src/HOL/arith_data.ML
author haftmann
Sun, 13 May 2007 18:15:22 +0200
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parent 22927 0b53bd36258b
child 22997 d4f3b015b50b
permissions -rw-r--r--
refined module rat
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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 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 HOLogic.Suc_zero) 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 => HOLogic.Suc_zero :: 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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(* 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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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 [@{thm "add_Suc"}, @{thm "add_Suc_right"},
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    @{thm "add_0"}, @{thm "add_0_right"}];
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  val norm_tac2 = simp_all_tac @{thms 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 @{thm 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 @{thm "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 @{thm "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 @{thm "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 @{thm "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 = @{thm linorder_not_less} RS iffD1;
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val not_leD = @{thm linorder_not_le} RS iffD1;
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val le0 = thm "le0";
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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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datatype arithtactic = ArithTactic of {name: string, tactic: int -> tactic, id: stamp};
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fun mk_arith_tactic name tactic = ArithTactic {name = name, tactic = tactic, id = stamp ()};
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fun eq_arith_tactic (ArithTactic {id = id1, ...}, ArithTactic {id = id2, ...}) = (id1 = id2);
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structure ArithTheoryData = TheoryDataFun
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(
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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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            tactics: arithtactic list};
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  val empty = {splits = [], inj_consts = [], discrete = [], tactics = []};
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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, tactics= tactics1},
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             {splits= splits2, inj_consts= inj_consts2, discrete= discrete2, tactics= tactics2}) =
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   {splits = Library.merge Thm.eq_thm_prop (splits1, splits2),
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    inj_consts = Library.merge (op =) (inj_consts1, inj_consts2),
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    discrete = Library.merge (op =) (discrete1, discrete2),
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    tactics = Library.merge eq_arith_tactic (tactics1, tactics2)};
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);
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val arith_split_add = Thm.declaration_attribute (fn thm =>
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  Context.mapping (ArithTheoryData.map (fn {splits,inj_consts,discrete,tactics} =>
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    {splits= insert Thm.eq_thm_prop thm splits, inj_consts= inj_consts, discrete= discrete, tactics= tactics})) I);
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fun arith_discrete d = ArithTheoryData.map (fn {splits,inj_consts,discrete,tactics} =>
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  {splits = splits, inj_consts = inj_consts, discrete = insert (op =) d discrete, tactics= tactics});
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fun arith_inj_const c = ArithTheoryData.map (fn {splits,inj_consts,discrete,tactics} =>
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  {splits = splits, inj_consts = insert (op =) c inj_consts, discrete = discrete, tactics= tactics});
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fun arith_tactic_add tac = ArithTheoryData.map (fn {splits,inj_consts,discrete,tactics} =>
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  {splits= splits, inj_consts= inj_consts, discrete= discrete, tactics= insert eq_arith_tactic tac tactics});
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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, dent) =
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  let
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    val num = HOLogic.dest_numeral numt
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    val den = HOLogic.dest_numeral 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_numeral 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_int (HOLogic.dest_numeral 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_int (~(HOLogic.dest_numeral n))))
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    | Const ("Suc", _) $ _ =>
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        demult (t, Rat.mult m (Rat.rat_of_int (HOLogic.dest_nat 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_numeral 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_int 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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   308
  )
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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_numeral dent
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      in
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        if den = 0 then
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          raise Zero
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   315
        else
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          demult (t, Rat.mult m (Rat.inv (Rat.rat_of_int den)))
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   317
      end
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   318
        handle TERM _ => (SOME atom, m))
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    | demult (Const ("HOL.zero", _), m) = (NONE, Rat.zero)
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    | demult (Const ("HOL.one", _), m) = (NONE, m)
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    | demult (t as Const ("Numeral.number_of", _) $ n, m) =
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        ((NONE, Rat.mult m (Rat.rat_of_int (HOLogic.dest_numeral n)))
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   323
          handle TERM _ => (SOME t, m))
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   324
    | demult (Const ("HOL.uminus", _) $ t, m) = demult (t, Rat.neg m)
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   325
    | demult (t as Const f $ x, m) =
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   326
        (if f mem inj_consts then SOME x else SOME t, m)
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   327
    | demult (atom, m) = (SOME atom, m)
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   328
and
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   329
  atomult (mC, atom, t, m) = (
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   330
    case demult (t, m) of (NONE, m')    => (SOME atom, m')
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   331
                        | (SOME t', m') => (SOME (mC $ atom $ t'), m')
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  )
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   333
in demult end;
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   334
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   335
fun decomp0 (inj_consts : (string * typ) list) (rel : string, lhs : term, rhs : term) :
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   336
            ((term * Rat.rat) list * Rat.rat * string * (term * Rat.rat) list * Rat.rat) option =
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   337
let
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   338
  (* Turn term into list of summand * multiplicity plus a constant *)
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   339
  fun poly (Const ("HOL.plus", _) $ s $ t, m : Rat.rat, pi : (term * Rat.rat) list * Rat.rat) =
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   340
        poly (s, m, poly (t, m, pi))
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    | poly (all as Const ("HOL.minus", T) $ s $ t, m, pi) =
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   342
        if nT T then add_atom all m pi else poly (s, m, poly (t, Rat.neg m, pi))
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   343
    | poly (all as Const ("HOL.uminus", T) $ t, m, pi) =
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   344
        if nT T then add_atom all m pi else poly (t, Rat.neg m, pi)
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    | poly (Const ("HOL.zero", _), _, pi) =
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   346
        pi
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    | poly (Const ("HOL.one", _), 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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   351
    | poly (all as Const ("HOL.times", _) $ _ $ _, m, pi as (p, i)) =
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   352
        (case demult inj_consts (all, m) of
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   353
           (NONE,   m') => (p, Rat.add i m')
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   354
         | (SOME u, m') => add_atom u m' pi)
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   355
    | poly (all as Const ("HOL.divide", _) $ _ $ _, m, pi as (p, i)) =
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   356
        (case demult inj_consts (all, m) of
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   357
           (NONE,   m') => (p, Rat.add i m')
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   358
         | (SOME u, m') => add_atom u m' pi)
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   359
    | poly (all as Const ("Numeral.number_of", Type(_,[_,T])) $ t, m, pi as (p, i)) =
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   360
        (let val k = HOLogic.dest_numeral t
20859
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   361
            val k2 = if k < 0 andalso T = HOLogic.natT then 0 else k
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   362
        in (p, Rat.add i (Rat.mult m (Rat.rat_of_int k2))) end
20859
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diff changeset
   363
        handle TERM _ => add_atom all m pi)
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   364
    | poly (all as Const f $ x, m, pi) =
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   365
        if f mem inj_consts then poly (x, m, pi) else add_atom all m pi
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   366
    | poly (all, m, pi) =
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   367
        add_atom all m pi
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   368
  val (p, i) = poly (lhs, Rat.one, ([], Rat.zero))
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   369
  val (q, j) = poly (rhs, Rat.one, ([], Rat.zero))
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   370
in
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   371
  case rel of
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   372
    "Orderings.less"    => SOME (p, i, "<", q, j)
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   373
  | "Orderings.less_eq" => SOME (p, i, "<=", q, j)
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   374
  | "op ="              => SOME (p, i, "=", q, j)
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   375
  | _                   => NONE
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   376
end handle Zero => NONE;
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   377
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   378
fun of_lin_arith_sort sg (U : typ) : bool =
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   379
  Type.of_sort (Sign.tsig_of sg) (U, ["Ring_and_Field.ordered_idom"])
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1198032bad25 Initial changes to extend arithmetic from individual types to type classes.
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   380
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   381
fun allows_lin_arith sg (discrete : string list) (U as Type (D, [])) : bool * bool =
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   382
  if of_lin_arith_sort sg U then
58b71535ed00 lin_arith_prover splits certain operators (e.g. min, max, abs)
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diff changeset
   383
    (true, D mem discrete)
58b71535ed00 lin_arith_prover splits certain operators (e.g. min, max, abs)
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diff changeset
   384
  else (* special cases *)
20271
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diff changeset
   385
    if D mem discrete then  (true, true)  else  (false, false)
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   386
  | allows_lin_arith sg discrete U =
58b71535ed00 lin_arith_prover splits certain operators (e.g. min, max, abs)
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diff changeset
   387
  (of_lin_arith_sort sg U, false);
15121
1198032bad25 Initial changes to extend arithmetic from individual types to type classes.
nipkow
parents: 14738
diff changeset
   388
20271
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diff changeset
   389
fun decomp_typecheck (sg, discrete, inj_consts) (T : typ, xxx) : decompT option =
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parents: 20268
diff changeset
   390
  case T of
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diff changeset
   391
    Type ("fun", [U, _]) =>
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diff changeset
   392
      (case allows_lin_arith sg discrete U of
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parents: 20268
diff changeset
   393
        (true, d) =>
e76e77e0d615 fixed a bug in function poly: decomposition of products
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diff changeset
   394
          (case decomp0 inj_consts xxx of
e76e77e0d615 fixed a bug in function poly: decomposition of products
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diff changeset
   395
            NONE                   => NONE
e76e77e0d615 fixed a bug in function poly: decomposition of products
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diff changeset
   396
          | SOME (p, i, rel, q, j) => SOME (p, i, rel, q, j, d))
e76e77e0d615 fixed a bug in function poly: decomposition of products
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diff changeset
   397
      | (false, _) =>
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diff changeset
   398
          NONE)
e76e77e0d615 fixed a bug in function poly: decomposition of products
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diff changeset
   399
  | _ => NONE;
9436
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   400
20271
e76e77e0d615 fixed a bug in function poly: decomposition of products
webertj
parents: 20268
diff changeset
   401
fun negate (SOME (x, i, rel, y, j, d)) = SOME (x, i, "~" ^ rel, y, j, d)
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webertj
parents: 20268
diff changeset
   402
  | negate NONE                        = NONE;
9436
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   403
20271
e76e77e0d615 fixed a bug in function poly: decomposition of products
webertj
parents: 20268
diff changeset
   404
fun decomp_negation data (_ $ (Const (rel, T) $ lhs $ rhs)) : decompT option =
e76e77e0d615 fixed a bug in function poly: decomposition of products
webertj
parents: 20268
diff changeset
   405
      decomp_typecheck data (T, (rel, lhs, rhs))
e76e77e0d615 fixed a bug in function poly: decomposition of products
webertj
parents: 20268
diff changeset
   406
  | decomp_negation data (_ $ (Const ("Not", _) $ (Const (rel, T) $ lhs $ rhs))) =
e76e77e0d615 fixed a bug in function poly: decomposition of products
webertj
parents: 20268
diff changeset
   407
      negate (decomp_typecheck data (T, (rel, lhs, rhs)))
e76e77e0d615 fixed a bug in function poly: decomposition of products
webertj
parents: 20268
diff changeset
   408
  | decomp_negation data _ =
e76e77e0d615 fixed a bug in function poly: decomposition of products
webertj
parents: 20268
diff changeset
   409
      NONE;
e76e77e0d615 fixed a bug in function poly: decomposition of products
webertj
parents: 20268
diff changeset
   410
e76e77e0d615 fixed a bug in function poly: decomposition of products
webertj
parents: 20268
diff changeset
   411
fun decomp sg : term -> decompT option =
20254
58b71535ed00 lin_arith_prover splits certain operators (e.g. min, max, abs)
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diff changeset
   412
let
58b71535ed00 lin_arith_prover splits certain operators (e.g. min, max, abs)
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parents: 20217
diff changeset
   413
  val {discrete, inj_consts, ...} = ArithTheoryData.get sg
58b71535ed00 lin_arith_prover splits certain operators (e.g. min, max, abs)
webertj
parents: 20217
diff changeset
   414
in
20271
e76e77e0d615 fixed a bug in function poly: decomposition of products
webertj
parents: 20268
diff changeset
   415
  decomp_negation (sg, discrete, inj_consts)
20254
58b71535ed00 lin_arith_prover splits certain operators (e.g. min, max, abs)
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parents: 20217
diff changeset
   416
end;
9436
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   417
20276
d94dc40673b1 possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents: 20271
diff changeset
   418
fun domain_is_nat (_ $ (Const (_, T) $ _ $ _))                      = nT T
d94dc40673b1 possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents: 20271
diff changeset
   419
  | domain_is_nat (_ $ (Const ("Not", _) $ (Const (_, T) $ _ $ _))) = nT T
d94dc40673b1 possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents: 20271
diff changeset
   420
  | domain_is_nat _                                                 = false;
d94dc40673b1 possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents: 20271
diff changeset
   421
21820
2f2b6a965ccc introduced mk/dest_numeral/number for mk/dest_binum etc.
haftmann
parents: 21621
diff changeset
   422
fun number_of (n, T) = HOLogic.mk_number T n;
10693
9e4a0e84d0d6 moved mk_bin from Numerals to HOLogic
nipkow
parents: 10574
diff changeset
   423
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
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parents: 20044
diff changeset
   424
(*---------------------------------------------------------------------------*)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
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parents: 20044
diff changeset
   425
(* code that performs certain goal transformations for linear arithmetic     *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
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diff changeset
   426
(*---------------------------------------------------------------------------*)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
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parents: 20044
diff changeset
   427
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   428
(* A "do nothing" variant of pre_decomp and pre_tac:
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   429
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   430
fun pre_decomp sg Ts termitems = [termitems];
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   431
fun pre_tac i = all_tac;
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   432
*)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   433
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   434
(*---------------------------------------------------------------------------*)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   435
(* 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
   436
(* 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
   437
(* to the proof state                                                        *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   438
(*---------------------------------------------------------------------------*)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   439
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   440
val fast_arith_split_limit = ref 9;
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   441
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   442
(* checks if splitting with 'thm' is implemented                             *)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   443
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   444
fun is_split_thm (thm : thm) : bool =
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   445
  case concl_of thm of _ $ (_ $ (_ $ lhs) $ _) => (
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   446
    (* Trueprop $ ((op =) $ (?P $ lhs) $ rhs) *)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   447
    case head_of lhs of
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   448
      Const (a, _) => a mem_string ["Orderings.max",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   449
                                    "Orderings.min",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   450
                                    "HOL.abs",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   451
                                    "HOL.minus",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   452
                                    "IntDef.nat",
21415
39f98c88f88a op div/op mod now named without leading op
haftmann
parents: 21243
diff changeset
   453
                                    "Divides.mod",
39f98c88f88a op div/op mod now named without leading op
haftmann
parents: 21243
diff changeset
   454
                                    "Divides.div"]
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   455
    | _            => (warning ("Lin. Arith.: wrong format for split rule " ^
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   456
                                 Display.string_of_thm thm);
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   457
                       false))
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   458
  | _ => (warning ("Lin. Arith.: wrong format for split rule " ^
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   459
                   Display.string_of_thm thm);
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   460
          false);
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   461
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   462
(* 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
   463
(* variables as needed when substituting inside an abstraction               *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   464
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   465
fun subst_term ([] : (term * term) list) (t : term) = t
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   466
  | subst_term pairs                     t          =
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   467
      (case AList.lookup (op aconv) pairs t of
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   468
        SOME new =>
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   469
          new
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   470
      | NONE     =>
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   471
          (case t of Abs (a, T, body) =>
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   472
            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
   473
            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
   474
          | t1 $ t2                   =>
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   475
            subst_term pairs t1 $ subst_term pairs t2
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   476
          | _ => t));
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   477
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   478
(* 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
   479
(* 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
   480
(* 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
   481
(* 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
   482
(* on the subgoal                                                            *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   483
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   484
(* 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
   485
(*        (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
   486
(*        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
   487
(*        theorem that can be applied, and modify the subgoal accordingly.   *)
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   488
(*        Or even better, the splitter should be extended to provide         *)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   489
(*        splitting on terms as well as splitting on theorems (where the     *)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   490
(*        former can have a faster implementation as it does not need to be  *)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   491
(*        proof-producing).                                                  *)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   492
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   493
fun split_once_items (sg : theory) (Ts : typ list, terms : term list) :
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   494
                     (typ list * term list) list option =
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   495
let
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   496
  (* takes a list  [t1, ..., tn]  to the term                                *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   497
  (*   tn' --> ... --> t1' --> False  ,                                      *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   498
  (* where ti' = HOLogic.dest_Trueprop ti                                    *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   499
  (* term list -> term *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   500
  fun REPEAT_DETERM_etac_rev_mp terms' =
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   501
    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
   502
  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
   503
  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
   504
  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
   505
in
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   506
  if length splits > !fast_arith_split_limit then (
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   507
    tracing ("fast_arith_split_limit exceeded (current value is " ^
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   508
              string_of_int (!fast_arith_split_limit) ^ ")");
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   509
    NONE
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   510
  ) else (
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   511
  case splits of [] =>
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   512
    (* split_tac would fail: no possible split *)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   513
    NONE
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   514
  | ((_, _, _, split_type, split_term) :: _) => (
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   515
    (* ignore all but the first possible split *)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   516
    case strip_comb split_term of
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   517
    (* ?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
   518
      (Const ("Orderings.max", _), [t1, t2]) =>
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   519
      let
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   520
        val rev_terms     = rev terms
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   521
        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
   522
        val terms2        = map (subst_term [(split_term, t2)]) rev_terms
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   523
        val t1_leq_t2     = Const ("Orderings.less_eq",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   524
                                    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
   525
        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
   526
        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
   527
        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
   528
        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
   529
      in
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   530
        SOME [(Ts, subgoal1), (Ts, subgoal2)]
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   531
      end
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   532
    (* ?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
   533
    | (Const ("Orderings.min", _), [t1, t2]) =>
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   534
      let
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   535
        val rev_terms     = rev terms
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   536
        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
   537
        val terms2        = map (subst_term [(split_term, t2)]) rev_terms
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   538
        val t1_leq_t2     = Const ("Orderings.less_eq",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   539
                                    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
   540
        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
   541
        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
   542
        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
   543
        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
   544
      in
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   545
        SOME [(Ts, subgoal1), (Ts, subgoal2)]
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   546
      end
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   547
    (* ?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
   548
    | (Const ("HOL.abs", _), [t1]) =>
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   549
      let
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   550
        val rev_terms   = rev terms
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   551
        val terms1      = map (subst_term [(split_term, t1)]) rev_terms
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   552
        val terms2      = map (subst_term [(split_term, Const ("HOL.uminus",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   553
                            split_type --> split_type) $ t1)]) rev_terms
20713
823967ef47f1 renamed 0 and 1 to HOL.zero and HOL.one respectivly; introduced corresponding syntactic classes
haftmann
parents: 20485
diff changeset
   554
        val zero        = Const ("HOL.zero", split_type)
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   555
        val zero_leq_t1 = Const ("Orderings.less_eq",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   556
                            split_type --> split_type --> HOLogic.boolT) $ zero $ t1
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   557
        val t1_lt_zero  = Const ("Orderings.less",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   558
                            split_type --> split_type --> HOLogic.boolT) $ t1 $ zero
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   559
        val not_false   = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   560
        val subgoal1    = (HOLogic.mk_Trueprop zero_leq_t1) :: terms1 @ [not_false]
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   561
        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
   562
      in
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   563
        SOME [(Ts, subgoal1), (Ts, subgoal2)]
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   564
      end
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   565
    (* ?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
   566
    | (Const ("HOL.minus", _), [t1, t2]) =>
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   567
      let
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   568
        (* "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
   569
        (* transformation, therefore some adjustment of indices is necessary *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   570
        val rev_terms       = rev terms
20713
823967ef47f1 renamed 0 and 1 to HOL.zero and HOL.one respectivly; introduced corresponding syntactic classes
haftmann
parents: 20485
diff changeset
   571
        val zero            = Const ("HOL.zero", split_type)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   572
        val d               = Bound 0
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   573
        val terms1          = map (subst_term [(split_term, zero)]) rev_terms
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   574
        val terms2          = map (subst_term [(incr_boundvars 1 split_term, d)])
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   575
                                (map (incr_boundvars 1) rev_terms)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   576
        val t1'             = incr_boundvars 1 t1
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   577
        val t2'             = incr_boundvars 1 t2
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   578
        val t1_lt_t2        = Const ("Orderings.less",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   579
                                split_type --> split_type --> HOLogic.boolT) $ t1 $ t2
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   580
        val t1_eq_t2_plus_d = Const ("op =", split_type --> split_type --> HOLogic.boolT) $ t1' $
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   581
                                (Const ("HOL.plus",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   582
                                  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
   583
        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
   584
        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
   585
        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
   586
      in
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   587
        SOME [(Ts, subgoal1), (split_type :: Ts, subgoal2)]
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   588
      end
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   589
    (* ?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
   590
    | (Const ("IntDef.nat", _), [t1]) =>
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   591
      let
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   592
        val rev_terms   = rev terms
20713
823967ef47f1 renamed 0 and 1 to HOL.zero and HOL.one respectivly; introduced corresponding syntactic classes
haftmann
parents: 20485
diff changeset
   593
        val zero_int    = Const ("HOL.zero", HOLogic.intT)
823967ef47f1 renamed 0 and 1 to HOL.zero and HOL.one respectivly; introduced corresponding syntactic classes
haftmann
parents: 20485
diff changeset
   594
        val zero_nat    = Const ("HOL.zero", HOLogic.natT)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   595
        val n           = Bound 0
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   596
        val terms1      = map (subst_term [(incr_boundvars 1 split_term, n)])
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   597
                            (map (incr_boundvars 1) rev_terms)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   598
        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
   599
        val t1'         = incr_boundvars 1 t1
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   600
        val t1_eq_int_n = Const ("op =", HOLogic.intT --> HOLogic.intT --> HOLogic.boolT) $ t1' $
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   601
                            (Const ("IntDef.int", HOLogic.natT --> HOLogic.intT) $ n)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   602
        val t1_lt_zero  = Const ("Orderings.less",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   603
                            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
   604
        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
   605
        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
   606
        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
   607
      in
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   608
        SOME [(HOLogic.natT :: Ts, subgoal1), (Ts, subgoal2)]
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   609
      end
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   610
    (* "?P ((?n::nat) mod (number_of ?k)) =
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   611
         ((number_of ?k = 0 --> ?P ?n) & (~ (number_of ?k = 0) -->
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   612
           (ALL i j. j < number_of ?k --> ?n = number_of ?k * i + j --> ?P j))) *)
21415
39f98c88f88a op div/op mod now named without leading op
haftmann
parents: 21243
diff changeset
   613
    | (Const ("Divides.mod", Type ("fun", [Type ("nat", []), _])), [t1, t2]) =>
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   614
      let
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   615
        val rev_terms               = rev terms
20713
823967ef47f1 renamed 0 and 1 to HOL.zero and HOL.one respectivly; introduced corresponding syntactic classes
haftmann
parents: 20485
diff changeset
   616
        val zero                    = Const ("HOL.zero", split_type)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   617
        val i                       = Bound 1
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   618
        val j                       = Bound 0
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   619
        val terms1                  = map (subst_term [(split_term, t1)]) rev_terms
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   620
        val terms2                  = map (subst_term [(incr_boundvars 2 split_term, j)])
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   621
                                        (map (incr_boundvars 2) rev_terms)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   622
        val t1'                     = incr_boundvars 2 t1
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   623
        val t2'                     = incr_boundvars 2 t2
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   624
        val t2_eq_zero              = Const ("op =",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   625
                                        split_type --> split_type --> HOLogic.boolT) $ t2 $ zero
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   626
        val t2_neq_zero             = HOLogic.mk_not (Const ("op =",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   627
                                        split_type --> split_type --> HOLogic.boolT) $ t2' $ zero)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   628
        val j_lt_t2                 = Const ("Orderings.less",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   629
                                        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
   630
        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
   631
                                       (Const ("HOL.plus", split_type --> split_type --> split_type) $
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   632
                                         (Const ("HOL.times",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   633
                                           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
   634
        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
   635
        val subgoal1                = (HOLogic.mk_Trueprop t2_eq_zero) :: terms1 @ [not_false]
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   636
        val subgoal2                = (map HOLogic.mk_Trueprop
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   637
                                        [t2_neq_zero, j_lt_t2, t1_eq_t2_times_i_plus_j])
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   638
                                          @ terms2 @ [not_false]
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   639
      in
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   640
        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
   641
      end
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   642
    (* "?P ((?n::nat) div (number_of ?k)) =
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   643
         ((number_of ?k = 0 --> ?P 0) & (~ (number_of ?k = 0) -->
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   644
           (ALL i j. j < number_of ?k --> ?n = number_of ?k * i + j --> ?P i))) *)
21415
39f98c88f88a op div/op mod now named without leading op
haftmann
parents: 21243
diff changeset
   645
    | (Const ("Divides.div", Type ("fun", [Type ("nat", []), _])), [t1, t2]) =>
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   646
      let
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   647
        val rev_terms               = rev terms
20713
823967ef47f1 renamed 0 and 1 to HOL.zero and HOL.one respectivly; introduced corresponding syntactic classes
haftmann
parents: 20485
diff changeset
   648
        val zero                    = Const ("HOL.zero", split_type)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   649
        val i                       = Bound 1
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   650
        val j                       = Bound 0
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   651
        val terms1                  = map (subst_term [(split_term, zero)]) rev_terms
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   652
        val terms2                  = map (subst_term [(incr_boundvars 2 split_term, i)])
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   653
                                        (map (incr_boundvars 2) rev_terms)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   654
        val t1'                     = incr_boundvars 2 t1
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   655
        val t2'                     = incr_boundvars 2 t2
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   656
        val t2_eq_zero              = Const ("op =",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   657
                                        split_type --> split_type --> HOLogic.boolT) $ t2 $ zero
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   658
        val t2_neq_zero             = HOLogic.mk_not (Const ("op =",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   659
                                        split_type --> split_type --> HOLogic.boolT) $ t2' $ zero)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   660
        val j_lt_t2                 = Const ("Orderings.less",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   661
                                        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
   662
        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
   663
                                       (Const ("HOL.plus", split_type --> split_type --> split_type) $
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   664
                                         (Const ("HOL.times",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   665
                                           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
   666
        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
   667
        val subgoal1                = (HOLogic.mk_Trueprop t2_eq_zero) :: terms1 @ [not_false]
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   668
        val subgoal2                = (map HOLogic.mk_Trueprop
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   669
                                        [t2_neq_zero, j_lt_t2, t1_eq_t2_times_i_plus_j])
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   670
                                          @ terms2 @ [not_false]
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   671
      in
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   672
        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
   673
      end
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   674
    (* "?P ((?n::int) mod (number_of ?k)) =
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   675
         ((iszero (number_of ?k) --> ?P ?n) &
20485
3078fd2eec7b got rid of Numeral.bin type
haftmann
parents: 20413
diff changeset
   676
          (neg (number_of (uminus ?k)) -->
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   677
            (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
   678
          (neg (number_of ?k) -->
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   679
            (ALL i j. number_of ?k < j & j <= 0 & ?n = number_of ?k * i + j --> ?P j))) *)
21415
39f98c88f88a op div/op mod now named without leading op
haftmann
parents: 21243
diff changeset
   680
    | (Const ("Divides.mod",
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   681
        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
   682
      let
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   683
        val rev_terms               = rev terms
20713
823967ef47f1 renamed 0 and 1 to HOL.zero and HOL.one respectivly; introduced corresponding syntactic classes
haftmann
parents: 20485
diff changeset
   684
        val zero                    = Const ("HOL.zero", split_type)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   685
        val i                       = Bound 1
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   686
        val j                       = Bound 0
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   687
        val terms1                  = map (subst_term [(split_term, t1)]) rev_terms
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   688
        val terms2_3                = map (subst_term [(incr_boundvars 2 split_term, j)])
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   689
                                        (map (incr_boundvars 2) rev_terms)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   690
        val t1'                     = incr_boundvars 2 t1
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   691
        val (t2' as (_ $ k'))       = incr_boundvars 2 t2
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   692
        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
   693
        val neg_minus_k             = Const ("IntDef.neg", split_type --> HOLogic.boolT) $
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   694
                                        (number_of $
20485
3078fd2eec7b got rid of Numeral.bin type
haftmann
parents: 20413
diff changeset
   695
                                          (Const ("HOL.uminus",
3078fd2eec7b got rid of Numeral.bin type
haftmann
parents: 20413
diff changeset
   696
                                            HOLogic.intT --> HOLogic.intT) $ k'))
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   697
        val zero_leq_j              = Const ("Orderings.less_eq",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   698
                                        split_type --> split_type --> HOLogic.boolT) $ zero $ j
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   699
        val j_lt_t2                 = Const ("Orderings.less",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   700
                                        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
   701
        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
   702
                                       (Const ("HOL.plus", split_type --> split_type --> split_type) $
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   703
                                         (Const ("HOL.times",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   704
                                           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
   705
        val neg_t2                  = Const ("IntDef.neg", split_type --> HOLogic.boolT) $ t2'
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   706
        val t2_lt_j                 = Const ("Orderings.less",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   707
                                        split_type --> split_type--> HOLogic.boolT) $ t2' $ j
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   708
        val j_leq_zero              = Const ("Orderings.less_eq",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   709
                                        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
   710
        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
   711
        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
   712
        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
   713
                                        @ hd terms2_3
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   714
                                        :: (if tl terms2_3 = [] then [not_false] else [])
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   715
                                        @ (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
   716
                                        @ (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
   717
        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
   718
                                        @ hd terms2_3
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   719
                                        :: (if tl terms2_3 = [] then [not_false] else [])
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   720
                                        @ (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
   721
                                        @ (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
   722
        val Ts'                     = split_type :: split_type :: Ts
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   723
      in
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   724
        SOME [(Ts, subgoal1), (Ts', subgoal2), (Ts', subgoal3)]
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   725
      end
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   726
    (* "?P ((?n::int) div (number_of ?k)) =
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   727
         ((iszero (number_of ?k) --> ?P 0) &
20485
3078fd2eec7b got rid of Numeral.bin type
haftmann
parents: 20413
diff changeset
   728
          (neg (number_of (uminus ?k)) -->
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   729
            (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
   730
          (neg (number_of ?k) -->
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   731
            (ALL i. (EX j. number_of ?k < j & j <= 0 & ?n = number_of ?k * i + j) --> ?P i))) *)
21415
39f98c88f88a op div/op mod now named without leading op
haftmann
parents: 21243
diff changeset
   732
    | (Const ("Divides.div",
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   733
        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
   734
      let
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   735
        val rev_terms               = rev terms
20713
823967ef47f1 renamed 0 and 1 to HOL.zero and HOL.one respectivly; introduced corresponding syntactic classes
haftmann
parents: 20485
diff changeset
   736
        val zero                    = Const ("HOL.zero", split_type)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   737
        val i                       = Bound 1
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   738
        val j                       = Bound 0
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   739
        val terms1                  = map (subst_term [(split_term, zero)]) rev_terms
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   740
        val terms2_3                = map (subst_term [(incr_boundvars 2 split_term, i)])
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   741
                                        (map (incr_boundvars 2) rev_terms)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   742
        val t1'                     = incr_boundvars 2 t1
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   743
        val (t2' as (_ $ k'))       = incr_boundvars 2 t2
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   744
        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
   745
        val neg_minus_k             = Const ("IntDef.neg", split_type --> HOLogic.boolT) $
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   746
                                        (number_of $
22927
0b53bd36258b fixed typo
haftmann
parents: 22900
diff changeset
   747
                                          (Const ("HOL.uminus",
20485
3078fd2eec7b got rid of Numeral.bin type
haftmann
parents: 20413
diff changeset
   748
                                            HOLogic.intT --> HOLogic.intT) $ k'))
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   749
        val zero_leq_j              = Const ("Orderings.less_eq",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   750
                                        split_type --> split_type --> HOLogic.boolT) $ zero $ j
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   751
        val j_lt_t2                 = Const ("Orderings.less",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   752
                                        split_type --> split_type--> HOLogic.boolT) $ j $ t2'
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   753
        val t1_eq_t2_times_i_plus_j = Const ("op =",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   754
                                        split_type --> split_type --> HOLogic.boolT) $ t1' $
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   755
                                       (Const ("HOL.plus", split_type --> split_type --> split_type) $
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   756
                                         (Const ("HOL.times",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   757
                                           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
   758
        val neg_t2                  = Const ("IntDef.neg", split_type --> HOLogic.boolT) $ t2'
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   759
        val t2_lt_j                 = Const ("Orderings.less",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   760
                                        split_type --> split_type--> HOLogic.boolT) $ t2' $ j
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   761
        val j_leq_zero              = Const ("Orderings.less_eq",
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   762
                                        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
   763
        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
   764
        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
   765
        val subgoal2                = (HOLogic.mk_Trueprop neg_minus_k)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   766
                                        :: terms2_3
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   767
                                        @ not_false
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   768
                                        :: (map HOLogic.mk_Trueprop
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   769
                                             [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
   770
        val subgoal3                = (HOLogic.mk_Trueprop neg_t2)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   771
                                        :: terms2_3
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   772
                                        @ not_false
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   773
                                        :: (map HOLogic.mk_Trueprop
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   774
                                             [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
   775
        val Ts'                     = split_type :: split_type :: Ts
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   776
      in
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   777
        SOME [(Ts, subgoal1), (Ts', subgoal2), (Ts', subgoal3)]
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   778
      end
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   779
    (* this will only happen if a split theorem can be applied for which no  *)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   780
    (* code exists above -- in which case either the split theorem should be *)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   781
    (* implemented above, or 'is_split_thm' should be modified to filter it  *)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   782
    (* out                                                                   *)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   783
    | (t, ts) => (
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   784
      warning ("Lin. Arith.: split rule for " ^ Sign.string_of_term sg t ^
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   785
               " (with " ^ Int.toString (length ts) ^
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   786
               " 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
   787
      NONE
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   788
    ))
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   789
  )
9436
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   790
end;
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   791
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   792
(* 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
   793
(* 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
   794
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   795
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
   796
let
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   797
  fun filter_prems (t, (left, right)) =
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   798
    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
   799
  val (left, right) = foldl filter_prems ([], []) terms
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   800
in
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   801
  right @ left
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   802
end;
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   803
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   804
(* 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
   805
(* subgoal that has 'terms' as premises                                      *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   806
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   807
fun negated_term_occurs_positively (terms : term list) : bool =
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   808
  List.exists
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   809
    (fn (Trueprop $ (Const ("Not", _) $ t)) => member (op aconv) terms (Trueprop $ t)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   810
      | _                                   => false)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   811
    terms;
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   812
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   813
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
   814
let
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   815
  (* 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
   816
  (* splitting is possible                                                   *)
20271
e76e77e0d615 fixed a bug in function poly: decomposition of products
webertj
parents: 20268
diff changeset
   817
  fun split_loop ([] : (typ list * term list) list) = ([] : (typ list * term list) list)
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   818
    | split_loop (subgoal::subgoals)                = (
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   819
        case split_once_items sg subgoal of
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   820
          SOME new_subgoals => split_loop (new_subgoals @ subgoals)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   821
        | NONE              => subgoal :: split_loop subgoals
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   822
      )
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   823
  fun is_relevant t  = isSome (decomp sg t)
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   824
  (* filter_prems_tac is_relevant: *)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   825
  val relevant_terms = filter_prems_tac_items is_relevant terms
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   826
  (* split_tac, NNF normalization: *)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   827
  val split_goals    = split_loop [(Ts, relevant_terms)]
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   828
  (* necessary because split_once_tac may normalize terms: *)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   829
  val beta_eta_norm  = map (apsnd (map (Envir.eta_contract o Envir.beta_norm))) split_goals
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   830
  (* TRY (etac notE) THEN eq_assume_tac: *)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   831
  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
   832
in
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   833
  result
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   834
end;
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   835
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   836
(* 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
   837
(* 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
   838
(* (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
   839
(* performs NNF-normalization of ~P, and eliminates conjunctions,            *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   840
(* 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
   841
(* 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
   842
(* 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
   843
(* !fast_arith_split_limit splits are possible.                              *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   844
20850
f43d36f1364a nnf_simpset built statically
webertj
parents: 20713
diff changeset
   845
local
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   846
  val nnf_simpset =
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   847
    empty_ss setmkeqTrue mk_eq_True
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   848
    setmksimps (mksimps mksimps_pairs)
20850
f43d36f1364a nnf_simpset built statically
webertj
parents: 20713
diff changeset
   849
    addsimps [imp_conv_disj, iff_conv_conj_imp, de_Morgan_disj, de_Morgan_conj,
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   850
      not_all, not_ex, not_not]
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   851
  fun prem_nnf_tac i st =
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   852
    full_simp_tac (Simplifier.theory_context (Thm.theory_of_thm st) nnf_simpset) i st
20850
f43d36f1364a nnf_simpset built statically
webertj
parents: 20713
diff changeset
   853
in
f43d36f1364a nnf_simpset built statically
webertj
parents: 20713
diff changeset
   854
f43d36f1364a nnf_simpset built statically
webertj
parents: 20713
diff changeset
   855
fun split_once_tac (split_thms : thm list) (i : int) : tactic =
f43d36f1364a nnf_simpset built statically
webertj
parents: 20713
diff changeset
   856
let
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   857
  fun cond_split_tac i st =
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   858
    let
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   859
      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
   860
      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
   861
      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
   862
      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
   863
      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
   864
    in
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   865
      if length splits > !fast_arith_split_limit then
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   866
        no_tac st
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   867
      else
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   868
        split_tac split_thms i st
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   869
    end
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   870
in
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   871
  EVERY' [
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   872
    REPEAT_DETERM o etac rev_mp,
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   873
    cond_split_tac,
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   874
    rtac ccontr,
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   875
    prem_nnf_tac,
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   876
    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
   877
  ] i
20850
f43d36f1364a nnf_simpset built statically
webertj
parents: 20713
diff changeset
   878
end
f43d36f1364a nnf_simpset built statically
webertj
parents: 20713
diff changeset
   879
f43d36f1364a nnf_simpset built statically
webertj
parents: 20713
diff changeset
   880
end;  (* local *)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   881
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   882
(* 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
   883
(* 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
   884
(* 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
   885
(* 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
   886
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   887
fun pre_tac i st =
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   888
let
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   889
  val sg            = theory_of_thm st
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   890
  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
   891
  fun is_relevant t = isSome (decomp sg t)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   892
in
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   893
  DETERM (
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   894
    TRY (filter_prems_tac is_relevant i)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   895
      THEN (
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   896
        (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
   897
          THEN_ALL_NEW
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   898
            ((fn j => PRIMITIVE
22900
f8a7c10e1bd0 moved conversions to structure Conv;
wenzelm
parents: 22887
diff changeset
   899
                        (Conv.fconv_rule
f8a7c10e1bd0 moved conversions to structure Conv;
wenzelm
parents: 22887
diff changeset
   900
                          (Conv.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
   901
              THEN'
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   902
            (TRY o (etac notE THEN' eq_assume_tac)))
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   903
      ) i
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   904
  ) st
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   905
end;
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   906
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   907
end;  (* LA_Data_Ref *)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   908
9436
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   909
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   910
structure Fast_Arith =
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   911
  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
   912
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   913
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
   914
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
   915
val trace_arith            = Fast_Arith.trace;
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   916
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
   917
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
   918
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   919
(* reduce contradictory <= to False.
22838
haftmann
parents: 22634
diff changeset
   920
   Most of the work is done by the cancel tactics. *)
9436
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   921
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   922
val init_lin_arith_data =
18708
4b3dadb4fe33 setup: theory -> theory;
wenzelm
parents: 18394
diff changeset
   923
 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
   924
   {add_mono_thms = add_mono_thms @
22838
haftmann
parents: 22634
diff changeset
   925
    @{thms add_mono_thms_ordered_semiring} @ @{thms add_mono_thms_ordered_field},
10693
9e4a0e84d0d6 moved mk_bin from Numerals to HOLogic
nipkow
parents: 10574
diff changeset
   926
    mult_mono_thms = mult_mono_thms,
10574
8f98f0301d67 Linear arithmetic now copes with mixed nat/int formulae.
nipkow
parents: 10516
diff changeset
   927
    inj_thms = inj_thms,
21243
afffe1f72143 removed theory NatArith (now part of Nat);
wenzelm
parents: 20897
diff changeset
   928
    lessD = lessD @ [thm "Suc_leI"],
22887
haftmann
parents: 22846
diff changeset
   929
    neqE = [@{thm linorder_neqE_nat}, @{thm linorder_neqE_ordered_idom}],
22838
haftmann
parents: 22634
diff changeset
   930
    simpset = HOL_basic_ss
haftmann
parents: 22634
diff changeset
   931
      addsimps [@{thm "add_zero_left"}, @{thm "add_zero_right"},
haftmann
parents: 22634
diff changeset
   932
        @{thm "Zero_not_Suc"}, @{thm "Suc_not_Zero"}, @{thm "le_0_eq"}, @{thm "One_nat_def"},
haftmann
parents: 22634
diff changeset
   933
        @{thm "order_less_irrefl"}, @{thm "zero_neq_one"}, @{thm "zero_less_one"},
haftmann
parents: 22634
diff changeset
   934
        @{thm "zero_le_one"}, @{thm "zero_neq_one"} RS not_sym, @{thm "not_one_le_zero"},
haftmann
parents: 22634
diff changeset
   935
        @{thm "not_one_less_zero"}]
haftmann
parents: 22634
diff changeset
   936
      addsimprocs [ab_group_add_cancel.sum_conv, ab_group_add_cancel.rel_conv]
haftmann
parents: 22634
diff changeset
   937
       (*abel_cancel helps it work in abstract algebraic domains*)
haftmann
parents: 22634
diff changeset
   938
      addsimprocs nat_cancel_sums_add}) #>
18708
4b3dadb4fe33 setup: theory -> theory;
wenzelm
parents: 18394
diff changeset
   939
  arith_discrete "nat";
9436
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   940
13462
56610e2ba220 sane interface for simprocs;
wenzelm
parents: 12949
diff changeset
   941
val fast_nat_arith_simproc =
16834
71d87aeebb57 HOL.Not;
wenzelm
parents: 16733
diff changeset
   942
  Simplifier.simproc (the_context ()) "fast_nat_arith"
13462
56610e2ba220 sane interface for simprocs;
wenzelm
parents: 12949
diff changeset
   943
    ["(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
   944
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   945
(* 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
   946
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
   947
*not* themselves (in)equalities, because the latter activate
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   948
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
   949
solver all the time rather than add the additional check. *)
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   950
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   951
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   952
(* arith proof method *)
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   953
10516
dc113303d101 arith_tac: atomize;
wenzelm
parents: 9893
diff changeset
   954
local
dc113303d101 arith_tac: atomize;
wenzelm
parents: 9893
diff changeset
   955
13499
f95f5818f24f Counter example generation mods.
nipkow
parents: 13462
diff changeset
   956
fun raw_arith_tac ex i st =
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   957
  (* 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
   958
     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
   959
     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
   960
     (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
   961
     (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
   962
  *)
13499
f95f5818f24f Counter example generation mods.
nipkow
parents: 13462
diff changeset
   963
  refute_tac (K true)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   964
    (* 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
   965
    (* split_tac may use split theorems that have not been implemented in    *)
20268
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   966
    (* fast_arith_tac (cf. pre_decomp and split_once_items above), and       *)
1fe9aed8fcac code reformatted
webertj
parents: 20254
diff changeset
   967
    (* fast_arith_split_limit may trigger.                                   *)
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   968
    (* 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
   969
    (* 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
   970
    (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
   971
    (fast_ex_arith_tac ex)
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   972
    i st;
9436
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
   973
20412
40757f475eb0 additional list of tactics that can be added to arith
webertj
parents: 20280
diff changeset
   974
fun arith_theory_tac i st =
40757f475eb0 additional list of tactics that can be added to arith
webertj
parents: 20280
diff changeset
   975
let
40757f475eb0 additional list of tactics that can be added to arith
webertj
parents: 20280
diff changeset
   976
  val tactics = #tactics (ArithTheoryData.get (Thm.theory_of_thm st))
40757f475eb0 additional list of tactics that can be added to arith
webertj
parents: 20280
diff changeset
   977
in
40757f475eb0 additional list of tactics that can be added to arith
webertj
parents: 20280
diff changeset
   978
  FIRST' (map (fn ArithTactic {tactic, ...} => tactic) tactics) i st
40757f475eb0 additional list of tactics that can be added to arith
webertj
parents: 20280
diff changeset
   979
end;
13877
a6b825ee48d9 Added hook for presburger arithmetic decision procedure.
berghofe
parents: 13517
diff changeset
   980
10516
dc113303d101 arith_tac: atomize;
wenzelm
parents: 9893
diff changeset
   981
in
dc113303d101 arith_tac: atomize;
wenzelm
parents: 9893
diff changeset
   982
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   983
  val simple_arith_tac = FIRST' [fast_arith_tac,
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   984
    ObjectLogic.atomize_tac THEN' raw_arith_tac true];
13877
a6b825ee48d9 Added hook for presburger arithmetic decision procedure.
berghofe
parents: 13517
diff changeset
   985
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   986
  val arith_tac = FIRST' [fast_arith_tac,
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   987
    ObjectLogic.atomize_tac THEN' raw_arith_tac true,
20412
40757f475eb0 additional list of tactics that can be added to arith
webertj
parents: 20280
diff changeset
   988
    arith_theory_tac];
13877
a6b825ee48d9 Added hook for presburger arithmetic decision procedure.
berghofe
parents: 13517
diff changeset
   989
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   990
  val silent_arith_tac = FIRST' [fast_arith_tac,
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   991
    ObjectLogic.atomize_tac THEN' raw_arith_tac false,
20412
40757f475eb0 additional list of tactics that can be added to arith
webertj
parents: 20280
diff changeset
   992
    arith_theory_tac];
10516
dc113303d101 arith_tac: atomize;
wenzelm
parents: 9893
diff changeset
   993
20217
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   994
  fun arith_method prems =
25b068a99d2b linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents: 20044
diff changeset
   995
    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
   996
10516
dc113303d101 arith_tac: atomize;
wenzelm
parents: 9893
diff changeset
   997
end;
dc113303d101 arith_tac: atomize;
wenzelm
parents: 9893
diff changeset
   998
15195
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
   999
(* antisymmetry:
15197
19e735596e51 Added antisymmetry simproc
nipkow
parents: 15195
diff changeset
  1000
   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
  1001
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1002
local
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1003
val antisym = mk_meta_eq order_antisym
22548
6ce4bddf3bcb dropped legacy ML bindings
haftmann
parents: 21879
diff changeset
  1004
val not_lessD = @{thm linorder_not_less} RS iffD1
15195
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1005
fun prp t thm = (#prop(rep_thm thm) = t)
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1006
in
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1007
fun antisym_eq prems thm =
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1008
  let
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1009
    val r = #prop(rep_thm thm);
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1010
  in
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1011
    case r of
19277
f7602e74d948 renamed op < <= to Orderings.less(_eq)
haftmann
parents: 19233
diff changeset
  1012
      Tr $ ((c as Const("Orderings.less_eq",T)) $ s $ t) =>
15195
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1013
        let val r' = Tr $ (c $ t $ s)
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1014
        in
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1015
          case Library.find_first (prp r') prems of
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15234
diff changeset
  1016
            NONE =>
19277
f7602e74d948 renamed op < <= to Orderings.less(_eq)
haftmann
parents: 19233
diff changeset
  1017
              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
  1018
              in case Library.find_first (prp r') prems of
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15234
diff changeset
  1019
                   NONE => []
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15234
diff changeset
  1020
                 | SOME thm' => [(thm' RS not_lessD) RS (thm RS antisym)]
15195
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1021
              end
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15234
diff changeset
  1022
          | SOME thm' => [thm' RS (thm RS antisym)]
15195
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1023
        end
19277
f7602e74d948 renamed op < <= to Orderings.less(_eq)
haftmann
parents: 19233
diff changeset
  1024
    | Tr $ (Const("Not",_) $ (Const("Orderings.less",T) $ s $ t)) =>
f7602e74d948 renamed op < <= to Orderings.less(_eq)
haftmann
parents: 19233
diff changeset
  1025
        let val r' = Tr $ (Const("Orderings.less_eq",T) $ s $ t)
15195
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1026
        in
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1027
          case Library.find_first (prp r') prems of
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15234
diff changeset
  1028
            NONE =>
19277
f7602e74d948 renamed op < <= to Orderings.less(_eq)
haftmann
parents: 19233
diff changeset
  1029
              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
  1030
              in case Library.find_first (prp r') prems of
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15234
diff changeset
  1031
                   NONE => []
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15234
diff changeset
  1032
                 | SOME thm' =>
15195
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1033
                     [(thm' RS not_lessD) RS ((thm RS not_lessD) RS antisym)]
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1034
              end
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15234
diff changeset
  1035
          | SOME thm' => [thm' RS ((thm RS not_lessD) RS antisym)]
15195
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1036
        end
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1037
    | _ => []
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1038
  end
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1039
  handle THM _ => []
197e00ce3f20 new forward deduction capability for simplifier
nipkow
parents: 15185
diff changeset
  1040
end;
15197
19e735596e51 Added antisymmetry simproc
nipkow
parents: 15195
diff changeset
  1041
*)
9436
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
  1042
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
  1043
(* theory setup *)
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
  1044
62bb04ab4b01 rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff changeset
  1045
val arith_setup =
18708
4b3dadb4fe33 setup: theory -> theory;
wenzelm
parents: 18394
diff changeset
  1046
  init_lin_arith_data #>
4b3dadb4fe33 setup: theory -> theory;
wenzelm
parents: 18394
diff changeset
  1047
  (fn thy => (Simplifier.change_simpset_of thy (fn ss => ss
17875
d81094515061 change_claset/simpset;
wenzelm
parents: 17611
diff changeset
  1048
    addsimprocs (nat_cancel_sums @ [fast_nat_arith_simproc])
18708
4b3dadb4fe33 setup: theory -> theory;
wenzelm
parents: 18394
diff changeset
  1049
    addSolver (mk_solver' "lin. arith." Fast_Arith.cut_lin_arith_tac)); thy)) #>
15221
8412cfdf3287 tweaking of arithmetic proofs
paulson
parents: 15197
diff changeset
  1050
  Method.add_methods
21879
a3efbae45735 switched argument order in *.syntax lifters
haftmann
parents: 21820
diff changeset
  1051
    [("arith", (arith_method o fst) oo Method.syntax Args.bang_facts,
18708
4b3dadb4fe33 setup: theory -> theory;
wenzelm
parents: 18394
diff changeset
  1052
      "decide linear arithmethic")] #>
18728
6790126ab5f6 simplified type attribute;
wenzelm
parents: 18708
diff changeset
  1053
  Attrib.add_attributes [("arith_split", Attrib.no_args arith_split_add,
18708
4b3dadb4fe33 setup: theory -> theory;
wenzelm
parents: 18394
diff changeset
  1054
    "declaration of split rules for arithmetic procedure")];