File ‹transfer_principle.ML›
signature TRANSFER_PRINCIPLE =
sig
val transfer_tac: Proof.context -> thm list -> int -> tactic
val add_const: string -> theory -> theory
end;
structure Transfer_Principle: TRANSFER_PRINCIPLE =
struct
structure Data = Generic_Data
(
type T = {
intros: thm list,
unfolds: thm list,
refolds: thm list,
consts: string list
};
val empty = {intros = [], unfolds = [], refolds = [], consts = []};
fun merge
({intros = intros1, unfolds = unfolds1,
refolds = refolds1, consts = consts1},
{intros = intros2, unfolds = unfolds2,
refolds = refolds2, consts = consts2}) : T =
{intros = Thm.merge_thms (intros1, intros2),
unfolds = Thm.merge_thms (unfolds1, unfolds2),
refolds = Thm.merge_thms (refolds1, refolds2),
consts = Library.merge (op =) (consts1, consts2)};
);
fun unstar_typ (Type (\<^type_name>‹star›, [t])) = unstar_typ t
| unstar_typ (Type (a, Ts)) = Type (a, map unstar_typ Ts)
| unstar_typ T = T
fun unstar_term consts term =
let
fun unstar (Const(a,T) $ t) = if member (op =) consts a then (unstar t)
else (Const(a,unstar_typ T) $ unstar t)
| unstar (f $ t) = unstar f $ unstar t
| unstar (Const(a,T)) = Const(a,unstar_typ T)
| unstar (Abs(a,T,t)) = Abs(a,unstar_typ T,unstar t)
| unstar t = t
in
unstar term
end
local exception MATCH
in
fun transfer_star_tac ctxt =
let
fun thm_of (Const (\<^const_name>‹Ifun›, _) $ t $ u) = @{thm transfer_Ifun} OF [thm_of t, thm_of u]
| thm_of (Const (\<^const_name>‹star_of›, _) $ _) = @{thm star_of_def}
| thm_of (Const (\<^const_name>‹star_n›, _) $ _) = @{thm Pure.reflexive}
| thm_of _ = raise MATCH;
fun thm_of_goal (Const (\<^const_name>‹Pure.eq›, _) $ t $ (Const (\<^const_name>‹star_n›, _) $ _)) =
thm_of t
| thm_of_goal _ = raise MATCH;
in
SUBGOAL (fn (t, i) =>
resolve_tac ctxt [thm_of_goal (strip_all_body t |> Logic.strip_imp_concl)] i
handle MATCH => no_tac)
end;
end;
fun transfer_thm_of ctxt ths t =
let
val {intros,unfolds,refolds,consts} = Data.get (Context.Proof ctxt);
val meta = Local_Defs.meta_rewrite_rule ctxt;
val ths' = map meta ths;
val unfolds' = map meta unfolds and refolds' = map meta refolds;
val (_$_$t') = Thm.concl_of (Raw_Simplifier.rewrite ctxt true unfolds' (Thm.cterm_of ctxt t))
val u = unstar_term consts t'
val tac =
rewrite_goals_tac ctxt (ths' @ refolds' @ unfolds') THEN
ALLGOALS (Object_Logic.full_atomize_tac ctxt) THEN
match_tac ctxt [transitive_thm] 1 THEN
resolve_tac ctxt [@{thm transfer_start}] 1 THEN
REPEAT_ALL_NEW (resolve_tac ctxt intros ORELSE' transfer_star_tac ctxt) 1 THEN
match_tac ctxt [reflexive_thm] 1
in Goal.prove ctxt [] [] (Logic.mk_equals (t,u)) (K tac) end;
fun transfer_tac ctxt ths = SUBGOAL (fn (t, _) => (fn th =>
let
val tr = transfer_thm_of ctxt ths t
val (_$ l $ r) = Thm.concl_of tr;
val trs = if l aconv r then [] else [tr];
in rewrite_goals_tac ctxt trs th end));
local
fun map_intros f = Data.map
(fn {intros,unfolds,refolds,consts} =>
{intros=f intros, unfolds=unfolds, refolds=refolds, consts=consts})
fun map_unfolds f = Data.map
(fn {intros,unfolds,refolds,consts} =>
{intros=intros, unfolds=f unfolds, refolds=refolds, consts=consts})
fun map_refolds f = Data.map
(fn {intros,unfolds,refolds,consts} =>
{intros=intros, unfolds=unfolds, refolds=f refolds, consts=consts})
in
val intro_add = Thm.declaration_attribute (map_intros o Thm.add_thm o Thm.trim_context);
val intro_del = Thm.declaration_attribute (map_intros o Thm.del_thm);
val unfold_add = Thm.declaration_attribute (map_unfolds o Thm.add_thm o Thm.trim_context);
val unfold_del = Thm.declaration_attribute (map_unfolds o Thm.del_thm);
val refold_add = Thm.declaration_attribute (map_refolds o Thm.add_thm o Thm.trim_context);
val refold_del = Thm.declaration_attribute (map_refolds o Thm.del_thm);
end
fun add_const c = Context.theory_map (Data.map
(fn {intros,unfolds,refolds,consts} =>
{intros=intros, unfolds=unfolds, refolds=refolds, consts=c::consts}))
val _ =
Theory.setup
(Attrib.setup \<^binding>‹transfer_intro› (Attrib.add_del intro_add intro_del)
"declaration of transfer introduction rule" #>
Attrib.setup \<^binding>‹transfer_unfold› (Attrib.add_del unfold_add unfold_del)
"declaration of transfer unfolding rule" #>
Attrib.setup \<^binding>‹transfer_refold› (Attrib.add_del refold_add refold_del)
"declaration of transfer refolding rule")
end;