moved abstract syntax operations to logic.ML;
maintain class parameters;
added params_of_sort;
added cert/read_classrel (from sign.ML), check class parameters;
tuned;
(* Title: Pure/axclass.ML
ID: $Id$
Author: Markus Wenzel, TU Muenchen
Axiomatic type classes.
*)
signature AX_CLASS =
sig
val print_axclasses: theory -> unit
val get_info: theory -> class -> {super_classes: class list, intro: thm, axioms: thm list}
val get_instances: theory ->
{classes: unit Graph.T,
classrel: ((class * class) * thm) list,
arities: ((string * sort list * class) * thm) list}
val class_intros: theory -> thm list
val add_axclass: bstring * xstring list -> string list ->
((bstring * string) * Attrib.src list) list -> theory -> class * theory
val add_axclass_i: bstring * class list -> string list ->
((bstring * term) * attribute list) list -> theory -> class * theory
val params_of_sort: theory -> sort -> string list
val cert_classrel: theory -> class * class -> class * class
val read_classrel: theory -> xstring * xstring -> class * class
val add_classrel: thm -> theory -> theory
val add_arity: thm -> theory -> theory
val prove_classrel: class * class -> tactic -> theory -> theory
val prove_arity: string * sort list * sort -> tactic -> theory -> theory
end;
structure AxClass: AX_CLASS =
struct
(** theory data **)
(* class parameters (canonical order) *)
type param = string * class;
fun add_param pp ((x, c): param) params =
(case AList.lookup (op =) params x of
NONE => (x, c) :: params
| SOME c' => error ("Duplicate class parameter " ^ quote x ^
" for " ^ Pretty.string_of_sort pp [c] ^
(if c = c' then "" else " and " ^ Pretty.string_of_sort pp [c'])));
fun merge_params _ ([], qs) = qs
| merge_params pp (ps, qs) =
fold_rev (fn q => if member (op =) ps q then I else add_param pp q) qs ps;
(* axclass *)
val introN = "intro";
val axiomsN = "axioms";
datatype axclass = AxClass of
{super_classes: class list,
intro: thm,
axioms: thm list};
fun make_axclass (super_classes, intro, axioms) =
AxClass {super_classes = super_classes, intro = intro, axioms = axioms};
type axclasses = axclass Symtab.table * param list;
fun merge_axclasses pp ((tab1, params1), (tab2, params2)) : axclasses =
(Symtab.merge (K true) (tab1, tab2), merge_params pp (params1, params2));
(* instances *)
datatype instances = Instances of
{classes: unit Graph.T, (*raw relation -- no closure!*)
classrel: ((class * class) * thm) list,
arities: ((string * sort list * class) * thm) list};
fun make_instances (classes, classrel, arities) =
Instances {classes = classes, classrel = classrel, arities = arities};
fun map_instances f (Instances {classes, classrel, arities}) =
make_instances (f (classes, classrel, arities));
fun merge_instances
(Instances {classes = classes1, classrel = classrel1, arities = arities1},
Instances {classes = classes2, classrel = classrel2, arities = arities2}) =
make_instances
(Graph.merge (K true) (classes1, classes2),
merge (eq_fst op =) (classrel1, classrel2),
merge (eq_fst op =) (arities1, arities2));
(* data *)
structure AxClassData = TheoryDataFun
(struct
val name = "Pure/axclass";
type T = axclasses * instances;
val empty : T = ((Symtab.empty, []), make_instances (Graph.empty, [], []));
val copy = I;
val extend = I;
fun merge pp ((axclasses1, instances1), (axclasses2, instances2)) =
(merge_axclasses pp (axclasses1, axclasses2), merge_instances (instances1, instances2));
fun print thy ((axclasses, params), _) =
let
val ctxt = ProofContext.init thy;
val prt_cls = ProofContext.pretty_sort ctxt o single;
fun pretty_class c [] = prt_cls c
| pretty_class c cs = Pretty.block
(prt_cls c :: Pretty.str " <" :: Pretty.brk 1 :: Pretty.commas (map prt_cls cs));
fun pretty_axclass (class, AxClass {super_classes, intro, axioms}) =
Pretty.block (Pretty.fbreaks
[pretty_class class super_classes,
Pretty.strs ("parameters:" ::
fold (fn (x, c) => if c = class then cons x else I) params []),
ProofContext.pretty_fact ctxt (introN, [intro]),
ProofContext.pretty_fact ctxt (axiomsN, axioms)]);
in
Pretty.writeln (Pretty.chunks (map pretty_axclass (Symtab.dest axclasses)))
end;
end);
val _ = Context.add_setup AxClassData.init;
val print_axclasses = AxClassData.print;
val get_instances = AxClassData.get #> (fn (_, Instances insts) => insts);
(** axclass definitions **)
(* lookup *)
val lookup_info = Symtab.lookup o #1 o #1 o AxClassData.get;
fun get_info thy c =
(case lookup_info thy c of
SOME (AxClass info) => info
| NONE => error ("Unknown axclass " ^ quote c));
fun class_intros thy =
let
fun add_intro c =
(case lookup_info thy c of SOME (AxClass {intro, ...}) => cons intro | _ => I);
val classes = Sign.classes thy;
in map (Thm.class_triv thy) classes @ fold add_intro classes [] end;
(* add_axclass(_i) *)
local
fun err_bad_axsort ax c =
error ("Sort constraint in axiom " ^ quote ax ^ " not supersort of " ^ quote c);
fun err_bad_tfrees ax =
error ("More than one type variable in axiom " ^ quote ax);
fun replace_tfree T = map_term_types (Term.map_atyps (fn TFree _ => T | U => U));
fun gen_axclass prep_class prep_axm prep_att
(bclass, raw_super_classes) params raw_axioms_atts thy =
let
val pp = Sign.pp thy;
val class = Sign.full_name thy bclass;
val super_classes = map (prep_class thy) raw_super_classes;
val axms = map (prep_axm thy o fst) raw_axioms_atts;
val atts = map (map (prep_att thy) o snd) raw_axioms_atts;
(*declare class*)
val class_thy =
thy |> Theory.add_classes_i [(bclass, super_classes)];
(*prepare abstract axioms*)
fun abs_axm ax =
if null (term_tfrees ax) then
Logic.mk_implies (Logic.mk_inclass (Term.aT [], class), ax)
else replace_tfree (Term.aT [class]) ax;
val abs_axms = map (abs_axm o snd) axms;
fun axm_sort (name, ax) =
(case term_tfrees ax of
[] => []
| [(_, S)] => if Sign.subsort class_thy ([class], S) then S else err_bad_axsort name class
| _ => err_bad_tfrees name);
val axS = Sign.certify_sort class_thy (List.concat (map axm_sort axms));
val int_axm = Logic.close_form o replace_tfree (Term.aT axS);
fun inclass c = Logic.mk_inclass (Term.aT axS, c);
val intro_axm = Logic.list_implies
(map inclass super_classes @ map (int_axm o #2) axms, inclass class);
(*declare axioms and rule*)
val (([intro], [axioms]), axms_thy) =
class_thy
|> Theory.add_path (Logic.const_of_class bclass)
|> PureThy.add_axioms_i [Thm.no_attributes (introN, intro_axm)]
||>> PureThy.add_axiomss_i [Thm.no_attributes (axiomsN, abs_axms)];
val info = make_axclass (super_classes, intro, axioms);
(*store info*)
val (_, final_thy) =
axms_thy
|> Theory.add_finals_i false [Const (Logic.const_of_class class, Term.a_itselfT --> propT)]
|> PureThy.add_thms ((map #1 axms ~~ axioms) ~~ atts)
||> Theory.restore_naming class_thy
||> AxClassData.map (apfst (fn (is, ps) =>
(Symtab.update (class, info) is, fold (fn x => add_param pp (x, class)) params ps)));
in (class, final_thy) end;
in
val add_axclass = gen_axclass Sign.intern_class Theory.read_axm Attrib.attribute;
val add_axclass_i = gen_axclass (K I) Theory.cert_axm (K I);
end;
(** instantiation proofs **)
(* parameters *)
fun params_of_sort thy S =
let
val range = Graph.all_succs (Sign.classes_of thy) (Sign.certify_sort thy S);
val params = #2 (#1 (AxClassData.get thy));
in fold (fn (x, c) => if member (op =) range c then cons x else I) params [] end;
fun cert_classrel thy raw_rel =
let
val (c1, c2) = pairself (Sign.certify_class thy) raw_rel;
val _ = Type.add_classrel (Sign.pp thy) [(c1, c2)] (Sign.tsig_of thy);
val _ =
(case subtract (op =) (params_of_sort thy [c1]) (params_of_sort thy [c2]) of
[] => ()
| xs => raise TYPE ("Class " ^ Sign.string_of_sort thy [c1] ^ " lacks parameter(s) " ^
commas_quote xs ^ " of " ^ Sign.string_of_sort thy [c2], [], []));
in (c1, c2) end;
fun read_classrel thy raw_rel =
cert_classrel thy (pairself (Sign.read_class thy) raw_rel)
handle TYPE (msg, _, _) => error msg;
(* primitive rules *)
fun add_classrel th thy =
let
fun err () = raise THM ("add_classrel: malformed class relation", 0, [th]);
val prop = Drule.plain_prop_of (Thm.transfer thy th);
val rel = Logic.dest_classrel prop handle TERM _ => err ();
val (c1, c2) = cert_classrel thy rel handle TYPE _ => err ();
in
thy
|> Theory.add_classrel_i [(c1, c2)]
|> AxClassData.map (apsnd (map_instances (fn (classes, classrel, arities) =>
(classes
|> Graph.default_node (c1, ())
|> Graph.default_node (c2, ())
|> Graph.add_edge (c1, c2),
((c1, c2), th) :: classrel, arities))))
end;
fun add_arity th thy =
let
val prop = Drule.plain_prop_of (Thm.transfer thy th);
val (t, Ss, c) = Logic.dest_arity prop handle TERM _ =>
raise THM ("add_arity: malformed type arity", 0, [th]);
in
thy
|> Theory.add_arities_i [(t, Ss, [c])]
|> AxClassData.map (apsnd (map_instances (fn (classes, classrel, arities) =>
(classes, classrel, ((t, Ss, c), th) :: arities))))
end;
(* tactical proofs *)
fun prove_classrel raw_rel tac thy =
let
val (c1, c2) = cert_classrel thy raw_rel;
val th = Goal.prove thy [] [] (Logic.mk_classrel (c1, c2)) (fn _ => tac) handle ERROR msg =>
cat_error msg ("The error(s) above occurred while trying to prove class relation " ^
quote (Sign.string_of_classrel thy [c1, c2]));
in add_classrel th thy end;
fun prove_arity raw_arity tac thy =
let
val arity = Sign.cert_arity thy raw_arity;
val props = Logic.mk_arities arity;
val ths = Goal.prove_multi thy [] [] props
(fn _ => Tactic.precise_conjunction_tac (length props) 1 THEN tac) handle ERROR msg =>
cat_error msg ("The error(s) above occurred while trying to prove type arity " ^
quote (Sign.string_of_arity thy arity));
in fold add_arity ths thy end;
end;