author | paulson |
Mon, 23 Sep 1996 18:18:18 +0200 | |
changeset 2010 | 0a22b9d63a18 |
parent 1498 | 7b7d20e89b1b |
child 2266 | 82aef6857c5b |
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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User interfaces for axiomatic type classes. |
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*) |
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signature AX_CLASS = |
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sig |
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val add_thms_as_axms: (string * thm) list -> theory -> theory |
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val add_classrel_thms: thm list -> theory -> theory |
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val add_arity_thms: thm list -> theory -> theory |
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val add_axclass: class * class list -> (string * string) list |
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-> theory -> theory |
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val add_axclass_i: class * class list -> (string * term) list |
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-> theory -> theory |
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val add_inst_subclass: class * class -> string list -> thm list |
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-> tactic option -> theory -> theory |
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val add_inst_arity: string * sort list * class list -> string list |
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-> thm list -> tactic option -> theory -> theory |
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val axclass_tac: theory -> thm list -> tactic |
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val prove_subclass: theory -> class * class -> thm list |
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-> tactic option -> thm |
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val prove_arity: theory -> string * sort list * class -> thm list |
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-> tactic option -> thm |
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val goal_subclass: theory -> class * class -> thm list |
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val goal_arity: theory -> string * sort list * class -> thm list |
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end; |
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structure AxClass : AX_CLASS = |
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struct |
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(** utilities **) |
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(* type vars *) |
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fun map_typ_frees f (Type (t, tys)) = Type (t, map (map_typ_frees f) tys) |
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| map_typ_frees f (TFree a) = f a |
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| map_typ_frees _ a = a; |
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val map_term_tfrees = map_term_types o map_typ_frees; |
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fun aT S = TFree ("'a", S); |
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(* get axioms and theorems *) |
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fun get_ax thy name = |
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Some (get_axiom thy name) handle THEORY _ => None; |
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val get_axioms = mapfilter o get_ax; |
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val is_def = Logic.is_equals o #prop o rep_thm; |
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fun witnesses thy axms thms = |
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map (get_axiom thy) axms @ thms @ filter is_def (map snd (axioms_of thy)); |
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(** abstract syntax operations **) |
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(* subclass relations as terms *) |
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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 "dest_classrel" [tm]; |
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val (ty, c2) = Logic.dest_inclass (Logic.freeze_vars tm) |
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handle TERM _ => err (); |
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val c1 = (case ty of TFree (_, [c]) => c | _ => err ()); |
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in |
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(c1, c2) |
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end; |
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(* arities as terms *) |
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fun mk_arity (t, ss, c) = |
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let |
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val names = tl (variantlist (replicate (length ss + 1) "'", [])); |
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val tfrees = map TFree (names ~~ ss); |
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in |
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Logic.mk_inclass (Type (t, tfrees), c) |
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end; |
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fun dest_arity tm = |
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let |
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fun err () = raise_term "dest_arity" [tm]; |
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val (ty, c) = Logic.dest_inclass (Logic.freeze_vars tm) |
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handle TERM _ => err (); |
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val (t, tfrees) = |
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(case ty of |
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Type (t, tys) => (t, map (fn TFree x => x | _ => err ()) tys) |
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| _ => err ()); |
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val ss = |
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if null (gen_duplicates eq_fst tfrees) |
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then map snd tfrees else err (); |
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in |
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(t, ss, c) |
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end; |
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(** add theorems as axioms **) |
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fun prep_thm_axm thy thm = |
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let |
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fun err msg = raise THM ("prep_thm_axm: " ^ msg, 0, [thm]); |
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val {sign, hyps, prop, ...} = rep_thm thm; |
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in |
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if not (Sign.subsig (sign, sign_of thy)) then |
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err "theorem not of same theory" |
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else if not (null (extra_shyps thm)) orelse not (null hyps) then |
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err "theorem may not contain hypotheses" |
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else prop |
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end; |
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(*general theorems*) |
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fun add_thms_as_axms thms thy = |
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add_axioms_i (map (apsnd (prep_thm_axm thy)) thms) thy; |
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(*theorems expressing class relations*) |
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fun add_classrel_thms thms thy = |
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let |
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fun prep_thm thm = |
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let |
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val prop = prep_thm_axm thy thm; |
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val (c1, c2) = dest_classrel prop handle TERM _ => |
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raise THM ("add_classrel_thms: theorem is not a class relation", 0, [thm]); |
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in (c1, c2) end; |
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in |
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add_classrel (map prep_thm thms) thy |
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end; |
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(*theorems expressing arities*) |
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fun add_arity_thms thms thy = |
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let |
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fun prep_thm thm = |
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let |
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val prop = prep_thm_axm thy thm; |
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val (t, ss, c) = dest_arity prop handle TERM _ => |
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raise THM ("add_arity_thms: theorem is not an arity", 0, [thm]); |
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in (t, ss, [c]) end; |
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in |
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add_arities (map prep_thm thms) thy |
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end; |
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(** add axiomatic type classes **) |
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(* errors *) |
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fun err_not_logic c = |
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error ("Axiomatic class " ^ quote c ^ " not subclass of \"logic\""); |
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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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(* ext_axclass *) |
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fun ext_axclass prep_axm (class, super_classes) raw_axioms old_thy = |
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let |
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val axioms = map (prep_axm (sign_of old_thy)) raw_axioms; |
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val thy = add_classes [(class, super_classes)] old_thy; |
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val sign = sign_of thy; |
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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 logicS, class), ax) |
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else |
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map_term_tfrees (K (aT [class])) ax; |
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val abs_axioms = map (apsnd abs_axm) axioms; |
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(* prepare introduction orule *) |
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val _ = |
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if Sign.subsort sign ([class], logicS) then () |
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else err_not_logic class; |
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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)] => |
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if Sign.subsort sign ([class], S) then S |
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else err_bad_axsort name class |
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| _ => err_bad_tfrees name); |
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val axS = Sign.norm_sort sign (logicC :: flat (map axm_sort axioms)); |
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val int_axm = Logic.close_form o map_term_tfrees (K (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 snd) axioms, inclass class); |
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in |
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add_axioms_i ((class ^ "I", intro_axm) :: abs_axioms) thy |
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end; |
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(* external interfaces *) |
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val add_axclass = ext_axclass read_axm; |
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val add_axclass_i = ext_axclass cert_axm; |
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(** prove class relations and type arities **) |
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(* class_axms *) |
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fun class_axms thy = |
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let |
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val classes = Sign.classes (sign_of thy); |
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val intros = map (fn c => c ^ "I") classes; |
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in |
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map (class_triv thy) classes @ |
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get_axioms thy intros |
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end; |
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(* axclass_tac *) |
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||
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(*(1) repeatedly resolve goals of form "OFCLASS(ty, c_class)", |
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try class_trivs first, then "cI" axioms |
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(2) rewrite goals using user supplied definitions |
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(3) repeatedly resolve goals with user supplied non-definitions*) |
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fun axclass_tac thy thms = |
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let |
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val defs = filter is_def thms; |
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val non_defs = filter_out is_def thms; |
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in |
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TRY (REPEAT_FIRST (resolve_tac (class_axms thy))) THEN |
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TRY (rewrite_goals_tac defs) THEN |
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TRY (REPEAT_FIRST (fn i => assume_tac i ORELSE resolve_tac non_defs i)) |
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end; |
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(* provers *) |
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fun prove term_of str_of thy sig_prop thms usr_tac = |
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let |
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val sign = sign_of thy; |
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val goal = cterm_of sign (term_of sig_prop); |
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val tac = axclass_tac thy thms THEN (if_none usr_tac all_tac); |
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in |
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prove_goalw_cterm [] goal (K [tac]) |
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end |
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handle ERROR => error ("The error(s) above occurred while trying to prove " |
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^ quote (str_of sig_prop)); |
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val prove_subclass = |
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prove mk_classrel (fn (c1, c2) => c1 ^ " < " ^ c2); |
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val prove_arity = |
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prove mk_arity (fn (t, ss, c) => Type.str_of_arity (t, ss, [c])); |
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(* make goals (for interactive use) *) |
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fun mk_goal term_of thy sig_prop = |
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goalw_cterm [] (cterm_of (sign_of thy) (term_of sig_prop)); |
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val goal_subclass = mk_goal mk_classrel; |
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val goal_arity = mk_goal mk_arity; |
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(** add proved subclass relations and arities **) |
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fun add_inst_subclass (c1, c2) axms thms usr_tac thy = |
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add_classrel_thms |
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[prove_subclass thy (c1, c2) (witnesses thy axms thms) usr_tac] thy; |
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fun add_inst_arity (t, ss, cs) axms thms usr_tac thy = |
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let |
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val wthms = witnesses thy axms thms; |
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fun prove c = |
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prove_arity thy (t, ss, c) wthms usr_tac; |
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in |
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add_arity_thms (map prove cs) thy |
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end; |
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end; |