(* Title: HOL/Tools/SMT/smt_replay_methods.ML
Author: Sascha Boehme, TU Muenchen
Author: Jasmin Blanchette, TU Muenchen
Author: Mathias Fleury, MPII
Proof methods for replaying SMT proofs.
*)
signature SMT_REPLAY_METHODS =
sig
(*Printing*)
val pretty_goal: Proof.context -> string -> string -> thm list -> term -> Pretty.T
val trace_goal: Proof.context -> string -> thm list -> term -> unit
val trace: Proof.context -> (unit -> string) -> unit
(*Replaying*)
val replay_error: Proof.context -> string -> string -> thm list -> term -> 'a
val replay_rule_error: string -> Proof.context -> string -> thm list -> term -> 'a
(*theory lemma methods*)
type th_lemma_method = Proof.context -> thm list -> term -> thm
val add_th_lemma_method: string * th_lemma_method -> Context.generic ->
Context.generic
val get_th_lemma_method: Proof.context -> th_lemma_method Symtab.table
val discharge: int -> thm list -> thm -> thm
val match_instantiate: Proof.context -> term -> thm -> thm
val prove: Proof.context -> term -> (Proof.context -> int -> tactic) -> thm
val prove_arith_rewrite: ((term -> int * term Termtab.table ->
term * (int * term Termtab.table)) -> term -> int * term Termtab.table ->
term * (int * term Termtab.table)) -> Proof.context -> term -> thm
(*abstraction*)
type abs_context = int * term Termtab.table
type 'a abstracter = term -> abs_context -> 'a * abs_context
val add_arith_abstracter: (term abstracter -> term option abstracter) ->
Context.generic -> Context.generic
val abstract_lit: term -> abs_context -> term * abs_context
val abstract_conj: term -> abs_context -> term * abs_context
val abstract_disj: term -> abs_context -> term * abs_context
val abstract_not: (term -> abs_context -> term * abs_context) ->
term -> abs_context -> term * abs_context
val abstract_unit: term -> abs_context -> term * abs_context
val abstract_bool: term -> abs_context -> term * abs_context
(* also abstracts over equivalences and conjunction and implication*)
val abstract_bool_shallow: term -> abs_context -> term * abs_context
(* abstracts down to equivalence symbols *)
val abstract_bool_shallow_equivalence: term -> abs_context -> term * abs_context
val abstract_prop: term -> abs_context -> term * abs_context
val abstract_term: term -> abs_context -> term * abs_context
val abstract_eq: (term -> int * term Termtab.table -> term * (int * term Termtab.table)) ->
term -> int * term Termtab.table -> term * (int * term Termtab.table)
val abstract_neq: (term -> int * term Termtab.table -> term * (int * term Termtab.table)) ->
term -> int * term Termtab.table -> term * (int * term Termtab.table)
val abstract_arith: Proof.context -> term -> abs_context -> term * abs_context
(* also abstracts over if-then-else *)
val abstract_arith_shallow: Proof.context -> term -> abs_context -> term * abs_context
val prove_abstract: Proof.context -> thm list -> term ->
(Proof.context -> thm list -> int -> tactic) ->
(abs_context -> (term list * term) * abs_context) -> thm
val prove_abstract': Proof.context -> term -> (Proof.context -> thm list -> int -> tactic) ->
(abs_context -> term * abs_context) -> thm
val try_provers: string -> Proof.context -> string -> (string * (term -> 'a)) list -> thm list ->
term -> 'a
(*shared tactics*)
val cong_unfolding_trivial: Proof.context -> thm list -> term -> thm
val cong_basic: Proof.context -> thm list -> term -> thm
val cong_full: Proof.context -> thm list -> term -> thm
val cong_unfolding_first: Proof.context -> thm list -> term -> thm
val arith_th_lemma: Proof.context -> thm list -> term -> thm
val arith_th_lemma_wo: Proof.context -> thm list -> term -> thm
val arith_th_lemma_wo_shallow: Proof.context -> thm list -> term -> thm
val arith_th_lemma_tac_with_wo: Proof.context -> thm list -> int -> tactic
val dest_thm: thm -> term
val prop_tac: Proof.context -> thm list -> int -> tactic
val certify_prop: Proof.context -> term -> cterm
val dest_prop: term -> term
end;
structure SMT_Replay_Methods: SMT_REPLAY_METHODS =
struct
(* utility functions *)
fun trace ctxt f = SMT_Config.trace_msg ctxt f ()
fun pretty_thm ctxt thm = Syntax.pretty_term ctxt (Thm.concl_of thm)
fun pretty_goal ctxt msg rule thms t =
let
val full_msg = msg ^ ": " ^ quote rule
val assms =
if null thms then []
else [Pretty.big_list "assumptions:" (map (pretty_thm ctxt) thms)]
val concl = Pretty.big_list "proposition:" [Syntax.pretty_term ctxt t]
in Pretty.big_list full_msg (assms @ [concl]) end
fun replay_error ctxt msg rule thms t = error (Pretty.string_of (pretty_goal ctxt msg rule thms t))
fun replay_rule_error name ctxt = replay_error ctxt ("Failed to replay" ^ name ^ " proof step")
fun trace_goal ctxt rule thms t =
trace ctxt (fn () => Pretty.string_of (pretty_goal ctxt "Goal" rule thms t))
fun as_prop (t as Const (\<^const_name>\<open>Trueprop\<close>, _) $ _) = t
| as_prop t = HOLogic.mk_Trueprop t
fun dest_prop (Const (\<^const_name>\<open>Trueprop\<close>, _) $ t) = t
| dest_prop t = t
fun dest_thm thm = dest_prop (Thm.concl_of thm)
(* plug-ins *)
type abs_context = int * term Termtab.table
type 'a abstracter = term -> abs_context -> 'a * abs_context
type th_lemma_method = Proof.context -> thm list -> term -> thm
fun id_ord ((id1, _), (id2, _)) = int_ord (id1, id2)
structure Plugins = Generic_Data
(
type T =
(int * (term abstracter -> term option abstracter)) list *
th_lemma_method Symtab.table
val empty = ([], Symtab.empty)
val extend = I
fun merge ((abss1, ths1), (abss2, ths2)) = (
Ord_List.merge id_ord (abss1, abss2),
Symtab.merge (K true) (ths1, ths2))
)
fun add_arith_abstracter abs = Plugins.map (apfst (Ord_List.insert id_ord (serial (), abs)))
fun get_arith_abstracters ctxt = map snd (fst (Plugins.get (Context.Proof ctxt)))
fun add_th_lemma_method method = Plugins.map (apsnd (Symtab.update_new method))
fun get_th_lemma_method ctxt = snd (Plugins.get (Context.Proof ctxt))
fun match ctxt pat t =
(Vartab.empty, Vartab.empty)
|> Pattern.first_order_match (Proof_Context.theory_of ctxt) (pat, t)
fun gen_certify_inst sel cert ctxt thm t =
let
val inst = match ctxt (dest_thm thm) (dest_prop t)
fun cert_inst (ix, (a, b)) = ((ix, a), cert b)
in Vartab.fold (cons o cert_inst) (sel inst) [] end
fun match_instantiateT ctxt t thm =
if Term.exists_type (Term.exists_subtype Term.is_TVar) (dest_thm thm) then
Thm.instantiate (gen_certify_inst fst (Thm.ctyp_of ctxt) ctxt thm t, []) thm
else thm
fun match_instantiate ctxt t thm =
let val thm' = match_instantiateT ctxt t thm in
Thm.instantiate ([], gen_certify_inst snd (Thm.cterm_of ctxt) ctxt thm' t) thm'
end
fun discharge _ [] thm = thm
| discharge i (rule :: rules) thm = discharge (i + Thm.nprems_of rule) rules (rule RSN (i, thm))
fun by_tac ctxt thms ns ts t tac =
Goal.prove ctxt [] (map as_prop ts) (as_prop t)
(fn {context, prems} => HEADGOAL (tac context prems))
|> Drule.generalize ([], ns)
|> discharge 1 thms
fun prove ctxt t tac = by_tac ctxt [] [] [] t (K o tac)
(* abstraction *)
fun prove_abstract ctxt thms t tac f =
let
val ((prems, concl), (_, ts)) = f (1, Termtab.empty)
val ns = Termtab.fold (fn (_, v) => cons (fst (Term.dest_Free v))) ts []
in
by_tac ctxt [] ns prems concl tac
|> match_instantiate ctxt t
|> discharge 1 thms
end
fun prove_abstract' ctxt t tac f =
prove_abstract ctxt [] t tac (f #>> pair [])
fun lookup_term (_, terms) t = Termtab.lookup terms t
fun abstract_sub t f cx =
(case lookup_term cx t of
SOME v => (v, cx)
| NONE => f cx)
fun mk_fresh_free t (i, terms) =
let val v = Free ("t" ^ string_of_int i, fastype_of t)
in (v, (i + 1, Termtab.update (t, v) terms)) end
fun apply_abstracters _ [] _ cx = (NONE, cx)
| apply_abstracters abs (abstracter :: abstracters) t cx =
(case abstracter abs t cx of
(NONE, _) => apply_abstracters abs abstracters t cx
| x as (SOME _, _) => x)
fun abstract_term (t as _ $ _) = abstract_sub t (mk_fresh_free t)
| abstract_term (t as Abs _) = abstract_sub t (mk_fresh_free t)
| abstract_term t = pair t
fun abstract_bin abs f t t1 t2 = abstract_sub t (abs t1 ##>> abs t2 #>> f)
fun abstract_ter abs f t t1 t2 t3 =
abstract_sub t (abs t1 ##>> abs t2 ##>> abs t3 #>> (Scan.triple1 #> f))
fun abstract_lit (\<^const>\<open>HOL.Not\<close> $ t) = abstract_term t #>> HOLogic.mk_not
| abstract_lit t = abstract_term t
fun abstract_not abs (t as \<^const>\<open>HOL.Not\<close> $ t1) =
abstract_sub t (abs t1 #>> HOLogic.mk_not)
| abstract_not _ t = abstract_lit t
fun abstract_conj (t as \<^const>\<open>HOL.conj\<close> $ t1 $ t2) =
abstract_bin abstract_conj HOLogic.mk_conj t t1 t2
| abstract_conj t = abstract_lit t
fun abstract_disj (t as \<^const>\<open>HOL.disj\<close> $ t1 $ t2) =
abstract_bin abstract_disj HOLogic.mk_disj t t1 t2
| abstract_disj t = abstract_lit t
fun abstract_prop (t as (c as @{const If (bool)}) $ t1 $ t2 $ t3) =
abstract_ter abstract_prop (fn (t1, t2, t3) => c $ t1 $ t2 $ t3) t t1 t2 t3
| abstract_prop (t as \<^const>\<open>HOL.disj\<close> $ t1 $ t2) =
abstract_bin abstract_prop HOLogic.mk_disj t t1 t2
| abstract_prop (t as \<^const>\<open>HOL.conj\<close> $ t1 $ t2) =
abstract_bin abstract_prop HOLogic.mk_conj t t1 t2
| abstract_prop (t as \<^const>\<open>HOL.implies\<close> $ t1 $ t2) =
abstract_bin abstract_prop HOLogic.mk_imp t t1 t2
| abstract_prop (t as \<^term>\<open>HOL.eq :: bool => _\<close> $ t1 $ t2) =
abstract_bin abstract_prop HOLogic.mk_eq t t1 t2
| abstract_prop t = abstract_not abstract_prop t
fun abstract_arith ctxt u =
let
fun abs (t as (Const (\<^const_name>\<open>HOL.The\<close>, _) $ Abs (_, _, _))) =
abstract_sub t (abstract_term t)
| abs (t as (c as Const _) $ Abs (s, T, t')) =
abstract_sub t (abs t' #>> (fn u' => c $ Abs (s, T, u')))
| abs (t as (c as Const (\<^const_name>\<open>If\<close>, _)) $ t1 $ t2 $ t3) =
abstract_ter abs (fn (t1, t2, t3) => c $ t1 $ t2 $ t3) t t1 t2 t3
| abs (t as \<^const>\<open>HOL.Not\<close> $ t1) = abstract_sub t (abs t1 #>> HOLogic.mk_not)
| abs (t as \<^const>\<open>HOL.disj\<close> $ t1 $ t2) =
abstract_sub t (abs t1 ##>> abs t2 #>> HOLogic.mk_disj)
| abs (t as (c as Const (\<^const_name>\<open>uminus_class.uminus\<close>, _)) $ t1) =
abstract_sub t (abs t1 #>> (fn u => c $ u))
| abs (t as (c as Const (\<^const_name>\<open>plus_class.plus\<close>, _)) $ t1 $ t2) =
abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
| abs (t as (c as Const (\<^const_name>\<open>minus_class.minus\<close>, _)) $ t1 $ t2) =
abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
| abs (t as (c as Const (\<^const_name>\<open>times_class.times\<close>, _)) $ t1 $ t2) =
abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
| abs (t as (c as Const (\<^const_name>\<open>z3div\<close>, _)) $ t1 $ t2) =
abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
| abs (t as (c as Const (\<^const_name>\<open>z3mod\<close>, _)) $ t1 $ t2) =
abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
| abs (t as (c as Const (\<^const_name>\<open>HOL.eq\<close>, _)) $ t1 $ t2) =
abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
| abs (t as (c as Const (\<^const_name>\<open>ord_class.less\<close>, _)) $ t1 $ t2) =
abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
| abs (t as (c as Const (\<^const_name>\<open>ord_class.less_eq\<close>, _)) $ t1 $ t2) =
abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
| abs t = abstract_sub t (fn cx =>
if can HOLogic.dest_number t then (t, cx)
else
(case apply_abstracters abs (get_arith_abstracters ctxt) t cx of
(SOME u, cx') => (u, cx')
| (NONE, _) => abstract_term t cx))
in abs u end
fun abstract_unit (t as (\<^const>\<open>HOL.Not\<close> $ (\<^const>\<open>HOL.disj\<close> $ t1 $ t2))) =
abstract_sub t (abstract_unit t1 ##>> abstract_unit t2 #>>
HOLogic.mk_not o HOLogic.mk_disj)
| abstract_unit (t as (\<^const>\<open>HOL.disj\<close> $ t1 $ t2)) =
abstract_sub t (abstract_unit t1 ##>> abstract_unit t2 #>>
HOLogic.mk_disj)
| abstract_unit (t as (Const(\<^const_name>\<open>HOL.eq\<close>, _) $ t1 $ t2)) =
if fastype_of t1 = \<^typ>\<open>bool\<close> then
abstract_sub t (abstract_unit t1 ##>> abstract_unit t2 #>>
HOLogic.mk_eq)
else abstract_lit t
| abstract_unit (t as (\<^const>\<open>HOL.Not\<close> $ (Const(\<^const_name>\<open>HOL.eq\<close>, _) $ t1 $ t2))) =
if fastype_of t1 = \<^typ>\<open>bool\<close> then
abstract_sub t (abstract_unit t1 ##>> abstract_unit t2 #>>
HOLogic.mk_eq #>> HOLogic.mk_not)
else abstract_lit t
| abstract_unit (t as (\<^const>\<open>HOL.Not\<close> $ t1)) =
abstract_sub t (abstract_unit t1 #>> HOLogic.mk_not)
| abstract_unit t = abstract_lit t
fun abstract_bool (t as (@{const HOL.disj} $ t1 $ t2)) =
abstract_sub t (abstract_bool t1 ##>> abstract_bool t2 #>>
HOLogic.mk_disj)
| abstract_bool (t as (@{const HOL.conj} $ t1 $ t2)) =
abstract_sub t (abstract_bool t1 ##>> abstract_bool t2 #>>
HOLogic.mk_conj)
| abstract_bool (t as (Const(@{const_name HOL.eq}, _) $ t1 $ t2)) =
if fastype_of t1 = @{typ bool} then
abstract_sub t (abstract_bool t1 ##>> abstract_bool t2 #>>
HOLogic.mk_eq)
else abstract_lit t
| abstract_bool (t as (@{const HOL.Not} $ t1)) =
abstract_sub t (abstract_bool t1 #>> HOLogic.mk_not)
| abstract_bool (t as (@{const HOL.implies} $ t1 $ t2)) =
abstract_sub t (abstract_bool t1 ##>> abstract_bool t2 #>>
HOLogic.mk_imp)
| abstract_bool t = abstract_lit t
fun abstract_bool_shallow (t as (@{const HOL.disj} $ t1 $ t2)) =
abstract_sub t (abstract_bool_shallow t1 ##>> abstract_bool_shallow t2 #>>
HOLogic.mk_disj)
| abstract_bool_shallow (t as (@{const HOL.Not} $ t1)) =
abstract_sub t (abstract_bool_shallow t1 #>> HOLogic.mk_not)
| abstract_bool_shallow t = abstract_term t
fun abstract_bool_shallow_equivalence (t as (@{const HOL.disj} $ t1 $ t2)) =
abstract_sub t (abstract_bool_shallow_equivalence t1 ##>> abstract_bool_shallow_equivalence t2 #>>
HOLogic.mk_disj)
| abstract_bool_shallow_equivalence (t as (Const(@{const_name HOL.eq}, _) $ t1 $ t2)) =
if fastype_of t1 = @{typ bool} then
abstract_sub t (abstract_lit t1 ##>> abstract_lit t2 #>>
HOLogic.mk_eq)
else abstract_lit t
| abstract_bool_shallow_equivalence (t as (@{const HOL.Not} $ t1)) =
abstract_sub t (abstract_bool_shallow_equivalence t1 #>> HOLogic.mk_not)
| abstract_bool_shallow_equivalence t = abstract_lit t
fun abstract_arith_shallow ctxt u =
let
fun abs (t as (Const (\<^const_name>\<open>HOL.The\<close>, _) $ Abs (_, _, _))) =
abstract_sub t (abstract_term t)
| abs (t as (c as Const _) $ Abs (s, T, t')) =
abstract_sub t (abs t' #>> (fn u' => c $ Abs (s, T, u')))
| abs (t as (Const (\<^const_name>\<open>If\<close>, _)) $ _ $ _ $ _) =
abstract_sub t (abstract_term t)
| abs (t as \<^const>\<open>HOL.Not\<close> $ t1) = abstract_sub t (abs t1 #>> HOLogic.mk_not)
| abs (t as \<^const>\<open>HOL.disj\<close> $ t1 $ t2) =
abstract_sub t (abs t1 ##>> abs t2 #>> HOLogic.mk_disj)
| abs (t as (c as Const (\<^const_name>\<open>uminus_class.uminus\<close>, _)) $ t1) =
abstract_sub t (abs t1 #>> (fn u => c $ u))
| abs (t as (c as Const (\<^const_name>\<open>plus_class.plus\<close>, _)) $ t1 $ t2) =
abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
| abs (t as (c as Const (\<^const_name>\<open>minus_class.minus\<close>, _)) $ t1 $ t2) =
abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
| abs (t as (c as Const (\<^const_name>\<open>times_class.times\<close>, _)) $ t1 $ t2) =
abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
| abs (t as (Const (\<^const_name>\<open>z3div\<close>, _)) $ _ $ _) =
abstract_sub t (abstract_term t)
| abs (t as (Const (\<^const_name>\<open>z3mod\<close>, _)) $ _ $ _) =
abstract_sub t (abstract_term t)
| abs (t as (c as Const (\<^const_name>\<open>HOL.eq\<close>, _)) $ t1 $ t2) =
abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
| abs (t as (c as Const (\<^const_name>\<open>ord_class.less\<close>, _)) $ t1 $ t2) =
abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
| abs (t as (c as Const (\<^const_name>\<open>ord_class.less_eq\<close>, _)) $ t1 $ t2) =
abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
| abs t = abstract_sub t (fn cx =>
if can HOLogic.dest_number t then (t, cx)
else
(case apply_abstracters abs (get_arith_abstracters ctxt) t cx of
(SOME u, cx') => (u, cx')
| (NONE, _) => abstract_term t cx))
in abs u end
(* theory lemmas *)
fun try_provers prover_name ctxt rule [] thms t = replay_rule_error prover_name ctxt rule thms t
| try_provers prover_name ctxt rule ((name, prover) :: named_provers) thms t =
(case (trace ctxt (K ("Trying prover " ^ quote name)); try prover t) of
SOME thm => thm
| NONE => try_provers prover_name ctxt rule named_provers thms t)
(*theory-lemma*)
fun arith_th_lemma_tac ctxt prems =
Method.insert_tac ctxt prems
THEN' SELECT_GOAL (Local_Defs.unfold0_tac ctxt @{thms z3div_def z3mod_def})
THEN' Arith_Data.arith_tac ctxt
fun arith_th_lemma ctxt thms t =
prove_abstract ctxt thms t arith_th_lemma_tac (
fold_map (abstract_arith ctxt o dest_thm) thms ##>>
abstract_arith ctxt (dest_prop t))
fun arith_th_lemma_tac_with_wo ctxt prems =
Method.insert_tac ctxt prems
THEN' SELECT_GOAL (Local_Defs.unfold0_tac ctxt @{thms z3div_def z3mod_def int_distrib})
THEN' Simplifier.asm_full_simp_tac
(empty_simpset ctxt addsimprocs [(*@{simproc linordered_ring_strict_eq_cancel_factor_poly},
@{simproc linordered_ring_strict_le_cancel_factor_poly},
@{simproc linordered_ring_strict_less_cancel_factor_poly},
@{simproc nat_eq_cancel_factor_poly},
@{simproc nat_le_cancel_factor_poly},
@{simproc nat_less_cancel_factor_poly}*)
THEN' (fn i => TRY (Arith_Data.arith_tac ctxt i))
fun arith_th_lemma_wo ctxt thms t =
prove_abstract ctxt thms t arith_th_lemma_tac_with_wo (
fold_map (abstract_arith ctxt o dest_thm) thms ##>>
abstract_arith ctxt (dest_prop t))
fun arith_th_lemma_wo_shallow ctxt thms t =
prove_abstract ctxt thms t arith_th_lemma_tac_with_wo (
fold_map (abstract_arith_shallow ctxt o dest_thm) thms ##>>
abstract_arith_shallow ctxt (dest_prop t))
val _ = Theory.setup (Context.theory_map (add_th_lemma_method ("arith", arith_th_lemma)))
(* congruence *)
fun certify_prop ctxt t = Thm.cterm_of ctxt (as_prop t)
fun ctac ctxt prems i st = st |> (
resolve_tac ctxt (@{thm refl} :: prems) i
ORELSE (cong_tac ctxt i THEN ctac ctxt prems (i + 1) THEN ctac ctxt prems i))
fun cong_basic ctxt thms t =
let val st = Thm.trivial (certify_prop ctxt t)
in
(case Seq.pull (ctac ctxt thms 1 st) of
SOME (thm, _) => thm
| NONE => raise THM ("cong", 0, thms @ [st]))
end
val cong_dest_rules = @{lemma
"(\ P \ Q) \ (P \ \ Q) \ P = Q"
"(P \ \ Q) \ (\ P \ Q) \ P = Q"
by fast+}
fun cong_full_core_tac ctxt =
eresolve_tac ctxt @{thms subst}
THEN' resolve_tac ctxt @{thms refl}
ORELSE' Classical.fast_tac ctxt
fun cong_full ctxt thms t = prove ctxt t (fn ctxt' =>
Method.insert_tac ctxt thms
THEN' (cong_full_core_tac ctxt'
ORELSE' dresolve_tac ctxt cong_dest_rules
THEN' cong_full_core_tac ctxt'))
local
val reorder_for_simp = try (fn thm =>
let val t = Thm.prop_of (@{thm eq_reflection} OF [thm])
val thm =
(case Logic.dest_equals t of
(t1, t2) =>
if t1 aconv t2 then raise TERM("identical terms", [t1, t2])
else if Term.size_of_term t1 > Term.size_of_term t2 then @{thm eq_reflection} OF [thm]
else @{thm eq_reflection} OF [@{thm sym} OF [thm]])
handle TERM("dest_equals", _) => @{thm eq_reflection} OF [thm]
in thm end)
in
fun cong_unfolding_trivial ctxt thms t =
prove ctxt t (fn _ =>
EVERY' (map (fn thm => K (unfold_tac ctxt [thm])) ((map_filter reorder_for_simp thms)))
THEN' (fn i => TRY (resolve_tac ctxt @{thms refl} i)))
fun cong_unfolding_first ctxt thms t =
let val ctxt =
ctxt
|> empty_simpset
|> put_simpset HOL_basic_ss
|> (fn ctxt => ctxt addsimps @{thms not_not eq_commute})
in
prove ctxt t (fn _ =>
EVERY' (map (fn thm => K (unfold_tac ctxt [thm])) ((map_filter reorder_for_simp thms)))
THEN' Method.insert_tac ctxt thms
THEN' (full_simp_tac ctxt)
THEN' K (ALLGOALS (K (Clasimp.auto_tac ctxt))))
end
end
fun arith_rewrite_tac ctxt _ =
let val backup_tac = Arith_Data.arith_tac ctxt ORELSE' Clasimp.force_tac ctxt in
(TRY o Simplifier.simp_tac ctxt) THEN_ALL_NEW backup_tac
ORELSE' backup_tac
end
fun abstract_eq f (Const (\<^const_name>\<open>HOL.eq\<close>, _) $ t1 $ t2) =
f t1 ##>> f t2 #>> HOLogic.mk_eq
| abstract_eq _ t = abstract_term t
fun abstract_neq f (Const (\<^const_name>\<open>HOL.eq\<close>, _) $ t1 $ t2) =
f t1 ##>> f t2 #>> HOLogic.mk_eq
| abstract_neq f (Const (\<^const_name>\<open>HOL.Not\<close>, _) $ (Const (\<^const_name>\<open>HOL.eq\<close>, _) $ t1 $ t2)) =
f t1 ##>> f t2 #>> HOLogic.mk_eq #>> curry (op $) HOLogic.Not
| abstract_neq f (Const (\<^const_name>\<open>HOL.disj\<close>, _) $ t1 $ t2) =
f t1 ##>> f t2 #>> HOLogic.mk_disj
| abstract_neq _ t = abstract_term t
fun prove_arith_rewrite abstracter ctxt t =
prove_abstract' ctxt t arith_rewrite_tac (
abstracter (abstract_arith ctxt) (dest_prop t))
fun prop_tac ctxt prems =
Method.insert_tac ctxt prems
THEN' SUBGOAL (fn (prop, i) =>
if Term.size_of_term prop > 100 then SAT.satx_tac ctxt i
else (Classical.fast_tac ctxt ORELSE' Clasimp.force_tac ctxt) i)
end;
¤ Dauer der Verarbeitung: 0.83 Sekunden
(vorverarbeitet)
¤
|
Haftungshinweis
Die Informationen auf dieser Webseite wurden
nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit,
noch Qualität der bereit gestellten Informationen zugesichert.
Bemerkung:
Die farbliche Syntaxdarstellung ist noch experimentell.
|
