(* Title: Pure/goal.ML
ID: $Id$
Author: Makarius and Lawrence C Paulson
Goals in tactical theorem proving.
*)
signature BASIC_GOAL =
sig
val SELECT_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: thm -> thm
val conclude: thm -> thm
val finish: thm -> thm
val norm_result: thm -> thm
val close_result: thm -> thm
val prove_raw: cterm list -> cterm -> (thm list -> tactic) -> thm
val prove_multi: Proof.context -> string list -> term list -> term list ->
({prems: thm list, context: Proof.context} -> tactic) -> thm list
val prove: Proof.context -> string list -> term list -> term ->
({prems: thm list, context: Proof.context} -> tactic) -> thm
val prove_global: theory -> string list -> term list -> term -> (thm list -> tactic) -> thm
val extract: int -> int -> thm -> thm Seq.seq
val retrofit: int -> int -> thm -> thm -> thm Seq.seq
val conjunction_tac: int -> tactic
val precise_conjunction_tac: int -> int -> tactic
val asm_rewrite_goal_tac: bool * bool * bool -> (simpset -> tactic) -> simpset -> int -> tactic
val rewrite_goal_tac: thm list -> int -> tactic
val norm_hhf_tac: int -> tactic
val compose_hhf: thm -> int -> thm -> thm Seq.seq
val compose_hhf_tac: thm -> int -> tactic
val comp_hhf: thm -> thm -> thm
end;
structure Goal: GOAL =
struct
(** goals **)
(*
-------- (init)
C ==> #C
*)
val init =
let val A = #1 (Drule.dest_implies (Thm.cprop_of Drule.protectI))
in fn C => Thm.instantiate ([], [(A, C)]) Drule.protectI end;
(*
C
--- (protect)
#C
*)
fun protect th = th COMP_INCR Drule.protectI;
(*
A ==> ... ==> #C
---------------- (conclude)
A ==> ... ==> C
*)
fun conclude th =
(case SINGLE (Thm.compose_no_flatten false (th, Thm.nprems_of th) 1)
(Drule.incr_indexes th Drule.protectD) of
SOME th' => th'
| NONE => raise THM ("Failed to conclude goal", 0, [th]));
(*
#C
--- (finish)
C
*)
fun finish th =
(case Thm.nprems_of th of
0 => conclude th
| n => raise THM ("Proof failed.\n" ^
Pretty.string_of (Pretty.chunks (Display.pretty_goals n th)) ^
("\n" ^ string_of_int n ^ " unsolved goal(s)!"), 0, [th]));
(** results **)
(* normal form *)
val norm_result =
Drule.flexflex_unique
#> MetaSimplifier.norm_hhf_protect
#> Thm.strip_shyps
#> Drule.zero_var_indexes;
val close_result =
Thm.compress
#> Drule.close_derivation;
(** tactical theorem proving **)
(* prove_raw -- no checks, no normalization of result! *)
fun prove_raw casms cprop tac =
(case SINGLE (tac (map Assumption.assume casms)) (init cprop) of
SOME th => Drule.implies_intr_list casms (finish th)
| NONE => error "Tactic failed.");
(* prove_multi *)
fun prove_multi ctxt xs asms props tac =
let
val thy = ProofContext.theory_of ctxt;
val string_of_term = Sign.string_of_term thy;
fun err msg = cat_error msg
("The error(s) above occurred for the goal statement:\n" ^
string_of_term (Logic.list_implies (asms, Logic.mk_conjunction_list props)));
fun cert_safe t = Thm.cterm_of thy (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_internal (asms @ props)
|> Assumption.add_assumes casms;
val goal = init (Conjunction.mk_conjunction_list cprops);
val res =
(case SINGLE (tac {prems = prems, context = ctxt'}) goal of
NONE => err "Tactic failed."
| SOME res => res);
val [results] = Conjunction.elim_precise [length props] (finish res)
handle THM (msg, _, _) => err msg;
val _ = Unify.matches_list thy (map Thm.term_of cprops) (map Thm.prop_of results)
orelse err ("Proved a different theorem: " ^ string_of_term (Thm.prop_of res));
in
results
|> map (Assumption.export false ctxt' ctxt)
|> Variable.export ctxt' ctxt
|> map Drule.zero_var_indexes
end;
(* prove *)
fun prove ctxt xs asms prop tac = hd (prove_multi ctxt xs asms [prop] tac);
fun prove_global thy xs asms prop tac =
Drule.standard (prove (ProofContext.init thy) xs asms prop (fn {prems, ...} => tac prems));
(** goal structure **)
(* nested goals *)
fun extract i n st =
(if i < 1 orelse n < 1 orelse i + n - 1 > Thm.nprems_of st then Seq.empty
else if n = 1 then Seq.single (Thm.cprem_of st i)
else Seq.single (foldr1 Conjunction.mk_conjunction (map (Thm.cprem_of st) (i upto i + n - 1))))
|> Seq.map (Thm.adjust_maxidx_cterm ~1 #> init);
fun retrofit i n st' st =
(if n = 1 then st
else st |> Drule.rotate_prems (i - 1) |> Conjunction.uncurry n |> Drule.rotate_prems (1 - i))
|> Thm.compose_no_flatten false (conclude st', Thm.nprems_of st') i;
fun SELECT_GOAL tac i st =
if Thm.nprems_of st = 1 andalso i = 1 then tac st
else Seq.lifts (retrofit i 1) (Seq.maps tac (extract i 1 st)) st;
(* multiple goals *)
val conj_tac = SUBGOAL (fn (goal, i) =>
if can Logic.dest_conjunction goal then rtac Conjunction.conjunctionI i
else no_tac);
val conjunction_tac = TRY o REPEAT_ALL_NEW conj_tac;
val precise_conjunction_tac =
let
fun tac 0 i = eq_assume_tac i
| tac 1 i = SUBGOAL (K all_tac) i
| tac n i = conj_tac i THEN TRY (fn st => tac (n - 1) (i + 1) st);
in TRY oo tac end;
fun CONJUNCTS tac =
SELECT_GOAL (conjunction_tac 1
THEN tac
THEN PRIMITIVE (Conjunction.uncurry ~1));
fun PRECISE_CONJUNCTS n tac =
SELECT_GOAL (precise_conjunction_tac n 1
THEN tac
THEN PRIMITIVE (Conjunction.uncurry ~1));
(* rewriting *)
(*Rewrite subgoal i only. SELECT_GOAL avoids inefficiencies in goals_conv.*)
fun asm_rewrite_goal_tac mode prover_tac ss =
SELECT_GOAL
(PRIMITIVE (MetaSimplifier.rewrite_goal_rule mode (SINGLE o prover_tac) ss 1));
fun rewrite_goal_tac rews =
let val ss = MetaSimplifier.empty_ss addsimps rews in
fn i => fn st => asm_rewrite_goal_tac (true, false, false) (K no_tac)
(MetaSimplifier.theory_context (Thm.theory_of_thm st) ss) i st
end;
(* hhf normal form *)
val norm_hhf_tac =
rtac 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 [Drule.norm_hhf_eq] i);
fun compose_hhf tha i thb =
Thm.bicompose false (false, Drule.lift_all (Thm.cprem_of thb i) tha, 0) i thb;
fun compose_hhf_tac th i = PRIMSEQ (compose_hhf th i);
fun comp_hhf tha thb =
(case Seq.chop 2 (compose_hhf tha 1 thb) of
([th], _) => th
| ([], _) => raise THM ("comp_hhf: no unifiers", 1, [tha, thb])
| _ => raise THM ("comp_hhf: multiple unifiers", 1, [tha, thb]));
end;
structure BasicGoal: BASIC_GOAL = Goal;
open BasicGoal;