src/HOL/Tools/lin_arith.ML
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(*  Title:      HOL/Tools/lin_arith.ML
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    Author:     Tjark Weber and Tobias Nipkow, TU Muenchen
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HOL setup for linear arithmetic (see Provers/Arith/fast_lin_arith.ML).
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*)
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signature LIN_ARITH =
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sig
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  val pre_tac: Proof.context -> int -> tactic
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  val simple_tac: Proof.context -> int -> tactic
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  val tac: Proof.context -> int -> tactic
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  val simproc: simpset -> term -> thm option
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  val add_inj_thms: thm list -> Context.generic -> Context.generic
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  val add_lessD: thm -> Context.generic -> Context.generic
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  val add_simps: thm list -> Context.generic -> Context.generic
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  val add_simprocs: simproc list -> Context.generic -> Context.generic
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  val add_inj_const: string * typ -> Context.generic -> Context.generic
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  val add_discrete_type: string -> Context.generic -> Context.generic
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  val set_number_of: (theory -> typ -> int -> cterm) -> Context.generic ->
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    Context.generic
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  val setup: Context.generic -> Context.generic
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  val global_setup: theory -> theory
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  val split_limit: int Config.T
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  val neq_limit: int Config.T
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  val warning_count: int Unsynchronized.ref
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  val trace: bool Unsynchronized.ref
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end;
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structure Lin_Arith: LIN_ARITH =
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struct
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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 trueI = TrueI;
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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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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 Thm.prop_of thm of
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    Const ("Trueprop", _) $ (Const (@{const_name "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 as Const("Trueprop", _)) $ (Const (@{const_name Not}, _) $ t)) = TP $ t
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  | neg_prop ((TP as Const("Trueprop", _)) $ t) = TP $ (HOLogic.Not $t)
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  | neg_prop t = raise TERM ("neg_prop", [t]);
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fun is_False thm =
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  let val _ $ t = Thm.prop_of thm
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  in t = HOLogic.false_const end;
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fun is_nat t = (fastype_of1 t = HOLogic.natT);
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fun mk_nat_thm thy t =
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  let
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    val cn = cterm_of thy (Var (("n", 0), HOLogic.natT))
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    and ct = cterm_of thy t
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  in instantiate ([], [(cn, ct)]) @{thm le0} end;
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end;  (* LA_Logic *)
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(* arith context data *)
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structure Lin_Arith_Data = GenericDataFun
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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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  val empty = {splits = [], inj_consts = [], discrete = []};
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  val extend = I;
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  fun merge _
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   ({splits= splits1, inj_consts= inj_consts1, discrete= discrete1},
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    {splits= splits2, inj_consts= inj_consts2, discrete= discrete2}) : T =
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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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);
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val get_arith_data = Lin_Arith_Data.get o Context.Proof;
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fun add_split thm = Lin_Arith_Data.map (fn {splits, inj_consts, discrete} =>
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  {splits = update Thm.eq_thm_prop thm splits,
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   inj_consts = inj_consts, discrete = discrete});
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fun add_discrete_type d = Lin_Arith_Data.map (fn {splits, inj_consts, discrete} =>
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  {splits = splits, inj_consts = inj_consts,
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   discrete = update (op =) d discrete});
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fun add_inj_const c = Lin_Arith_Data.map (fn {splits, inj_consts, discrete} =>
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  {splits = splits, inj_consts = update (op =) c inj_consts,
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   discrete = discrete});
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val (split_limit, setup_split_limit) = Attrib.config_int "linarith_split_limit" 9;
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val (neq_limit, setup_neq_limit) = Attrib.config_int "linarith_neq_limit" 9;
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structure LA_Data =
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struct
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val fast_arith_neq_limit = neq_limit;
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(* Decomposition of terms *)
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(*internal representation of linear (in-)equations*)
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type decomp =
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  ((term * Rat.rat) list * Rat.rat * string * (term * Rat.rat) list * Rat.rat * bool);
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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 Pattern.aeconv p t of
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      NONE   => ((t, m) :: p, i)
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    | SOME n => (AList.update Pattern.aeconv (t, Rat.add n m) p, i);
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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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   inj_consts: list of constants to be ignored when encountered
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               (e.g. arithmetic type conversions that preserve value)
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   m: multiplicity associated with the entire product
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   returns either (SOME term, associated multiplicity) or (NONE, constant)
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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 (@{const_name HOL.times}, _)) $ s $ t, m) =
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      (case s of Const (@{const_name HOL.times}, _) $ s1 $ s2 =>
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        (* bracketing to the right: '(s1 * s2) * t' becomes 's1 * (s2 * t)' *)
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        demult (mC $ s1 $ (mC $ s2 $ t), m)
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      | _ =>
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        (* product 's * t', where either factor can be 'NONE' *)
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        (case demult (s, m) of
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          (SOME s', m') =>
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            (case demult (t, m') of
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              (SOME t', m'') => (SOME (mC $ s' $ t'), m'')
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            | (NONE,    m'') => (SOME s', m''))
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        | (NONE,    m') => demult (t, m')))
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    | demult ((mC as Const (@{const_name HOL.divide}, _)) $ s $ t, m) =
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      (* FIXME: Shouldn't we simplify nested quotients, e.g. '(s/t)/u' could
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         become 's/(t*u)', and '(s*t)/u' could become 's*(t/u)' ?   Note that
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         if we choose to do so here, the simpset used by arith must be able to
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         perform the same simplifications. *)
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      (* FIXME: Currently we treat the numerator as atomic unless the
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         denominator can be reduced to a numeric constant.  It might be better
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         to demult the numerator in any case, and invent a new term of the form
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         '1 / t' if the numerator can be reduced, but the denominator cannot. *)
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      (* FIXME: Currently we even treat the whole fraction as atomic unless the
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         denominator can be reduced to a numeric constant.  It might be better
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         to use the partially reduced denominator (i.e. 's / (2*t)' could be
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         demult'ed to 's / t' with multiplicity .5).   This would require a
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         very simple change only below, but it breaks existing proofs. *)
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      (* quotient 's / t', where the denominator t can be NONE *)
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      (* Note: will raise Rat.DIVZERO iff m' is Rat.zero *)
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      (case demult (t, Rat.one) of
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        (SOME _, _) => (SOME (mC $ s $ t), m)
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      | (NONE,  m') => apsnd (Rat.mult (Rat.inv m')) (demult (s, m)))
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    (* terms that evaluate to numeric constants *)
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    | demult (Const (@{const_name HOL.uminus}, _) $ t, m) = demult (t, Rat.neg m)
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    | demult (Const (@{const_name HOL.zero}, _), m) = (NONE, Rat.zero)
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    | demult (Const (@{const_name HOL.one}, _), m) = (NONE, m)
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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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    | demult (t as Const ("Int.number_class.number_of", _) $ n, m) =
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      ((NONE, Rat.mult m (Rat.rat_of_int (HOLogic.dest_numeral n)))
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        handle TERM _ => (SOME t, m))
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    | demult (t as Const (@{const_name Suc}, _) $ _, m) =
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      ((NONE, Rat.mult m (Rat.rat_of_int (HOLogic.dest_nat t)))
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        handle TERM _ => (SOME t, m))
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    (* injection constants are ignored *)
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    | demult (t as Const f $ x, m) =
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      if member (op =) inj_consts f then demult (x, m) else (SOME t, m)
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    (* everything else is considered atomic *)
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    | demult (atom, m) = (SOME atom, m)
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in demult end;
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fun decomp0 (inj_consts : (string * typ) list) (rel : string, lhs : term, rhs : term) :
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            ((term * Rat.rat) list * Rat.rat * string * (term * Rat.rat) list * Rat.rat) option =
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let
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  (* Turns a term 'all' and associated multiplicity 'm' into a list 'p' of
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     summands and associated multiplicities, plus a constant 'i' (with implicit
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     multiplicity 1) *)
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  fun poly (Const (@{const_name HOL.plus}, _) $ s $ t,
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        m : Rat.rat, pi : (term * Rat.rat) list * Rat.rat) = poly (s, m, poly (t, m, pi))
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    | poly (all as Const (@{const_name HOL.minus}, T) $ s $ t, m, pi) =
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        if nT T then add_atom all m pi else poly (s, m, poly (t, Rat.neg m, pi))
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    | poly (all as Const (@{const_name HOL.uminus}, T) $ t, m, pi) =
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        if nT T then add_atom all m pi else poly (t, Rat.neg m, pi)
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    | poly (Const (@{const_name HOL.zero}, _), _, pi) =
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        pi
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    | poly (Const (@{const_name HOL.one}, _), m, (p, i)) =
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        (p, Rat.add i m)
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    | poly (Const (@{const_name Suc}, _) $ t, m, (p, i)) =
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        poly (t, m, (p, Rat.add i m))
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    | poly (all as Const (@{const_name HOL.times}, _) $ _ $ _, m, pi as (p, i)) =
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        (case demult inj_consts (all, m) of
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           (NONE,   m') => (p, Rat.add i m')
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         | (SOME u, m') => add_atom u m' pi)
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    | poly (all as Const (@{const_name HOL.divide}, _) $ _ $ _, m, pi as (p, i)) =
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        (case demult inj_consts (all, m) of
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           (NONE,   m') => (p, Rat.add i m')
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         | (SOME u, m') => add_atom u m' pi)
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    | poly (all as Const ("Int.number_class.number_of", Type(_,[_,T])) $ t, m, pi as (p, i)) =
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        (let val k = HOLogic.dest_numeral t
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            val k2 = if k < 0 andalso T = HOLogic.natT then 0 else k
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        in (p, Rat.add i (Rat.mult m (Rat.rat_of_int k2))) end
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        handle TERM _ => add_atom all m pi)
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    | poly (all as Const f $ x, m, pi) =
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        if f mem inj_consts then poly (x, m, pi) else add_atom all m pi
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    | poly (all, m, pi) =
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        add_atom all m pi
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  val (p, i) = poly (lhs, Rat.one, ([], Rat.zero))
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  val (q, j) = poly (rhs, Rat.one, ([], Rat.zero))
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in
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  case rel of
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    @{const_name HOL.less}    => SOME (p, i, "<", q, j)
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  | @{const_name HOL.less_eq} => SOME (p, i, "<=", q, j)
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  | "op ="              => SOME (p, i, "=", q, j)
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  | _                   => NONE
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end handle Rat.DIVZERO => NONE;
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fun of_lin_arith_sort thy U =
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  Sign.of_sort thy (U, @{sort Ring_and_Field.ordered_idom});
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fun allows_lin_arith thy (discrete : string list) (U as Type (D, [])) : bool * bool =
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      if of_lin_arith_sort thy U then (true, member (op =) discrete D)
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      else if member (op =) discrete D then (true, true) else (false, false)
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  | allows_lin_arith sg discrete U = (of_lin_arith_sort sg U, false);
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fun decomp_typecheck (thy, discrete, inj_consts) (T : typ, xxx) : decomp option =
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  case T of
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    Type ("fun", [U, _]) =>
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      (case allows_lin_arith thy discrete U of
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        (true, d) =>
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          (case decomp0 inj_consts xxx of
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            NONE                   => NONE
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          | SOME (p, i, rel, q, j) => SOME (p, i, rel, q, j, d))
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      | (false, _) =>
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          NONE)
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  | _ => NONE;
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fun negate (SOME (x, i, rel, y, j, d)) = SOME (x, i, "~" ^ rel, y, j, d)
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  | negate NONE                        = NONE;
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fun decomp_negation data
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  ((Const ("Trueprop", _)) $ (Const (rel, T) $ lhs $ rhs)) : decomp option =
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      decomp_typecheck data (T, (rel, lhs, rhs))
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  | decomp_negation data ((Const ("Trueprop", _)) $
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  (Const ("Not", _) $ (Const (rel, T) $ lhs $ rhs))) =
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      negate (decomp_typecheck data (T, (rel, lhs, rhs)))
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  | decomp_negation data _ =
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      NONE;
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fun decomp ctxt : term -> decomp option =
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  let
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    val thy = ProofContext.theory_of ctxt
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    val {discrete, inj_consts, ...} = get_arith_data ctxt
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  in decomp_negation (thy, discrete, inj_consts) end;
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fun domain_is_nat (_ $ (Const (_, T) $ _ $ _))                      = nT T
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  | domain_is_nat (_ $ (Const ("Not", _) $ (Const (_, T) $ _ $ _))) = nT T
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  | domain_is_nat _                                                 = false;
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(*---------------------------------------------------------------------------*)
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(* the following code performs splitting of certain constants (e.g., min,    *)
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(* max) in a linear arithmetic problem; similar to what split_tac later does *)
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(* to the proof state                                                        *)
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(*---------------------------------------------------------------------------*)
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(* checks if splitting with 'thm' is implemented                             *)
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fun is_split_thm thm =
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  case concl_of thm of _ $ (_ $ (_ $ lhs) $ _) => (
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    (* Trueprop $ ((op =) $ (?P $ lhs) $ rhs) *)
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    case head_of lhs of
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      Const (a, _) => member (op =) [@{const_name Orderings.max},
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                                    @{const_name Orderings.min},
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                                    @{const_name HOL.abs},
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                                    @{const_name HOL.minus},
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                                    "Int.nat",
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                                    "Divides.div_class.mod",
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                                    "Divides.div_class.div"] a
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    | _            => (warning ("Lin. Arith.: wrong format for split rule " ^
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                                 Display.string_of_thm_without_context thm);
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                       false))
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  | _ => (warning ("Lin. Arith.: wrong format for split rule " ^
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                   Display.string_of_thm_without_context thm);
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          false);
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(* substitute new for occurrences of old in a term, incrementing bound       *)
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(* variables as needed when substituting inside an abstraction               *)
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fun subst_term ([] : (term * term) list) (t : term) = t
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  | subst_term pairs                     t          =
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      (case AList.lookup Pattern.aeconv pairs t of
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        SOME new =>
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          new
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      | NONE     =>
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          (case t of Abs (a, T, body) =>
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            let val pairs' = map (pairself (incr_boundvars 1)) pairs
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            in  Abs (a, T, subst_term pairs' body)  end
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          | t1 $ t2                   =>
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            subst_term pairs t1 $ subst_term pairs t2
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          | _ => t));
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(* approximates the effect of one application of split_tac (followed by NNF  *)
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(* normalization) on the subgoal represented by '(Ts, terms)'; returns a     *)
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(* list of new subgoals (each again represented by a typ list for bound      *)
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(* variables and a term list for premises), or NONE if split_tac would fail  *)
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(* on the subgoal                                                            *)
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(* FIXME: currently only the effect of certain split theorems is reproduced  *)
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(*        (which is why we need 'is_split_thm').  A more canonical           *)
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(*        implementation should analyze the right-hand side of the split     *)
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(*        theorem that can be applied, and modify the subgoal accordingly.   *)
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(*        Or even better, the splitter should be extended to provide         *)
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(*        splitting on terms as well as splitting on theorems (where the     *)
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(*        former can have a faster implementation as it does not need to be  *)
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(*        proof-producing).                                                  *)
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fun split_once_items ctxt (Ts : typ list, terms : term list) :
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                     (typ list * term list) list option =
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let
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  val thy = ProofContext.theory_of ctxt
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  (* takes a list  [t1, ..., tn]  to the term                                *)
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  (*   tn' --> ... --> t1' --> False  ,                                      *)
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  (* where ti' = HOLogic.dest_Trueprop ti                                    *)
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  fun REPEAT_DETERM_etac_rev_mp tms =
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    fold (curry HOLogic.mk_imp) (map HOLogic.dest_Trueprop tms)
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      HOLogic.false_const
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  val split_thms  = filter is_split_thm (#splits (get_arith_data ctxt))
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  val cmap        = Splitter.cmap_of_split_thms split_thms
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  val goal_tm     = REPEAT_DETERM_etac_rev_mp terms
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  val splits      = Splitter.split_posns cmap thy Ts goal_tm
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  val split_limit = Config.get ctxt split_limit
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in
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  if length splits > split_limit then (
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    tracing ("linarith_split_limit exceeded (current value is " ^
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      string_of_int split_limit ^ ")");
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    NONE
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  ) else case splits of
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    [] =>
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    (* split_tac would fail: no possible split *)
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    NONE
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  | (_, _::_, _, _, _) :: _ =>
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    (* disallow a split that involves non-locally bound variables (except    *)
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    (* when bound by outermost meta-quantifiers)                             *)
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    NONE
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  | (_, [], _, split_type, split_term) :: _ =>
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    (* ignore all but the first possible split                               *)
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    (case strip_comb split_term of
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    (* ?P (max ?i ?j) = ((?i <= ?j --> ?P ?j) & (~ ?i <= ?j --> ?P ?i)) *)
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      (Const (@{const_name Orderings.max}, _), [t1, t2]) =>
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      let
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        val rev_terms     = rev terms
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        val terms1        = map (subst_term [(split_term, t1)]) rev_terms
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        val terms2        = map (subst_term [(split_term, t2)]) rev_terms
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        val t1_leq_t2     = Const (@{const_name HOL.less_eq},
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                                    split_type --> split_type --> HOLogic.boolT) $ t1 $ t2
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        val not_t1_leq_t2 = HOLogic.Not $ t1_leq_t2
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        val not_false     = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const)
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        val subgoal1      = (HOLogic.mk_Trueprop t1_leq_t2) :: terms2 @ [not_false]
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        val subgoal2      = (HOLogic.mk_Trueprop not_t1_leq_t2) :: terms1 @ [not_false]
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      in
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        SOME [(Ts, subgoal1), (Ts, subgoal2)]
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      end
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    (* ?P (min ?i ?j) = ((?i <= ?j --> ?P ?i) & (~ ?i <= ?j --> ?P ?j)) *)
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    | (Const (@{const_name Orderings.min}, _), [t1, t2]) =>
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      let
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        val rev_terms     = rev terms
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        val terms1        = map (subst_term [(split_term, t1)]) rev_terms
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        val terms2        = map (subst_term [(split_term, t2)]) rev_terms
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        val t1_leq_t2     = Const (@{const_name HOL.less_eq},
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                                    split_type --> split_type --> HOLogic.boolT) $ t1 $ t2
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        val not_t1_leq_t2 = HOLogic.Not $ t1_leq_t2
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        val not_false     = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const)
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        val subgoal1      = (HOLogic.mk_Trueprop t1_leq_t2) :: terms1 @ [not_false]
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diff changeset
   395
        val subgoal2      = (HOLogic.mk_Trueprop not_t1_leq_t2) :: terms2 @ [not_false]
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   396
      in
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   397
        SOME [(Ts, subgoal1), (Ts, subgoal2)]
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   398
      end
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   399
    (* ?P (abs ?a) = ((0 <= ?a --> ?P ?a) & (?a < 0 --> ?P (- ?a))) *)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   400
    | (Const (@{const_name HOL.abs}, _), [t1]) =>
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   401
      let
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   402
        val rev_terms   = rev terms
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   403
        val terms1      = map (subst_term [(split_term, t1)]) rev_terms
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   404
        val terms2      = map (subst_term [(split_term, Const (@{const_name HOL.uminus},
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   405
                            split_type --> split_type) $ t1)]) rev_terms
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   406
        val zero        = Const (@{const_name HOL.zero}, split_type)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   407
        val zero_leq_t1 = Const (@{const_name HOL.less_eq},
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   408
                            split_type --> split_type --> HOLogic.boolT) $ zero $ t1
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   409
        val t1_lt_zero  = Const (@{const_name HOL.less},
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   410
                            split_type --> split_type --> HOLogic.boolT) $ t1 $ zero
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   411
        val not_false   = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   412
        val subgoal1    = (HOLogic.mk_Trueprop zero_leq_t1) :: terms1 @ [not_false]
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   413
        val subgoal2    = (HOLogic.mk_Trueprop t1_lt_zero) :: terms2 @ [not_false]
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   414
      in
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   415
        SOME [(Ts, subgoal1), (Ts, subgoal2)]
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   416
      end
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   417
    (* ?P (?a - ?b) = ((?a < ?b --> ?P 0) & (ALL d. ?a = ?b + d --> ?P d)) *)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   418
    | (Const (@{const_name HOL.minus}, _), [t1, t2]) =>
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   419
      let
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   420
        (* "d" in the above theorem becomes a new bound variable after NNF   *)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   421
        (* transformation, therefore some adjustment of indices is necessary *)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   422
        val rev_terms       = rev terms
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   423
        val zero            = Const (@{const_name HOL.zero}, split_type)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   424
        val d               = Bound 0
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   425
        val terms1          = map (subst_term [(split_term, zero)]) rev_terms
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   426
        val terms2          = map (subst_term [(incr_boundvars 1 split_term, d)])
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   427
                                (map (incr_boundvars 1) rev_terms)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   428
        val t1'             = incr_boundvars 1 t1
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   429
        val t2'             = incr_boundvars 1 t2
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   430
        val t1_lt_t2        = Const (@{const_name HOL.less},
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   431
                                split_type --> split_type --> HOLogic.boolT) $ t1 $ t2
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   432
        val t1_eq_t2_plus_d = Const ("op =", split_type --> split_type --> HOLogic.boolT) $ t1' $
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   433
                                (Const (@{const_name HOL.plus},
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   434
                                  split_type --> split_type --> split_type) $ t2' $ d)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   435
        val not_false       = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   436
        val subgoal1        = (HOLogic.mk_Trueprop t1_lt_t2) :: terms1 @ [not_false]
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   437
        val subgoal2        = (HOLogic.mk_Trueprop t1_eq_t2_plus_d) :: terms2 @ [not_false]
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   438
      in
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   439
        SOME [(Ts, subgoal1), (split_type :: Ts, subgoal2)]
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   440
      end
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   441
    (* ?P (nat ?i) = ((ALL n. ?i = int n --> ?P n) & (?i < 0 --> ?P 0)) *)
25919
8b1c0d434824 joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents: 25015
diff changeset
   442
    | (Const ("Int.nat", _), [t1]) =>
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   443
      let
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   444
        val rev_terms   = rev terms
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   445
        val zero_int    = Const (@{const_name HOL.zero}, HOLogic.intT)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   446
        val zero_nat    = Const (@{const_name HOL.zero}, HOLogic.natT)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   447
        val n           = Bound 0
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   448
        val terms1      = map (subst_term [(incr_boundvars 1 split_term, n)])
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   449
                            (map (incr_boundvars 1) rev_terms)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   450
        val terms2      = map (subst_term [(split_term, zero_nat)]) rev_terms
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   451
        val t1'         = incr_boundvars 1 t1
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   452
        val t1_eq_int_n = Const ("op =", HOLogic.intT --> HOLogic.intT --> HOLogic.boolT) $ t1' $
24196
f1dbfd7e3223 localized of_nat
haftmann
parents: 24112
diff changeset
   453
                            (Const (@{const_name of_nat}, HOLogic.natT --> HOLogic.intT) $ n)
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   454
        val t1_lt_zero  = Const (@{const_name HOL.less},
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   455
                            HOLogic.intT --> HOLogic.intT --> HOLogic.boolT) $ t1 $ zero_int
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   456
        val not_false   = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   457
        val subgoal1    = (HOLogic.mk_Trueprop t1_eq_int_n) :: terms1 @ [not_false]
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   458
        val subgoal2    = (HOLogic.mk_Trueprop t1_lt_zero) :: terms2 @ [not_false]
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   459
      in
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   460
        SOME [(HOLogic.natT :: Ts, subgoal1), (Ts, subgoal2)]
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   461
      end
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   462
    (* "?P ((?n::nat) mod (number_of ?k)) =
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   463
         ((number_of ?k = 0 --> ?P ?n) & (~ (number_of ?k = 0) -->
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   464
           (ALL i j. j < number_of ?k --> ?n = number_of ?k * i + j --> ?P j))) *)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   465
    | (Const ("Divides.div_class.mod", Type ("fun", [Type ("nat", []), _])), [t1, t2]) =>
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   466
      let
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   467
        val rev_terms               = rev terms
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   468
        val zero                    = Const (@{const_name HOL.zero}, split_type)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   469
        val i                       = Bound 1
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   470
        val j                       = Bound 0
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   471
        val terms1                  = map (subst_term [(split_term, t1)]) rev_terms
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   472
        val terms2                  = map (subst_term [(incr_boundvars 2 split_term, j)])
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   473
                                        (map (incr_boundvars 2) rev_terms)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   474
        val t1'                     = incr_boundvars 2 t1
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   475
        val t2'                     = incr_boundvars 2 t2
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   476
        val t2_eq_zero              = Const ("op =",
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   477
                                        split_type --> split_type --> HOLogic.boolT) $ t2 $ zero
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   478
        val t2_neq_zero             = HOLogic.mk_not (Const ("op =",
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   479
                                        split_type --> split_type --> HOLogic.boolT) $ t2' $ zero)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   480
        val j_lt_t2                 = Const (@{const_name HOL.less},
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   481
                                        split_type --> split_type--> HOLogic.boolT) $ j $ t2'
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   482
        val t1_eq_t2_times_i_plus_j = Const ("op =", split_type --> split_type --> HOLogic.boolT) $ t1' $
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   483
                                       (Const (@{const_name HOL.plus}, split_type --> split_type --> split_type) $
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   484
                                         (Const (@{const_name HOL.times},
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   485
                                           split_type --> split_type --> split_type) $ t2' $ i) $ j)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   486
        val not_false               = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   487
        val subgoal1                = (HOLogic.mk_Trueprop t2_eq_zero) :: terms1 @ [not_false]
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   488
        val subgoal2                = (map HOLogic.mk_Trueprop
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   489
                                        [t2_neq_zero, j_lt_t2, t1_eq_t2_times_i_plus_j])
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   490
                                          @ terms2 @ [not_false]
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   491
      in
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   492
        SOME [(Ts, subgoal1), (split_type :: split_type :: Ts, subgoal2)]
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   493
      end
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   494
    (* "?P ((?n::nat) div (number_of ?k)) =
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   495
         ((number_of ?k = 0 --> ?P 0) & (~ (number_of ?k = 0) -->
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   496
           (ALL i j. j < number_of ?k --> ?n = number_of ?k * i + j --> ?P i))) *)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   497
    | (Const ("Divides.div_class.div", Type ("fun", [Type ("nat", []), _])), [t1, t2]) =>
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   498
      let
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   499
        val rev_terms               = rev terms
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   500
        val zero                    = Const (@{const_name HOL.zero}, split_type)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   501
        val i                       = Bound 1
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   502
        val j                       = Bound 0
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   503
        val terms1                  = map (subst_term [(split_term, zero)]) rev_terms
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   504
        val terms2                  = map (subst_term [(incr_boundvars 2 split_term, i)])
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   505
                                        (map (incr_boundvars 2) rev_terms)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   506
        val t1'                     = incr_boundvars 2 t1
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   507
        val t2'                     = incr_boundvars 2 t2
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   508
        val t2_eq_zero              = Const ("op =",
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   509
                                        split_type --> split_type --> HOLogic.boolT) $ t2 $ zero
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   510
        val t2_neq_zero             = HOLogic.mk_not (Const ("op =",
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   511
                                        split_type --> split_type --> HOLogic.boolT) $ t2' $ zero)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   512
        val j_lt_t2                 = Const (@{const_name HOL.less},
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   513
                                        split_type --> split_type--> HOLogic.boolT) $ j $ t2'
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   514
        val t1_eq_t2_times_i_plus_j = Const ("op =", split_type --> split_type --> HOLogic.boolT) $ t1' $
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   515
                                       (Const (@{const_name HOL.plus}, split_type --> split_type --> split_type) $
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   516
                                         (Const (@{const_name HOL.times},
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   517
                                           split_type --> split_type --> split_type) $ t2' $ i) $ j)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   518
        val not_false               = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   519
        val subgoal1                = (HOLogic.mk_Trueprop t2_eq_zero) :: terms1 @ [not_false]
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   520
        val subgoal2                = (map HOLogic.mk_Trueprop
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   521
                                        [t2_neq_zero, j_lt_t2, t1_eq_t2_times_i_plus_j])
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   522
                                          @ terms2 @ [not_false]
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   523
      in
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   524
        SOME [(Ts, subgoal1), (split_type :: split_type :: Ts, subgoal2)]
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   525
      end
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   526
    (* "?P ((?n::int) mod (number_of ?k)) =
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   527
         ((iszero (number_of ?k) --> ?P ?n) &
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   528
          (neg (number_of (uminus ?k)) -->
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   529
            (ALL i j. 0 <= j & j < number_of ?k & ?n = number_of ?k * i + j --> ?P j)) &
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   530
          (neg (number_of ?k) -->
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   531
            (ALL i j. number_of ?k < j & j <= 0 & ?n = number_of ?k * i + j --> ?P j))) *)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   532
    | (Const ("Divides.div_class.mod",
25919
8b1c0d434824 joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents: 25015
diff changeset
   533
        Type ("fun", [Type ("Int.int", []), _])), [t1, t2 as (number_of $ k)]) =>
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   534
      let
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   535
        val rev_terms               = rev terms
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   536
        val zero                    = Const (@{const_name HOL.zero}, split_type)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   537
        val i                       = Bound 1
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   538
        val j                       = Bound 0
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   539
        val terms1                  = map (subst_term [(split_term, t1)]) rev_terms
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   540
        val terms2_3                = map (subst_term [(incr_boundvars 2 split_term, j)])
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   541
                                        (map (incr_boundvars 2) rev_terms)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   542
        val t1'                     = incr_boundvars 2 t1
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   543
        val (t2' as (_ $ k'))       = incr_boundvars 2 t2
25919
8b1c0d434824 joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents: 25015
diff changeset
   544
        val iszero_t2               = Const ("Int.iszero", split_type --> HOLogic.boolT) $ t2
8b1c0d434824 joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents: 25015
diff changeset
   545
        val neg_minus_k             = Const ("Int.neg", split_type --> HOLogic.boolT) $
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   546
                                        (number_of $
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   547
                                          (Const (@{const_name HOL.uminus},
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   548
                                            HOLogic.intT --> HOLogic.intT) $ k'))
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   549
        val zero_leq_j              = Const (@{const_name HOL.less_eq},
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   550
                                        split_type --> split_type --> HOLogic.boolT) $ zero $ j
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   551
        val j_lt_t2                 = Const (@{const_name HOL.less},
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   552
                                        split_type --> split_type--> HOLogic.boolT) $ j $ t2'
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   553
        val t1_eq_t2_times_i_plus_j = Const ("op =", split_type --> split_type --> HOLogic.boolT) $ t1' $
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   554
                                       (Const (@{const_name HOL.plus}, split_type --> split_type --> split_type) $
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   555
                                         (Const (@{const_name HOL.times},
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   556
                                           split_type --> split_type --> split_type) $ t2' $ i) $ j)
25919
8b1c0d434824 joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents: 25015
diff changeset
   557
        val neg_t2                  = Const ("Int.neg", split_type --> HOLogic.boolT) $ t2'
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   558
        val t2_lt_j                 = Const (@{const_name HOL.less},
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   559
                                        split_type --> split_type--> HOLogic.boolT) $ t2' $ j
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   560
        val j_leq_zero              = Const (@{const_name HOL.less_eq},
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   561
                                        split_type --> split_type --> HOLogic.boolT) $ j $ zero
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   562
        val not_false               = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   563
        val subgoal1                = (HOLogic.mk_Trueprop iszero_t2) :: terms1 @ [not_false]
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   564
        val subgoal2                = (map HOLogic.mk_Trueprop [neg_minus_k, zero_leq_j])
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   565
                                        @ hd terms2_3
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   566
                                        :: (if tl terms2_3 = [] then [not_false] else [])
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   567
                                        @ (map HOLogic.mk_Trueprop [j_lt_t2, t1_eq_t2_times_i_plus_j])
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   568
                                        @ (if tl terms2_3 = [] then [] else tl terms2_3 @ [not_false])
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   569
        val subgoal3                = (map HOLogic.mk_Trueprop [neg_t2, t2_lt_j])
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   570
                                        @ hd terms2_3
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   571
                                        :: (if tl terms2_3 = [] then [not_false] else [])
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   572
                                        @ (map HOLogic.mk_Trueprop [j_leq_zero, t1_eq_t2_times_i_plus_j])
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   573
                                        @ (if tl terms2_3 = [] then [] else tl terms2_3 @ [not_false])
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   574
        val Ts'                     = split_type :: split_type :: Ts
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   575
      in
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   576
        SOME [(Ts, subgoal1), (Ts', subgoal2), (Ts', subgoal3)]
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   577
      end
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   578
    (* "?P ((?n::int) div (number_of ?k)) =
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   579
         ((iszero (number_of ?k) --> ?P 0) &
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   580
          (neg (number_of (uminus ?k)) -->
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   581
            (ALL i. (EX j. 0 <= j & j < number_of ?k & ?n = number_of ?k * i + j) --> ?P i)) &
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   582
          (neg (number_of ?k) -->
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   583
            (ALL i. (EX j. number_of ?k < j & j <= 0 & ?n = number_of ?k * i + j) --> ?P i))) *)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   584
    | (Const ("Divides.div_class.div",
25919
8b1c0d434824 joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents: 25015
diff changeset
   585
        Type ("fun", [Type ("Int.int", []), _])), [t1, t2 as (number_of $ k)]) =>
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   586
      let
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   587
        val rev_terms               = rev terms
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   588
        val zero                    = Const (@{const_name HOL.zero}, split_type)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   589
        val i                       = Bound 1
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   590
        val j                       = Bound 0
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   591
        val terms1                  = map (subst_term [(split_term, zero)]) rev_terms
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   592
        val terms2_3                = map (subst_term [(incr_boundvars 2 split_term, i)])
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   593
                                        (map (incr_boundvars 2) rev_terms)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   594
        val t1'                     = incr_boundvars 2 t1
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   595
        val (t2' as (_ $ k'))       = incr_boundvars 2 t2
25919
8b1c0d434824 joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents: 25015
diff changeset
   596
        val iszero_t2               = Const ("Int.iszero", split_type --> HOLogic.boolT) $ t2
8b1c0d434824 joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents: 25015
diff changeset
   597
        val neg_minus_k             = Const ("Int.neg", split_type --> HOLogic.boolT) $
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   598
                                        (number_of $
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   599
                                          (Const (@{const_name HOL.uminus},
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   600
                                            HOLogic.intT --> HOLogic.intT) $ k'))
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   601
        val zero_leq_j              = Const (@{const_name HOL.less_eq},
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   602
                                        split_type --> split_type --> HOLogic.boolT) $ zero $ j
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   603
        val j_lt_t2                 = Const (@{const_name HOL.less},
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   604
                                        split_type --> split_type--> HOLogic.boolT) $ j $ t2'
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   605
        val t1_eq_t2_times_i_plus_j = Const ("op =",
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   606
                                        split_type --> split_type --> HOLogic.boolT) $ t1' $
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   607
                                       (Const (@{const_name HOL.plus}, split_type --> split_type --> split_type) $
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   608
                                         (Const (@{const_name HOL.times},
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   609
                                           split_type --> split_type --> split_type) $ t2' $ i) $ j)
25919
8b1c0d434824 joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents: 25015
diff changeset
   610
        val neg_t2                  = Const ("Int.neg", split_type --> HOLogic.boolT) $ t2'
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   611
        val t2_lt_j                 = Const (@{const_name HOL.less},
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   612
                                        split_type --> split_type--> HOLogic.boolT) $ t2' $ j
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   613
        val j_leq_zero              = Const (@{const_name HOL.less_eq},
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   614
                                        split_type --> split_type --> HOLogic.boolT) $ j $ zero
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   615
        val not_false               = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   616
        val subgoal1                = (HOLogic.mk_Trueprop iszero_t2) :: terms1 @ [not_false]
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   617
        val subgoal2                = (HOLogic.mk_Trueprop neg_minus_k)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   618
                                        :: terms2_3
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   619
                                        @ not_false
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   620
                                        :: (map HOLogic.mk_Trueprop
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   621
                                             [zero_leq_j, j_lt_t2, t1_eq_t2_times_i_plus_j])
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   622
        val subgoal3                = (HOLogic.mk_Trueprop neg_t2)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   623
                                        :: terms2_3
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   624
                                        @ not_false
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   625
                                        :: (map HOLogic.mk_Trueprop
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   626
                                             [t2_lt_j, j_leq_zero, t1_eq_t2_times_i_plus_j])
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   627
        val Ts'                     = split_type :: split_type :: Ts
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   628
      in
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   629
        SOME [(Ts, subgoal1), (Ts', subgoal2), (Ts', subgoal3)]
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   630
      end
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   631
    (* this will only happen if a split theorem can be applied for which no  *)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   632
    (* code exists above -- in which case either the split theorem should be *)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   633
    (* implemented above, or 'is_split_thm' should be modified to filter it  *)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   634
    (* out                                                                   *)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   635
    | (t, ts) => (
24920
2a45e400fdad generic Syntax.pretty/string_of operations;
wenzelm
parents: 24328
diff changeset
   636
      warning ("Lin. Arith.: split rule for " ^ Syntax.string_of_term ctxt t ^
32369
04af689ce721 Fixed a bug where the simplifier would hang on
webertj
parents: 32091
diff changeset
   637
        " (with " ^ string_of_int (length ts) ^
04af689ce721 Fixed a bug where the simplifier would hang on
webertj
parents: 32091
diff changeset
   638
        " argument(s)) not implemented; proof reconstruction is likely to fail");
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   639
      NONE
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   640
    ))
32369
04af689ce721 Fixed a bug where the simplifier would hang on
webertj
parents: 32091
diff changeset
   641
end;  (* split_once_items *)
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   642
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   643
(* remove terms that do not satisfy 'p'; change the order of the remaining   *)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   644
(* terms in the same way as filter_prems_tac does                            *)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   645
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   646
fun filter_prems_tac_items (p : term -> bool) (terms : term list) : term list =
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   647
let
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   648
  fun filter_prems (t, (left, right)) =
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   649
    if  p t  then  (left, right @ [t])  else  (left @ right, [])
30190
479806475f3c use long names for old-style fold combinators;
wenzelm
parents: 29850
diff changeset
   650
  val (left, right) = List.foldl filter_prems ([], []) terms
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   651
in
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   652
  right @ left
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   653
end;
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   654
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   655
(* return true iff TRY (etac notE) THEN eq_assume_tac would succeed on a     *)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   656
(* subgoal that has 'terms' as premises                                      *)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   657
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   658
fun negated_term_occurs_positively (terms : term list) : bool =
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   659
  List.exists
32369
04af689ce721 Fixed a bug where the simplifier would hang on
webertj
parents: 32091
diff changeset
   660
    (fn (Trueprop $ (Const ("Not", _) $ t)) =>
04af689ce721 Fixed a bug where the simplifier would hang on
webertj
parents: 32091
diff changeset
   661
      member Pattern.aeconv terms (Trueprop $ t)
04af689ce721 Fixed a bug where the simplifier would hang on
webertj
parents: 32091
diff changeset
   662
      | _ => false)
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   663
    terms;
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   664
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   665
fun pre_decomp ctxt (Ts : typ list, terms : term list) : (typ list * term list) list =
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   666
let
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   667
  (* repeatedly split (including newly emerging subgoals) until no further   *)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   668
  (* splitting is possible                                                   *)
32369
04af689ce721 Fixed a bug where the simplifier would hang on
webertj
parents: 32091
diff changeset
   669
  fun split_loop ([] : (typ list * term list) list) =
04af689ce721 Fixed a bug where the simplifier would hang on
webertj
parents: 32091
diff changeset
   670
      ([] : (typ list * term list) list)
04af689ce721 Fixed a bug where the simplifier would hang on
webertj
parents: 32091
diff changeset
   671
    | split_loop (subgoal::subgoals) =
04af689ce721 Fixed a bug where the simplifier would hang on
webertj
parents: 32091
diff changeset
   672
      (case split_once_items ctxt subgoal of
04af689ce721 Fixed a bug where the simplifier would hang on
webertj
parents: 32091
diff changeset
   673
        SOME new_subgoals => split_loop (new_subgoals @ subgoals)
04af689ce721 Fixed a bug where the simplifier would hang on
webertj
parents: 32091
diff changeset
   674
      | NONE              => subgoal :: split_loop subgoals)
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   675
  fun is_relevant t  = isSome (decomp ctxt t)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   676
  (* filter_prems_tac is_relevant: *)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   677
  val relevant_terms = filter_prems_tac_items is_relevant terms
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   678
  (* split_tac, NNF normalization: *)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   679
  val split_goals    = split_loop [(Ts, relevant_terms)]
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   680
  (* necessary because split_once_tac may normalize terms: *)
32369
04af689ce721 Fixed a bug where the simplifier would hang on
webertj
parents: 32091
diff changeset
   681
  val beta_eta_norm  = map (apsnd (map (Envir.eta_contract o Envir.beta_norm)))
04af689ce721 Fixed a bug where the simplifier would hang on
webertj
parents: 32091
diff changeset
   682
    split_goals
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   683
  (* TRY (etac notE) THEN eq_assume_tac: *)
32369
04af689ce721 Fixed a bug where the simplifier would hang on
webertj
parents: 32091
diff changeset
   684
  val result         = List.filter (not o negated_term_occurs_positively o snd)
04af689ce721 Fixed a bug where the simplifier would hang on
webertj
parents: 32091
diff changeset
   685
    beta_eta_norm
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   686
in
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   687
  result
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   688
end;
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   689
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   690
(* takes the i-th subgoal  [| A1; ...; An |] ==> B  to                       *)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   691
(* An --> ... --> A1 --> B,  performs splitting with the given 'split_thms'  *)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   692
(* (resulting in a different subgoal P), takes  P  to  ~P ==> False,         *)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   693
(* performs NNF-normalization of ~P, and eliminates conjunctions,            *)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   694
(* disjunctions and existential quantifiers from the premises, possibly (in  *)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   695
(* the case of disjunctions) resulting in several new subgoals, each of the  *)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   696
(* general form  [| Q1; ...; Qm |] ==> False.  Fails if more than            *)
31082
54a442b2d727 interface changes in linarith.ML
haftmann
parents: 30722
diff changeset
   697
(* !split_limit splits are possible.                              *)
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   698
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   699
local
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   700
  val nnf_simpset =
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   701
    empty_ss setmkeqTrue mk_eq_True
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   702
    setmksimps (mksimps mksimps_pairs)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   703
    addsimps [imp_conv_disj, iff_conv_conj_imp, de_Morgan_disj, de_Morgan_conj,
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   704
      not_all, not_ex, not_not]
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   705
  fun prem_nnf_tac i st =
32369
04af689ce721 Fixed a bug where the simplifier would hang on
webertj
parents: 32091
diff changeset
   706
    full_simp_tac (Simplifier.theory_context (Thm.theory_of_thm st) nnf_simpset)
04af689ce721 Fixed a bug where the simplifier would hang on
webertj
parents: 32091
diff changeset
   707
      i st
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   708
in
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   709
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   710
fun split_once_tac ctxt split_thms =
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   711
  let
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   712
    val thy = ProofContext.theory_of ctxt
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   713
    val cond_split_tac = SUBGOAL (fn (subgoal, i) =>
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   714
      let
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   715
        val Ts = rev (map snd (Logic.strip_params subgoal))
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   716
        val concl = HOLogic.dest_Trueprop (Logic.strip_assums_concl subgoal)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   717
        val cmap = Splitter.cmap_of_split_thms split_thms
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   718
        val splits = Splitter.split_posns cmap thy Ts concl
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   719
      in
32369
04af689ce721 Fixed a bug where the simplifier would hang on
webertj
parents: 32091
diff changeset
   720
        if null splits orelse length splits > Config.get ctxt split_limit then
04af689ce721 Fixed a bug where the simplifier would hang on
webertj
parents: 32091
diff changeset
   721
          no_tac
04af689ce721 Fixed a bug where the simplifier would hang on
webertj
parents: 32091
diff changeset
   722
        else if null (#2 (hd splits)) then
04af689ce721 Fixed a bug where the simplifier would hang on
webertj
parents: 32091
diff changeset
   723
          split_tac split_thms i
04af689ce721 Fixed a bug where the simplifier would hang on
webertj
parents: 32091
diff changeset
   724
        else
04af689ce721 Fixed a bug where the simplifier would hang on
webertj
parents: 32091
diff changeset
   725
          (* disallow a split that involves non-locally bound variables      *)
04af689ce721 Fixed a bug where the simplifier would hang on
webertj
parents: 32091
diff changeset
   726
          (* (except when bound by outermost meta-quantifiers)               *)
04af689ce721 Fixed a bug where the simplifier would hang on
webertj
parents: 32091
diff changeset
   727
          no_tac
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   728
      end)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   729
  in
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   730
    EVERY' [
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   731
      REPEAT_DETERM o etac rev_mp,
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   732
      cond_split_tac,
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   733
      rtac ccontr,
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   734
      prem_nnf_tac,
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   735
      TRY o REPEAT_ALL_NEW (DETERM o (eresolve_tac [conjE, exE] ORELSE' etac disjE))
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   736
    ]
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   737
  end;
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   738
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   739
end;  (* local *)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   740
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   741
(* remove irrelevant premises, then split the i-th subgoal (and all new      *)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   742
(* subgoals) by using 'split_once_tac' repeatedly.  Beta-eta-normalize new   *)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   743
(* subgoals and finally attempt to solve them by finding an immediate        *)
32369
04af689ce721 Fixed a bug where the simplifier would hang on
webertj
parents: 32091
diff changeset
   744
(* contradiction (i.e., a term and its negation) in their premises.          *)
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   745
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   746
fun pre_tac ctxt i =
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   747
let
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   748
  val split_thms = filter is_split_thm (#splits (get_arith_data ctxt))
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   749
  fun is_relevant t = isSome (decomp ctxt t)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   750
in
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   751
  DETERM (
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   752
    TRY (filter_prems_tac is_relevant i)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   753
      THEN (
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   754
        (TRY o REPEAT_ALL_NEW (split_once_tac ctxt split_thms))
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   755
          THEN_ALL_NEW
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   756
            (CONVERSION Drule.beta_eta_conversion
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   757
              THEN'
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   758
            (TRY o (etac notE THEN' eq_assume_tac)))
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   759
      ) i
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   760
  )
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   761
end;
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   762
31100
6a2e67fe4488 tuned interface of Lin_Arith
haftmann
parents: 31082
diff changeset
   763
end;  (* LA_Data *)
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   764
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   765
31100
6a2e67fe4488 tuned interface of Lin_Arith
haftmann
parents: 31082
diff changeset
   766
val pre_tac = LA_Data.pre_tac;
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   767
31100
6a2e67fe4488 tuned interface of Lin_Arith
haftmann
parents: 31082
diff changeset
   768
structure Fast_Arith = Fast_Lin_Arith(structure LA_Logic = LA_Logic and LA_Data = LA_Data);
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   769
31510
e0f2bb4b0021 fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents: 31101
diff changeset
   770
fun map_inj_thms f {add_mono_thms, mult_mono_thms, inj_thms, lessD, neqE, simpset, number_of} =
31100
6a2e67fe4488 tuned interface of Lin_Arith
haftmann
parents: 31082
diff changeset
   771
  {add_mono_thms = add_mono_thms, mult_mono_thms = mult_mono_thms, inj_thms = f inj_thms,
31510
e0f2bb4b0021 fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents: 31101
diff changeset
   772
    lessD = lessD, neqE = neqE, simpset = simpset, number_of = number_of};
31100
6a2e67fe4488 tuned interface of Lin_Arith
haftmann
parents: 31082
diff changeset
   773
31510
e0f2bb4b0021 fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents: 31101
diff changeset
   774
fun map_lessD f {add_mono_thms, mult_mono_thms, inj_thms, lessD, neqE, simpset, number_of} =
31100
6a2e67fe4488 tuned interface of Lin_Arith
haftmann
parents: 31082
diff changeset
   775
  {add_mono_thms = add_mono_thms, mult_mono_thms = mult_mono_thms, inj_thms = inj_thms,
31510
e0f2bb4b0021 fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents: 31101
diff changeset
   776
    lessD = f lessD, neqE = neqE, simpset = simpset, number_of = number_of};
31100
6a2e67fe4488 tuned interface of Lin_Arith
haftmann
parents: 31082
diff changeset
   777
31510
e0f2bb4b0021 fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents: 31101
diff changeset
   778
fun map_simpset f {add_mono_thms, mult_mono_thms, inj_thms, lessD, neqE, simpset, number_of} =
31100
6a2e67fe4488 tuned interface of Lin_Arith
haftmann
parents: 31082
diff changeset
   779
  {add_mono_thms = add_mono_thms, mult_mono_thms = mult_mono_thms, inj_thms = inj_thms,
31510
e0f2bb4b0021 fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents: 31101
diff changeset
   780
    lessD = lessD, neqE = neqE, simpset = f simpset, number_of = number_of};
e0f2bb4b0021 fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents: 31101
diff changeset
   781
e0f2bb4b0021 fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents: 31101
diff changeset
   782
fun map_number_of f {add_mono_thms, mult_mono_thms, inj_thms, lessD, neqE, simpset, number_of} =
e0f2bb4b0021 fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents: 31101
diff changeset
   783
  {add_mono_thms = add_mono_thms, mult_mono_thms = mult_mono_thms, inj_thms = inj_thms,
e0f2bb4b0021 fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents: 31101
diff changeset
   784
    lessD = lessD, neqE = neqE, simpset = simpset, number_of = f number_of};
31100
6a2e67fe4488 tuned interface of Lin_Arith
haftmann
parents: 31082
diff changeset
   785
6a2e67fe4488 tuned interface of Lin_Arith
haftmann
parents: 31082
diff changeset
   786
fun add_inj_thms thms = Fast_Arith.map_data (map_inj_thms (append thms));
6a2e67fe4488 tuned interface of Lin_Arith
haftmann
parents: 31082
diff changeset
   787
fun add_lessD thm = Fast_Arith.map_data (map_lessD (fn thms => thms @ [thm]));
6a2e67fe4488 tuned interface of Lin_Arith
haftmann
parents: 31082
diff changeset
   788
fun add_simps thms = Fast_Arith.map_data (map_simpset (fn simpset => simpset addsimps thms));
6a2e67fe4488 tuned interface of Lin_Arith
haftmann
parents: 31082
diff changeset
   789
fun add_simprocs procs = Fast_Arith.map_data (map_simpset (fn simpset => simpset addsimprocs procs));
6a2e67fe4488 tuned interface of Lin_Arith
haftmann
parents: 31082
diff changeset
   790
31510
e0f2bb4b0021 fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents: 31101
diff changeset
   791
fun set_number_of f = Fast_Arith.map_data (map_number_of (K (serial (), f)))
e0f2bb4b0021 fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents: 31101
diff changeset
   792
e0f2bb4b0021 fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents: 31101
diff changeset
   793
31101
26c7bb764a38 qualified names for Lin_Arith tactics and simprocs
haftmann
parents: 31100
diff changeset
   794
fun simple_tac ctxt = Fast_Arith.lin_arith_tac ctxt false;
26c7bb764a38 qualified names for Lin_Arith tactics and simprocs
haftmann
parents: 31100
diff changeset
   795
val lin_arith_tac = Fast_Arith.lin_arith_tac;
31082
54a442b2d727 interface changes in linarith.ML
haftmann
parents: 30722
diff changeset
   796
val trace = Fast_Arith.trace;
27017
1e0e8c1adf8c added warning_count for issued reconstruction failure messages;
wenzelm
parents: 26942
diff changeset
   797
val warning_count = Fast_Arith.warning_count;
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   798
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   799
(* reduce contradictory <= to False.
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   800
   Most of the work is done by the cancel tactics. *)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   801
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   802
val init_arith_data =
31510
e0f2bb4b0021 fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents: 31101
diff changeset
   803
  Fast_Arith.map_data (fn {add_mono_thms, mult_mono_thms, inj_thms, lessD, number_of, ...} =>
31082
54a442b2d727 interface changes in linarith.ML
haftmann
parents: 30722
diff changeset
   804
   {add_mono_thms = @{thms add_mono_thms_ordered_semiring} @ @{thms add_mono_thms_ordered_field} @ add_mono_thms,
31510
e0f2bb4b0021 fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents: 31101
diff changeset
   805
    mult_mono_thms = @{thm mult_strict_left_mono} :: @{thm mult_left_mono} ::
e0f2bb4b0021 fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents: 31101
diff changeset
   806
      @{lemma "a = b ==> c*a = c*b" by (rule arg_cong)} :: mult_mono_thms,
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   807
    inj_thms = inj_thms,
31082
54a442b2d727 interface changes in linarith.ML
haftmann
parents: 30722
diff changeset
   808
    lessD = lessD @ [@{thm "Suc_leI"}],
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   809
    neqE = [@{thm linorder_neqE_nat}, @{thm linorder_neqE_ordered_idom}],
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   810
    simpset = HOL_basic_ss
31510
e0f2bb4b0021 fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents: 31101
diff changeset
   811
      addsimps @{thms ring_distribs}
e0f2bb4b0021 fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents: 31101
diff changeset
   812
      addsimps [@{thm if_True}, @{thm if_False}]
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   813
      addsimps
28053
a2106c0d8c45 no parameter prefix for class interpretation
haftmann
parents: 27017
diff changeset
   814
       [@{thm "monoid_add_class.add_0_left"},
a2106c0d8c45 no parameter prefix for class interpretation
haftmann
parents: 27017
diff changeset
   815
        @{thm "monoid_add_class.add_0_right"},
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   816
        @{thm "Zero_not_Suc"}, @{thm "Suc_not_Zero"}, @{thm "le_0_eq"}, @{thm "One_nat_def"},
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   817
        @{thm "order_less_irrefl"}, @{thm "zero_neq_one"}, @{thm "zero_less_one"},
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   818
        @{thm "zero_le_one"}, @{thm "zero_neq_one"} RS not_sym, @{thm "not_one_le_zero"},
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   819
        @{thm "not_one_less_zero"}]
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   820
      addsimprocs [ab_group_add_cancel.sum_conv, ab_group_add_cancel.rel_conv]
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   821
       (*abel_cancel helps it work in abstract algebraic domains*)
31082
54a442b2d727 interface changes in linarith.ML
haftmann
parents: 30722
diff changeset
   822
      addsimprocs Nat_Arith.nat_cancel_sums_add
31510
e0f2bb4b0021 fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents: 31101
diff changeset
   823
      addcongs [if_weak_cong],
e0f2bb4b0021 fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents: 31101
diff changeset
   824
    number_of = number_of}) #>
31082
54a442b2d727 interface changes in linarith.ML
haftmann
parents: 30722
diff changeset
   825
  add_discrete_type @{type_name nat};
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   826
29849
a2baf1b221be new attribute "arith" for facts supplied to arith.
nipkow
parents: 29548
diff changeset
   827
fun add_arith_facts ss =
30686
47a32dd1b86e moved generic arith_tac (formerly silent_arith_tac), verbose_arith_tac (formerly arith_tac) to Arith_Data; simple_arith-tac now named linear_arith_tac
haftmann
parents: 30528
diff changeset
   828
  add_prems (Arith_Data.get_arith_facts (MetaSimplifier.the_context ss)) ss;
29849
a2baf1b221be new attribute "arith" for facts supplied to arith.
nipkow
parents: 29548
diff changeset
   829
31101
26c7bb764a38 qualified names for Lin_Arith tactics and simprocs
haftmann
parents: 31100
diff changeset
   830
val simproc = add_arith_facts #> Fast_Arith.lin_arith_simproc;
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   831
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   832
26110
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   833
(* generic refutation procedure *)
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   834
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   835
(* parameters:
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   836
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   837
   test: term -> bool
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   838
   tests if a term is at all relevant to the refutation proof;
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   839
   if not, then it can be discarded. Can improve performance,
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   840
   esp. if disjunctions can be discarded (no case distinction needed!).
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   841
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   842
   prep_tac: int -> tactic
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   843
   A preparation tactic to be applied to the goal once all relevant premises
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   844
   have been moved to the conclusion.
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   845
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   846
   ref_tac: int -> tactic
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   847
   the actual refutation tactic. Should be able to deal with goals
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   848
   [| A1; ...; An |] ==> False
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   849
   where the Ai are atomic, i.e. no top-level &, | or EX
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   850
*)
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   851
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   852
local
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   853
  val nnf_simpset =
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   854
    empty_ss setmkeqTrue mk_eq_True
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   855
    setmksimps (mksimps mksimps_pairs)
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   856
    addsimps [@{thm imp_conv_disj}, @{thm iff_conv_conj_imp}, @{thm de_Morgan_disj},
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   857
      @{thm de_Morgan_conj}, @{thm not_all}, @{thm not_ex}, @{thm not_not}];
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   858
  fun prem_nnf_tac i st =
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   859
    full_simp_tac (Simplifier.theory_context (Thm.theory_of_thm st) nnf_simpset) i st;
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   860
in
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   861
fun refute_tac test prep_tac ref_tac =
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   862
  let val refute_prems_tac =
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   863
        REPEAT_DETERM
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   864
              (eresolve_tac [@{thm conjE}, @{thm exE}] 1 ORELSE
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   865
               filter_prems_tac test 1 ORELSE
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   866
               etac @{thm disjE} 1) THEN
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   867
        (DETERM (etac @{thm notE} 1 THEN eq_assume_tac 1) ORELSE
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   868
         ref_tac 1);
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   869
  in EVERY'[TRY o filter_prems_tac test,
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   870
            REPEAT_DETERM o etac @{thm rev_mp}, prep_tac, rtac @{thm ccontr}, prem_nnf_tac,
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   871
            SELECT_GOAL (DEPTH_SOLVE refute_prems_tac)]
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   872
  end;
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   873
end;
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   874
06eacfd8dd9f moved refute_tac to linarith.ML
haftmann
parents: 26101
diff changeset
   875
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   876
(* arith proof method *)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   877
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   878
local
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   879
31101
26c7bb764a38 qualified names for Lin_Arith tactics and simprocs
haftmann
parents: 31100
diff changeset
   880
fun raw_tac ctxt ex =
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   881
  (* FIXME: K true should be replaced by a sensible test (perhaps "isSome o
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   882
     decomp sg"? -- but note that the test is applied to terms already before
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   883
     they are split/normalized) to speed things up in case there are lots of
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   884
     irrelevant terms involved; elimination of min/max can be optimized:
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   885
     (max m n + k <= r) = (m+k <= r & n+k <= r)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   886
     (l <= min m n + k) = (l <= m+k & l <= n+k)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   887
  *)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   888
  refute_tac (K true)
31101
26c7bb764a38 qualified names for Lin_Arith tactics and simprocs
haftmann
parents: 31100
diff changeset
   889
    (* Splitting is also done inside simple_tac, but not completely --   *)
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   890
    (* split_tac may use split theorems that have not been implemented in    *)
31101
26c7bb764a38 qualified names for Lin_Arith tactics and simprocs
haftmann
parents: 31100
diff changeset
   891
    (* simple_tac (cf. pre_decomp and split_once_items above), and       *)
31082
54a442b2d727 interface changes in linarith.ML
haftmann
parents: 30722
diff changeset
   892
    (* split_limit may trigger.                                   *)
31101
26c7bb764a38 qualified names for Lin_Arith tactics and simprocs
haftmann
parents: 31100
diff changeset
   893
    (* Therefore splitting outside of simple_tac may allow us to prove   *)
26c7bb764a38 qualified names for Lin_Arith tactics and simprocs
haftmann
parents: 31100
diff changeset
   894
    (* some goals that simple_tac alone would fail on.                   *)
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   895
    (REPEAT_DETERM o split_tac (#splits (get_arith_data ctxt)))
31101
26c7bb764a38 qualified names for Lin_Arith tactics and simprocs
haftmann
parents: 31100
diff changeset
   896
    (lin_arith_tac ctxt ex);
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   897
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   898
in
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   899
31101
26c7bb764a38 qualified names for Lin_Arith tactics and simprocs
haftmann
parents: 31100
diff changeset
   900
fun gen_tac ex ctxt = FIRST' [simple_tac ctxt,
26c7bb764a38 qualified names for Lin_Arith tactics and simprocs
haftmann
parents: 31100
diff changeset
   901
  ObjectLogic.full_atomize_tac THEN' (REPEAT_DETERM o rtac impI) THEN' raw_tac ctxt ex];
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   902
31101
26c7bb764a38 qualified names for Lin_Arith tactics and simprocs
haftmann
parents: 31100
diff changeset
   903
val tac = gen_tac true;
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   904
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   905
end;
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   906
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   907
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   908
(* context setup *)
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   909
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   910
val setup =
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   911
  init_arith_data #>
31101
26c7bb764a38 qualified names for Lin_Arith tactics and simprocs
haftmann
parents: 31100
diff changeset
   912
  Simplifier.map_ss (fn ss => ss addsimprocs [Simplifier.simproc (@{theory}) "fast_nat_arith"
26c7bb764a38 qualified names for Lin_Arith tactics and simprocs
haftmann
parents: 31100
diff changeset
   913
    ["(m::nat) < n","(m::nat) <= n", "(m::nat) = n"] (K simproc)]
26c7bb764a38 qualified names for Lin_Arith tactics and simprocs
haftmann
parents: 31100
diff changeset
   914
    (* Because of fast_nat_arith_simproc, the arithmetic solver is really only
26c7bb764a38 qualified names for Lin_Arith tactics and simprocs
haftmann
parents: 31100
diff changeset
   915
    useful to detect inconsistencies among the premises for subgoals which are
26c7bb764a38 qualified names for Lin_Arith tactics and simprocs
haftmann
parents: 31100
diff changeset
   916
    *not* themselves (in)equalities, because the latter activate
26c7bb764a38 qualified names for Lin_Arith tactics and simprocs
haftmann
parents: 31100
diff changeset
   917
    fast_nat_arith_simproc anyway. However, it seems cheaper to activate the
26c7bb764a38 qualified names for Lin_Arith tactics and simprocs
haftmann
parents: 31100
diff changeset
   918
    solver all the time rather than add the additional check. *)
29850
14d9891c917b fix to [arith]
nipkow
parents: 29849
diff changeset
   919
    addSolver (mk_solver' "lin_arith"
31100
6a2e67fe4488 tuned interface of Lin_Arith
haftmann
parents: 31082
diff changeset
   920
      (add_arith_facts #> Fast_Arith.cut_lin_arith_tac)))
6a2e67fe4488 tuned interface of Lin_Arith
haftmann
parents: 31082
diff changeset
   921
6a2e67fe4488 tuned interface of Lin_Arith
haftmann
parents: 31082
diff changeset
   922
val global_setup =
6a2e67fe4488 tuned interface of Lin_Arith
haftmann
parents: 31082
diff changeset
   923
  setup_split_limit #> setup_neq_limit #>
6a2e67fe4488 tuned interface of Lin_Arith
haftmann
parents: 31082
diff changeset
   924
  Attrib.setup @{binding arith_split} (Scan.succeed (Thm.declaration_attribute add_split))
6a2e67fe4488 tuned interface of Lin_Arith
haftmann
parents: 31082
diff changeset
   925
    "declaration of split rules for arithmetic procedure" #>
6a2e67fe4488 tuned interface of Lin_Arith
haftmann
parents: 31082
diff changeset
   926
  Method.setup @{binding linarith}
6a2e67fe4488 tuned interface of Lin_Arith
haftmann
parents: 31082
diff changeset
   927
    (Args.bang_facts >> (fn prems => fn ctxt =>
6a2e67fe4488 tuned interface of Lin_Arith
haftmann
parents: 31082
diff changeset
   928
      METHOD (fn facts =>
6a2e67fe4488 tuned interface of Lin_Arith
haftmann
parents: 31082
diff changeset
   929
        HEADGOAL (Method.insert_tac (prems @ Arith_Data.get_arith_facts ctxt @ facts)
31101
26c7bb764a38 qualified names for Lin_Arith tactics and simprocs
haftmann
parents: 31100
diff changeset
   930
          THEN' tac ctxt)))) "linear arithmetic" #>
26c7bb764a38 qualified names for Lin_Arith tactics and simprocs
haftmann
parents: 31100
diff changeset
   931
  Arith_Data.add_tactic "linear arithmetic" gen_tac;
24092
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   932
71c27b320610 HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff changeset
   933
end;