(* Title: HOL/Eisbach/eisbach_rule_insts.ML
Author: Daniel Matichuk, NICTA/UNSW
Eisbach-aware variants of the "where" and "of" attributes.
Alternate syntax for rule_insts.ML participates in token closures by
examining the behaviour of Rule_Insts.where_rule and instantiating token
values accordingly. Instantiations in re-interpretation are done with
Drule.cterm_instantiate.
*)
structure Eisbach_Rule_Insts : sig end =
struct
fun restore_tags thm = Thm.map_tags (K (Thm.get_tags thm));
fun add_thm_insts thm =
let
val thy = Thm.theory_of_thm thm;
val tyvars = Thm.fold_terms Term.add_tvars thm [];
val tyvars' = tyvars |> map (Logic.mk_term o Logic.mk_type o TVar);
val tvars = Thm.fold_terms Term.add_vars thm [];
val tvars' = tvars |> map (Logic.mk_term o Var);
val conj =
Logic.mk_conjunction_list (tyvars' @ tvars') |> Thm.global_cterm_of thy |> Drule.mk_term;
in
((tyvars, tvars), Conjunction.intr thm conj)
end;
fun get_thm_insts thm =
let
val (thm', insts) = Conjunction.elim thm;
val insts' = insts
|> Drule.dest_term
|> Thm.term_of
|> Logic.dest_conjunction_list
|> map Logic.dest_term
|> (fn f => fold (fn t => fn (tys, ts) =>
(case try Logic.dest_type t of
SOME T => (T :: tys, ts)
| NONE => (tys, t :: ts))) f ([], []))
||> rev
|>> rev;
in
(thm', insts')
end;
fun instantiate_xis insts thm =
let
val tyvars = Thm.fold_terms Term.add_tvars thm [];
val tvars = Thm.fold_terms Term.add_vars thm [];
val cert = Thm.global_cterm_of (Thm.theory_of_thm thm);
val certT = Thm.global_ctyp_of (Thm.theory_of_thm thm);
fun add_inst (xi, t) (Ts, ts) =
(case AList.lookup (op =) tyvars xi of
SOME S => ((certT (TVar (xi, S)), certT (Logic.dest_type t)) :: Ts, ts)
| NONE =>
(case AList.lookup (op =) tvars xi of
SOME T => (Ts, (cert (Var (xi, T)), cert t) :: ts)
| NONE => error "indexname not found in thm"));
val (cTinsts, cinsts) = fold add_inst insts ([], []);
in
(Thm.instantiate (cTinsts, []) thm
|> Drule.cterm_instantiate cinsts
COMP_INCR asm_rl)
|> Thm.adjust_maxidx_thm ~1
|> restore_tags thm
end;
datatype rule_inst =
Named_Insts of ((indexname * string) * (term -> unit)) list
| Term_Insts of (indexname * term) list;
fun embed_indexname ((xi, s), f) =
let
fun wrap_xi xi t =
Logic.mk_conjunction (Logic.mk_term (Var (xi, fastype_of t)), Logic.mk_term t);
in ((xi, s), f o wrap_xi xi) end;
fun unembed_indexname t =
let
val (t, t') = apply2 Logic.dest_term (Logic.dest_conjunction t);
val (xi, _) = Term.dest_Var t;
in (xi, t') end;
fun read_where_insts toks =
let
val parser =
Parse.!!!
(Parse.and_list1 (Args.var -- (Args.$$$ "=" |-- Parse_Tools.name_term)) -- Parse.for_fixes)
--| Scan.ahead Parse.eof;
val (insts, fixes) = the (Scan.read Token.stopper parser toks);
val insts' =
if forall (fn (_, v) => Parse_Tools.is_real_val v) insts
then Term_Insts (map (fn (_, t) => unembed_indexname (Parse_Tools.the_real_val t)) insts)
else Named_Insts (map (fn (xi, p) => embed_indexname
((xi, Parse_Tools.the_parse_val p), Parse_Tools.the_parse_fun p)) insts);
in
(insts', fixes)
end;
fun of_rule thm (args, concl_args) =
let
fun zip_vars _ [] = []
| zip_vars (_ :: xs) (NONE :: rest) = zip_vars xs rest
| zip_vars ((x, _) :: xs) (SOME t :: rest) = (x, t) :: zip_vars xs rest
| zip_vars [] _ = error "More instantiations than variables in theorem";
val insts =
zip_vars (rev (Term.add_vars (Thm.full_prop_of thm) [])) args @
zip_vars (rev (Term.add_vars (Thm.concl_of thm) [])) concl_args;
in insts end;
val inst = Args.maybe Parse_Tools.name_term;
val concl = Args.$$$ "concl" -- Args.colon;
fun read_of_insts toks thm =
let
val parser =
Parse.!!!
((Scan.repeat (Scan.unless concl inst) -- Scan.optional (concl |-- Scan.repeat inst) [])
-- Parse.for_fixes) --| Scan.ahead Parse.eof;
val ((insts, concl_insts), fixes) =
the (Scan.read Token.stopper parser toks);
val insts' =
if forall (fn SOME t => Parse_Tools.is_real_val t | NONE => true) (insts @ concl_insts)
then
Term_Insts
(map_filter
(Option.map (Parse_Tools.the_real_val #> unembed_indexname)) (insts @ concl_insts))
else
Named_Insts
(apply2
(map (Option.map (fn p => (Parse_Tools.the_parse_val p, Parse_Tools.the_parse_fun p))))
(insts, concl_insts)
|> of_rule thm |> map ((fn (xi, (nm, tok)) => embed_indexname ((xi, nm), tok))));
in
(insts', fixes)
end;
fun read_instantiate_closed ctxt ((Named_Insts insts), fixes) thm =
let
val insts' = map (fn ((v, t), _) => ((v, Position.none), t)) insts;
val (thm_insts, thm') = add_thm_insts thm
val (thm'', thm_insts') =
Rule_Insts.where_rule ctxt insts' fixes thm'
|> get_thm_insts;
val tyinst =
ListPair.zip (fst thm_insts, fst thm_insts') |> map (fn ((xi, _), typ) => (xi, typ));
val tinst =
ListPair.zip (snd thm_insts, snd thm_insts') |> map (fn ((xi, _), t) => (xi, t));
val _ =
map (fn ((xi, _), f) =>
(case AList.lookup (op =) tyinst xi of
SOME typ => f (Logic.mk_type typ)
| NONE =>
(case AList.lookup (op =) tinst xi of
SOME t => f t
| NONE => error "Lost indexname in instantiated theorem"))) insts;
in
(thm'' |> restore_tags thm)
end
| read_instantiate_closed _ ((Term_Insts insts), _) thm = instantiate_xis insts thm;
val parse_all : Token.T list context_parser = Scan.lift (Scan.many Token.not_eof);
val _ =
Theory.setup
(Attrib.setup @{binding "where"} (parse_all >>
(fn toks => Thm.rule_attribute (fn context =>
read_instantiate_closed (Context.proof_of context) (read_where_insts toks))))
"named instantiation of theorem");
val _ =
Theory.setup
(Attrib.setup @{binding "of"} (parse_all >>
(fn toks => Thm.rule_attribute (fn context => fn thm =>
read_instantiate_closed (Context.proof_of context) (read_of_insts toks thm) thm)))
"positional instantiation of theorem");
end;