wenzelm@404: (*  Title:      Pure/axclass.ML
wenzelm@404:     ID:         $Id$
wenzelm@404:     Author:     Markus Wenzel, TU Muenchen
wenzelm@404: 
wenzelm@19405: Axiomatic type classes.
wenzelm@404: *)
wenzelm@404: 
wenzelm@404: signature AX_CLASS =
wenzelm@3938: sig
wenzelm@6379:   val print_axclasses: theory -> unit
wenzelm@19418:   val get_info: theory -> class -> {super: sort, def: thm, intro: thm, axioms: thm list}
wenzelm@19392:   val get_instances: theory ->
wenzelm@19405:    {classes: unit Graph.T,
wenzelm@19405:     classrel: ((class * class) * thm) list,
wenzelm@19405:     arities: ((string * sort list * class) * thm) list}
wenzelm@19243:   val class_intros: theory -> thm list
wenzelm@19405:   val params_of_sort: theory -> sort -> string list
wenzelm@19405:   val cert_classrel: theory -> class * class -> class * class
wenzelm@19405:   val read_classrel: theory -> xstring * xstring -> class * class
wenzelm@19405:   val add_classrel: thm -> theory -> theory
wenzelm@19405:   val add_arity: thm -> theory -> theory
wenzelm@19405:   val prove_classrel: class * class -> tactic -> theory -> theory
wenzelm@19243:   val prove_arity: string * sort list * sort -> tactic -> theory -> theory
wenzelm@19418:   val add_axclass: bstring * xstring list -> string list ->
wenzelm@19418:     ((bstring * Attrib.src list) * string list) list -> theory -> class * theory
wenzelm@19418:   val add_axclass_i: bstring * class list -> string list ->
wenzelm@19418:     ((bstring * attribute list) * term list) list -> theory -> class * theory
wenzelm@3938: end;
wenzelm@404: 
wenzelm@15801: structure AxClass: AX_CLASS =
wenzelm@404: struct
wenzelm@404: 
wenzelm@19405: (** theory data **)
wenzelm@423: 
wenzelm@19405: (* class parameters (canonical order) *)
wenzelm@423: 
wenzelm@19405: type param = string * class;
wenzelm@423: 
wenzelm@19405: fun add_param pp ((x, c): param) params =
wenzelm@19405:   (case AList.lookup (op =) params x of
wenzelm@19405:     NONE => (x, c) :: params
wenzelm@19405:   | SOME c' => error ("Duplicate class parameter " ^ quote x ^
wenzelm@19405:       " for " ^ Pretty.string_of_sort pp [c] ^
wenzelm@19405:       (if c = c' then "" else " and " ^ Pretty.string_of_sort pp [c'])));
wenzelm@423: 
wenzelm@19405: fun merge_params _ ([], qs) = qs
wenzelm@19405:   | merge_params pp (ps, qs) =
wenzelm@19405:       fold_rev (fn q => if member (op =) ps q then I else add_param pp q) qs ps;
wenzelm@423: 
wenzelm@423: 
wenzelm@19392: (* axclass *)
wenzelm@6379: 
wenzelm@19243: val introN = "intro";
wenzelm@19243: val axiomsN = "axioms";
wenzelm@19243: 
wenzelm@19392: datatype axclass = AxClass of
wenzelm@19418:  {super: sort,
wenzelm@19418:   def: thm,
wenzelm@19392:   intro: thm,
wenzelm@19392:   axioms: thm list};
wenzelm@19392: 
wenzelm@19418: fun make_axclass (super, def, intro, axioms) =
wenzelm@19418:   AxClass {super = super, def = def, intro = intro, axioms = axioms};
wenzelm@19392: 
wenzelm@19405: type axclasses = axclass Symtab.table * param list;
wenzelm@19405: 
wenzelm@19405: fun merge_axclasses pp ((tab1, params1), (tab2, params2)) : axclasses =
wenzelm@19405:   (Symtab.merge (K true) (tab1, tab2), merge_params pp (params1, params2));
wenzelm@19405: 
wenzelm@19392: 
wenzelm@19392: (* instances *)
wenzelm@19392: 
wenzelm@19392: datatype instances = Instances of
wenzelm@19405:  {classes: unit Graph.T,                 (*raw relation -- no closure!*)
wenzelm@19405:   classrel: ((class * class) * thm) list,
wenzelm@19405:   arities: ((string * sort list * class) * thm) list};
wenzelm@19392: 
wenzelm@19405: fun make_instances (classes, classrel, arities) =
wenzelm@19405:   Instances {classes = classes, classrel = classrel, arities = arities};
wenzelm@6379: 
wenzelm@19405: fun map_instances f (Instances {classes, classrel, arities}) =
wenzelm@19405:   make_instances (f (classes, classrel, arities));
wenzelm@19392: 
wenzelm@19392: fun merge_instances
wenzelm@19405:    (Instances {classes = classes1, classrel = classrel1, arities = arities1},
wenzelm@19405:     Instances {classes = classes2, classrel = classrel2, arities = arities2}) =
wenzelm@19392:   make_instances
wenzelm@19405:    (Graph.merge (K true) (classes1, classes2),
wenzelm@19405:     merge (eq_fst op =) (classrel1, classrel2),
wenzelm@19392:     merge (eq_fst op =) (arities1, arities2));
wenzelm@19392: 
wenzelm@19392: 
wenzelm@19405: (* data *)
wenzelm@19392: 
wenzelm@19392: structure AxClassData = TheoryDataFun
wenzelm@16458: (struct
wenzelm@19392:   val name = "Pure/axclass";
wenzelm@19405:   type T = axclasses * instances;
wenzelm@19405:   val empty : T = ((Symtab.empty, []), make_instances (Graph.empty, [], []));
wenzelm@6546:   val copy = I;
wenzelm@16458:   val extend = I;
wenzelm@6379: 
wenzelm@19405:   fun merge pp ((axclasses1, instances1), (axclasses2, instances2)) =
wenzelm@19405:     (merge_axclasses pp (axclasses1, axclasses2), merge_instances (instances1, instances2));
wenzelm@19392: 
wenzelm@19405:   fun print thy ((axclasses, params), _) =
wenzelm@6379:     let
wenzelm@19405:       val ctxt = ProofContext.init thy;
wenzelm@19405:       val prt_cls = ProofContext.pretty_sort ctxt o single;
wenzelm@19405: 
wenzelm@19405:       fun pretty_class c [] = prt_cls c
wenzelm@19405:         | pretty_class c cs = Pretty.block
wenzelm@19405:             (prt_cls c :: Pretty.str " <" :: Pretty.brk 1 :: Pretty.commas (map prt_cls cs));
wenzelm@6379: 
wenzelm@19418:       fun pretty_axclass (class, AxClass {super, def, intro, axioms}) =
wenzelm@19392:         Pretty.block (Pretty.fbreaks
wenzelm@19418:          [pretty_class class super,
wenzelm@19405:           Pretty.strs ("parameters:" ::
wenzelm@19405:             fold (fn (x, c) => if c = class then cons x else I) params []),
wenzelm@19418:           ProofContext.pretty_fact ctxt ("def", [def]),
wenzelm@19405:           ProofContext.pretty_fact ctxt (introN, [intro]),
wenzelm@19405:           ProofContext.pretty_fact ctxt (axiomsN, axioms)]);
wenzelm@19405:     in
wenzelm@19405:       Pretty.writeln (Pretty.chunks (map pretty_axclass (Symtab.dest axclasses)))
wenzelm@19405:     end;
wenzelm@16458: end);
wenzelm@6379: 
wenzelm@19392: val _ = Context.add_setup AxClassData.init;
wenzelm@19392: val print_axclasses = AxClassData.print;
wenzelm@19392: 
wenzelm@19392: val get_instances = AxClassData.get #> (fn (_, Instances insts) => insts);
wenzelm@6379: 
wenzelm@6379: 
wenzelm@19392: (* lookup *)
wenzelm@19392: 
wenzelm@19405: val lookup_info = Symtab.lookup o #1 o #1 o AxClassData.get;
wenzelm@6379: 
wenzelm@17281: fun get_info thy c =
wenzelm@17281:   (case lookup_info thy c of
wenzelm@19392:     SOME (AxClass info) => info
wenzelm@19392:   | NONE => error ("Unknown axclass " ^ quote c));
wenzelm@6379: 
wenzelm@19123: fun class_intros thy =
wenzelm@19392:   let
wenzelm@19392:     fun add_intro c =
wenzelm@19392:       (case lookup_info thy c of SOME (AxClass {intro, ...}) => cons intro | _ => I);
wenzelm@19392:     val classes = Sign.classes thy;
wenzelm@19392:   in map (Thm.class_triv thy) classes @ fold add_intro classes [] end;
wenzelm@15876: 
wenzelm@15876: 
wenzelm@404: 
wenzelm@19418: (** instances **)
wenzelm@15876: 
wenzelm@19405: (* parameters *)
wenzelm@15876: 
wenzelm@19405: fun params_of_sort thy S =
wenzelm@19405:   let
wenzelm@19405:     val range = Graph.all_succs (Sign.classes_of thy) (Sign.certify_sort thy S);
wenzelm@19405:     val params = #2 (#1 (AxClassData.get thy));
wenzelm@19405:   in fold (fn (x, c) => if member (op =) range c then cons x else I) params [] end;
wenzelm@19405: 
wenzelm@19418: 
wenzelm@19418: (* class relations *)
wenzelm@19418: 
wenzelm@19405: fun cert_classrel thy raw_rel =
wenzelm@15876:   let
wenzelm@19405:     val (c1, c2) = pairself (Sign.certify_class thy) raw_rel;
wenzelm@19405:     val _ = Type.add_classrel (Sign.pp thy) [(c1, c2)] (Sign.tsig_of thy);
wenzelm@19405:     val _ =
wenzelm@19405:       (case subtract (op =) (params_of_sort thy [c1]) (params_of_sort thy [c2]) of
wenzelm@19405:         [] => ()
wenzelm@19405:       | xs => raise TYPE ("Class " ^ Sign.string_of_sort thy [c1] ^ " lacks parameter(s) " ^
wenzelm@19405:           commas_quote xs ^ " of " ^ Sign.string_of_sort thy [c2], [], []));
wenzelm@19405:   in (c1, c2) end;
wenzelm@19405: 
wenzelm@19405: fun read_classrel thy raw_rel =
wenzelm@19405:   cert_classrel thy (pairself (Sign.read_class thy) raw_rel)
wenzelm@19405:     handle TYPE (msg, _, _) => error msg;
wenzelm@19405: 
wenzelm@19405: 
wenzelm@19405: (* primitive rules *)
wenzelm@19405: 
wenzelm@19405: fun add_classrel th thy =
wenzelm@19405:   let
wenzelm@19405:     fun err () = raise THM ("add_classrel: malformed class relation", 0, [th]);
wenzelm@19405:     val prop = Drule.plain_prop_of (Thm.transfer thy th);
wenzelm@19405:     val rel = Logic.dest_classrel prop handle TERM _ => err ();
wenzelm@19405:     val (c1, c2) = cert_classrel thy rel handle TYPE _ => err ();
wenzelm@19392:   in
wenzelm@19392:     thy
wenzelm@19405:     |> Theory.add_classrel_i [(c1, c2)]
wenzelm@19405:     |> AxClassData.map (apsnd (map_instances (fn (classes, classrel, arities) =>
wenzelm@19418:         (classes
wenzelm@19418:             |> Graph.default_node (c1, ())
wenzelm@19418:             |> Graph.default_node (c2, ())
wenzelm@19418:             |> Graph.add_edge (c1, c2),
wenzelm@19418:           ((c1, c2), th) :: classrel, arities))))
wenzelm@19392:   end;
wenzelm@15876: 
wenzelm@19405: fun add_arity th thy =
wenzelm@15876:   let
wenzelm@19405:     val prop = Drule.plain_prop_of (Thm.transfer thy th);
wenzelm@19405:     val (t, Ss, c) = Logic.dest_arity prop handle TERM _ =>
wenzelm@19405:       raise THM ("add_arity: malformed type arity", 0, [th]);
wenzelm@19392:   in
wenzelm@19392:     thy
wenzelm@19405:     |> Theory.add_arities_i [(t, Ss, [c])]
wenzelm@19405:     |> AxClassData.map (apsnd (map_instances (fn (classes, classrel, arities) =>
wenzelm@19405:       (classes, classrel, ((t, Ss, c), th) :: arities))))
wenzelm@19392:   end;
wenzelm@404: 
wenzelm@404: 
wenzelm@19243: (* tactical proofs *)
wenzelm@15876: 
wenzelm@19405: fun prove_classrel raw_rel tac thy =
wenzelm@15876:   let
wenzelm@19405:     val (c1, c2) = cert_classrel thy raw_rel;
wenzelm@19405:     val th = Goal.prove thy [] [] (Logic.mk_classrel (c1, c2)) (fn _ => tac) handle ERROR msg =>
wenzelm@19243:       cat_error msg ("The error(s) above occurred while trying to prove class relation " ^
wenzelm@19243:         quote (Sign.string_of_classrel thy [c1, c2]));
wenzelm@19405:   in add_classrel th thy end;
wenzelm@404: 
wenzelm@19243: fun prove_arity raw_arity tac thy =
wenzelm@15876:   let
wenzelm@19243:     val arity = Sign.cert_arity thy raw_arity;
wenzelm@19405:     val props = Logic.mk_arities arity;
wenzelm@17956:     val ths = Goal.prove_multi thy [] [] props
wenzelm@18678:       (fn _ => Tactic.precise_conjunction_tac (length props) 1 THEN tac) handle ERROR msg =>
wenzelm@19243:         cat_error msg ("The error(s) above occurred while trying to prove type arity " ^
wenzelm@19243:           quote (Sign.string_of_arity thy arity));
wenzelm@19405:   in fold add_arity ths thy end;
wenzelm@19392: 
wenzelm@19418: 
wenzelm@19418: 
wenzelm@19418: (** axclass definitions **)
wenzelm@19418: 
wenzelm@19418: (* add_axclass(_i) *)
wenzelm@19418: 
wenzelm@19418: fun gen_axclass prep_class prep_att prep_propp
wenzelm@19418:     (bclass, raw_super) params raw_specs thy =
wenzelm@19418:   let
wenzelm@19418:     val ctxt = ProofContext.init thy;
wenzelm@19418:     val pp = ProofContext.pp ctxt;
wenzelm@19418: 
wenzelm@19418: 
wenzelm@19418:     (* prepare specification *)
wenzelm@19418: 
wenzelm@19418:     val bconst = Logic.const_of_class bclass;
wenzelm@19418:     val class = Sign.full_name thy bclass;
wenzelm@19418:     val super = map (prep_class thy) raw_super |> Sign.certify_sort thy;
wenzelm@19418: 
wenzelm@19418:     fun prep_axiom t =
wenzelm@19418:       (case Term.add_tfrees t [] of
wenzelm@19418:         [(a, S)] =>
wenzelm@19418:           if Sign.subsort thy (super, S) then t
wenzelm@19418:           else error ("Sort constraint of type variable " ^
wenzelm@19418:             setmp show_sorts true (Pretty.string_of_typ pp) (TFree (a, S)) ^
wenzelm@19418:             " needs to be weaker than " ^ Pretty.string_of_sort pp super)
wenzelm@19418:       | [] => t
wenzelm@19418:       | _ => error ("Multiple type variables in class axiom:\n" ^ Pretty.string_of_term pp t))
wenzelm@19418:       |> map_term_types (Term.map_atyps (fn TFree _ => Term.aT [] | U => U))
wenzelm@19418:       |> Logic.close_form;
wenzelm@19418: 
wenzelm@19418:     val axiomss = prep_propp (ctxt, map (map (rpair ([], [])) o snd) raw_specs)
wenzelm@19418:       |> snd |> map (map (prep_axiom o fst));
wenzelm@19418:     val name_atts = Attrib.map_specs (prep_att thy) raw_specs |> map fst;
wenzelm@19418: 
wenzelm@19418: 
wenzelm@19418:     (* definition *)
wenzelm@19418: 
wenzelm@19418:     val conjs = map (curry Logic.mk_inclass (Term.aT [])) super @ List.concat axiomss;
wenzelm@19418:     val class_eq =
wenzelm@19418:       Logic.mk_equals (Logic.mk_inclass (Term.aT [], class), Logic.mk_conjunction_list conjs);
wenzelm@19418: 
wenzelm@19418:     val ([def], def_thy) =
wenzelm@19418:       thy
wenzelm@19418:       |> Theory.add_classes_i [(bclass, super)]
wenzelm@19418:       |> PureThy.add_defs_i false [((Thm.def_name bconst, class_eq), [])];
wenzelm@19418:     val (raw_intro, (raw_classrel, raw_axioms)) =
wenzelm@19418:       (Conjunction.split_defined (length conjs) def) ||> chop (length super);
wenzelm@19418: 
wenzelm@19418: 
wenzelm@19418:     (* facts *)
wenzelm@19418: 
wenzelm@19418:     val class_triv = Thm.class_triv def_thy class;
wenzelm@19418:     val ([(_, [intro]), (_, axioms)], facts_thy) =
wenzelm@19418:       def_thy
wenzelm@19418:       |> PureThy.note_thmss_qualified "" bconst
wenzelm@19418:         [((introN, []), [([Drule.standard raw_intro], [])]),
wenzelm@19418:          ((axiomsN, []), [(map (fn th => Drule.standard (class_triv RS th)) raw_axioms, [])])]
wenzelm@19418:       ||> fold (fn th => add_classrel (Drule.standard' (class_triv RS th))) raw_classrel;
wenzelm@19418: 
wenzelm@19418: 
wenzelm@19418:     (* result *)
wenzelm@19418: 
wenzelm@19418:     val result_thy =
wenzelm@19418:       facts_thy
wenzelm@19418:       |> Sign.add_path bconst
wenzelm@19418:       |> PureThy.note_thmss_i "" (name_atts ~~ map Thm.simple_fact (unflat axiomss axioms)) |> snd
wenzelm@19418:       |> Sign.restore_naming facts_thy
wenzelm@19418:       |> AxClassData.map (apfst (fn (is, ps) =>
wenzelm@19418:         (Symtab.update (class, make_axclass (super, def, intro, axioms)) is,
wenzelm@19418:           fold (fn x => add_param pp (x, class)) params ps)));
wenzelm@19418: 
wenzelm@19418:   in (class, result_thy) end;
wenzelm@19418: 
wenzelm@19418: val add_axclass = gen_axclass Sign.read_class Attrib.attribute ProofContext.read_propp;
wenzelm@19418: val add_axclass_i = gen_axclass Sign.certify_class (K I) ProofContext.cert_propp;
wenzelm@19418: 
wenzelm@15876: end;