(* Title: Pure/goal.ML
Author: Makarius
Goals in tactical theorem proving, with support for forked proofs.
*)
signature BASIC_GOAL =
sig
val quick_and_dirty: bool Config.T
val parallel_proofs: int Unsynchronized.ref
val SELECT_GOAL: tactic -> int -> tactic
val PREFER_GOAL: tactic -> int -> tactic
val CONJUNCTS: tactic -> int -> tactic
val PRECISE_CONJUNCTS: int -> tactic -> int -> tactic
end;
signature GOAL =
sig
include BASIC_GOAL
val init: cterm -> thm
val protect: int -> thm -> thm
val conclude: thm -> thm
val check_finished: Proof.context -> thm -> thm
val finish: Proof.context -> thm -> thm
val norm_result: Proof.context -> thm -> thm
val skip_proofs_enabled: unit -> bool
val future_enabled: int -> bool
val future_enabled_timing: Time.time -> bool
val future_result: Proof.context -> thm future -> term -> thm
val prove_internal: Proof.context -> cterm list -> cterm -> (thm list -> tactic) -> thm
val is_schematic: term -> bool
val prove_common: Proof.context -> int option -> string list -> term list -> term list ->
({prems: thm list, context: Proof.context} -> tactic) -> thm list
val prove_future: Proof.context -> string list -> term list -> term ->
({prems: thm list, context: Proof.context} -> tactic) -> thm
val prove: Proof.context -> string list -> term list -> term ->
({prems: thm list, context: Proof.context} -> tactic) -> thm
val prove_global_future: theory -> string list -> term list -> term ->
({prems: thm list, context: Proof.context} -> tactic) -> thm
val prove_global: theory -> string list -> term list -> term ->
({prems: thm list, context: Proof.context} -> tactic) -> thm
val quick_and_dirty_raw: Config.raw
val prove_sorry: Proof.context -> string list -> term list -> term ->
({prems: thm list, context: Proof.context} -> tactic) -> thm
val prove_sorry_global: theory -> string list -> term list -> term ->
({prems: thm list, context: Proof.context} -> tactic) -> thm
val restrict: int -> int -> thm -> thm
val unrestrict: int -> thm -> thm
val conjunction_tac: int -> tactic
val precise_conjunction_tac: int -> int -> tactic
val recover_conjunction_tac: tactic
val norm_hhf_tac: Proof.context -> int -> tactic
val assume_rule_tac: Proof.context -> int -> tactic
end;
structure Goal: GOAL =
struct
(** goals **)
(*
-------- (init)
C ==> #C
*)
fun init C = Thm.instantiate ([], [((("A", 0), propT), C)]) Drule.protectI;
(*
A1 ==> ... ==> An ==> C
------------------------ (protect n)
A1 ==> ... ==> An ==> #C
*)
fun protect n th = Drule.comp_no_flatten (th, n) 1 Drule.protectI;
(*
A ==> ... ==> #C
---------------- (conclude)
A ==> ... ==> C
*)
fun conclude th = Drule.comp_no_flatten (th, Thm.nprems_of th) 1 Drule.protectD;
(*
#C
--- (finish)
C
*)
fun check_finished ctxt th =
if Thm.no_prems th then th
else
raise THM ("Proof failed.\n" ^ Pretty.string_of (Goal_Display.pretty_goal ctxt th), 0, [th]);
fun finish ctxt = check_finished ctxt #> conclude;
(** results **)
(* normal form *)
fun norm_result ctxt =
Drule.flexflex_unique (SOME ctxt)
#> Raw_Simplifier.norm_hhf_protect ctxt
#> Thm.strip_shyps
#> Drule.zero_var_indexes;
(* scheduling parameters *)
fun skip_proofs_enabled () =
let val skip = Options.default_bool "skip_proofs" in
if Proofterm.proofs_enabled () andalso skip then
(warning "Proof terms enabled -- cannot skip proofs"; false)
else skip
end;
val parallel_proofs = Unsynchronized.ref 1;
fun future_enabled n =
Multithreading.enabled () andalso ! parallel_proofs >= n andalso
is_some (Future.worker_task ());
fun future_enabled_timing t =
future_enabled 1 andalso
Time.toReal t >= Options.default_real "parallel_subproofs_threshold";
(* future_result *)
fun future_result ctxt result prop =
let
val assms = Assumption.all_assms_of ctxt;
val As = map Thm.term_of assms;
val xs = map Free (fold Term.add_frees (prop :: As) []);
val fixes = map (Thm.cterm_of ctxt) xs;
val tfrees = fold Term.add_tfrees (prop :: As) [];
val instT = map (fn (a, S) => (((a, 0), S), Thm.ctyp_of ctxt (TFree (a, S)))) tfrees;
val global_prop =
Logic.varify_types_global (fold_rev Logic.all xs (Logic.list_implies (As, prop)))
|> Thm.cterm_of ctxt
|> Thm.weaken_sorts' ctxt;
val global_result = result |> Future.map
(Drule.flexflex_unique (SOME ctxt) #>
Thm.adjust_maxidx_thm ~1 #>
Drule.implies_intr_list assms #>
Drule.forall_intr_list fixes #>
Thm.generalize (map #1 tfrees, []) 0 #>
Thm.strip_shyps);
val local_result =
Thm.future global_result global_prop
|> Thm.close_derivation
|> Thm.instantiate (instT, [])
|> Drule.forall_elim_list fixes
|> fold (Thm.elim_implies o Thm.assume) assms;
in local_result end;
(** tactical theorem proving **)
(* prove_internal -- minimal checks, no normalization of result! *)
fun prove_internal ctxt casms cprop tac =
(case SINGLE (tac (map (Assumption.assume ctxt) casms)) (init cprop) of
SOME th => Drule.implies_intr_list casms (finish ctxt th)
| NONE => error "Tactic failed");
(* prove variations *)
fun is_schematic t =
Term.exists_subterm Term.is_Var t orelse
Term.exists_type (Term.exists_subtype Term.is_TVar) t;
fun prove_common ctxt fork_pri xs asms props tac =
let
val thy = Proof_Context.theory_of ctxt;
val schematic = exists is_schematic props;
val immediate = is_none fork_pri;
val future = future_enabled 1;
val skip = not immediate andalso not schematic andalso future andalso skip_proofs_enabled ();
val pos = Position.thread_data ();
fun err msg =
cat_error msg
("The error(s) above occurred for the goal statement" ^ Position.here pos ^ ":\n" ^
Syntax.string_of_term ctxt (Logic.list_implies (asms, Logic.mk_conjunction_list props)));
fun cert_safe t = Thm.cterm_of ctxt (Envir.beta_norm (Term.no_dummy_patterns t))
handle TERM (msg, _) => err msg | TYPE (msg, _, _) => err msg;
val casms = map cert_safe asms;
val cprops = map cert_safe props;
val (prems, ctxt') = ctxt
|> Variable.add_fixes_direct xs
|> fold Variable.declare_term (asms @ props)
|> Assumption.add_assumes casms
||> Variable.set_body true;
val stmt = Thm.weaken_sorts' ctxt' (Conjunction.mk_conjunction_balanced cprops);
fun tac' args st =
if skip then ALLGOALS (Skip_Proof.cheat_tac ctxt) st before Skip_Proof.report ctxt
else tac args st;
fun result () =
(case SINGLE (tac' {prems = prems, context = ctxt'}) (init stmt) of
NONE => err "Tactic failed"
| SOME st =>
let
val _ =
Context.subthy_id (Thm.theory_id st, Context.theory_id thy) orelse
err "Bad background theory of goal state";
val res =
(finish ctxt' st
|> Drule.flexflex_unique (SOME ctxt')
|> Thm.check_shyps ctxt'
|> Thm.check_hyps (Context.Proof ctxt'))
handle THM (msg, _, _) => err msg | ERROR msg => err msg;
in
if Unify.matches_list (Context.Proof ctxt') [Thm.term_of stmt] [Thm.prop_of res]
then res
else err ("Proved a different theorem: " ^ Syntax.string_of_term ctxt' (Thm.prop_of res))
end);
val res =
if immediate orelse schematic orelse not future orelse skip then result ()
else
future_result ctxt'
(Execution.fork {name = "Goal.prove", pos = Position.thread_data (), pri = the fork_pri}
result)
(Thm.term_of stmt);
in
res
|> Thm.close_derivation
|> Conjunction.elim_balanced (length props)
|> map (Assumption.export false ctxt' ctxt)
|> Variable.export ctxt' ctxt
|> map Drule.zero_var_indexes
end;
fun prove_future_pri ctxt pri xs asms prop tac =
hd (prove_common ctxt (SOME pri) xs asms [prop] tac);
fun prove_future ctxt = prove_future_pri ctxt ~1;
fun prove ctxt xs asms prop tac = hd (prove_common ctxt NONE xs asms [prop] tac);
fun prove_global_future thy xs asms prop tac =
Drule.export_without_context (prove_future (Proof_Context.init_global thy) xs asms prop tac);
fun prove_global thy xs asms prop tac =
Drule.export_without_context (prove (Proof_Context.init_global thy) xs asms prop tac);
(* skip proofs *)
val quick_and_dirty_raw = Config.declare_option ("quick_and_dirty", \<^here>);
val quick_and_dirty = Config.bool quick_and_dirty_raw;
fun prove_sorry ctxt xs asms prop tac =
if Config.get ctxt quick_and_dirty then
prove ctxt xs asms prop (fn _ => ALLGOALS (Skip_Proof.cheat_tac ctxt))
else (if future_enabled 1 then prove_future_pri ctxt ~2 else prove ctxt) xs asms prop tac;
fun prove_sorry_global thy xs asms prop tac =
Drule.export_without_context
(prove_sorry (Proof_Context.init_global thy) xs asms prop tac);
(** goal structure **)
(* rearrange subgoals *)
fun restrict i n st =
if i < 1 orelse n < 1 orelse i + n - 1 > Thm.nprems_of st
then raise THM ("Goal.restrict", i, [st])
else rotate_prems (i - 1) st |> protect n;
fun unrestrict i = conclude #> rotate_prems (1 - i);
(*with structural marker*)
fun SELECT_GOAL tac i st =
if Thm.nprems_of st = 1 andalso i = 1 then tac st
else (PRIMITIVE (restrict i 1) THEN tac THEN PRIMITIVE (unrestrict i)) st;
(*without structural marker*)
fun PREFER_GOAL tac i st =
if i < 1 orelse i > Thm.nprems_of st then Seq.empty
else (PRIMITIVE (rotate_prems (i - 1)) THEN tac THEN PRIMITIVE (rotate_prems (1 - i))) st;
(* multiple goals *)
fun precise_conjunction_tac 0 i = eq_assume_tac i
| precise_conjunction_tac 1 i = SUBGOAL (K all_tac) i
| precise_conjunction_tac n i = PRIMITIVE (Drule.with_subgoal i (Conjunction.curry_balanced n));
val adhoc_conjunction_tac = REPEAT_ALL_NEW
(SUBGOAL (fn (goal, i) =>
if can Logic.dest_conjunction goal then resolve0_tac [Conjunction.conjunctionI] i
else no_tac));
val conjunction_tac = SUBGOAL (fn (goal, i) =>
precise_conjunction_tac (length (Logic.dest_conjunctions goal)) i ORELSE
TRY (adhoc_conjunction_tac i));
val recover_conjunction_tac = PRIMITIVE (fn th =>
Conjunction.uncurry_balanced (Thm.nprems_of th) th);
fun PRECISE_CONJUNCTS n tac =
SELECT_GOAL (precise_conjunction_tac n 1
THEN tac
THEN recover_conjunction_tac);
fun CONJUNCTS tac =
SELECT_GOAL (conjunction_tac 1
THEN tac
THEN recover_conjunction_tac);
(* hhf normal form *)
fun norm_hhf_tac ctxt =
resolve_tac ctxt [Drule.asm_rl] (*cheap approximation -- thanks to builtin Logic.flatten_params*)
THEN' SUBGOAL (fn (t, i) =>
if Drule.is_norm_hhf t then all_tac
else rewrite_goal_tac ctxt Drule.norm_hhf_eqs i);
(* non-atomic goal assumptions *)
fun non_atomic (Const ("Pure.imp", _) $ _ $ _) = true
| non_atomic (Const ("Pure.all", _) $ _) = true
| non_atomic _ = false;
fun assume_rule_tac ctxt = norm_hhf_tac ctxt THEN' CSUBGOAL (fn (goal, i) =>
let
val ((_, goal'), ctxt') = Variable.focus_cterm NONE goal ctxt;
val goal'' = Drule.cterm_rule (singleton (Variable.export ctxt' ctxt)) goal';
val Rs = filter (non_atomic o Thm.term_of) (Drule.strip_imp_prems goal'');
val tacs = Rs |> map (fn R =>
eresolve_tac ctxt [Raw_Simplifier.norm_hhf ctxt (Thm.trivial R)] THEN_ALL_NEW assume_tac ctxt);
in fold_rev (curry op APPEND') tacs (K no_tac) i end);
end;
structure Basic_Goal: BASIC_GOAL = Goal;
open Basic_Goal;