wenzelm@404: (*  Title:      Pure/axclass.ML
wenzelm@404:     ID:         $Id$
wenzelm@404:     Author:     Markus Wenzel, TU Muenchen
wenzelm@404: 
wenzelm@423: Higher level user interfaces for axiomatic type classes.
wenzelm@404: *)
wenzelm@404: 
wenzelm@404: signature AX_CLASS =
wenzelm@404: sig
wenzelm@404:   structure Tactical: TACTICAL
wenzelm@423:   local open Tactical Tactical.Thm Tactical.Thm.Sign.Syntax.Mixfix in
wenzelm@423:     val add_thms_as_axms: (string * thm) list -> theory -> theory
wenzelm@423:     val add_classrel_thms: thm list -> theory -> theory
wenzelm@423:     val add_arity_thms: thm list -> theory -> theory
wenzelm@404:     val add_axclass: class * class list -> (string * string) list
wenzelm@404:       -> theory -> theory
wenzelm@404:     val add_axclass_i: class * class list -> (string * term) list
wenzelm@404:       -> theory -> theory
wenzelm@423:     val add_sigclass: class * class list -> (string * string * mixfix) list
wenzelm@423:       -> theory -> theory
wenzelm@423:     val add_sigclass_i: class * class list -> (string * typ * mixfix) list
wenzelm@423:       -> theory -> theory
wenzelm@423:     val axclass_tac: theory -> thm list -> tactic
wenzelm@423:     val prove_classrel: theory -> class * class -> thm list
wenzelm@423:       -> tactic option -> thm
wenzelm@423:     val prove_arity: theory -> string * sort list * class -> thm list
wenzelm@423:       -> tactic option -> thm
wenzelm@423:     val add_subclass: class * class -> string list -> thm list
wenzelm@404:       -> tactic option -> theory -> theory
wenzelm@423:     val add_instance: string * sort list * class list -> string list
wenzelm@423:       -> thm list -> tactic option -> theory -> theory
wenzelm@404:   end
wenzelm@404: end;
wenzelm@404: 
wenzelm@404: functor AxClassFun(structure Logic: LOGIC and Goals: GOALS and Tactic: TACTIC
wenzelm@404:   sharing Goals.Tactical = Tactic.Tactical)(*: AX_CLASS *) = (* FIXME *)
wenzelm@404: struct
wenzelm@404: 
wenzelm@404: structure Tactical = Goals.Tactical;
wenzelm@404: structure Thm = Tactical.Thm;
wenzelm@404: structure Sign = Thm.Sign;
wenzelm@404: structure Type = Sign.Type;
wenzelm@404: 
wenzelm@404: open Logic Thm Tactical Tactic Goals;
wenzelm@404: 
wenzelm@404: 
wenzelm@423: (* FIXME fake! - remove *)
wenzelm@404: 
wenzelm@404: val add_defns = add_axioms;
wenzelm@404: val add_defns_i = add_axioms_i;
wenzelm@404: 
wenzelm@404: 
wenzelm@423: 
wenzelm@404: (** utilities **)
wenzelm@404: 
wenzelm@404: (* type vars *)
wenzelm@404: 
wenzelm@404: fun map_typ_frees f (Type (t, tys)) = Type (t, map (map_typ_frees f) tys)
wenzelm@404:   | map_typ_frees f (TFree a) = f a
wenzelm@404:   | map_typ_frees _ a = a;
wenzelm@404: 
wenzelm@404: val map_term_tfrees = map_term_types o map_typ_frees;
wenzelm@404: 
wenzelm@404: fun aT S = TFree ("'a", S);
wenzelm@404: 
wenzelm@404: 
wenzelm@404: (* get axioms *)
wenzelm@404: 
wenzelm@404: fun get_ax thy name =
wenzelm@404:   Some (get_axiom thy name) handle THEORY _ => None;
wenzelm@404: 
wenzelm@404: val get_axioms = mapfilter o get_ax;
wenzelm@404: 
wenzelm@404: 
wenzelm@404: (* is_defn *)
wenzelm@404: 
wenzelm@404: fun is_defn thm =
wenzelm@404:   (case #prop (rep_thm thm) of
wenzelm@404:     Const ("==", _) $ _ $ _ => true
wenzelm@404:   | _ => false);
wenzelm@404: 
wenzelm@404: 
wenzelm@404: 
wenzelm@423: (** abstract syntax operations **)    (* FIXME -> logic.ML (?) *)
wenzelm@423: 
wenzelm@423: (* subclass relations as terms *)
wenzelm@423: 
wenzelm@423: fun mk_classrel (c1, c2) = mk_inclass (aT [c1], c2);
wenzelm@423: 
wenzelm@423: fun dest_classrel tm =
wenzelm@423:   let
wenzelm@423:     fun err () = raise_term "dest_classrel" [tm];
wenzelm@423: 
wenzelm@423:     val (ty, c2) = dest_inclass (freeze_vars tm) handle TERM _ => err ();
wenzelm@423:     val c1 = (case ty of TFree (_, [c]) => c | _ => err ());
wenzelm@423:   in
wenzelm@423:     (c1, c2)
wenzelm@423:   end;
wenzelm@423: 
wenzelm@423: 
wenzelm@423: (* arities as terms *)
wenzelm@423: 
wenzelm@423: fun mk_arity (t, ss, c) =
wenzelm@423:   let
wenzelm@423:     val names = variantlist (replicate (length ss) "'a", []);
wenzelm@423:     val tfrees = map TFree (names ~~ ss);
wenzelm@423:   in
wenzelm@423:     mk_inclass (Type (t, tfrees), c)
wenzelm@423:   end;
wenzelm@423: 
wenzelm@423: fun dest_arity tm =
wenzelm@423:   let
wenzelm@423:     fun err () = raise_term "dest_arity" [tm];
wenzelm@423: 
wenzelm@423:     val (ty, c) = dest_inclass (freeze_vars tm) handle TERM _ => err ();
wenzelm@423:     val (t, tfrees) =
wenzelm@423:       (case ty of
wenzelm@423:         Type (t, tys) => (t, map (fn TFree x => x | _ => err ()) tys)
wenzelm@423:       | _ => err ());
wenzelm@423:     val ss =
wenzelm@423:       if null (gen_duplicates eq_fst tfrees)
wenzelm@423:       then map snd tfrees else err ();
wenzelm@423:   in
wenzelm@423:     (t, ss, c)
wenzelm@423:   end;
wenzelm@423: 
wenzelm@423: 
wenzelm@423: 
wenzelm@423: (** add theorems as axioms **)    (* FIXME -> drule.ML (?) *)
wenzelm@423: 
wenzelm@423: fun prep_thm_axm thy thm =
wenzelm@423:   let
wenzelm@423:     fun err msg = raise THM ("prep_thm_axm: " ^ msg, 0, [thm]);
wenzelm@423: 
wenzelm@423:     val {sign, hyps, prop, ...} = rep_thm thm;
wenzelm@423:   in
wenzelm@423:     if not (Sign.subsig (sign, sign_of thy)) then
wenzelm@423:       err "theorem not of same theory"
wenzelm@423:     else if not (null hyps) then
wenzelm@423:       err "theorem may not contain hypotheses"
wenzelm@423:     else prop
wenzelm@423:   end;
wenzelm@423: 
wenzelm@423: (*general theorems*)
wenzelm@423: fun add_thms_as_axms thms thy =
wenzelm@423:   add_axioms_i (map (apsnd (prep_thm_axm thy)) thms) thy;
wenzelm@423: 
wenzelm@423: (*theorems expressing class relations*)
wenzelm@423: fun add_classrel_thms thms thy =
wenzelm@423:   let
wenzelm@423:     fun prep_thm thm =
wenzelm@423:       let
wenzelm@423:         val prop = prep_thm_axm thy thm;
wenzelm@423:         val (c1, c2) = dest_classrel prop handle TERM _ =>
wenzelm@423:           raise THM ("add_classrel_thms: theorem is not a class relation", 0, [thm]);
wenzelm@423:       in (c1, c2) end;
wenzelm@423:   in
wenzelm@423:     add_classrel (map prep_thm thms) thy
wenzelm@423:   end;
wenzelm@423: 
wenzelm@423: (*theorems expressing arities*)
wenzelm@423: fun add_arity_thms thms thy =
wenzelm@423:   let
wenzelm@423:     fun prep_thm thm =
wenzelm@423:       let
wenzelm@423:         val prop = prep_thm_axm thy thm;
wenzelm@423:         val (t, ss, c) = dest_arity prop handle TERM _ =>
wenzelm@423:           raise THM ("add_arity_thms: theorem is not an arity", 0, [thm]);
wenzelm@423:       in (t, ss, [c]) end;
wenzelm@423:   in
wenzelm@423:     add_arities (map prep_thm thms) thy
wenzelm@423:   end;
wenzelm@423: 
wenzelm@423: 
wenzelm@423: 
wenzelm@423: (** add axiomatic type classes **)
wenzelm@404: 
wenzelm@404: (* errors *)
wenzelm@404: 
wenzelm@404: fun err_not_logic c =
wenzelm@404:   error ("Axiomatic class " ^ quote c ^ " not subclass of \"logic\"");
wenzelm@404: 
wenzelm@404: fun err_bad_axsort ax c =
wenzelm@404:   error ("Sort constraint in axiom " ^ quote ax ^ " not supersort of " ^ quote c);
wenzelm@404: 
wenzelm@404: fun err_bad_tfrees ax =
wenzelm@404:   error ("More than one type variable in axiom " ^ quote ax);
wenzelm@404: 
wenzelm@404: 
wenzelm@404: (* ext_axclass *)
wenzelm@404: 
wenzelm@404: fun ext_axclass prep_axm (class, super_classes) raw_axioms old_thy =
wenzelm@404:   let
wenzelm@404:     val axioms = map (prep_axm (sign_of old_thy)) raw_axioms;
wenzelm@404:     val thy = add_classes [([], class, super_classes)] old_thy;
wenzelm@404:     val sign = sign_of thy;
wenzelm@404: 
wenzelm@404: 
wenzelm@404:     (* prepare abstract axioms *)
wenzelm@404: 
wenzelm@404:     fun abs_axm ax =
wenzelm@404:       if null (term_tfrees ax) then
wenzelm@404:         mk_implies (mk_inclass (aT logicS, class), ax)
wenzelm@404:       else
wenzelm@404:         map_term_tfrees (K (aT [class])) ax;
wenzelm@404: 
wenzelm@404:     val abs_axioms = map (apsnd abs_axm) axioms;
wenzelm@404: 
wenzelm@404: 
wenzelm@404:     (* prepare introduction orule *)
wenzelm@404: 
wenzelm@404:     val _ =
wenzelm@404:       if Sign.subsort sign ([class], logicS) then ()
wenzelm@404:       else err_not_logic class;
wenzelm@404: 
wenzelm@404:     fun axm_sort (name, ax) =
wenzelm@404:       (case term_tfrees ax of
wenzelm@404:         [] => []
wenzelm@404:       | [(_, S)] =>
wenzelm@404:           if Sign.subsort sign ([class], S) then S
wenzelm@404:           else err_bad_axsort name class
wenzelm@404:       | _ => err_bad_tfrees name);
wenzelm@404: 
wenzelm@404:     val axS = Sign.norm_sort sign (logicC :: flat (map axm_sort axioms));
wenzelm@404: 
wenzelm@404:     val int_axm = close_form o map_term_tfrees (K (aT axS));
wenzelm@404:     fun inclass c = mk_inclass (aT axS, c);
wenzelm@404: 
wenzelm@404:     val intro_axm = list_implies
wenzelm@404:       (map inclass super_classes @ map (int_axm o snd) axioms, inclass class);
wenzelm@404:   in
wenzelm@404:     add_axioms_i ((class ^ "I", intro_axm) :: abs_axioms) thy
wenzelm@404:   end;
wenzelm@404: 
wenzelm@404: 
wenzelm@404: (* external interfaces *)
wenzelm@404: 
wenzelm@404: val add_axclass = ext_axclass read_axm;
wenzelm@404: val add_axclass_i = ext_axclass cert_axm;
wenzelm@404: 
wenzelm@404: 
wenzelm@423: (* add signature classes *)
wenzelm@404: 
wenzelm@423: fun ext_sigclass add_cnsts (class, super_classes) consts old_thy =
wenzelm@423:   old_thy
wenzelm@423:   |> add_axclass (class, super_classes) []
wenzelm@423:   |> add_defsort [class]
wenzelm@423:   |> add_cnsts consts
wenzelm@423:   |> add_defsort (Type.defaultS (#tsig (Sign.rep_sg (sign_of old_thy))));
wenzelm@404: 
wenzelm@423: val add_sigclass = ext_sigclass add_consts;
wenzelm@423: val add_sigclass_i = ext_sigclass add_consts_i;
wenzelm@404: 
wenzelm@404: 
wenzelm@404: 
wenzelm@423: (** prove class relations and type arities **)
wenzelm@423: 
wenzelm@423: (* class_axms *)
wenzelm@404: 
wenzelm@404: fun class_axms thy =
wenzelm@404:   let
wenzelm@404:     val classes = Sign.classes (sign_of thy);
wenzelm@404:     val intros = map (fn c => c ^ "I") classes;
wenzelm@404:   in
wenzelm@404:     get_axioms thy intros @
wenzelm@404:     map (class_triv thy) classes
wenzelm@404:   end;
wenzelm@404: 
wenzelm@423: 
wenzelm@423: (* axclass_tac *)
wenzelm@423: 
wenzelm@423: (*(1) repeatedly resolve goals of form "(| ty : c_class |)",
wenzelm@423:       try "cI" axioms first and use class_triv as last resort
wenzelm@423:   (2) rewrite goals using user supplied definitions
wenzelm@423:   (3) repeatedly resolve goals with user supplied non-definitions*)
wenzelm@423: 
wenzelm@423: fun axclass_tac thy thms =
wenzelm@423:   TRY (REPEAT_FIRST (resolve_tac (class_axms thy))) THEN
wenzelm@423:   TRY (rewrite_goals_tac (filter is_defn thms)) THEN
wenzelm@423:   TRY (REPEAT_FIRST (resolve_tac (filter_out is_defn thms)));
wenzelm@404: 
wenzelm@404: 
wenzelm@423: (* provers *)
wenzelm@404: 
wenzelm@423: fun prove term_of str_of thy sig_prop thms usr_tac =
wenzelm@404:   let
wenzelm@404:     val sign = sign_of thy;
wenzelm@423:     val goal = cterm_of sign (term_of sig_prop);
wenzelm@423:     val tac = axclass_tac thy thms THEN (if_none usr_tac all_tac);
wenzelm@423:   in
wenzelm@423:     prove_goalw_cterm [] goal (K [tac])
wenzelm@423:   end
wenzelm@423:   handle ERROR => error ("The error(s) above occurred while trying to prove "
wenzelm@423:     ^ quote (str_of sig_prop));
wenzelm@404: 
wenzelm@423: val prove_classrel =
wenzelm@423:   prove mk_classrel (fn (c1, c2) => c1 ^ " < " ^ c2);
wenzelm@404: 
wenzelm@423: val prove_arity =
wenzelm@423:   prove mk_arity (fn (t, ss, c) => Type.str_of_arity (t, ss, [c]));
wenzelm@404: 
wenzelm@404: 
wenzelm@423: (* make goals (for interactive use) *)
wenzelm@423: 
wenzelm@423: fun mk_goal term_of thy sig_prop =
wenzelm@423:   goalw_cterm [] (cterm_of (sign_of thy) (term_of sig_prop));
wenzelm@423: 
wenzelm@423: val goal_subclass = mk_goal mk_classrel;
wenzelm@423: val goal_arity = mk_goal mk_arity;
wenzelm@423: 
wenzelm@423: 
wenzelm@423: 
wenzelm@423: (** add proved class relations and instances **)
wenzelm@404: 
wenzelm@423: fun add_subclass (c1, c2) axms thms usr_tac thy =
wenzelm@423:   add_classrel_thms
wenzelm@423:   [prove_classrel thy (c1, c2) (get_axioms thy axms @ thms) usr_tac] thy;
wenzelm@423: 
wenzelm@423: fun add_instance (t, ss, cs) axms thms usr_tac thy =
wenzelm@423:   let
wenzelm@423:     val usr_thms = get_axioms thy axms @ thms;
wenzelm@423:     fun prove c =
wenzelm@423:       prove_arity thy (t, ss, c) usr_thms usr_tac;
wenzelm@423:   in
wenzelm@423:     add_arity_thms (map prove cs) thy
wenzelm@423:   end;
wenzelm@404: 
wenzelm@404: 
wenzelm@404: end;
wenzelm@404: