author | wenzelm |
Tue, 14 Mar 2006 22:07:33 +0100 | |
changeset 19273 | 05b6d220e509 |
parent 19243 | 5dcb899a8486 |
child 19392 | a631cd2117a8 |
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 -> string -> {super_classes: class list, intro: thm, axioms: 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 -> {intro: thm, axioms: thm list} * theory |
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val add_axclass_i: bstring * class list -> ((bstring * term) * attribute list) list -> |
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theory -> {intro: thm, axioms: thm list} * 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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fun aT S = TFree ("'a", S); |
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fun dest_varT (TFree (x, S)) = ((x, ~1), S) |
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| dest_varT (TVar a) = a |
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| dest_varT T = raise TYPE ("AxClass.dest_varT", [T], []); |
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(* subclass propositions *) |
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fun mk_classrel (c1, c2) = Logic.mk_inclass (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_varT 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_varT 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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(** axclass info **) |
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||
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val introN = "intro"; |
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val axiomsN = "axioms"; |
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type axclass_info = |
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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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structure AxclassesData = TheoryDataFun |
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(struct |
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val name = "Pure/axclasses"; |
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type T = axclass_info Symtab.table; |
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val empty = Symtab.empty; |
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val copy = I; |
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val extend = I; |
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fun merge _ = Symtab.merge (K true); |
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fun print thy tab = |
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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, {super_classes, intro, axioms}) = 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 tab))) end; |
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end); |
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val _ = Context.add_setup AxclassesData.init; |
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val print_axclasses = AxclassesData.print; |
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val lookup_info = Symtab.lookup o AxclassesData.get; |
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fun get_info thy c = |
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(case lookup_info thy c of |
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NONE => error ("Unknown axclass " ^ quote c) |
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| SOME info => info); |
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fun class_intros thy = |
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let val classes = Sign.classes thy in |
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map (Thm.class_triv thy) classes @ |
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List.mapPartial (Option.map #intro o lookup_info thy) classes |
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end; |
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(** add axiomatic type classes **) |
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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 (aT [], class), ax) |
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else replace_tfree (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 (aT axS); |
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fun inclass c = Logic.mk_inclass (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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177 |
(*declare axioms and rule*) |
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18377 | 178 |
val (([intro], [axioms]), axms_thy) = |
6379 | 179 |
class_thy |
18932 | 180 |
|> Theory.add_path (Logic.const_of_class bclass) |
6379 | 181 |
|> PureThy.add_axioms_i [Thm.no_attributes (introN, intro_axm)] |
18377 | 182 |
||>> PureThy.add_axiomss_i [Thm.no_attributes (axiomsN, abs_axms)]; |
6379 | 183 |
val info = {super_classes = super_classes, intro = intro, axioms = axioms}; |
184 |
||
185 |
(*store info*) |
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18377 | 186 |
val (_, final_thy) = |
6379 | 187 |
axms_thy |
18932 | 188 |
|> Theory.add_finals_i false [Const (Logic.const_of_class class, a_itselfT --> propT)] |
18377 | 189 |
|> PureThy.add_thms ((map #1 axms ~~ axioms) ~~ atts) |
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||> Theory.restore_naming class_thy |
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||> AxclassesData.map (Symtab.update (class, info)); |
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in ({intro = intro, axioms = axioms}, 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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(** proven class instantiation **) |
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(* primitive rules *) |
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|
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fun add_classrel ths thy = |
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let |
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fun prep_thm 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 Theory.add_classrel_i (map prep_thm ths) thy end; |
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|
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fun add_arity ths thy = |
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let |
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fun prep_thm 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 Theory.add_arities_i (map prep_thm ths) thy end; |
404
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|
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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; |