Reimplemented algebra method; now controlled by attribute.
(* 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
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_hhf: thm -> thm
val norm_hhf_protect: thm -> thm
val compose_hhf: thm -> int -> thm -> thm Seq.seq
val compose_hhf_tac: thm -> int -> tactic
val comp_hhf: thm -> thm -> thm
val prove_multi: Context.proof -> string list -> term list -> term list ->
(thm list -> tactic) -> thm list
val prove: Context.proof -> string list -> term list -> term -> (thm list -> tactic) -> thm
val prove_global: theory -> string list -> term list -> term -> (thm list -> tactic) -> thm
val prove_raw: cterm list -> cterm -> (thm list -> tactic) -> thm
val extract: int -> int -> thm -> thm Seq.seq
val retrofit: int -> int -> thm -> thm -> thm Seq.seq
end;
structure Goal: GOAL =
struct
(** goals **)
(*
-------- (init)
C ==> #C
*)
fun init ct = Drule.instantiate' [] [SOME ct] Drule.protectI;
(*
C
--- (protect)
#C
*)
fun protect th = th COMP Drule.incr_indexes th 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 **)
(* HHF normal form: !! before ==>, outermost !! generalized *)
local
fun gen_norm_hhf ss =
(not o Drule.is_norm_hhf o Thm.prop_of) ?
Drule.fconv_rule (MetaSimplifier.rewrite_cterm (true, false, false) (K (K NONE)) ss)
#> Thm.adjust_maxidx_thm
#> Drule.gen_all;
val ss =
MetaSimplifier.theory_context ProtoPure.thy MetaSimplifier.empty_ss
addsimps [Drule.norm_hhf_eq];
in
val norm_hhf = gen_norm_hhf ss;
val norm_hhf_protect = gen_norm_hhf (ss addeqcongs [Drule.protect_cong]);
end;
(* composition of normal results *)
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]));
(** tactical theorem proving **)
(* prove_multi *)
fun prove_multi ctxt xs asms props tac =
let
val thy = Context.theory_of_proof ctxt;
val string_of_term = Sign.string_of_term thy;
val prop = Logic.mk_conjunction_list props;
val statement = Logic.list_implies (asms, prop);
fun err msg = cat_error msg
("The error(s) above occurred for the goal statement:\n" ^ string_of_term statement);
fun cert_safe t = Thm.cterm_of thy (Envir.beta_norm t)
handle TERM (msg, _) => err msg | TYPE (msg, _, _) => err msg;
val _ = cert_safe statement;
val _ = Term.no_dummy_patterns statement handle TERM (msg, _) => err msg;
val casms = map cert_safe asms;
val prems = map (norm_hhf o Thm.assume) casms;
val ctxt' = ctxt
|> Variable.set_body false
|> (snd o Variable.add_fixes xs)
|> fold Variable.declare_internal (asms @ props);
val res =
(case SINGLE (tac prems) (init (cert_safe prop)) 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 o cert_safe) props) (map Thm.prop_of results)
orelse err ("Proved a different theorem: " ^ string_of_term (Thm.prop_of res));
in
results
|> map (Drule.implies_intr_list casms)
|> Variable.export ctxt' ctxt
|> map (norm_hhf #> 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 (Context.init_proof thy) xs asms prop tac);
(* prove_raw -- no checks, no normalization of result! *)
fun prove_raw casms cprop tac =
(case SINGLE (tac (map (norm_hhf o Thm.assume) casms)) (init cprop) of
SOME th => Drule.implies_intr_list casms (finish th)
| NONE => error "Tactic failed.");
(** local goal states **)
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 #> 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;
end;
structure BasicGoal: BASIC_GOAL = Goal;
open BasicGoal;