(* Title: HOL/Decision_Procs/ferrack_tac.ML
Author: Amine Chaieb, TU Muenchen
*)
signature FERRACK_TAC =
sig
val linr_tac: Proof.context -> bool -> int -> tactic
end
structure Ferrack_Tac: FERRACK_TAC =
struct
val ferrack_ss = let val ths = [@{thm real_of_int_inject}, @{thm real_of_int_less_iff},
@{thm real_of_int_le_iff}]
in @{context} delsimps ths addsimps (map (fn th => th RS sym) ths)
end |> simpset_of;
val binarith = @{thms arith_simps}
val comp_arith = binarith @ @{thms simp_thms}
fun prepare_for_linr q fm =
let
val ps = Logic.strip_params fm
val hs = map HOLogic.dest_Trueprop (Logic.strip_assums_hyp fm)
val c = HOLogic.dest_Trueprop (Logic.strip_assums_concl fm)
fun mk_all ((s, T), (P,n)) =
if Term.is_dependent P then
(HOLogic.all_const T $ Abs (s, T, P), n)
else (incr_boundvars ~1 P, n-1)
fun mk_all2 (v, t) = HOLogic.all_const (fastype_of v) $ lambda v t;
val rhs = hs
(* val (rhs,irhs) = List.partition (relevant (rev ps)) hs *)
val np = length ps
val (fm',np) = List.foldr (fn ((x, T), (fm,n)) => mk_all ((x, T), (fm,n)))
(List.foldr HOLogic.mk_imp c rhs, np) ps
val (vs, _) = List.partition (fn t => q orelse (type_of t) = HOLogic.natT)
(Misc_Legacy.term_frees fm' @ Misc_Legacy.term_vars fm');
val fm2 = List.foldr mk_all2 fm' vs
in (fm2, np + length vs, length rhs) end;
(*Object quantifier to meta --*)
fun spec_step n th = if (n=0) then th else (spec_step (n-1) th) RS spec ;
(* object implication to meta---*)
fun mp_step n th = if (n=0) then th else (mp_step (n-1) th) RS mp;
fun linr_tac ctxt q =
Object_Logic.atomize_prems_tac ctxt
THEN' (REPEAT_DETERM o split_tac ctxt [@{thm split_min}, @{thm split_max}, @{thm abs_split}])
THEN' SUBGOAL (fn (g, i) =>
let
val thy = Proof_Context.theory_of ctxt
(* Transform the term*)
val (t,np,nh) = prepare_for_linr q g
(* Some simpsets for dealing with mod div abs and nat*)
val simpset0 = put_simpset HOL_basic_ss ctxt addsimps comp_arith
val ct = Thm.global_cterm_of thy (HOLogic.mk_Trueprop t)
(* Theorem for the nat --> int transformation *)
val pre_thm = Seq.hd (EVERY
[simp_tac simpset0 1,
TRY (simp_tac (put_simpset ferrack_ss ctxt) 1)]
(Thm.trivial ct))
fun assm_tac i = REPEAT_DETERM_N nh (assume_tac ctxt i)
(* The result of the quantifier elimination *)
val (th, tac) = case Thm.prop_of pre_thm of
Const (@{const_name Pure.imp}, _) $ (Const (@{const_name Trueprop}, _) $ t1) $ _ =>
let val pth = linr_oracle (ctxt, Envir.eta_long [] t1)
in
((pth RS iffD2) RS pre_thm,
assm_tac (i + 1) THEN (if q then I else TRY) (rtac TrueI i))
end
| _ => (pre_thm, assm_tac i)
in rtac ((mp_step nh o spec_step np) th) i THEN tac end);
end