(* Title: Pure/axclass.ML
ID: $Id$
Author: Markus Wenzel, TU Muenchen
User interface for axiomatic type classes.
TODO:
arity_tac: FILTER is_arity (?), assume_tac (?) (no?)
*)
signature AX_CLASS =
sig
structure Tactical: TACTICAL
local open Tactical Tactical.Thm in
val add_axclass: class * class list -> (string * string) list
-> theory -> theory
val add_axclass_i: class * class list -> (string * term) list
-> theory -> theory
val add_instance: string * sort list * class -> string list -> thm list
-> tactic option -> theory -> theory
val axclass_tac: theory -> tactic
end
end;
functor AxClassFun(structure Logic: LOGIC and Goals: GOALS and Tactic: TACTIC
sharing Goals.Tactical = Tactic.Tactical)(*: AX_CLASS *) = (* FIXME *)
struct
structure Tactical = Goals.Tactical;
structure Thm = Tactical.Thm;
structure Sign = Thm.Sign;
structure Type = Sign.Type;
open Logic Thm Tactical Tactic Goals;
(* FIXME -> type.ML *)
structure Type =
struct
open Type;
fun str_of_sort [c] = c
| str_of_sort cs = parents "{" "}" (commas cs);
fun str_of_dom dom = parents "(" ")" (commas (map str_of_sort dom));
fun str_of_arity (t, [], S) = t ^ " :: " ^ str_of_sort S
| str_of_arity (t, SS, S) =
t ^ " :: " ^ str_of_dom SS ^ " " ^ str_of_sort S;
end;
(** add constant definitions **) (* FIXME -> drule.ML (?) *)
(* FIXME fake! *)
val add_defns = add_axioms;
val add_defns_i = add_axioms_i;
(** utilities **)
(* type vars *)
fun map_typ_frees f (Type (t, tys)) = Type (t, map (map_typ_frees f) tys)
| map_typ_frees f (TFree a) = f a
| map_typ_frees _ a = a;
val map_term_tfrees = map_term_types o map_typ_frees;
fun aT S = TFree ("'a", S);
(* get axioms *)
fun get_ax thy name =
Some (get_axiom thy name) handle THEORY _ => None;
val get_axioms = mapfilter o get_ax;
(* is_defn *)
fun is_defn thm =
(case #prop (rep_thm thm) of
Const ("==", _) $ _ $ _ => true
| _ => false);
(** add axiomatic type class **)
(* errors *)
fun err_not_logic c =
error ("Axiomatic class " ^ quote c ^ " not subclass of \"logic\"");
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);
(* ext_axclass *)
fun ext_axclass prep_axm (class, super_classes) raw_axioms old_thy =
let
val axioms = map (prep_axm (sign_of old_thy)) raw_axioms;
val thy = add_classes [([], class, super_classes)] old_thy;
val sign = sign_of thy;
(* prepare abstract axioms *)
fun abs_axm ax =
if null (term_tfrees ax) then
mk_implies (mk_inclass (aT logicS, class), ax)
else
map_term_tfrees (K (aT [class])) ax;
val abs_axioms = map (apsnd abs_axm) axioms;
(* prepare introduction orule *)
val _ =
if Sign.subsort sign ([class], logicS) then ()
else err_not_logic class;
fun axm_sort (name, ax) =
(case term_tfrees ax of
[] => []
| [(_, S)] =>
if Sign.subsort sign ([class], S) then S
else err_bad_axsort name class
| _ => err_bad_tfrees name);
val axS = Sign.norm_sort sign (logicC :: flat (map axm_sort axioms));
val int_axm = close_form o map_term_tfrees (K (aT axS));
fun inclass c = mk_inclass (aT axS, c);
val intro_axm = list_implies
(map inclass super_classes @ map (int_axm o snd) axioms, inclass class);
in
add_axioms_i ((class ^ "I", intro_axm) :: abs_axioms) thy
end;
(* external interfaces *)
val add_axclass = ext_axclass read_axm;
val add_axclass_i = ext_axclass cert_axm;
(** add class instance **)
(* arities as terms *)
fun mk_arity (t, ss, c) =
let
val names = variantlist (replicate (length ss) "'a", []);
val tvars = map (fn a => TVar ((a, 0), logicS)) names;
in
mk_inclass (Type (t, tvars), c)
end;
fun dest_arity tm =
let
fun err () = raise_term "dest_arity" [tm];
val (ty, c) = dest_inclass tm handle TERM _ => err ();
val (t, tvars) =
(case ty of
Type (t, tys) => (t, map (fn TVar x => x | _ => err ()) tys)
| _ => err ());
val ss =
if null (gen_duplicates eq_fst tvars)
then map snd tvars else err ();
in
(t, ss, c)
end;
(* axclass_tac *)
(*repeatedly resolve subgoals of form "(| ty : c_class |)";
try "cI" axioms first and use class_triv as last resort*)
fun class_axms thy =
let
val classes = Sign.classes (sign_of thy);
val intros = map (fn c => c ^ "I") classes;
in
get_axioms thy intros @
map (class_triv thy) classes
end;
fun axclass_tac thy =
REPEAT_FIRST (resolve_tac (class_axms thy));
(* prove_arity *)
(*(* FIXME *)
(* FIXME state sign vs sign (!?) *)
fun weaker_arity state =
all_subsort (ss, #2 (dest_arity (concl_of state)))
handle TERM _ => false;
*)
fun prove_arity thy (arity as (t, ss, c)) thms usr_tac =
let
val sign = sign_of thy;
val all_subsort = forall2 (Sign.subsort sign);
val arity_goal = cterm_of sign (mk_arity arity);
val arity_tac =
axclass_tac thy THEN
TRY (rewrite_goals_tac (filter is_defn thms)) THEN
TRY (REPEAT_FIRST (resolve_tac (filter_out is_defn thms))) THEN
(if_none usr_tac all_tac);
val arity_thm = prove_goalw_cterm [] arity_goal (K [arity_tac]);
val (t', ss', c') = dest_arity (#prop (rep_thm arity_thm))
handle TERM _ => error "Result is not an arity";
in
if t = t' andalso all_subsort (ss, ss') andalso c = c' then ()
else error ("Proved different arity: " ^ Type.str_of_arity (t', ss', [c']))
end
handle ERROR => error ("The error(s) above occurred while trying to prove: " ^
Type.str_of_arity (t, ss, [c]));
(* external interface *)
fun add_instance (t, ss, c) axms thms usr_tac thy =
(prove_arity thy (t, ss, c) (get_axioms thy axms @ thms) usr_tac;
add_arities [(t, ss, [c])] thy);
end;