(* Title: HOL/Tools/Transfer/transfer.ML
Author: Brian Huffman, TU Muenchen
Author: Ondrej Kuncar, TU Muenchen
Generic theorem transfer method.
*)
signature TRANSFER =
sig
type pred_data
val rel_eq_onp: pred_data -> thm
val bottom_rewr_conv: thm list -> conv
val top_rewr_conv: thm list -> conv
val prep_conv: conv
val get_transfer_raw: Proof.context -> thm list
val get_relator_eq_item_net: Proof.context -> thm Item_Net.T
val get_relator_eq: Proof.context -> thm list
val get_sym_relator_eq: Proof.context -> thm list
val get_relator_eq_raw: Proof.context -> thm list
val get_relator_domain: Proof.context -> thm list
val morph_pred_data: morphism -> pred_data -> pred_data
val lookup_pred_data: Proof.context -> string -> pred_data option
val update_pred_data: string -> pred_data -> Context.generic -> Context.generic
val get_compound_lhs: Proof.context -> (term * thm) Item_Net.T
val get_compound_rhs: Proof.context -> (term * thm) Item_Net.T
val transfer_add: attribute
val transfer_del: attribute
val transfer_raw_add: thm -> Context.generic -> Context.generic
val transfer_raw_del: thm -> Context.generic -> Context.generic
val transferred_attribute: thm list -> attribute
val untransferred_attribute: thm list -> attribute
val prep_transfer_domain_thm: Proof.context -> thm -> thm
val transfer_domain_add: attribute
val transfer_domain_del: attribute
val transfer_rule_of_term: Proof.context -> bool -> term -> thm
val transfer_rule_of_lhs: Proof.context -> term -> thm
val eq_tac: Proof.context -> int -> tactic
val transfer_step_tac: Proof.context -> int -> tactic
val transfer_tac: bool -> Proof.context -> int -> tactic
val transfer_prover_tac: Proof.context -> int -> tactic
val gen_frees_tac: (string * typ) list -> Proof.context -> int -> tactic
end
structure Transfer : TRANSFER =
struct
(** Theory Data **)
val compound_xhs_empty_net = Item_Net.init (Thm.eq_thm_prop o apply2 snd) (single o fst);
val rewr_rules = Item_Net.init Thm.eq_thm_prop (single o fst o HOLogic.dest_eq
o HOLogic.dest_Trueprop o Thm.concl_of);
type pred_data = {rel_eq_onp: thm}
val rel_eq_onp: pred_data -> thm = #rel_eq_onp
structure Data = Generic_Data
(
type T =
{ transfer_raw : thm Item_Net.T,
known_frees : (string * typ) list,
compound_lhs : (term * thm) Item_Net.T,
compound_rhs : (term * thm) Item_Net.T,
relator_eq : thm Item_Net.T,
relator_eq_raw : thm Item_Net.T,
relator_domain : thm Item_Net.T,
pred_data : pred_data Symtab.table }
val empty =
{ transfer_raw = Thm.intro_rules,
known_frees = [],
compound_lhs = compound_xhs_empty_net,
compound_rhs = compound_xhs_empty_net,
relator_eq = rewr_rules,
relator_eq_raw = Thm.full_rules,
relator_domain = Thm.full_rules,
pred_data = Symtab.empty }
val extend = I
fun merge
( { transfer_raw = t1, known_frees = k1,
compound_lhs = l1,
compound_rhs = c1, relator_eq = r1,
relator_eq_raw = rw1, relator_domain = rd1,
pred_data = pd1 },
{ transfer_raw = t2, known_frees = k2,
compound_lhs = l2,
compound_rhs = c2, relator_eq = r2,
relator_eq_raw = rw2, relator_domain = rd2,
pred_data = pd2 } ) =
{ transfer_raw = Item_Net.merge (t1, t2),
known_frees = Library.merge (op =) (k1, k2),
compound_lhs = Item_Net.merge (l1, l2),
compound_rhs = Item_Net.merge (c1, c2),
relator_eq = Item_Net.merge (r1, r2),
relator_eq_raw = Item_Net.merge (rw1, rw2),
relator_domain = Item_Net.merge (rd1, rd2),
pred_data = Symtab.merge (K true) (pd1, pd2) }
)
fun get_transfer_raw ctxt = ctxt
|> (Item_Net.content o #transfer_raw o Data.get o Context.Proof)
fun get_known_frees ctxt = ctxt
|> (#known_frees o Data.get o Context.Proof)
fun get_compound_lhs ctxt = ctxt
|> (#compound_lhs o Data.get o Context.Proof)
fun get_compound_rhs ctxt = ctxt
|> (#compound_rhs o Data.get o Context.Proof)
fun get_relator_eq_item_net ctxt = (#relator_eq o Data.get o Context.Proof) ctxt
fun get_relator_eq ctxt = ctxt
|> (Item_Net.content o #relator_eq o Data.get o Context.Proof)
|> map safe_mk_meta_eq
fun get_sym_relator_eq ctxt = ctxt
|> (Item_Net.content o #relator_eq o Data.get o Context.Proof)
|> map (Thm.symmetric o safe_mk_meta_eq)
fun get_relator_eq_raw ctxt = ctxt
|> (Item_Net.content o #relator_eq_raw o Data.get o Context.Proof)
fun get_relator_domain ctxt = ctxt
|> (Item_Net.content o #relator_domain o Data.get o Context.Proof)
fun get_pred_data ctxt = ctxt
|> (#pred_data o Data.get o Context.Proof)
fun map_data f1 f2 f3 f4 f5 f6 f7 f8
{ transfer_raw, known_frees, compound_lhs, compound_rhs,
relator_eq, relator_eq_raw, relator_domain, pred_data } =
{ transfer_raw = f1 transfer_raw,
known_frees = f2 known_frees,
compound_lhs = f3 compound_lhs,
compound_rhs = f4 compound_rhs,
relator_eq = f5 relator_eq,
relator_eq_raw = f6 relator_eq_raw,
relator_domain = f7 relator_domain,
pred_data = f8 pred_data }
fun map_transfer_raw f = map_data f I I I I I I I
fun map_known_frees f = map_data I f I I I I I I
fun map_compound_lhs f = map_data I I f I I I I I
fun map_compound_rhs f = map_data I I I f I I I I
fun map_relator_eq f = map_data I I I I f I I I
fun map_relator_eq_raw f = map_data I I I I I f I I
fun map_relator_domain f = map_data I I I I I I f I
fun map_pred_data f = map_data I I I I I I I f
fun add_transfer_thm thm = Data.map
(map_transfer_raw (Item_Net.update thm) o
map_compound_lhs
(case HOLogic.dest_Trueprop (Thm.concl_of thm) of
Const (@{const_name Rel}, _) $ _ $ (lhs as (_ $ _)) $ _ =>
Item_Net.update (lhs, thm)
| _ => I) o
map_compound_rhs
(case HOLogic.dest_Trueprop (Thm.concl_of thm) of
Const (@{const_name Rel}, _) $ _ $ _ $ (rhs as (_ $ _)) =>
Item_Net.update (rhs, thm)
| _ => I) o
map_known_frees (Term.add_frees (Thm.concl_of thm)))
fun del_transfer_thm thm = Data.map
(map_transfer_raw (Item_Net.remove thm) o
map_compound_lhs
(case HOLogic.dest_Trueprop (Thm.concl_of thm) of
Const (@{const_name Rel}, _) $ _ $ (lhs as (_ $ _)) $ _ =>
Item_Net.remove (lhs, thm)
| _ => I) o
map_compound_rhs
(case HOLogic.dest_Trueprop (Thm.concl_of thm) of
Const (@{const_name Rel}, _) $ _ $ _ $ (rhs as (_ $ _)) =>
Item_Net.remove (rhs, thm)
| _ => I))
fun transfer_raw_add thm ctxt = add_transfer_thm thm ctxt
fun transfer_raw_del thm ctxt = del_transfer_thm thm ctxt
(** Conversions **)
fun bottom_rewr_conv rewrs = Conv.bottom_conv (K (Conv.try_conv (Conv.rewrs_conv rewrs))) @{context}
fun top_rewr_conv rewrs = Conv.top_conv (K (Conv.try_conv (Conv.rewrs_conv rewrs))) @{context}
fun transfer_rel_conv conv =
Conv.concl_conv ~1 (HOLogic.Trueprop_conv (Conv.fun2_conv (Conv.arg_conv conv)))
val Rel_rule = Thm.symmetric @{thm Rel_def}
fun dest_funcT cT =
(case Thm.dest_ctyp cT of [T, U] => (T, U)
| _ => raise TYPE ("dest_funcT", [Thm.typ_of cT], []))
fun Rel_conv ct =
let val (cT, cT') = dest_funcT (Thm.ctyp_of_cterm ct)
val (cU, _) = dest_funcT cT'
in Drule.instantiate' [SOME cT, SOME cU] [SOME ct] Rel_rule end
(* Conversion to preprocess a transfer rule *)
fun safe_Rel_conv ct =
Conv.try_conv (HOLogic.Trueprop_conv (Conv.fun_conv (Conv.fun_conv Rel_conv))) ct
fun prep_conv ct = (
Conv.implies_conv safe_Rel_conv prep_conv
else_conv
safe_Rel_conv
else_conv
Conv.all_conv) ct
(** Replacing explicit equalities with is_equality premises **)
fun mk_is_equality t =
Const (@{const_name is_equality}, Term.fastype_of t --> HOLogic.boolT) $ t
val is_equality_lemma =
@{lemma "(!!R. is_equality R ==> PROP (P R)) == PROP (P (op =))"
by (unfold is_equality_def, rule, drule meta_spec,
erule meta_mp, rule refl, simp)}
fun gen_abstract_equalities ctxt (dest : term -> term * (term -> term)) thm =
let
val thy = Thm.theory_of_thm thm
val prop = Thm.prop_of thm
val (t, mk_prop') = dest prop
(* Only consider "op =" at non-base types *)
fun is_eq (Const (@{const_name HOL.eq}, Type ("fun", [T, _]))) =
(case T of Type (_, []) => false | _ => true)
| is_eq _ = false
val add_eqs = Term.fold_aterms (fn t => if is_eq t then insert (op =) t else I)
val eq_consts = rev (add_eqs t [])
val eqTs = map (snd o dest_Const) eq_consts
val used = Term.add_free_names prop []
val names = map (K "") eqTs |> Name.variant_list used
val frees = map Free (names ~~ eqTs)
val prems = map (HOLogic.mk_Trueprop o mk_is_equality) frees
val prop1 = mk_prop' (Term.subst_atomic (eq_consts ~~ frees) t)
val prop2 = fold Logic.all frees (Logic.list_implies (prems, prop1))
val cprop = Thm.global_cterm_of thy prop2
val equal_thm = Raw_Simplifier.rewrite ctxt false [is_equality_lemma] cprop
fun forall_elim thm = Thm.forall_elim_vars (Thm.maxidx_of thm + 1) thm
in
forall_elim (thm COMP (equal_thm COMP @{thm equal_elim_rule2}))
end
handle TERM _ => thm
fun abstract_equalities_transfer ctxt thm =
let
fun dest prop =
let
val prems = Logic.strip_imp_prems prop
val concl = HOLogic.dest_Trueprop (Logic.strip_imp_concl prop)
val ((rel, x), y) = apfst Term.dest_comb (Term.dest_comb concl)
in
(rel, fn rel' =>
Logic.list_implies (prems, HOLogic.mk_Trueprop (rel' $ x $ y)))
end
val contracted_eq_thm =
Conv.fconv_rule (transfer_rel_conv (bottom_rewr_conv (get_relator_eq ctxt))) thm
handle CTERM _ => thm
in
gen_abstract_equalities ctxt dest contracted_eq_thm
end
fun abstract_equalities_relator_eq ctxt rel_eq_thm =
gen_abstract_equalities ctxt (fn x => (x, I))
(rel_eq_thm RS @{thm is_equality_def [THEN iffD2]})
fun abstract_equalities_domain ctxt thm =
let
fun dest prop =
let
val prems = Logic.strip_imp_prems prop
val concl = HOLogic.dest_Trueprop (Logic.strip_imp_concl prop)
val ((eq, dom), y) = apfst Term.dest_comb (Term.dest_comb concl)
in
(dom, fn dom' => Logic.list_implies (prems, HOLogic.mk_Trueprop (eq $ dom' $ y)))
end
fun transfer_rel_conv conv =
Conv.concl_conv ~1 (HOLogic.Trueprop_conv (Conv.arg1_conv (Conv.arg_conv conv)))
val contracted_eq_thm =
Conv.fconv_rule (transfer_rel_conv (bottom_rewr_conv (get_relator_eq ctxt))) thm
in
gen_abstract_equalities ctxt dest contracted_eq_thm
end
(** Replacing explicit Domainp predicates with Domainp assumptions **)
fun mk_Domainp_assm (T, R) =
HOLogic.mk_eq ((Const (@{const_name Domainp}, Term.fastype_of T --> Term.fastype_of R) $ T), R)
val Domainp_lemma =
@{lemma "(!!R. Domainp T = R ==> PROP (P R)) == PROP (P (Domainp T))"
by (rule, drule meta_spec,
erule meta_mp, rule refl, simp)}
fun fold_Domainp f (t as Const (@{const_name Domainp},_) $ (Var (_,_))) = f t
| fold_Domainp f (t $ u) = fold_Domainp f t #> fold_Domainp f u
| fold_Domainp f (Abs (_, _, t)) = fold_Domainp f t
| fold_Domainp _ _ = I
fun subst_terms tab t =
let
val t' = Termtab.lookup tab t
in
case t' of
SOME t' => t'
| NONE =>
(case t of
u $ v => (subst_terms tab u) $ (subst_terms tab v)
| Abs (a, T, t) => Abs (a, T, subst_terms tab t)
| t => t)
end
fun gen_abstract_domains ctxt (dest : term -> term * (term -> term)) thm =
let
val thy = Thm.theory_of_thm thm
val prop = Thm.prop_of thm
val (t, mk_prop') = dest prop
val Domainp_tms = rev (fold_Domainp (fn t => insert op= t) t [])
val Domainp_Ts = map (snd o dest_funT o snd o dest_Const o fst o dest_comb) Domainp_tms
val used = Term.add_free_names t []
val rels = map (snd o dest_comb) Domainp_tms
val rel_names = map (fst o fst o dest_Var) rels
val names = map (fn name => ("D" ^ name)) rel_names |> Name.variant_list used
val frees = map Free (names ~~ Domainp_Ts)
val prems = map (HOLogic.mk_Trueprop o mk_Domainp_assm) (rels ~~ frees);
val t' = subst_terms (fold Termtab.update (Domainp_tms ~~ frees) Termtab.empty) t
val prop1 = fold Logic.all frees (Logic.list_implies (prems, mk_prop' t'))
val prop2 = Logic.list_rename_params (rev names) prop1
val cprop = Thm.global_cterm_of thy prop2
val equal_thm = Raw_Simplifier.rewrite ctxt false [Domainp_lemma] cprop
fun forall_elim thm = Thm.forall_elim_vars (Thm.maxidx_of thm + 1) thm;
in
forall_elim (thm COMP (equal_thm COMP @{thm equal_elim_rule2}))
end
handle TERM _ => thm
fun abstract_domains_transfer ctxt thm =
let
fun dest prop =
let
val prems = Logic.strip_imp_prems prop
val concl = HOLogic.dest_Trueprop (Logic.strip_imp_concl prop)
val ((rel, x), y) = apfst Term.dest_comb (Term.dest_comb concl)
in
(x, fn x' =>
Logic.list_implies (prems, HOLogic.mk_Trueprop (rel $ x' $ y)))
end
in
gen_abstract_domains ctxt dest thm
end
fun abstract_domains_relator_domain ctxt thm =
let
fun dest prop =
let
val prems = Logic.strip_imp_prems prop
val concl = HOLogic.dest_Trueprop (Logic.strip_imp_concl prop)
val ((rel, x), y) = apfst Term.dest_comb (Term.dest_comb concl)
in
(y, fn y' =>
Logic.list_implies (prems, HOLogic.mk_Trueprop (rel $ x $ y')))
end
in
gen_abstract_domains ctxt dest thm
end
fun detect_transfer_rules thm =
let
fun is_transfer_rule tm = case (HOLogic.dest_Trueprop tm) of
(Const (@{const_name HOL.eq}, _)) $ ((Const (@{const_name Domainp}, _)) $ _) $ _ => false
| _ $ _ $ _ => true
| _ => false
fun safe_transfer_rule_conv ctm =
if is_transfer_rule (Thm.term_of ctm) then safe_Rel_conv ctm else Conv.all_conv ctm
in
Conv.fconv_rule (Conv.prems_conv ~1 safe_transfer_rule_conv) thm
end
(** Adding transfer domain rules **)
fun prep_transfer_domain_thm ctxt thm =
(abstract_equalities_domain ctxt o detect_transfer_rules) thm
fun add_transfer_domain_thm thm ctxt = (add_transfer_thm o
prep_transfer_domain_thm (Context.proof_of ctxt)) thm ctxt
fun del_transfer_domain_thm thm ctxt = (del_transfer_thm o
prep_transfer_domain_thm (Context.proof_of ctxt)) thm ctxt
(** Transfer proof method **)
val post_simps =
@{thms transfer_forall_eq [symmetric]
transfer_implies_eq [symmetric] transfer_bforall_unfold}
fun gen_frees_tac keepers ctxt = SUBGOAL (fn (t, i) =>
let
val keepers = keepers @ get_known_frees ctxt
val vs = rev (Term.add_frees t [])
val vs' = filter_out (member (op =) keepers) vs
in
Induct.arbitrary_tac ctxt 0 vs' i
end)
fun mk_relT (T, U) = T --> U --> HOLogic.boolT
fun mk_Rel t =
let val T = fastype_of t
in Const (@{const_name Transfer.Rel}, T --> T) $ t end
fun transfer_rule_of_terms (prj : typ * typ -> typ) ctxt tab t u =
let
val thy = Proof_Context.theory_of ctxt
(* precondition: prj(T,U) must consist of only TFrees and type "fun" *)
fun rel (T as Type ("fun", [T1, T2])) (U as Type ("fun", [U1, U2])) =
let
val r1 = rel T1 U1
val r2 = rel T2 U2
val rT = fastype_of r1 --> fastype_of r2 --> mk_relT (T, U)
in
Const (@{const_name rel_fun}, rT) $ r1 $ r2
end
| rel T U =
let
val (a, _) = dest_TFree (prj (T, U))
in
Free (the (AList.lookup (op =) tab a), mk_relT (T, U))
end
fun zip _ thms (Bound i) (Bound _) = (nth thms i, [])
| zip ctxt thms (Abs (x, T, t)) (Abs (y, U, u)) =
let
val ([x', y'], ctxt') = Variable.variant_fixes [x, y] ctxt
val prop = mk_Rel (rel T U) $ Free (x', T) $ Free (y', U)
val cprop = Thm.global_cterm_of thy (HOLogic.mk_Trueprop prop)
val thm0 = Thm.assume cprop
val (thm1, hyps) = zip ctxt' (thm0 :: thms) t u
val ((r1, x), y) = apfst Thm.dest_comb (Thm.dest_comb (Thm.dest_arg cprop))
val r2 = Thm.dest_fun2 (Thm.dest_arg (Thm.cprop_of thm1))
val (a1, (b1, _)) = apsnd dest_funcT (dest_funcT (Thm.ctyp_of_cterm r1))
val (a2, (b2, _)) = apsnd dest_funcT (dest_funcT (Thm.ctyp_of_cterm r2))
val tinsts = [SOME a1, SOME b1, SOME a2, SOME b2]
val insts = [SOME (Thm.dest_arg r1), SOME (Thm.dest_arg r2)]
val rule = Drule.instantiate' tinsts insts @{thm Rel_abs}
val thm2 = Thm.forall_intr x (Thm.forall_intr y (Thm.implies_intr cprop thm1))
in
(thm2 COMP rule, hyps)
end
| zip ctxt thms (f $ t) (g $ u) =
let
val (thm1, hyps1) = zip ctxt thms f g
val (thm2, hyps2) = zip ctxt thms t u
in
(thm2 RS (thm1 RS @{thm Rel_app}), hyps1 @ hyps2)
end
| zip _ _ t u =
let
val T = fastype_of t
val U = fastype_of u
val prop = mk_Rel (rel T U) $ t $ u
val cprop = Thm.global_cterm_of thy (HOLogic.mk_Trueprop prop)
in
(Thm.assume cprop, [cprop])
end
val r = mk_Rel (rel (fastype_of t) (fastype_of u))
val goal = HOLogic.mk_Trueprop (r $ t $ u)
val rename = Thm.trivial (Thm.global_cterm_of thy goal)
val (thm, hyps) = zip ctxt [] t u
in
Drule.implies_intr_list hyps (thm RS rename)
end
(* create a lambda term of the same shape as the given term *)
fun skeleton (is_atom : term -> bool) ctxt t =
let
fun dummy ctxt =
let
val (c, ctxt) = yield_singleton Variable.variant_fixes "a" ctxt
in
(Free (c, dummyT), ctxt)
end
fun go (Bound i) ctxt = (Bound i, ctxt)
| go (Abs (x, _, t)) ctxt =
let
val (t', ctxt) = go t ctxt
in
(Abs (x, dummyT, t'), ctxt)
end
| go (tu as (t $ u)) ctxt =
if is_atom tu andalso not (Term.is_open tu) then dummy ctxt else
let
val (t', ctxt) = go t ctxt
val (u', ctxt) = go u ctxt
in
(t' $ u', ctxt)
end
| go _ ctxt = dummy ctxt
in
go t ctxt |> fst |> Syntax.check_term ctxt |>
map_types (map_type_tfree (fn (a, _) => TFree (a, @{sort type})))
end
(** Monotonicity analysis **)
(* TODO: Put extensible table in theory data *)
val monotab =
Symtab.make
[(@{const_name transfer_implies}, [~1, 1]),
(@{const_name transfer_forall}, [1])(*,
(@{const_name implies}, [~1, 1]),
(@{const_name All}, [1])*)]
(*
Function bool_insts determines the set of boolean-relation variables
that can be instantiated to implies, rev_implies, or iff.
Invariants: bool_insts p (t, u) requires that
u :: _ => _ => ... => bool, and
t is a skeleton of u
*)
fun bool_insts p (t, u) =
let
fun strip2 (t1 $ t2, u1 $ u2, tus) =
strip2 (t1, u1, (t2, u2) :: tus)
| strip2 x = x
fun or3 ((a, b, c), (x, y, z)) = (a orelse x, b orelse y, c orelse z)
fun go Ts p (Abs (_, T, t), Abs (_, _, u)) tab = go (T :: Ts) p (t, u) tab
| go Ts p (t, u) tab =
let
val (a, _) = dest_TFree (Term.body_type (Term.fastype_of1 (Ts, t)))
val (_, tf, tus) = strip2 (t, u, [])
val ps_opt = case tf of Const (c, _) => Symtab.lookup monotab c | _ => NONE
val tab1 =
case ps_opt of
SOME ps =>
let
val ps' = map (fn x => p * x) (take (length tus) ps)
in
fold I (map2 (go Ts) ps' tus) tab
end
| NONE => tab
val tab2 = Symtab.make [(a, (p >= 0, p <= 0, is_none ps_opt))]
in
Symtab.join (K or3) (tab1, tab2)
end
val tab = go [] p (t, u) Symtab.empty
fun f (a, (true, false, false)) = SOME (a, @{const implies})
| f (a, (false, true, false)) = SOME (a, @{const rev_implies})
| f (a, (true, true, _)) = SOME (a, HOLogic.eq_const HOLogic.boolT)
| f _ = NONE
in
map_filter f (Symtab.dest tab)
end
fun retrieve_terms t net = map fst (Item_Net.retrieve net t)
fun matches_list ctxt term =
is_some o find_first (fn pat => Pattern.matches (Proof_Context.theory_of ctxt) (pat, term))
fun transfer_rule_of_term ctxt equiv t : thm =
let
val compound_rhs = get_compound_rhs ctxt
fun is_rhs t = compound_rhs |> retrieve_terms t |> matches_list ctxt t
val s = skeleton is_rhs ctxt t
val frees = map fst (Term.add_frees s [])
val tfrees = map fst (Term.add_tfrees s [])
fun prep a = "R" ^ Library.unprefix "'" a
val (rnames, ctxt') = Variable.variant_fixes (map prep tfrees) ctxt
val tab = tfrees ~~ rnames
fun prep a = the (AList.lookup (op =) tab a)
val thm = transfer_rule_of_terms fst ctxt' tab s t
val binsts = bool_insts (if equiv then 0 else 1) (s, t)
val cbool = @{ctyp bool}
val relT = @{typ "bool => bool => bool"}
val idx = Thm.maxidx_of thm + 1
val thy = Proof_Context.theory_of ctxt
fun tinst (a, _) = (Thm.global_ctyp_of thy (TVar ((a, idx), @{sort type})), cbool)
fun inst (a, t) =
(Thm.global_cterm_of thy (Var (Name.clean_index (prep a, idx), relT)), Thm.global_cterm_of thy t)
in
thm
|> Thm.generalize (tfrees, rnames @ frees) idx
|> Thm.instantiate (map tinst binsts, map inst binsts)
end
fun transfer_rule_of_lhs ctxt t : thm =
let
val compound_lhs = get_compound_lhs ctxt
fun is_lhs t = compound_lhs |> retrieve_terms t |> matches_list ctxt t
val s = skeleton is_lhs ctxt t
val frees = map fst (Term.add_frees s [])
val tfrees = map fst (Term.add_tfrees s [])
fun prep a = "R" ^ Library.unprefix "'" a
val (rnames, ctxt') = Variable.variant_fixes (map prep tfrees) ctxt
val tab = tfrees ~~ rnames
fun prep a = the (AList.lookup (op =) tab a)
val thm = transfer_rule_of_terms snd ctxt' tab t s
val binsts = bool_insts 1 (s, t)
val cbool = @{ctyp bool}
val relT = @{typ "bool => bool => bool"}
val idx = Thm.maxidx_of thm + 1
val thy = Proof_Context.theory_of ctxt
fun tinst (a, _) = (Thm.global_ctyp_of thy (TVar ((a, idx), @{sort type})), cbool)
fun inst (a, t) =
(Thm.global_cterm_of thy (Var (Name.clean_index (prep a, idx), relT)), Thm.global_cterm_of thy t)
in
thm
|> Thm.generalize (tfrees, rnames @ frees) idx
|> Thm.instantiate (map tinst binsts, map inst binsts)
end
fun eq_rules_tac ctxt eq_rules =
TRY o REPEAT_ALL_NEW (resolve_tac ctxt eq_rules)
THEN_ALL_NEW rtac @{thm is_equality_eq}
fun eq_tac ctxt = eq_rules_tac ctxt (get_relator_eq_raw ctxt)
fun transfer_step_tac ctxt =
REPEAT_ALL_NEW (resolve_tac ctxt (get_transfer_raw ctxt)
THEN_ALL_NEW (DETERM o eq_rules_tac ctxt (get_relator_eq_raw ctxt)))
fun transfer_tac equiv ctxt i =
let
val pre_simps = @{thms transfer_forall_eq transfer_implies_eq}
val start_rule =
if equiv then @{thm transfer_start} else @{thm transfer_start'}
val rules = get_transfer_raw ctxt
val eq_rules = get_relator_eq_raw ctxt
(* allow unsolved subgoals only for standard transfer method, not for transfer' *)
val end_tac = if equiv then K all_tac else K no_tac
val err_msg = "Transfer failed to convert goal to an object-logic formula"
fun main_tac (t, i) =
rtac start_rule i THEN
(rtac (transfer_rule_of_term ctxt equiv (HOLogic.dest_Trueprop t))
THEN_ALL_NEW
(SOLVED'
(REPEAT_ALL_NEW (resolve_tac ctxt rules) THEN_ALL_NEW
(DETERM o eq_rules_tac ctxt eq_rules))
ORELSE' end_tac)) (i + 1)
handle TERM (_, ts) => raise TERM (err_msg, ts)
in
EVERY
[rewrite_goal_tac ctxt pre_simps i THEN
SUBGOAL main_tac i,
(* FIXME: rewrite_goal_tac does unwanted eta-contraction *)
rewrite_goal_tac ctxt post_simps i,
Goal.norm_hhf_tac ctxt i]
end
fun transfer_prover_tac ctxt = SUBGOAL (fn (t, i) =>
let
val rhs = (snd o Term.dest_comb o HOLogic.dest_Trueprop) t
val rule1 = transfer_rule_of_term ctxt false rhs
val rules = get_transfer_raw ctxt
val eq_rules = get_relator_eq_raw ctxt
val expand_eq_in_rel = transfer_rel_conv (top_rewr_conv [@{thm rel_fun_eq[symmetric,THEN eq_reflection]}])
in
EVERY
[CONVERSION prep_conv i,
rtac @{thm transfer_prover_start} i,
((rtac rule1 ORELSE' (CONVERSION expand_eq_in_rel THEN' rtac rule1))
THEN_ALL_NEW
(REPEAT_ALL_NEW (resolve_tac ctxt rules) THEN_ALL_NEW
(DETERM o eq_rules_tac ctxt eq_rules))) (i + 1),
rtac @{thm refl} i]
end)
(** Transfer attribute **)
fun transferred ctxt extra_rules thm =
let
val start_rule = @{thm transfer_start}
val start_rule' = @{thm transfer_start'}
val rules = extra_rules @ get_transfer_raw ctxt
val eq_rules = get_relator_eq_raw ctxt
val err_msg = "Transfer failed to convert goal to an object-logic formula"
val pre_simps = @{thms transfer_forall_eq transfer_implies_eq}
val thm1 = Drule.forall_intr_vars thm
val instT = rev (Term.add_tvars (Thm.full_prop_of thm1) [])
|> map (fn v as ((a, _), S) => (v, TFree (a, S)))
val thm2 = thm1
|> Thm.certify_instantiate (instT, [])
|> Raw_Simplifier.rewrite_rule ctxt pre_simps
val ctxt' = Variable.declare_names (Thm.full_prop_of thm2) ctxt
val t = HOLogic.dest_Trueprop (Thm.concl_of thm2)
val rule = transfer_rule_of_lhs ctxt' t
val tac =
resolve_tac ctxt' [thm2 RS start_rule', thm2 RS start_rule] 1 THEN
(rtac rule
THEN_ALL_NEW
(SOLVED' (REPEAT_ALL_NEW (resolve_tac ctxt' rules)
THEN_ALL_NEW (DETERM o eq_rules_tac ctxt' eq_rules)))) 1
handle TERM (_, ts) => raise TERM (err_msg, ts)
val thm3 = Goal.prove_internal ctxt' [] @{cpat "Trueprop ?P"} (K tac)
val tnames = map (fst o dest_TFree o snd) instT
in
thm3
|> Raw_Simplifier.rewrite_rule ctxt' post_simps
|> Simplifier.norm_hhf ctxt'
|> Drule.generalize (tnames, [])
|> Drule.zero_var_indexes
end
(*
handle THM _ => thm
*)
fun untransferred ctxt extra_rules thm =
let
val start_rule = @{thm untransfer_start}
val rules = extra_rules @ get_transfer_raw ctxt
val eq_rules = get_relator_eq_raw ctxt
val err_msg = "Transfer failed to convert goal to an object-logic formula"
val pre_simps = @{thms transfer_forall_eq transfer_implies_eq}
val thm1 = Drule.forall_intr_vars thm
val instT = rev (Term.add_tvars (Thm.full_prop_of thm1) [])
|> map (fn v as ((a, _), S) => (v, TFree (a, S)))
val thm2 = thm1
|> Thm.certify_instantiate (instT, [])
|> Raw_Simplifier.rewrite_rule ctxt pre_simps
val ctxt' = Variable.declare_names (Thm.full_prop_of thm2) ctxt
val t = HOLogic.dest_Trueprop (Thm.concl_of thm2)
val rule = transfer_rule_of_term ctxt' true t
val tac =
rtac (thm2 RS start_rule) 1 THEN
(rtac rule
THEN_ALL_NEW
(SOLVED' (REPEAT_ALL_NEW (resolve_tac ctxt' rules)
THEN_ALL_NEW (DETERM o eq_rules_tac ctxt' eq_rules)))) 1
handle TERM (_, ts) => raise TERM (err_msg, ts)
val thm3 = Goal.prove_internal ctxt' [] @{cpat "Trueprop ?P"} (K tac)
val tnames = map (fst o dest_TFree o snd) instT
in
thm3
|> Raw_Simplifier.rewrite_rule ctxt' post_simps
|> Simplifier.norm_hhf ctxt'
|> Drule.generalize (tnames, [])
|> Drule.zero_var_indexes
end
(** Methods and attributes **)
val free = Args.context -- Args.term >> (fn (_, Free v) => v | (ctxt, t) =>
error ("Bad free variable: " ^ Syntax.string_of_term ctxt t))
val fixing = Scan.optional (Scan.lift (Args.$$$ "fixing" -- Args.colon)
|-- Scan.repeat free) []
fun transfer_method equiv : (Proof.context -> Proof.method) context_parser =
fixing >> (fn vs => fn ctxt =>
SIMPLE_METHOD' (gen_frees_tac vs ctxt THEN' transfer_tac equiv ctxt))
val transfer_prover_method : (Proof.context -> Proof.method) context_parser =
Scan.succeed (fn ctxt => SIMPLE_METHOD' (transfer_prover_tac ctxt))
(* Attribute for transfer rules *)
fun prep_rule ctxt =
abstract_domains_transfer ctxt o abstract_equalities_transfer ctxt o Conv.fconv_rule prep_conv
val transfer_add =
Thm.declaration_attribute (fn thm => fn ctxt =>
(add_transfer_thm o prep_rule (Context.proof_of ctxt)) thm ctxt)
val transfer_del =
Thm.declaration_attribute (fn thm => fn ctxt =>
(del_transfer_thm o prep_rule (Context.proof_of ctxt)) thm ctxt)
val transfer_attribute =
Attrib.add_del transfer_add transfer_del
(* Attributes for transfer domain rules *)
val transfer_domain_add = Thm.declaration_attribute add_transfer_domain_thm
val transfer_domain_del = Thm.declaration_attribute del_transfer_domain_thm
val transfer_domain_attribute =
Attrib.add_del transfer_domain_add transfer_domain_del
(* Attributes for transferred rules *)
fun transferred_attribute thms = Thm.rule_attribute
(fn context => transferred (Context.proof_of context) thms)
fun untransferred_attribute thms = Thm.rule_attribute
(fn context => untransferred (Context.proof_of context) thms)
val transferred_attribute_parser =
Attrib.thms >> transferred_attribute
val untransferred_attribute_parser =
Attrib.thms >> untransferred_attribute
fun morph_pred_data phi {rel_eq_onp} = {rel_eq_onp = Morphism.thm phi rel_eq_onp}
fun lookup_pred_data ctxt type_name = Symtab.lookup (get_pred_data ctxt) type_name
|> Option.map (morph_pred_data (Morphism.transfer_morphism (Proof_Context.theory_of ctxt)))
fun update_pred_data type_name qinfo ctxt =
Data.map (map_pred_data (Symtab.update (type_name, qinfo))) ctxt
(* Theory setup *)
val _ =
Theory.setup
let
val name = @{binding relator_eq}
fun add_thm thm context = context
|> Data.map (map_relator_eq (Item_Net.update thm))
|> Data.map (map_relator_eq_raw
(Item_Net.update (abstract_equalities_relator_eq (Context.proof_of context) thm)))
fun del_thm thm context = context
|> Data.map (map_relator_eq (Item_Net.remove thm))
|> Data.map (map_relator_eq_raw
(Item_Net.remove (abstract_equalities_relator_eq (Context.proof_of context) thm)))
val add = Thm.declaration_attribute add_thm
val del = Thm.declaration_attribute del_thm
val text = "declaration of relator equality rule (used by transfer method)"
val content = Item_Net.content o #relator_eq o Data.get
in
Attrib.setup name (Attrib.add_del add del) text
#> Global_Theory.add_thms_dynamic (name, content)
end
val _ =
Theory.setup
let
val name = @{binding relator_domain}
fun add_thm thm context =
let
val thm = abstract_domains_relator_domain (Context.proof_of context) thm
in
context |> Data.map (map_relator_domain (Item_Net.update thm)) |> add_transfer_domain_thm thm
end
fun del_thm thm context =
let
val thm = abstract_domains_relator_domain (Context.proof_of context) thm
in
context |> Data.map (map_relator_domain (Item_Net.remove thm)) |> del_transfer_domain_thm thm
end
val add = Thm.declaration_attribute add_thm
val del = Thm.declaration_attribute del_thm
val text = "declaration of relator domain rule (used by transfer method)"
val content = Item_Net.content o #relator_domain o Data.get
in
Attrib.setup name (Attrib.add_del add del) text
#> Global_Theory.add_thms_dynamic (name, content)
end
val _ =
Theory.setup
(Attrib.setup @{binding transfer_rule} transfer_attribute
"transfer rule for transfer method"
#> Global_Theory.add_thms_dynamic
(@{binding transfer_raw}, Item_Net.content o #transfer_raw o Data.get)
#> Attrib.setup @{binding transfer_domain_rule} transfer_domain_attribute
"transfer domain rule for transfer method"
#> Attrib.setup @{binding transferred} transferred_attribute_parser
"raw theorem transferred to abstract theorem using transfer rules"
#> Attrib.setup @{binding untransferred} untransferred_attribute_parser
"abstract theorem transferred to raw theorem using transfer rules"
#> Global_Theory.add_thms_dynamic
(@{binding relator_eq_raw}, Item_Net.content o #relator_eq_raw o Data.get)
#> Method.setup @{binding transfer} (transfer_method true)
"generic theorem transfer method"
#> Method.setup @{binding transfer'} (transfer_method false)
"generic theorem transfer method"
#> Method.setup @{binding transfer_prover} transfer_prover_method
"for proving transfer rules")
end