src/HOL/arith_data.ML
author webertj
Mon, 31 Jul 2006 20:56:49 +0200
changeset 20271 e76e77e0d615
parent 20268 1fe9aed8fcac
child 20276 d94dc40673b1
permissions -rw-r--r--
fixed a bug in function poly: decomposition of products
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(*  Title:      HOL/arith_data.ML
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    ID:         $Id$
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    Author:     Markus Wenzel, Stefan Berghofer and Tobias Nipkow
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Various arithmetic proof procedures.
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*)
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(*---------------------------------------------------------------------------*)
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(* 1. Cancellation of common terms                                           *)
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(*---------------------------------------------------------------------------*)
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structure NatArithUtils =
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struct
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(** abstract syntax of structure nat: 0, Suc, + **)
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(* mk_sum, mk_norm_sum *)
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val one = HOLogic.mk_nat 1;
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val mk_plus = HOLogic.mk_binop "HOL.plus";
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fun mk_sum [] = HOLogic.zero
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  | mk_sum [t] = t
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  | mk_sum (t :: ts) = mk_plus (t, mk_sum ts);
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(*normal form of sums: Suc (... (Suc (a + (b + ...))))*)
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fun mk_norm_sum ts =
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  let val (ones, sums) = List.partition (equal one) ts in
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    funpow (length ones) HOLogic.mk_Suc (mk_sum sums)
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  end;
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(* dest_sum *)
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val dest_plus = HOLogic.dest_bin "HOL.plus" HOLogic.natT;
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fun dest_sum tm =
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  if HOLogic.is_zero tm then []
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  else
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    (case try HOLogic.dest_Suc tm of
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      SOME t => one :: dest_sum t
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    | NONE =>
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        (case try dest_plus tm of
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          SOME (t, u) => dest_sum t @ dest_sum u
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        | NONE => [tm]));
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(** generic proof tools **)
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(* prove conversions *)
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fun prove_conv expand_tac norm_tac ss tu =  (* FIXME avoid standard *)
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  mk_meta_eq (standard (Goal.prove (Simplifier.the_context ss) [] []
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      (HOLogic.mk_Trueprop (HOLogic.mk_eq tu))
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    (K (EVERY [expand_tac, norm_tac ss]))));
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val subst_equals = prove_goal HOL.thy "[| t = s; u = t |] ==> u = s"
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  (fn prems => [cut_facts_tac prems 1, SIMPSET' asm_simp_tac 1]);
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(* rewriting *)
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fun simp_all_tac rules =
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  let val ss0 = HOL_ss addsimps rules
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  in fn ss => ALLGOALS (simp_tac (Simplifier.inherit_context ss ss0)) end;
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val add_rules = [add_Suc, add_Suc_right, add_0, add_0_right];
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val mult_rules = [mult_Suc, mult_Suc_right, mult_0, mult_0_right];
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fun prep_simproc (name, pats, proc) =
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  Simplifier.simproc (the_context ()) name pats proc;
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end;  (* NatArithUtils *)
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signature ARITH_DATA =
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sig
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  val nat_cancel_sums_add: simproc list
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  val nat_cancel_sums: simproc list
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end;
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structure ArithData: ARITH_DATA =
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struct
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open NatArithUtils;
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(** cancel common summands **)
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structure Sum =
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struct
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  val mk_sum = mk_norm_sum;
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  val dest_sum = dest_sum;
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  val prove_conv = prove_conv;
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  val norm_tac1 = simp_all_tac add_rules;
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  val norm_tac2 = simp_all_tac add_ac;
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  fun norm_tac ss = norm_tac1 ss THEN norm_tac2 ss;
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end;
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fun gen_uncancel_tac rule ct =
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  rtac (instantiate' [] [NONE, SOME ct] (rule RS subst_equals)) 1;
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(* nat eq *)
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structure EqCancelSums = CancelSumsFun
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(struct
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  open Sum;
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  val mk_bal = HOLogic.mk_eq;
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  val dest_bal = HOLogic.dest_bin "op =" HOLogic.natT;
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  val uncancel_tac = gen_uncancel_tac nat_add_left_cancel;
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end);
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(* nat less *)
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structure LessCancelSums = CancelSumsFun
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(struct
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  open Sum;
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  val mk_bal = HOLogic.mk_binrel "Orderings.less";
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  val dest_bal = HOLogic.dest_bin "Orderings.less" HOLogic.natT;
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  val uncancel_tac = gen_uncancel_tac nat_add_left_cancel_less;
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end);
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(* nat le *)
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structure LeCancelSums = CancelSumsFun
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(struct
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  open Sum;
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  val mk_bal = HOLogic.mk_binrel "Orderings.less_eq";
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  val dest_bal = HOLogic.dest_bin "Orderings.less_eq" HOLogic.natT;
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  val uncancel_tac = gen_uncancel_tac nat_add_left_cancel_le;
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end);
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(* nat diff *)
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structure DiffCancelSums = CancelSumsFun
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(struct
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  open Sum;
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  val mk_bal = HOLogic.mk_binop "HOL.minus";
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  val dest_bal = HOLogic.dest_bin "HOL.minus" HOLogic.natT;
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  val uncancel_tac = gen_uncancel_tac diff_cancel;
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end);
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(** prepare nat_cancel simprocs **)
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val nat_cancel_sums_add = map prep_simproc
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  [("nateq_cancel_sums",
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     ["(l::nat) + m = n", "(l::nat) = m + n", "Suc m = n", "m = Suc n"],
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     K EqCancelSums.proc),
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   ("natless_cancel_sums",
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     ["(l::nat) + m < n", "(l::nat) < m + n", "Suc m < n", "m < Suc n"],
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     K LessCancelSums.proc),
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   ("natle_cancel_sums",
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     ["(l::nat) + m <= n", "(l::nat) <= m + n", "Suc m <= n", "m <= Suc n"],
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     K LeCancelSums.proc)];
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val nat_cancel_sums = nat_cancel_sums_add @
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  [prep_simproc ("natdiff_cancel_sums",
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    ["((l::nat) + m) - n", "(l::nat) - (m + n)", "Suc m - n", "m - Suc n"],
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    K DiffCancelSums.proc)];
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end;  (* ArithData *)
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open ArithData;
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(*---------------------------------------------------------------------------*)
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(* 2. Linear arithmetic                                                      *)
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(*---------------------------------------------------------------------------*)
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(* Parameters data for general linear arithmetic functor *)
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structure LA_Logic: LIN_ARITH_LOGIC =
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struct
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val ccontr = ccontr;
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val conjI = conjI;
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val notI = notI;
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val sym = sym;
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val not_lessD = linorder_not_less RS iffD1;
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val not_leD = linorder_not_le RS iffD1;
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fun mk_Eq thm = (thm RS Eq_FalseI) handle THM _ => (thm RS Eq_TrueI);
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val mk_Trueprop = HOLogic.mk_Trueprop;
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fun atomize thm = case #prop(rep_thm thm) of
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    Const("Trueprop",_) $ (Const("op &",_) $ _ $ _) =>
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    atomize(thm RS conjunct1) @ atomize(thm RS conjunct2)
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  | _ => [thm];
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fun neg_prop(TP$(Const("Not",_)$t)) = TP$t
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  | neg_prop(TP$t) = TP $ (Const("Not",HOLogic.boolT-->HOLogic.boolT)$t);
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fun is_False thm =
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  let val _ $ t = #prop(rep_thm thm)
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  in t = Const("False",HOLogic.boolT) end;
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fun is_nat(t) = fastype_of1 t = HOLogic.natT;
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fun mk_nat_thm sg t =
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  let val ct = cterm_of sg t  and cn = cterm_of sg (Var(("n",0),HOLogic.natT))
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  in instantiate ([],[(cn,ct)]) le0 end;
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end;  (* LA_Logic *)
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(* arith theory data *)
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structure ArithTheoryData = TheoryDataFun
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(struct
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  val name = "HOL/arith";
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  type T = {splits: thm list,
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            inj_consts: (string * typ) list,
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            discrete: string list,
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            presburger: (int -> tactic) option};
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  val empty = {splits = [], inj_consts = [], discrete = [], presburger = NONE};
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  val copy = I;
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  val extend = I;
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  fun merge _ ({splits= splits1, inj_consts= inj_consts1, discrete= discrete1, presburger= presburger1},
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             {splits= splits2, inj_consts= inj_consts2, discrete= discrete2, presburger= presburger2}) =
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   {splits = Drule.merge_rules (splits1, splits2),
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    inj_consts = merge_lists inj_consts1 inj_consts2,
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    discrete = merge_lists discrete1 discrete2,
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    presburger = (case presburger1 of NONE => presburger2 | p => p)};
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  fun print _ _ = ();
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end);
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val arith_split_add = Thm.declaration_attribute (fn thm =>
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  Context.map_theory (ArithTheoryData.map (fn {splits,inj_consts,discrete,presburger} =>
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    {splits= thm::splits, inj_consts= inj_consts, discrete= discrete, presburger= presburger})));
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fun arith_discrete d = ArithTheoryData.map (fn {splits,inj_consts,discrete,presburger} =>
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  {splits = splits, inj_consts = inj_consts, discrete = d :: discrete, presburger= presburger});
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fun arith_inj_const c = ArithTheoryData.map (fn {splits,inj_consts,discrete,presburger} =>
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  {splits = splits, inj_consts = c :: inj_consts, discrete = discrete, presburger = presburger});
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signature HOL_LIN_ARITH_DATA =
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sig
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  include LIN_ARITH_DATA
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  val fast_arith_split_limit : int ref
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end;
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structure LA_Data_Ref: HOL_LIN_ARITH_DATA =
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struct
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(* internal representation of linear (in-)equations *)
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type decompT = ((term * Rat.rat) list * Rat.rat * string * (term * Rat.rat) list * Rat.rat * bool);
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(* Decomposition of terms *)
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fun nT (Type ("fun", [N, _])) = (N = HOLogic.natT)
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  | nT _                      = false;
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fun add_atom (t : term) (m : Rat.rat) (p : (term * Rat.rat) list, i : Rat.rat) :
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             (term * Rat.rat) list * Rat.rat =
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  case AList.lookup (op =) p t of NONE   => ((t, m) :: p, i)
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                                | SOME n => (AList.update (op =) (t, Rat.add (n, m)) p, i);
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exception Zero;
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fun rat_of_term (numt : term, dent : term) : Rat.rat =
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let
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  val num = HOLogic.dest_binum numt
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  val den = HOLogic.dest_binum dent
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in
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  if den = 0 then raise Zero else Rat.rat_of_quotient (num, den)
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end;
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(* Warning: in rare cases number_of encloses a non-numeral,
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   in which case dest_binum raises TERM; hence all the handles below.
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   Same for Suc-terms that turn out not to be numerals -
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   although the simplifier should eliminate those anyway ...
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*)
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fun number_of_Sucs (Const ("Suc", _) $ n) : int =
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      number_of_Sucs n + 1
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  | number_of_Sucs t =
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      if HOLogic.is_zero t then 0 else raise TERM ("number_of_Sucs", []);
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(* decompose nested multiplications, bracketing them to the right and combining
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   all their coefficients
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*)
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fun demult (inj_consts : (string * typ) list) : term * Rat.rat -> term option * Rat.rat =
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let
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  fun demult ((mC as Const ("HOL.times", _)) $ s $ t, m) = (
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    (case s of
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      Const ("Numeral.number_of", _) $ n =>
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        demult (t, Rat.mult (m, Rat.rat_of_intinf (HOLogic.dest_binum n)))
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    | Const ("HOL.uminus", _) $ (Const ("Numeral.number_of", _) $ n) =>
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        demult (t, Rat.mult (m, Rat.rat_of_intinf (~(HOLogic.dest_binum n))))
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    | Const("Suc", _) $ _ =>
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        demult (t, Rat.mult (m, Rat.rat_of_int (number_of_Sucs s)))
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    | Const ("HOL.times", _) $ s1 $ s2 =>
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        demult (mC $ s1 $ (mC $ s2 $ t), m)
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    | Const ("HOL.divide", _) $ numt $ (Const ("Numeral.number_of", _) $ dent) =>
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        let
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          val den = HOLogic.dest_binum dent
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        in
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          if den = 0 then
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            raise Zero
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          else
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            demult (mC $ numt $ t, Rat.mult (m, Rat.inv (Rat.rat_of_intinf den)))
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        end
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    | _ =>
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        atomult (mC, s, t, m)
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    ) handle TERM _ => atomult (mC, s, t, m)
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  )
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    | demult (atom as Const("HOL.divide", _) $ t $ (Const ("Numeral.number_of", _) $ dent), m) =
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      (let
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        val den = HOLogic.dest_binum dent
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   309
      in
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        if den = 0 then
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          raise Zero
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        else
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          demult (t, Rat.mult (m, Rat.inv (Rat.rat_of_intinf den)))
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      end
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        handle TERM _ => (SOME atom, m))
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    | demult (Const ("0", _), m) = (NONE, Rat.rat_of_int 0)
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    | demult (Const ("1", _), m) = (NONE, m)
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    | demult (t as Const ("Numeral.number_of", _) $ n, m) =
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   319
        ((NONE, Rat.mult (m, Rat.rat_of_intinf (HOLogic.dest_binum n)))
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          handle TERM _ => (SOME t,m))
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   321
    | demult (Const ("HOL.uminus", _) $ t, m) = demult(t,Rat.mult(m,Rat.rat_of_int(~1)))
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    | demult (t as Const f $ x, m) =
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        (if f mem inj_consts then SOME x else SOME t, m)
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   324
    | demult (atom, m) = (SOME atom, m)
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and
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  atomult (mC, atom, t, m) = (
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    case demult (t, m) of (NONE, m')    => (SOME atom, m')
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                        | (SOME t', m') => (SOME (mC $ atom $ t'), m')
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   329
  )
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in demult end;
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   331
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fun decomp0 (inj_consts : (string * typ) list) (rel : string, lhs : term, rhs : term) :
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   333
            ((term * Rat.rat) list * Rat.rat * string * (term * Rat.rat) list * Rat.rat) option =
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let
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  (* Turn term into list of summand * multiplicity plus a constant *)
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   336
  fun poly (Const ("HOL.plus", _) $ s $ t, m : Rat.rat, pi : (term * Rat.rat) list * Rat.rat) =
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   337
        poly (s, m, poly (t, m, pi))
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   338
    | poly (all as Const ("HOL.minus", T) $ s $ t, m, pi) =
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   339
        if nT T then add_atom all m pi else poly (s, m, poly (t, Rat.neg m, pi))
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   340
    | poly (all as Const ("HOL.uminus", T) $ t, m, pi) =
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   341
        if nT T then add_atom all m pi else poly (t, Rat.neg m, pi)
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   342
    | poly (Const ("0", _), _, pi) =
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   343
        pi
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    | poly (Const ("1", _), m, (p, i)) =
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        (p, Rat.add (i, m))
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    | poly (Const ("Suc", _) $ t, m, (p, i)) =
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        poly (t, m, (p, Rat.add (i, m)))
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    | poly (all as Const ("HOL.times", _) $ _ $ _, m, pi as (p, i)) =
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        (case demult inj_consts (all, m) of
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           (NONE,   m') => (p, Rat.add (i, m'))
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         | (SOME u, m') => add_atom u m' pi)
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   352
    | poly (all as Const ("HOL.divide", _) $ _ $ _, m, pi as (p, i)) =
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   353
        (case demult inj_consts (all, m) of
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   354
           (NONE,   m') => (p, Rat.add (i, m'))
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   355
         | (SOME u, m') => add_atom u m' pi)
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   356
    | poly (all as Const ("Numeral.number_of", _) $ t, m, pi as (p, i)) =
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   357
        ((p, Rat.add (i, Rat.mult (m, Rat.rat_of_intinf (HOLogic.dest_binum t))))
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   358
         handle TERM _ => add_atom all m pi)
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   359
    | poly (all as Const f $ x, m, pi) =
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   360
        if f mem inj_consts then poly (x, m, pi) else add_atom all m pi
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   361
    | poly (all, m, pi) =
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   362
        add_atom all m pi
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   363
  val (p, i) = poly (lhs, Rat.rat_of_int 1, ([], Rat.rat_of_int 0))
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   364
  val (q, j) = poly (rhs, Rat.rat_of_int 1, ([], Rat.rat_of_int 0))
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   365
in
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   366
  case rel of
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   367
    "Orderings.less"    => SOME (p, i, "<", q, j)
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   368
  | "Orderings.less_eq" => SOME (p, i, "<=", q, j)
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   369
  | "op ="              => SOME (p, i, "=", q, j)
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   370
  | _                   => NONE
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   371
end handle Zero => NONE;
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   372
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   373
fun of_lin_arith_sort sg (U : typ) : bool =
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   374
  Type.of_sort (Sign.tsig_of sg) (U, ["Ring_and_Field.ordered_idom"])
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   375
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   376
fun allows_lin_arith sg (discrete : string list) (U as Type (D, [])) : bool * bool =
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   377
  if of_lin_arith_sort sg U then
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   378
    (true, D mem discrete)
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   379
  else (* special cases *)
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   380
    if D mem discrete then  (true, true)  else  (false, false)
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   381
  | allows_lin_arith sg discrete U =
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   382
  (of_lin_arith_sort sg U, false);
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diff changeset
   383
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   384
fun decomp_typecheck (sg, discrete, inj_consts) (T : typ, xxx) : decompT option =
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   385
  case T of
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   386
    Type ("fun", [U, _]) =>
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   387
      (case allows_lin_arith sg discrete U of
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   388
        (true, d) =>
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   389
          (case decomp0 inj_consts xxx of
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   390
            NONE                   => NONE
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   391
          | SOME (p, i, rel, q, j) => SOME (p, i, rel, q, j, d))
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diff changeset
   392
      | (false, _) =>
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diff changeset
   393
          NONE)
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   394
  | _ => NONE;
9436
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
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diff changeset
   395
20271
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diff changeset
   396
fun negate (SOME (x, i, rel, y, j, d)) = SOME (x, i, "~" ^ rel, y, j, d)
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diff changeset
   397
  | negate NONE                        = NONE;
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62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
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parents:
diff changeset
   398
20271
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diff changeset
   399
fun decomp_negation data (_ $ (Const (rel, T) $ lhs $ rhs)) : decompT option =
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diff changeset
   400
      decomp_typecheck data (T, (rel, lhs, rhs))
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diff changeset
   401
  | decomp_negation data (_ $ (Const ("Not", _) $ (Const (rel, T) $ lhs $ rhs))) =
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diff changeset
   402
      negate (decomp_typecheck data (T, (rel, lhs, rhs)))
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diff changeset
   403
  | decomp_negation data _ =
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diff changeset
   404
      NONE;
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diff changeset
   405
e76e77e0d615 fixed a bug in function poly: decomposition of products
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diff changeset
   406
fun decomp sg : term -> decompT option =
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58b71535ed00 lin_arith_prover splits certain operators (e.g. min, max, abs)
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diff changeset
   407
let
58b71535ed00 lin_arith_prover splits certain operators (e.g. min, max, abs)
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diff changeset
   408
  val {discrete, inj_consts, ...} = ArithTheoryData.get sg
58b71535ed00 lin_arith_prover splits certain operators (e.g. min, max, abs)
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diff changeset
   409
in
20271
e76e77e0d615 fixed a bug in function poly: decomposition of products
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diff changeset
   410
  decomp_negation (sg, discrete, inj_consts)
20254
58b71535ed00 lin_arith_prover splits certain operators (e.g. min, max, abs)
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diff changeset
   411
end;
9436
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   412
20271
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diff changeset
   413
fun number_of (n : int, T : typ) =
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diff changeset
   414
  HOLogic.number_of_const T $ (HOLogic.mk_binum n);
10693
9e4a0e84d0d6 moved mk_bin from Numerals to HOLogic
nipkow
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diff changeset
   415
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
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   416
(*---------------------------------------------------------------------------*)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
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diff changeset
   417
(* code that performs certain goal transformations for linear arithmetic     *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
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diff changeset
   418
(*---------------------------------------------------------------------------*)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
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diff changeset
   419
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
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diff changeset
   420
(* A "do nothing" variant of pre_decomp and pre_tac:
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diff changeset
   421
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
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diff changeset
   422
fun pre_decomp sg Ts termitems = [termitems];
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
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diff changeset
   423
fun pre_tac i = all_tac;
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
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diff changeset
   424
*)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
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diff changeset
   425
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
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diff changeset
   426
(*---------------------------------------------------------------------------*)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
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diff changeset
   427
(* the following code performs splitting of certain constants (e.g. min,     *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   428
(* max) in a linear arithmetic problem; similar to what split_tac later does *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   429
(* to the proof state                                                        *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
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diff changeset
   430
(*---------------------------------------------------------------------------*)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
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diff changeset
   431
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
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diff changeset
   432
val fast_arith_split_limit = ref 9;
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
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diff changeset
   433
20268
1fe9aed8fcac code reformatted
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diff changeset
   434
(* checks if splitting with 'thm' is implemented                             *)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
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parents: 20044
diff changeset
   435
20268
1fe9aed8fcac code reformatted
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diff changeset
   436
fun is_split_thm (thm : thm) : bool =
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diff changeset
   437
  case concl_of thm of _ $ (_ $ (_ $ lhs) $ _) => (
1fe9aed8fcac code reformatted
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diff changeset
   438
    (* Trueprop $ ((op =) $ (?P $ lhs) $ rhs) *)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   439
    case head_of lhs of
1fe9aed8fcac code reformatted
webertj
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diff changeset
   440
      Const (a, _) => a mem_string ["Orderings.max",
1fe9aed8fcac code reformatted
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diff changeset
   441
                                    "Orderings.min",
1fe9aed8fcac code reformatted
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diff changeset
   442
                                    "HOL.abs",
1fe9aed8fcac code reformatted
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diff changeset
   443
                                    "HOL.minus",
1fe9aed8fcac code reformatted
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diff changeset
   444
                                    "IntDef.nat",
1fe9aed8fcac code reformatted
webertj
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diff changeset
   445
                                    "Divides.op mod",
1fe9aed8fcac code reformatted
webertj
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diff changeset
   446
                                    "Divides.op div"]
1fe9aed8fcac code reformatted
webertj
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diff changeset
   447
    | _            => (warning ("Lin. Arith.: wrong format for split rule " ^
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   448
                                 Display.string_of_thm thm);
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   449
                       false))
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   450
  | _ => (warning ("Lin. Arith.: wrong format for split rule " ^
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   451
                   Display.string_of_thm thm);
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   452
          false);
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   453
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   454
(* substitute new for occurrences of old in a term, incrementing bound       *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   455
(* variables as needed when substituting inside an abstraction               *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   456
20268
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webertj
parents: 20254
diff changeset
   457
fun subst_term ([] : (term * term) list) (t : term) = t
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   458
  | subst_term pairs                     t          =
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   459
      (case AList.lookup (op aconv) pairs t of
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   460
        SOME new =>
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   461
          new
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   462
      | NONE     =>
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   463
          (case t of Abs (a, T, body) =>
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   464
            let val pairs' = map (pairself (incr_boundvars 1)) pairs
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   465
            in  Abs (a, T, subst_term pairs' body)  end
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   466
          | t1 $ t2                   =>
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   467
            subst_term pairs t1 $ subst_term pairs t2
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   468
          | _ => t));
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   469
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   470
(* approximates the effect of one application of split_tac (followed by NNF  *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   471
(* normalization) on the subgoal represented by '(Ts, terms)'; returns a     *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   472
(* list of new subgoals (each again represented by a typ list for bound      *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   473
(* variables and a term list for premises), or NONE if split_tac would fail  *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   474
(* on the subgoal                                                            *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   475
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   476
(* FIXME: currently only the effect of certain split theorems is reproduced  *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   477
(*        (which is why we need 'is_split_thm').  A more canonical           *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   478
(*        implementation should analyze the right-hand side of the split     *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   479
(*        theorem that can be applied, and modify the subgoal accordingly.   *)
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   480
(*        Or even better, the splitter should be extended to provide         *)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   481
(*        splitting on terms as well as splitting on theorems (where the     *)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   482
(*        former can have a faster implementation as it does not need to be  *)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   483
(*        proof-producing).                                                  *)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   484
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   485
fun split_once_items (sg : theory) (Ts : typ list, terms : term list) :
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   486
                     (typ list * term list) list option =
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   487
let
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   488
  (* takes a list  [t1, ..., tn]  to the term                                *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   489
  (*   tn' --> ... --> t1' --> False  ,                                      *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   490
  (* where ti' = HOLogic.dest_Trueprop ti                                    *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   491
  (* term list -> term *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   492
  fun REPEAT_DETERM_etac_rev_mp terms' =
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   493
    fold (curry HOLogic.mk_imp) (map HOLogic.dest_Trueprop terms') HOLogic.false_const
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   494
  val split_thms = filter is_split_thm (#splits (ArithTheoryData.get sg))
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   495
  val cmap       = Splitter.cmap_of_split_thms split_thms
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   496
  val splits     = Splitter.split_posns cmap sg Ts (REPEAT_DETERM_etac_rev_mp terms)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   497
in
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   498
  if length splits > !fast_arith_split_limit then (
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   499
    tracing ("fast_arith_split_limit exceeded (current value is " ^
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   500
              string_of_int (!fast_arith_split_limit) ^ ")");
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   501
    NONE
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   502
  ) else (
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   503
  case splits of [] =>
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   504
    (* split_tac would fail: no possible split *)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   505
    NONE
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   506
  | ((_, _, _, split_type, split_term) :: _) => (
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   507
    (* ignore all but the first possible split *)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   508
    case strip_comb split_term of
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   509
    (* ?P (max ?i ?j) = ((?i <= ?j --> ?P ?j) & (~ ?i <= ?j --> ?P ?i)) *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   510
      (Const ("Orderings.max", _), [t1, t2]) =>
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   511
      let
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   512
        val rev_terms     = rev terms
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   513
        val terms1        = map (subst_term [(split_term, t1)]) rev_terms
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   514
        val terms2        = map (subst_term [(split_term, t2)]) rev_terms
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   515
        val t1_leq_t2     = Const ("Orderings.less_eq",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   516
                                    split_type --> split_type --> HOLogic.boolT) $ t1 $ t2
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   517
        val not_t1_leq_t2 = HOLogic.Not $ t1_leq_t2
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   518
        val not_false     = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   519
        val subgoal1      = (HOLogic.mk_Trueprop t1_leq_t2) :: terms2 @ [not_false]
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   520
        val subgoal2      = (HOLogic.mk_Trueprop not_t1_leq_t2) :: terms1 @ [not_false]
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   521
      in
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   522
        SOME [(Ts, subgoal1), (Ts, subgoal2)]
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   523
      end
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   524
    (* ?P (min ?i ?j) = ((?i <= ?j --> ?P ?i) & (~ ?i <= ?j --> ?P ?j)) *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   525
    | (Const ("Orderings.min", _), [t1, t2]) =>
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   526
      let
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   527
        val rev_terms     = rev terms
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   528
        val terms1        = map (subst_term [(split_term, t1)]) rev_terms
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   529
        val terms2        = map (subst_term [(split_term, t2)]) rev_terms
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   530
        val t1_leq_t2     = Const ("Orderings.less_eq",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   531
                                    split_type --> split_type --> HOLogic.boolT) $ t1 $ t2
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   532
        val not_t1_leq_t2 = HOLogic.Not $ t1_leq_t2
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   533
        val not_false     = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   534
        val subgoal1      = (HOLogic.mk_Trueprop t1_leq_t2) :: terms1 @ [not_false]
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   535
        val subgoal2      = (HOLogic.mk_Trueprop not_t1_leq_t2) :: terms2 @ [not_false]
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   536
      in
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   537
        SOME [(Ts, subgoal1), (Ts, subgoal2)]
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   538
      end
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   539
    (* ?P (abs ?a) = ((0 <= ?a --> ?P ?a) & (?a < 0 --> ?P (- ?a))) *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   540
    | (Const ("HOL.abs", _), [t1]) =>
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   541
      let
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   542
        val rev_terms   = rev terms
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   543
        val terms1      = map (subst_term [(split_term, t1)]) rev_terms
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   544
        val terms2      = map (subst_term [(split_term, Const ("HOL.uminus",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   545
                            split_type --> split_type) $ t1)]) rev_terms
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   546
        val zero        = Const ("0", split_type)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   547
        val zero_leq_t1 = Const ("Orderings.less_eq",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   548
                            split_type --> split_type --> HOLogic.boolT) $ zero $ t1
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   549
        val t1_lt_zero  = Const ("Orderings.less",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   550
                            split_type --> split_type --> HOLogic.boolT) $ t1 $ zero
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   551
        val not_false   = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   552
        val subgoal1    = (HOLogic.mk_Trueprop zero_leq_t1) :: terms1 @ [not_false]
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   553
        val subgoal2    = (HOLogic.mk_Trueprop t1_lt_zero) :: terms2 @ [not_false]
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   554
      in
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   555
        SOME [(Ts, subgoal1), (Ts, subgoal2)]
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   556
      end
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   557
    (* ?P (?a - ?b) = ((?a < ?b --> ?P 0) & (ALL d. ?a = ?b + d --> ?P d)) *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   558
    | (Const ("HOL.minus", _), [t1, t2]) =>
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   559
      let
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   560
        (* "d" in the above theorem becomes a new bound variable after NNF   *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   561
        (* transformation, therefore some adjustment of indices is necessary *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   562
        val rev_terms       = rev terms
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   563
        val zero            = Const ("0", split_type)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   564
        val d               = Bound 0
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   565
        val terms1          = map (subst_term [(split_term, zero)]) rev_terms
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   566
        val terms2          = map (subst_term [(incr_boundvars 1 split_term, d)])
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   567
                                (map (incr_boundvars 1) rev_terms)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   568
        val t1'             = incr_boundvars 1 t1
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   569
        val t2'             = incr_boundvars 1 t2
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   570
        val t1_lt_t2        = Const ("Orderings.less",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   571
                                split_type --> split_type --> HOLogic.boolT) $ t1 $ t2
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   572
        val t1_eq_t2_plus_d = Const ("op =", split_type --> split_type --> HOLogic.boolT) $ t1' $
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   573
                                (Const ("HOL.plus",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   574
                                  split_type --> split_type --> split_type) $ t2' $ d)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   575
        val not_false       = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   576
        val subgoal1        = (HOLogic.mk_Trueprop t1_lt_t2) :: terms1 @ [not_false]
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   577
        val subgoal2        = (HOLogic.mk_Trueprop t1_eq_t2_plus_d) :: terms2 @ [not_false]
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   578
      in
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   579
        SOME [(Ts, subgoal1), (split_type :: Ts, subgoal2)]
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   580
      end
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   581
    (* ?P (nat ?i) = ((ALL n. ?i = int n --> ?P n) & (?i < 0 --> ?P 0)) *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   582
    | (Const ("IntDef.nat", _), [t1]) =>
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   583
      let
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   584
        val rev_terms   = rev terms
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   585
        val zero_int    = Const ("0", HOLogic.intT)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   586
        val zero_nat    = Const ("0", HOLogic.natT)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   587
        val n           = Bound 0
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   588
        val terms1      = map (subst_term [(incr_boundvars 1 split_term, n)])
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   589
                            (map (incr_boundvars 1) rev_terms)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   590
        val terms2      = map (subst_term [(split_term, zero_nat)]) rev_terms
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   591
        val t1'         = incr_boundvars 1 t1
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   592
        val t1_eq_int_n = Const ("op =", HOLogic.intT --> HOLogic.intT --> HOLogic.boolT) $ t1' $
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   593
                            (Const ("IntDef.int", HOLogic.natT --> HOLogic.intT) $ n)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   594
        val t1_lt_zero  = Const ("Orderings.less",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   595
                            HOLogic.intT --> HOLogic.intT --> HOLogic.boolT) $ t1 $ zero_int
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   596
        val not_false   = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   597
        val subgoal1    = (HOLogic.mk_Trueprop t1_eq_int_n) :: terms1 @ [not_false]
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   598
        val subgoal2    = (HOLogic.mk_Trueprop t1_lt_zero) :: terms2 @ [not_false]
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   599
      in
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   600
        SOME [(HOLogic.natT :: Ts, subgoal1), (Ts, subgoal2)]
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   601
      end
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   602
    (* "?P ((?n::nat) mod (number_of ?k)) =
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   603
         ((number_of ?k = 0 --> ?P ?n) & (~ (number_of ?k = 0) -->
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   604
           (ALL i j. j < number_of ?k --> ?n = number_of ?k * i + j --> ?P j))) *)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   605
    | (Const ("Divides.op mod", Type ("fun", [Type ("nat", []), _])), [t1, t2]) =>
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   606
      let
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   607
        val rev_terms               = rev terms
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   608
        val zero                    = Const ("0", split_type)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   609
        val i                       = Bound 1
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   610
        val j                       = Bound 0
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   611
        val terms1                  = map (subst_term [(split_term, t1)]) rev_terms
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   612
        val terms2                  = map (subst_term [(incr_boundvars 2 split_term, j)])
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   613
                                        (map (incr_boundvars 2) rev_terms)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   614
        val t1'                     = incr_boundvars 2 t1
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   615
        val t2'                     = incr_boundvars 2 t2
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   616
        val t2_eq_zero              = Const ("op =",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   617
                                        split_type --> split_type --> HOLogic.boolT) $ t2 $ zero
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   618
        val t2_neq_zero             = HOLogic.mk_not (Const ("op =",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   619
                                        split_type --> split_type --> HOLogic.boolT) $ t2' $ zero)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   620
        val j_lt_t2                 = Const ("Orderings.less",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   621
                                        split_type --> split_type--> HOLogic.boolT) $ j $ t2'
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   622
        val t1_eq_t2_times_i_plus_j = Const ("op =", split_type --> split_type --> HOLogic.boolT) $ t1' $
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   623
                                       (Const ("HOL.plus", split_type --> split_type --> split_type) $
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   624
                                         (Const ("HOL.times",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   625
                                           split_type --> split_type --> split_type) $ t2' $ i) $ j)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   626
        val not_false               = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   627
        val subgoal1                = (HOLogic.mk_Trueprop t2_eq_zero) :: terms1 @ [not_false]
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   628
        val subgoal2                = (map HOLogic.mk_Trueprop
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   629
                                        [t2_neq_zero, j_lt_t2, t1_eq_t2_times_i_plus_j])
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   630
                                          @ terms2 @ [not_false]
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   631
      in
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   632
        SOME [(Ts, subgoal1), (split_type :: split_type :: Ts, subgoal2)]
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   633
      end
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   634
    (* "?P ((?n::nat) div (number_of ?k)) =
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   635
         ((number_of ?k = 0 --> ?P 0) & (~ (number_of ?k = 0) -->
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   636
           (ALL i j. j < number_of ?k --> ?n = number_of ?k * i + j --> ?P i))) *)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   637
    | (Const ("Divides.op div", Type ("fun", [Type ("nat", []), _])), [t1, t2]) =>
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   638
      let
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   639
        val rev_terms               = rev terms
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   640
        val zero                    = Const ("0", split_type)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   641
        val i                       = Bound 1
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   642
        val j                       = Bound 0
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   643
        val terms1                  = map (subst_term [(split_term, zero)]) rev_terms
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   644
        val terms2                  = map (subst_term [(incr_boundvars 2 split_term, i)])
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   645
                                        (map (incr_boundvars 2) rev_terms)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   646
        val t1'                     = incr_boundvars 2 t1
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   647
        val t2'                     = incr_boundvars 2 t2
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   648
        val t2_eq_zero              = Const ("op =",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   649
                                        split_type --> split_type --> HOLogic.boolT) $ t2 $ zero
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   650
        val t2_neq_zero             = HOLogic.mk_not (Const ("op =",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   651
                                        split_type --> split_type --> HOLogic.boolT) $ t2' $ zero)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   652
        val j_lt_t2                 = Const ("Orderings.less",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   653
                                        split_type --> split_type--> HOLogic.boolT) $ j $ t2'
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   654
        val t1_eq_t2_times_i_plus_j = Const ("op =", split_type --> split_type --> HOLogic.boolT) $ t1' $
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   655
                                       (Const ("HOL.plus", split_type --> split_type --> split_type) $
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   656
                                         (Const ("HOL.times",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   657
                                           split_type --> split_type --> split_type) $ t2' $ i) $ j)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   658
        val not_false               = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   659
        val subgoal1                = (HOLogic.mk_Trueprop t2_eq_zero) :: terms1 @ [not_false]
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   660
        val subgoal2                = (map HOLogic.mk_Trueprop
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   661
                                        [t2_neq_zero, j_lt_t2, t1_eq_t2_times_i_plus_j])
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   662
                                          @ terms2 @ [not_false]
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   663
      in
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   664
        SOME [(Ts, subgoal1), (split_type :: split_type :: Ts, subgoal2)]
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   665
      end
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   666
    (* "?P ((?n::int) mod (number_of ?k)) =
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   667
         ((iszero (number_of ?k) --> ?P ?n) &
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   668
          (neg (number_of (bin_minus ?k)) -->
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   669
            (ALL i j. 0 <= j & j < number_of ?k & ?n = number_of ?k * i + j --> ?P j)) &
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   670
          (neg (number_of ?k) -->
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   671
            (ALL i j. number_of ?k < j & j <= 0 & ?n = number_of ?k * i + j --> ?P j))) *)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   672
    | (Const ("Divides.op mod",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   673
        Type ("fun", [Type ("IntDef.int", []), _])), [t1, t2 as (number_of $ k)]) =>
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   674
      let
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   675
        val rev_terms               = rev terms
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   676
        val zero                    = Const ("0", split_type)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   677
        val i                       = Bound 1
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   678
        val j                       = Bound 0
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   679
        val terms1                  = map (subst_term [(split_term, t1)]) rev_terms
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   680
        val terms2_3                = map (subst_term [(incr_boundvars 2 split_term, j)])
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   681
                                        (map (incr_boundvars 2) rev_terms)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   682
        val t1'                     = incr_boundvars 2 t1
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   683
        val (t2' as (_ $ k'))       = incr_boundvars 2 t2
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   684
        val iszero_t2               = Const ("IntDef.iszero", split_type --> HOLogic.boolT) $ t2
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   685
        val neg_minus_k             = Const ("IntDef.neg", split_type --> HOLogic.boolT) $
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   686
                                        (number_of $
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   687
                                          (Const ("Numeral.bin_minus",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   688
                                            HOLogic.binT --> HOLogic.binT) $ k'))
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   689
        val zero_leq_j              = Const ("Orderings.less_eq",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   690
                                        split_type --> split_type --> HOLogic.boolT) $ zero $ j
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   691
        val j_lt_t2                 = Const ("Orderings.less",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   692
                                        split_type --> split_type--> HOLogic.boolT) $ j $ t2'
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   693
        val t1_eq_t2_times_i_plus_j = Const ("op =", split_type --> split_type --> HOLogic.boolT) $ t1' $
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   694
                                       (Const ("HOL.plus", split_type --> split_type --> split_type) $
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   695
                                         (Const ("HOL.times",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   696
                                           split_type --> split_type --> split_type) $ t2' $ i) $ j)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   697
        val neg_t2                  = Const ("IntDef.neg", split_type --> HOLogic.boolT) $ t2'
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   698
        val t2_lt_j                 = Const ("Orderings.less",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   699
                                        split_type --> split_type--> HOLogic.boolT) $ t2' $ j
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   700
        val j_leq_zero              = Const ("Orderings.less_eq",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   701
                                        split_type --> split_type --> HOLogic.boolT) $ j $ zero
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   702
        val not_false               = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   703
        val subgoal1                = (HOLogic.mk_Trueprop iszero_t2) :: terms1 @ [not_false]
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   704
        val subgoal2                = (map HOLogic.mk_Trueprop [neg_minus_k, zero_leq_j])
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   705
                                        @ hd terms2_3
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   706
                                        :: (if tl terms2_3 = [] then [not_false] else [])
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   707
                                        @ (map HOLogic.mk_Trueprop [j_lt_t2, t1_eq_t2_times_i_plus_j])
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   708
                                        @ (if tl terms2_3 = [] then [] else tl terms2_3 @ [not_false])
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   709
        val subgoal3                = (map HOLogic.mk_Trueprop [neg_t2, t2_lt_j])
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   710
                                        @ hd terms2_3
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   711
                                        :: (if tl terms2_3 = [] then [not_false] else [])
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   712
                                        @ (map HOLogic.mk_Trueprop [j_leq_zero, t1_eq_t2_times_i_plus_j])
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   713
                                        @ (if tl terms2_3 = [] then [] else tl terms2_3 @ [not_false])
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   714
        val Ts'                     = split_type :: split_type :: Ts
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   715
      in
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   716
        SOME [(Ts, subgoal1), (Ts', subgoal2), (Ts', subgoal3)]
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   717
      end
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   718
    (* "?P ((?n::int) div (number_of ?k)) =
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   719
         ((iszero (number_of ?k) --> ?P 0) &
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   720
          (neg (number_of (bin_minus ?k)) -->
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   721
            (ALL i. (EX j. 0 <= j & j < number_of ?k & ?n = number_of ?k * i + j) --> ?P i)) &
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   722
          (neg (number_of ?k) -->
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   723
            (ALL i. (EX j. number_of ?k < j & j <= 0 & ?n = number_of ?k * i + j) --> ?P i))) *)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   724
    | (Const ("Divides.op div",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   725
        Type ("fun", [Type ("IntDef.int", []), _])), [t1, t2 as (number_of $ k)]) =>
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   726
      let
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   727
        val rev_terms               = rev terms
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   728
        val zero                    = Const ("0", split_type)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   729
        val i                       = Bound 1
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   730
        val j                       = Bound 0
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   731
        val terms1                  = map (subst_term [(split_term, zero)]) rev_terms
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   732
        val terms2_3                = map (subst_term [(incr_boundvars 2 split_term, i)])
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   733
                                        (map (incr_boundvars 2) rev_terms)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   734
        val t1'                     = incr_boundvars 2 t1
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   735
        val (t2' as (_ $ k'))       = incr_boundvars 2 t2
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   736
        val iszero_t2               = Const ("IntDef.iszero", split_type --> HOLogic.boolT) $ t2
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   737
        val neg_minus_k             = Const ("IntDef.neg", split_type --> HOLogic.boolT) $
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   738
                                        (number_of $
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   739
                                          (Const ("Numeral.bin_minus",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   740
                                            HOLogic.binT --> HOLogic.binT) $ k'))
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   741
        val zero_leq_j              = Const ("Orderings.less_eq",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   742
                                        split_type --> split_type --> HOLogic.boolT) $ zero $ j
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   743
        val j_lt_t2                 = Const ("Orderings.less",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   744
                                        split_type --> split_type--> HOLogic.boolT) $ j $ t2'
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   745
        val t1_eq_t2_times_i_plus_j = Const ("op =",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   746
                                        split_type --> split_type --> HOLogic.boolT) $ t1' $
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   747
                                       (Const ("HOL.plus", split_type --> split_type --> split_type) $
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   748
                                         (Const ("HOL.times",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   749
                                           split_type --> split_type --> split_type) $ t2' $ i) $ j)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   750
        val neg_t2                  = Const ("IntDef.neg", split_type --> HOLogic.boolT) $ t2'
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   751
        val t2_lt_j                 = Const ("Orderings.less",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   752
                                        split_type --> split_type--> HOLogic.boolT) $ t2' $ j
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   753
        val j_leq_zero              = Const ("Orderings.less_eq",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   754
                                        split_type --> split_type --> HOLogic.boolT) $ j $ zero
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   755
        val not_false               = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   756
        val subgoal1                = (HOLogic.mk_Trueprop iszero_t2) :: terms1 @ [not_false]
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   757
        val subgoal2                = (HOLogic.mk_Trueprop neg_minus_k)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   758
                                        :: terms2_3
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   759
                                        @ not_false
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   760
                                        :: (map HOLogic.mk_Trueprop
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   761
                                             [zero_leq_j, j_lt_t2, t1_eq_t2_times_i_plus_j])
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   762
        val subgoal3                = (HOLogic.mk_Trueprop neg_t2)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   763
                                        :: terms2_3
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   764
                                        @ not_false
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   765
                                        :: (map HOLogic.mk_Trueprop
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   766
                                             [t2_lt_j, j_leq_zero, t1_eq_t2_times_i_plus_j])
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   767
        val Ts'                     = split_type :: split_type :: Ts
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   768
      in
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   769
        SOME [(Ts, subgoal1), (Ts', subgoal2), (Ts', subgoal3)]
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   770
      end
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   771
    (* this will only happen if a split theorem can be applied for which no  *)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   772
    (* code exists above -- in which case either the split theorem should be *)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   773
    (* implemented above, or 'is_split_thm' should be modified to filter it  *)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   774
    (* out                                                                   *)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   775
    | (t, ts) => (
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   776
      warning ("Lin. Arith.: split rule for " ^ Sign.string_of_term sg t ^
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   777
               " (with " ^ Int.toString (length ts) ^
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   778
               " argument(s)) not implemented; proof reconstruction is likely to fail");
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   779
      NONE
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   780
    ))
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   781
  )
9436
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   782
end;
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   783
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   784
(* remove terms that do not satisfy 'p'; change the order of the remaining   *)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   785
(* terms in the same way as filter_prems_tac does                            *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   786
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   787
fun filter_prems_tac_items (p : term -> bool) (terms : term list) : term list =
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   788
let
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   789
  fun filter_prems (t, (left, right)) =
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   790
    if  p t  then  (left, right @ [t])  else  (left @ right, [])
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   791
  val (left, right) = foldl filter_prems ([], []) terms
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   792
in
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   793
  right @ left
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   794
end;
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   795
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   796
(* return true iff TRY (etac notE) THEN eq_assume_tac would succeed on a     *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   797
(* subgoal that has 'terms' as premises                                      *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   798
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   799
fun negated_term_occurs_positively (terms : term list) : bool =
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   800
  List.exists
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   801
    (fn (Trueprop $ (Const ("Not", _) $ t)) => member (op aconv) terms (Trueprop $ t)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   802
      | _                                   => false)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   803
    terms;
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   804
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   805
fun pre_decomp sg (Ts : typ list, terms : term list) : (typ list * term list) list =
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   806
let
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   807
  (* repeatedly split (including newly emerging subgoals) until no further   *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   808
  (* splitting is possible                                                   *)
20271
e76e77e0d615 fixed a bug in function poly: decomposition of products
webertj
parents: 20268
diff changeset
   809
  fun split_loop ([] : (typ list * term list) list) = ([] : (typ list * term list) list)
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   810
    | split_loop (subgoal::subgoals)                = (
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   811
        case split_once_items sg subgoal of
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   812
          SOME new_subgoals => split_loop (new_subgoals @ subgoals)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   813
        | NONE              => subgoal :: split_loop subgoals
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   814
      )
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   815
  fun is_relevant t  = isSome (decomp sg t)
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   816
  (* filter_prems_tac is_relevant: *)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   817
  val relevant_terms = filter_prems_tac_items is_relevant terms
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   818
  (* split_tac, NNF normalization: *)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   819
  val split_goals    = split_loop [(Ts, relevant_terms)]
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   820
  (* necessary because split_once_tac may normalize terms: *)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   821
  val beta_eta_norm  = map (apsnd (map (Envir.eta_contract o Envir.beta_norm))) split_goals
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   822
  (* TRY (etac notE) THEN eq_assume_tac: *)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   823
  val result         = List.filter (not o negated_term_occurs_positively o snd) beta_eta_norm
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   824
in
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   825
  result
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   826
end;
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   827
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   828
(* takes the i-th subgoal  [| A1; ...; An |] ==> B  to                       *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   829
(* An --> ... --> A1 --> B,  performs splitting with the given 'split_thms'  *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   830
(* (resulting in a different subgoal P), takes  P  to  ~P ==> False,         *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   831
(* performs NNF-normalization of ~P, and eliminates conjunctions,            *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   832
(* disjunctions and existential quantifiers from the premises, possibly (in  *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   833
(* the case of disjunctions) resulting in several new subgoals, each of the  *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   834
(* general form  [| Q1; ...; Qm |] ==> False.  Fails if more than            *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   835
(* !fast_arith_split_limit splits are possible.                              *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   836
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   837
fun split_once_tac (split_thms : thm list) (i : int) : tactic =
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   838
let
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   839
  val nnf_simpset =
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   840
    empty_ss setmkeqTrue mk_eq_True
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   841
    setmksimps (mksimps mksimps_pairs)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   842
    addsimps [imp_conv_disj, iff_conv_conj_imp, de_Morgan_disj, de_Morgan_conj, 
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   843
      not_all, not_ex, not_not]
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   844
  fun prem_nnf_tac i st =
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   845
    full_simp_tac (Simplifier.theory_context (Thm.theory_of_thm st) nnf_simpset) i st
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   846
  fun cond_split_tac i st =
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   847
    let
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   848
      val subgoal = Logic.nth_prem (i, Thm.prop_of st)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   849
      val Ts      = rev (map snd (Logic.strip_params subgoal))
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   850
      val concl   = HOLogic.dest_Trueprop (Logic.strip_assums_concl subgoal)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   851
      val cmap    = Splitter.cmap_of_split_thms split_thms
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   852
      val splits  = Splitter.split_posns cmap (theory_of_thm st) Ts concl
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   853
    in
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   854
      if length splits > !fast_arith_split_limit then
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   855
        no_tac st
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   856
      else
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   857
        split_tac split_thms i st
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   858
    end
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   859
in
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   860
  EVERY' [
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   861
    REPEAT_DETERM o etac rev_mp,
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   862
    cond_split_tac,
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   863
    rtac ccontr,
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   864
    prem_nnf_tac,
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   865
    TRY o REPEAT_ALL_NEW (DETERM o (eresolve_tac [conjE, exE] ORELSE' etac disjE))
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   866
  ] i
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   867
end;
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   868
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   869
(* remove irrelevant premises, then split the i-th subgoal (and all new      *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   870
(* subgoals) by using 'split_once_tac' repeatedly.  Beta-eta-normalize new   *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   871
(* subgoals and finally attempt to solve them by finding an immediate        *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   872
(* contradiction (i.e. a term and its negation) in their premises.           *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   873
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   874
fun pre_tac i st =
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   875
let
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   876
  val sg            = theory_of_thm st
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   877
  val split_thms    = filter is_split_thm (#splits (ArithTheoryData.get sg))
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   878
  fun is_relevant t = isSome (decomp sg t)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   879
in
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   880
  DETERM (
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   881
    TRY (filter_prems_tac is_relevant i)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   882
      THEN (
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   883
        (TRY o REPEAT_ALL_NEW (split_once_tac split_thms))
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   884
          THEN_ALL_NEW
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   885
            ((fn j => PRIMITIVE
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   886
                        (Drule.fconv_rule
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   887
                          (Drule.goals_conv (equal j) (Drule.beta_eta_conversion))))
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   888
              THEN'
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   889
            (TRY o (etac notE THEN' eq_assume_tac)))
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   890
      ) i
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   891
  ) st
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   892
end;
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   893
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   894
end;  (* LA_Data_Ref *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   895
9436
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   896
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   897
structure Fast_Arith =
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   898
  Fast_Lin_Arith(structure LA_Logic=LA_Logic and LA_Data=LA_Data_Ref);
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   899
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   900
val fast_arith_tac         = Fast_Arith.lin_arith_tac false;
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   901
val fast_ex_arith_tac      = Fast_Arith.lin_arith_tac;
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   902
val trace_arith            = Fast_Arith.trace;
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   903
val fast_arith_neq_limit   = Fast_Arith.fast_arith_neq_limit;
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   904
val fast_arith_split_limit = LA_Data_Ref.fast_arith_split_limit;
9436
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   905
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   906
local
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   907
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   908
(* reduce contradictory <= to False.
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   909
   Most of the work is done by the cancel tactics.
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   910
*)
12931
2c0251fada94 solved the problem that Larry's simproce cancle_numerals(?) returns
nipkow
parents: 12480
diff changeset
   911
val add_rules =
14368
2763da611ad9 converted Real/Lubs to Isar script. Converting arithmetic setup
paulson
parents: 14356
diff changeset
   912
 [add_zero_left,add_zero_right,Zero_not_Suc,Suc_not_Zero,le_0_eq,
19297
8f6e097d7b23 Removal of unnecessary simprules: simproc cancel_numerals now works without
paulson
parents: 19285
diff changeset
   913
  One_nat_def,
17875
d81094515061 change_claset/simpset;
wenzelm
parents: 17611
diff changeset
   914
  order_less_irrefl, zero_neq_one, zero_less_one, zero_le_one,
16473
b24c820a0b85 moving some generic inequalities from integer arith to nat arith
paulson
parents: 16424
diff changeset
   915
  zero_neq_one RS not_sym, not_one_le_zero, not_one_less_zero];
9436
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   916
14368
2763da611ad9 converted Real/Lubs to Isar script. Converting arithmetic setup
paulson
parents: 14356
diff changeset
   917
val add_mono_thms_ordered_semiring = map (fn s => prove_goal (the_context ()) s
9436
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   918
 (fn prems => [cut_facts_tac prems 1,
14368
2763da611ad9 converted Real/Lubs to Isar script. Converting arithmetic setup
paulson
parents: 14356
diff changeset
   919
               blast_tac (claset() addIs [add_mono]) 1]))
15121
1198032bad25 Initial changes to extend arithmetic from individual types to type classes.
nipkow
parents: 14738
diff changeset
   920
["(i <= j) & (k <= l) ==> i + k <= j + (l::'a::pordered_ab_semigroup_add)",
1198032bad25 Initial changes to extend arithmetic from individual types to type classes.
nipkow
parents: 14738
diff changeset
   921
 "(i  = j) & (k <= l) ==> i + k <= j + (l::'a::pordered_ab_semigroup_add)",
1198032bad25 Initial changes to extend arithmetic from individual types to type classes.
nipkow
parents: 14738
diff changeset
   922
 "(i <= j) & (k  = l) ==> i + k <= j + (l::'a::pordered_ab_semigroup_add)",
1198032bad25 Initial changes to extend arithmetic from individual types to type classes.
nipkow
parents: 14738
diff changeset
   923
 "(i  = j) & (k  = l) ==> i + k  = j + (l::'a::pordered_ab_semigroup_add)"
9436
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   924
];
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   925
15121
1198032bad25 Initial changes to extend arithmetic from individual types to type classes.
nipkow
parents: 14738
diff changeset
   926
val mono_ss = simpset() addsimps
1198032bad25 Initial changes to extend arithmetic from individual types to type classes.
nipkow
parents: 14738
diff changeset
   927
                [add_mono,add_strict_mono,add_less_le_mono,add_le_less_mono];
1198032bad25 Initial changes to extend arithmetic from individual types to type classes.
nipkow
parents: 14738
diff changeset
   928
1198032bad25 Initial changes to extend arithmetic from individual types to type classes.
nipkow
parents: 14738
diff changeset
   929
val add_mono_thms_ordered_field =
1198032bad25 Initial changes to extend arithmetic from individual types to type classes.
nipkow
parents: 14738
diff changeset
   930
  map (fn s => prove_goal (the_context ()) s
1198032bad25 Initial changes to extend arithmetic from individual types to type classes.
nipkow
parents: 14738
diff changeset
   931
                 (fn prems => [cut_facts_tac prems 1, asm_simp_tac mono_ss 1]))
1198032bad25 Initial changes to extend arithmetic from individual types to type classes.
nipkow
parents: 14738
diff changeset
   932
    ["(i<j) & (k=l)   ==> i+k < j+(l::'a::pordered_cancel_ab_semigroup_add)",
1198032bad25 Initial changes to extend arithmetic from individual types to type classes.
nipkow
parents: 14738
diff changeset
   933
     "(i=j) & (k<l)   ==> i+k < j+(l::'a::pordered_cancel_ab_semigroup_add)",
1198032bad25 Initial changes to extend arithmetic from individual types to type classes.
nipkow
parents: 14738
diff changeset
   934
     "(i<j) & (k<=l)  ==> i+k < j+(l::'a::pordered_cancel_ab_semigroup_add)",
1198032bad25 Initial changes to extend arithmetic from individual types to type classes.
nipkow
parents: 14738
diff changeset
   935
     "(i<=j) & (k<l)  ==> i+k < j+(l::'a::pordered_cancel_ab_semigroup_add)",
1198032bad25 Initial changes to extend arithmetic from individual types to type classes.
nipkow
parents: 14738
diff changeset
   936
     "(i<j) & (k<l)   ==> i+k < j+(l::'a::pordered_cancel_ab_semigroup_add)"];
1198032bad25 Initial changes to extend arithmetic from individual types to type classes.
nipkow
parents: 14738
diff changeset
   937
9436
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   938
in
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   939
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   940
val init_lin_arith_data =
18708
4b3dadb4fe33 setup: theory -> theory;
wenzelm
parents: 18394
diff changeset
   941
 Fast_Arith.setup #>
4b3dadb4fe33 setup: theory -> theory;
wenzelm
parents: 18394
diff changeset
   942
 Fast_Arith.map_data (fn {add_mono_thms, mult_mono_thms, inj_thms, lessD, ...} =>
15121
1198032bad25 Initial changes to extend arithmetic from individual types to type classes.
nipkow
parents: 14738
diff changeset
   943
   {add_mono_thms = add_mono_thms @
1198032bad25 Initial changes to extend arithmetic from individual types to type classes.
nipkow
parents: 14738
diff changeset
   944
    add_mono_thms_ordered_semiring @ add_mono_thms_ordered_field,
10693
9e4a0e84d0d6 moved mk_bin from Numerals to HOLogic
nipkow
parents: 10574
diff changeset
   945
    mult_mono_thms = mult_mono_thms,
10574
8f98f0301d67 Linear arithmetic now copes with mixed nat/int formulae.
nipkow
parents: 10516
diff changeset
   946
    inj_thms = inj_thms,
9436
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   947
    lessD = lessD @ [Suc_leI],
15923
01d5d0c1c078 fixed lin.arith
nipkow
parents: 15921
diff changeset
   948
    neqE = [linorder_neqE_nat,
16485
77ae3bfa8b76 get_thm instead of obsolete Goals.get_thm;
wenzelm
parents: 16473
diff changeset
   949
      get_thm (theory "Ring_and_Field") (Name "linorder_neqE_ordered_idom")],
15234
ec91a90c604e simplification tweaks for better arithmetic reasoning
paulson
parents: 15221
diff changeset
   950
    simpset = HOL_basic_ss addsimps add_rules
17875
d81094515061 change_claset/simpset;
wenzelm
parents: 17611
diff changeset
   951
                   addsimprocs [ab_group_add_cancel.sum_conv,
15234
ec91a90c604e simplification tweaks for better arithmetic reasoning
paulson
parents: 15221
diff changeset
   952
                                ab_group_add_cancel.rel_conv]
ec91a90c604e simplification tweaks for better arithmetic reasoning
paulson
parents: 15221
diff changeset
   953
                   (*abel_cancel helps it work in abstract algebraic domains*)
18708
4b3dadb4fe33 setup: theory -> theory;
wenzelm
parents: 18394
diff changeset
   954
                   addsimprocs nat_cancel_sums_add}) #>
4b3dadb4fe33 setup: theory -> theory;
wenzelm
parents: 18394
diff changeset
   955
  ArithTheoryData.init #>
4b3dadb4fe33 setup: theory -> theory;
wenzelm
parents: 18394
diff changeset
   956
  arith_discrete "nat";
9436
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   957
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   958
end;
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   959
13462
56610e2ba220 sane interface for simprocs;
wenzelm
parents: 12949
diff changeset
   960
val fast_nat_arith_simproc =
16834
71d87aeebb57 HOL.Not;
wenzelm
parents: 16733
diff changeset
   961
  Simplifier.simproc (the_context ()) "fast_nat_arith"
13462
56610e2ba220 sane interface for simprocs;
wenzelm
parents: 12949
diff changeset
   962
    ["(m::nat) < n","(m::nat) <= n", "(m::nat) = n"] Fast_Arith.lin_arith_prover;
9436
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   963
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   964
(* Because of fast_nat_arith_simproc, the arithmetic solver is really only
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   965
useful to detect inconsistencies among the premises for subgoals which are
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   966
*not* themselves (in)equalities, because the latter activate
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   967
fast_nat_arith_simproc anyway. However, it seems cheaper to activate the
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   968
solver all the time rather than add the additional check. *)
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   969
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   970
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   971
(* arith proof method *)
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   972
10516
dc113303d101 arith_tac: atomize;
wenzelm
parents: 9893
diff changeset
   973
local
dc113303d101 arith_tac: atomize;
wenzelm
parents: 9893
diff changeset
   974
13499
f95f5818f24f Counter example generation mods.
nipkow
parents: 13462
diff changeset
   975
fun raw_arith_tac ex i st =
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   976
  (* FIXME: K true should be replaced by a sensible test (perhaps "isSome o
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   977
     decomp sg"?) to speed things up in case there are lots of irrelevant
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   978
     terms involved; elimination of min/max can be optimized:
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   979
     (max m n + k <= r) = (m+k <= r & n+k <= r)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   980
     (l <= min m n + k) = (l <= m+k & l <= n+k)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   981
  *)
13499
f95f5818f24f Counter example generation mods.
nipkow
parents: 13462
diff changeset
   982
  refute_tac (K true)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   983
    (* Splitting is also done inside fast_arith_tac, but not completely --   *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   984
    (* split_tac may use split theorems that have not been implemented in    *)
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   985
    (* fast_arith_tac (cf. pre_decomp and split_once_items above), and       *)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   986
    (* fast_arith_split_limit may trigger.                                   *)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   987
    (* Therefore splitting outside of fast_arith_tac may allow us to prove   *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   988
    (* some goals that fast_arith_tac alone would fail on.                   *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   989
    (REPEAT_DETERM o split_tac (#splits (ArithTheoryData.get (Thm.theory_of_thm st))))
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   990
    (fast_ex_arith_tac ex)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   991
    i st;
9436
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   992
13877
a6b825ee48d9 Added hook for presburger arithmetic decision procedure.
berghofe
parents: 13517
diff changeset
   993
fun presburger_tac i st =
16834
71d87aeebb57 HOL.Not;
wenzelm
parents: 16733
diff changeset
   994
  (case ArithTheoryData.get (Thm.theory_of_thm st) of
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15234
diff changeset
   995
     {presburger = SOME tac, ...} =>
16970
c1ef99e08c39 tuned msg;
wenzelm
parents: 16834
diff changeset
   996
       (warning "Trying full Presburger arithmetic ..."; tac i st)
13877
a6b825ee48d9 Added hook for presburger arithmetic decision procedure.
berghofe
parents: 13517
diff changeset
   997
   | _ => no_tac st);
a6b825ee48d9 Added hook for presburger arithmetic decision procedure.
berghofe
parents: 13517
diff changeset
   998
10516
dc113303d101 arith_tac: atomize;
wenzelm
parents: 9893
diff changeset
   999
in
dc113303d101 arith_tac: atomize;
wenzelm
parents: 9893
diff changeset
  1000
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
  1001
  val simple_arith_tac = FIRST' [fast_arith_tac,
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
  1002
    ObjectLogic.atomize_tac THEN' raw_arith_tac true];
13877
a6b825ee48d9 Added hook for presburger arithmetic decision procedure.
berghofe
parents: 13517
diff changeset
  1003
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
  1004
  val arith_tac = FIRST' [fast_arith_tac,
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
  1005
    ObjectLogic.atomize_tac THEN' raw_arith_tac true,
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
  1006
    presburger_tac];
13877
a6b825ee48d9 Added hook for presburger arithmetic decision procedure.
berghofe
parents: 13517
diff changeset
  1007
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
  1008
  val silent_arith_tac = FIRST' [fast_arith_tac,
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
  1009
    ObjectLogic.atomize_tac THEN' raw_arith_tac false,
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
  1010
    presburger_tac];
10516
dc113303d101 arith_tac: atomize;
wenzelm
parents: 9893
diff changeset
  1011
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
  1012
  fun arith_method prems =
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
  1013
    Method.METHOD (fn facts => HEADGOAL (Method.insert_tac (prems @ facts) THEN' arith_tac));
9436
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
  1014
10516
dc113303d101 arith_tac: atomize;
wenzelm
parents: 9893
diff changeset
  1015
end;
dc113303d101 arith_tac: atomize;
wenzelm
parents: 9893
diff changeset
  1016
15195
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1017
(* antisymmetry:
15197
19e735596e51 Added antisymmetry simproc
nipkow
parents: 15195
diff changeset
  1018
   combines x <= y (or ~(y < x)) and y <= x (or ~(x < y)) into x = y
15195
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1019
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1020
local
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1021
val antisym = mk_meta_eq order_antisym
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1022
val not_lessD = linorder_not_less RS iffD1
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1023
fun prp t thm = (#prop(rep_thm thm) = t)
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1024
in
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1025
fun antisym_eq prems thm =
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1026
  let
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1027
    val r = #prop(rep_thm thm);
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1028
  in
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1029
    case r of
19277
f7602e74d948 renamed op < <= to Orderings.less(_eq)
haftmann
parents: 19233
diff changeset
  1030
      Tr $ ((c as Const("Orderings.less_eq",T)) $ s $ t) =>
15195
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1031
        let val r' = Tr $ (c $ t $ s)
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1032
        in
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1033
          case Library.find_first (prp r') prems of
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15234
diff changeset
  1034
            NONE =>
19277
f7602e74d948 renamed op < <= to Orderings.less(_eq)
haftmann
parents: 19233
diff changeset
  1035
              let val r' = Tr $ (HOLogic.Not $ (Const("Orderings.less",T) $ s $ t))
15195
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1036
              in case Library.find_first (prp r') prems of
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15234
diff changeset
  1037
                   NONE => []
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15234
diff changeset
  1038
                 | SOME thm' => [(thm' RS not_lessD) RS (thm RS antisym)]
15195
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1039
              end
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15234
diff changeset
  1040
          | SOME thm' => [thm' RS (thm RS antisym)]
15195
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1041
        end
19277
f7602e74d948 renamed op < <= to Orderings.less(_eq)
haftmann
parents: 19233
diff changeset
  1042
    | Tr $ (Const("Not",_) $ (Const("Orderings.less",T) $ s $ t)) =>
f7602e74d948 renamed op < <= to Orderings.less(_eq)
haftmann
parents: 19233
diff changeset
  1043
        let val r' = Tr $ (Const("Orderings.less_eq",T) $ s $ t)
15195
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1044
        in
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1045
          case Library.find_first (prp r') prems of
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15234
diff changeset
  1046
            NONE =>
19277
f7602e74d948 renamed op < <= to Orderings.less(_eq)
haftmann
parents: 19233
diff changeset
  1047
              let val r' = Tr $ (HOLogic.Not $ (Const("Orderings.less",T) $ t $ s))
15195
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1048
              in case Library.find_first (prp r') prems of
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15234
diff changeset
  1049
                   NONE => []
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15234
diff changeset
  1050
                 | SOME thm' =>
15195
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1051
                     [(thm' RS not_lessD) RS ((thm RS not_lessD) RS antisym)]
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1052
              end
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15234
diff changeset
  1053
          | SOME thm' => [thm' RS ((thm RS not_lessD) RS antisym)]
15195
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1054
        end
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1055
    | _ => []
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1056
  end
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1057
  handle THM _ => []
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1058
end;
15197
19e735596e51 Added antisymmetry simproc
nipkow
parents: 15195
diff changeset
  1059
*)
9436
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
  1060
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
  1061
(* theory setup *)
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
  1062
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
  1063
val arith_setup =
18708
4b3dadb4fe33 setup: theory -> theory;
wenzelm
parents: 18394
diff changeset
  1064
  init_lin_arith_data #>
4b3dadb4fe33 setup: theory -> theory;
wenzelm
parents: 18394
diff changeset
  1065
  (fn thy => (Simplifier.change_simpset_of thy (fn ss => ss
17875
d81094515061 change_claset/simpset;
wenzelm
parents: 17611
diff changeset
  1066
    addsimprocs (nat_cancel_sums @ [fast_nat_arith_simproc])
18708
4b3dadb4fe33 setup: theory -> theory;
wenzelm
parents: 18394
diff changeset
  1067
    addSolver (mk_solver' "lin. arith." Fast_Arith.cut_lin_arith_tac)); thy)) #>
15221
8412cfdf3287 tweaking of arithmetic proofs
paulson
parents: 15197
diff changeset
  1068
  Method.add_methods
17875
d81094515061 change_claset/simpset;
wenzelm
parents: 17611
diff changeset
  1069
    [("arith", (arith_method o #2) oo Method.syntax Args.bang_facts,
18708
4b3dadb4fe33 setup: theory -> theory;
wenzelm
parents: 18394
diff changeset
  1070
      "decide linear arithmethic")] #>
18728
6790126ab5f6 simplified type attribute;
wenzelm
parents: 18708
diff changeset
  1071
  Attrib.add_attributes [("arith_split", Attrib.no_args arith_split_add,
18708
4b3dadb4fe33 setup: theory -> theory;
wenzelm
parents: 18394
diff changeset
  1072
    "declaration of split rules for arithmetic procedure")];