author | haftmann |
Mon, 10 Apr 2006 08:30:26 +0200 | |
changeset 19398 | 8ad34412ea97 |
parent 19392 | a631cd2117a8 |
child 19405 | a551256aba15 |
permissions | -rw-r--r-- |
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(* Title: Pure/axclass.ML |
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ID: $Id$ |
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Author: Markus Wenzel, TU Muenchen |
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Axiomatic type classes: pure logical content. |
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*) |
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signature AX_CLASS = |
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sig |
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val mk_classrel: class * class -> term |
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val dest_classrel: term -> class * class |
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val mk_arity: string * sort list * class -> term |
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val mk_arities: string * sort list * sort -> term list |
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val dest_arity: term -> string * sort list * class |
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val print_axclasses: theory -> unit |
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val get_info: theory -> class -> {super_classes: class list, intro: thm, axioms: thm list} |
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val get_instances: theory -> |
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{classrel: unit Graph.T, subsorts: ((sort * sort) * thm) list, arities: (arity * thm) list} |
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val class_intros: theory -> thm list |
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val add_axclass: bstring * xstring list -> ((bstring * string) * Attrib.src list) list -> |
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theory -> class * theory |
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val add_axclass_i: bstring * class list -> ((bstring * term) * attribute list) list -> |
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theory -> class * theory |
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val add_classrel: thm list -> theory -> theory |
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val add_arity: thm list -> theory -> theory |
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val prove_subclass: class * class -> tactic -> theory -> theory |
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val prove_arity: string * sort list * sort -> tactic -> theory -> theory |
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end; |
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structure AxClass: AX_CLASS = |
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struct |
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(** abstract syntax operations **) |
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(* subclass propositions *) |
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fun mk_classrel (c1, c2) = Logic.mk_inclass (Term.aT [c1], c2); |
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fun dest_classrel tm = |
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let |
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fun err () = raise TERM ("AxClass.dest_classrel", [tm]); |
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val (ty, c2) = Logic.dest_inclass tm handle TERM _ => err (); |
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val c1 = (case dest_TVar ty of (_, [c]) => c | _ => err ()) |
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handle TYPE _ => err (); |
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in (c1, c2) end; |
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||
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(* arity propositions *) |
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fun mk_arity (t, Ss, c) = |
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let |
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val tfrees = ListPair.map TFree (Term.invent_names [] "'a" (length Ss), Ss); |
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in Logic.mk_inclass (Type (t, tfrees), c) end; |
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fun mk_arities (t, Ss, S) = map (fn c => mk_arity (t, Ss, c)) S; |
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fun dest_arity tm = |
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let |
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fun err () = raise TERM ("AxClass.dest_arity", [tm]); |
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val (ty, c) = Logic.dest_inclass tm handle TERM _ => err (); |
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val (t, tvars) = |
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(case ty of |
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Type (t, tys) => (t, map dest_TVar tys handle TYPE _ => err ()) |
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| _ => err ()); |
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val ss = |
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if has_duplicates (eq_fst (op =)) tvars then err () |
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else map snd tvars; |
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in (t, ss, c) end; |
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(** theory data **) |
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||
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(* axclass *) |
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val introN = "intro"; |
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val axiomsN = "axioms"; |
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datatype axclass = AxClass of |
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{super_classes: class list, |
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intro: thm, |
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axioms: thm list}; |
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fun make_axclass (super_classes, intro, axioms) = |
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AxClass {super_classes = super_classes, intro = intro, axioms = axioms}; |
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(* instances *) |
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datatype instances = Instances of |
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{classrel: unit Graph.T, (*raw relation -- no closure!*) |
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subsorts: ((sort * sort) * thm) list, |
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arities: (arity * thm) list}; |
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fun make_instances (classrel, subsorts, arities) = |
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Instances {classrel = classrel, subsorts = subsorts, arities = arities}; |
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fun map_instances f (Instances {classrel, subsorts, arities}) = |
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make_instances (f (classrel, subsorts, arities)); |
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fun merge_instances |
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(Instances {classrel = classrel1, subsorts = subsorts1, arities = arities1}, |
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Instances {classrel = classrel2, subsorts = subsorts2, arities = arities2}) = |
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make_instances |
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(Graph.merge (K true) (classrel1, classrel2), |
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merge (eq_fst op =) (subsorts1, subsorts2), |
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merge (eq_fst op =) (arities1, arities2)); |
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(* setup data *) |
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structure AxClassData = TheoryDataFun |
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(struct |
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val name = "Pure/axclass"; |
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type T = axclass Symtab.table * instances; |
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val empty = (Symtab.empty, make_instances (Graph.empty, [], [])) : T; |
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val copy = I; |
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val extend = I; |
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fun merge _ ((axclasses1, instances1), (axclasses2, instances2)) = |
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(Symtab.merge (K true) (axclasses1, axclasses2), merge_instances (instances1, instances2)); |
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fun print thy (axclasses, _) = |
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let |
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fun pretty_class c cs = Pretty.block |
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(Pretty.str (Sign.extern_class thy c) :: Pretty.str " <" :: Pretty.brk 1 :: |
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Pretty.breaks (map (Pretty.str o Sign.extern_class thy) cs)); |
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fun pretty_thms name thms = Pretty.big_list (name ^ ":") |
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(map (Display.pretty_thm_sg thy) thms); |
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fun pretty_axclass (name, AxClass {super_classes, intro, axioms}) = |
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Pretty.block (Pretty.fbreaks |
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[pretty_class name super_classes, pretty_thms introN [intro], pretty_thms axiomsN axioms]); |
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in Pretty.writeln (Pretty.chunks (map pretty_axclass (Symtab.dest axclasses))) end; |
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end); |
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val _ = Context.add_setup AxClassData.init; |
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val print_axclasses = AxClassData.print; |
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val get_instances = AxClassData.get #> (fn (_, Instances insts) => insts); |
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(** axclass definitions **) |
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(* lookup *) |
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val lookup_info = Symtab.lookup o #1 o AxClassData.get; |
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fun get_info thy c = |
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(case lookup_info thy c of |
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SOME (AxClass info) => info |
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| NONE => error ("Unknown axclass " ^ quote c)); |
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fun class_intros thy = |
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let |
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fun add_intro c = |
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(case lookup_info thy c of SOME (AxClass {intro, ...}) => cons intro | _ => I); |
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val classes = Sign.classes thy; |
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in map (Thm.class_triv thy) classes @ fold add_intro classes [] end; |
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(* add_axclass(_i) *) |
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local |
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fun err_bad_axsort ax c = |
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error ("Sort constraint in axiom " ^ quote ax ^ " not supersort of " ^ quote c); |
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fun err_bad_tfrees ax = |
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error ("More than one type variable in axiom " ^ quote ax); |
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fun replace_tfree T = map_term_types (Term.map_atyps (fn TFree _ => T | U => U)); |
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fun gen_axclass prep_class prep_axm prep_att |
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(bclass, raw_super_classes) raw_axioms_atts thy = |
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let |
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val class = Sign.full_name thy bclass; |
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val super_classes = map (prep_class thy) raw_super_classes; |
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val axms = map (prep_axm thy o fst) raw_axioms_atts; |
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val atts = map (map (prep_att thy) o snd) raw_axioms_atts; |
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(*declare class*) |
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val class_thy = |
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thy |> Theory.add_classes_i [(bclass, super_classes)]; |
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(*prepare abstract axioms*) |
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fun abs_axm ax = |
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if null (term_tfrees ax) then |
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Logic.mk_implies (Logic.mk_inclass (Term.aT [], class), ax) |
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else replace_tfree (Term.aT [class]) ax; |
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val abs_axms = map (abs_axm o snd) axms; |
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fun axm_sort (name, ax) = |
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(case term_tfrees ax of |
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[] => [] |
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| [(_, S)] => if Sign.subsort class_thy ([class], S) then S else err_bad_axsort name class |
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| _ => err_bad_tfrees name); |
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val axS = Sign.certify_sort class_thy (List.concat (map axm_sort axms)); |
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val int_axm = Logic.close_form o replace_tfree (Term.aT axS); |
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fun inclass c = Logic.mk_inclass (Term.aT axS, c); |
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val intro_axm = Logic.list_implies |
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(map inclass super_classes @ map (int_axm o #2) axms, inclass class); |
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(*declare axioms and rule*) |
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val (([intro], [axioms]), axms_thy) = |
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class_thy |
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|> Theory.add_path (Logic.const_of_class bclass) |
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|> PureThy.add_axioms_i [Thm.no_attributes (introN, intro_axm)] |
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||>> PureThy.add_axiomss_i [Thm.no_attributes (axiomsN, abs_axms)]; |
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val info = make_axclass (super_classes, intro, axioms); |
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|
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(*store info*) |
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val (_, final_thy) = |
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axms_thy |
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|> Theory.add_finals_i false [Const (Logic.const_of_class class, Term.a_itselfT --> propT)] |
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|> PureThy.add_thms ((map #1 axms ~~ axioms) ~~ atts) |
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||> Theory.restore_naming class_thy |
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||> AxClassData.map (apfst (Symtab.update (class, info))); |
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in (class, final_thy) end; |
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in |
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val add_axclass = gen_axclass Sign.intern_class Theory.read_axm Attrib.attribute; |
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val add_axclass_i = gen_axclass (K I) Theory.cert_axm (K I); |
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end; |
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(** instantiation proofs **) |
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(* primitives *) |
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fun add_classrel ths thy = |
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let |
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fun add_rel (c1, c2) = |
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Graph.default_node (c1, ()) #> Graph.default_node (c2, ()) #> Graph.add_edge (c1, c2); |
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val rels = ths |> map (fn th => |
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let |
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val prop = Drule.plain_prop_of (Thm.transfer thy th); |
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val (c1, c2) = dest_classrel prop handle TERM _ => |
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raise THM ("AxClass.add_classrel: not a class relation", 0, [th]); |
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in (c1, c2) end); |
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in |
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thy |
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|> Theory.add_classrel_i rels |
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|> AxClassData.map (apsnd (map_instances (fn (classrel, subsorts, arities) => |
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(classrel |> fold add_rel rels, (map (pairself single) rels ~~ ths) @ subsorts, arities)))) |
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end; |
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|
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fun add_arity ths thy = |
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let |
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val ars = ths |> map (fn th => |
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let |
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val prop = Drule.plain_prop_of (Thm.transfer thy th); |
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val (t, ss, c) = dest_arity prop handle TERM _ => |
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raise THM ("AxClass.add_arity: not a type arity", 0, [th]); |
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in (t, ss, [c]) end); |
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in |
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thy |
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|> Theory.add_arities_i ars |
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|> AxClassData.map (apsnd (map_instances (fn (classrel, subsorts, arities) => |
|
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(classrel, subsorts, (ars ~~ ths) @ arities)))) |
|
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end; |
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|
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(* tactical proofs *) |
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|
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fun prove_subclass raw_rel tac thy = |
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let |
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val (c1, c2) = Sign.cert_classrel thy raw_rel; |
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val th = Goal.prove thy [] [] (mk_classrel (c1, c2)) (fn _ => tac) handle ERROR msg => |
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cat_error msg ("The error(s) above occurred while trying to prove class relation " ^ |
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quote (Sign.string_of_classrel thy [c1, c2])); |
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in add_classrel [th] thy end; |
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|
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fun prove_arity raw_arity tac thy = |
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let |
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val arity = Sign.cert_arity thy raw_arity; |
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val props = mk_arities arity; |
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val ths = Goal.prove_multi thy [] [] props |
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(fn _ => Tactic.precise_conjunction_tac (length props) 1 THEN tac) handle ERROR msg => |
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cat_error msg ("The error(s) above occurred while trying to prove type arity " ^ |
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quote (Sign.string_of_arity thy arity)); |
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in add_arity ths thy end; |
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|
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end; |