnd SOME) base_constraints 
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> add_typ_check ~1 "singleton_infer_param" singleton_infer_param 
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> add_typ_check ~2 "singleton_fixate" singleton_fixate 
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> prep_decl supexpr raw_elems; 
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(*FIXME check for *all* side conditions here, extra check function for elements, 
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less sidecondition checks in check phase*) 
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val base_sort = if null inferred_elems then given_basesort else 
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case fold add_tfrees_of_element 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 sup_sort = inter_sort base_sort sups 
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(* process elements as class specification *) 
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val begin_ctxt = begin sups base_sort 
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#> fold (Variable.declare_constraints o Free) ((map o apsnd o map_atyps) 
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(K (TFree (Name.aT, base_sort))) supparams) 
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(*FIXME should constraints be issued in begin?*) 
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val ((_, _, syntax_elems), _) = ProofContext.init thy 
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> begin_ctxt 
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> Expression.cert_declaration supexpr inferred_elems; 
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val (elems, global_syntax) = fold_map fork_syn syntax_elems []; 
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val constrain = Element.Constrains ((map o apsnd o map_atyps) 
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(K (TFree (Name.aT, base_sort))) supparams); 
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(*FIXME 2009 perhaps better: control type variable by explicit 
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parameter instantiation of import expression*) 
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in (((sups, supparam_names), (sup_sort, base_sort, supexpr)), (constrain :: elems, global_syntax)) end; 
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val cert_class_spec = prep_class_spec (K I) Expression.cert_declaration; 
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val read_class_spec = prep_class_spec Sign.intern_class Expression.cert_read_declaration; 
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fun add_consts bname class base_sort sups supparams global_syntax thy = 
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let 
29526  175 
(*FIXME 2009 simplify*) 
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val supconsts = supparams 
26518  177 
> AList.make (snd o the o AList.lookup (op =) (these_params thy sups)) 
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> (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; 
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val raw_params = (snd o chop (length supparams)) all_params; 
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fun add_const (b, SOME raw_ty, _) thy = 
25683  182 
let 
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val v = Binding.base_name b; 
28965  184 
val c = Sign.full_bname thy v; 
25683  185 
val ty = map_atyps (K (TFree (Name.aT, base_sort))) raw_ty; 
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val ty0 = Type.strip_sorts ty; 

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val ty' = map_atyps (K (TFree (Name.aT, [class]))) ty0; 

188 
val syn = (the_default NoSyn o AList.lookup (op =) global_syntax) v; 

189 
in 

190 
thy 

28965  191 
> Sign.declare_const [] ((Binding.name v, ty0), syn) 
25683  192 
> snd 
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> pair ((v, ty), (c, ty')) 

194 
end; 

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in 
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thy 
29547  197 
> 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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fun adjungate_axclass bname class base_sort sups supsort supparams global_syntax thy = 
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let 
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(*FIXME 2009 simplify*) 
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fun globalize param_map = map_aterms 
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(fn Free (v, ty) => Const ((fst o the o AList.lookup (op =) param_map) v, ty) 

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 t => t); 

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val raw_pred = Locale.intros_of thy class 
25683  210 
> fst 
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> Option.map (Logic.unvarify o Logic.strip_imp_concl o Thm.prop_of); 
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fun get_axiom thy = case (#axioms o AxClass.get_info thy) class 
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of [] => NONE 

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 [thm] => SOME thm; 

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in 
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thy 
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> add_consts bname class base_sort sups supparams global_syntax 
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> (fn (param_map, params) => AxClass.define_class (bname, supsort) 
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(map (fst o snd) params) 
29526  220 
[((Binding.empty, []), 
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Option.map (globalize param_map) raw_pred > the_list)] 
25683  222 
#> snd 
223 
#> `get_axiom 

224 
#> (fn assm_axiom => fold (Sign.add_const_constraint o apsnd SOME o snd) params 

29526  225 
#> pair (param_map, params, assm_axiom))) 
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end; 
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26518  228 
fun gen_class prep_spec bname raw_supclasses raw_elems thy = 
24748  229 
let 
28965  230 
val class = Sign.full_bname thy bname; 
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val (((sups, supparams), (supsort, base_sort, supexpr)), (elems, global_syntax)) = 
26247  232 
prep_spec thy raw_supclasses raw_elems; 
24218  233 
in 
234 
thy 

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> Expression.add_locale bname "" supexpr elems 
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> snd > LocalTheory.exit_global 
26518  237 
> adjungate_axclass bname class base_sort sups supsort supparams global_syntax 
29526  238 
> (fn (param_map, params, assm_axiom) => 
29547  239 
`(fn thy => calculate thy class sups base_sort param_map assm_axiom) 
240 
#> (fn (base_morph, morph, export_morph, axiom, assm_intro, of_class) => 

241 
Locale.add_registration (class, (morph, export_morph)) 

242 
#> Locale.activate_global_facts (class, morph $> export_morph) 

243 
#> register class sups params base_sort base_morph axiom assm_intro of_class)) 

29378  244 
> TheoryTarget.init (SOME class) 
25038  245 
> pair class 
24218  246 
end; 
247 

248 
in 

249 

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val class = gen_class cert_class_spec; 
26518  251 
val class_cmd = gen_class read_class_spec; 
24218  252 

253 
end; (*local*) 

254 

255 

29358  256 
(** subclass relations **) 
25462  257 

29358  258 
local 
25462  259 

29358  260 
fun gen_subclass prep_class do_proof raw_sup lthy = 
25462  261 
let 
29358  262 
val thy = ProofContext.theory_of lthy; 
29558  263 
val proto_sup = prep_class thy raw_sup; 
264 
val proto_sub = case TheoryTarget.peek lthy 

265 
of {is_class = false, ...} => error "Not in a class context" 

29358  266 
 {target, ...} => target; 
29558  267 
val (sub, sup) = AxClass.cert_classrel thy (proto_sub, proto_sup) 
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val expr = ([(sup, (("", false), Expression.Positional []))], []); 
29558  270 
val (([props], deps, export), goal_ctxt) = 
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Expression.cert_goal_expression expr lthy; 
29526  272 
val some_prop = try the_single props; 
29558  273 
val some_dep_morph = try the_single (map snd deps); 
274 
fun after_qed some_wit = 

275 
ProofContext.theory (register_subclass (sub, sup) 

276 
some_dep_morph some_wit export) 

277 
#> ProofContext.theory_of #> TheoryTarget.init (SOME sub); 

278 
in do_proof after_qed some_prop goal_ctxt end; 

25485  279 

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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  283 

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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  287 

29358  288 
in 
28666  289 

29358  290 
val subclass = gen_subclass (K I) user_proof; 
291 
fun prove_subclass tac = gen_subclass (K I) (tactic_proof tac); 

292 
val subclass_cmd = gen_subclass Sign.read_class user_proof; 

25462  293 

29358  294 
end; (*local*) 
295 

24218  296 
end; 