src/HOL/Tools/numeral_simprocs.ML
author haftmann
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dedicated theory for loading numeral simprocs
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(* Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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   Copyright   2000  University of Cambridge
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Simprocs for the integer numerals.
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*)
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(*To quote from Provers/Arith/cancel_numeral_factor.ML:
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Cancels common coefficients in balanced expressions:
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     u*#m ~~ u'*#m'  ==  #n*u ~~ #n'*u'
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where ~~ is an appropriate balancing operation (e.g. =, <=, <, div, /)
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and d = gcd(m,m') and n=m/d and n'=m'/d.
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*)
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signature NUMERAL_SIMPROCS =
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sig
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  val assoc_fold_simproc: simproc
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  val combine_numerals: simproc
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  val cancel_numerals: simproc list
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  val cancel_factors: simproc list
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  val cancel_numeral_factors: simproc list
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  val field_combine_numerals: simproc
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  val field_cancel_numeral_factors: simproc list
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  val num_ss: simpset
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end;
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structure Numeral_Simprocs : NUMERAL_SIMPROCS =
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struct
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val mk_number = Arith_Data.mk_number;
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val mk_sum = Arith_Data.mk_sum;
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val long_mk_sum = Arith_Data.long_mk_sum;
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val dest_sum = Arith_Data.dest_sum;
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val mk_diff = HOLogic.mk_binop @{const_name HOL.minus};
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val dest_diff = HOLogic.dest_bin @{const_name HOL.minus} Term.dummyT;
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val mk_times = HOLogic.mk_binop @{const_name HOL.times};
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fun one_of T = Const(@{const_name HOL.one},T);
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(* build product with trailing 1 rather than Numeral 1 in order to avoid the
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   unnecessary restriction to type class number_ring
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   which is not required for cancellation of common factors in divisions.
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*)
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fun mk_prod T = 
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  let val one = one_of T
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  fun mk [] = one
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    | mk [t] = t
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    | mk (t :: ts) = if t = one then mk ts else mk_times (t, mk ts)
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  in mk end;
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(*This version ALWAYS includes a trailing one*)
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fun long_mk_prod T []        = one_of T
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  | long_mk_prod T (t :: ts) = mk_times (t, mk_prod T ts);
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val dest_times = HOLogic.dest_bin @{const_name HOL.times} Term.dummyT;
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fun dest_prod t =
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      let val (t,u) = dest_times t
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      in dest_prod t @ dest_prod u end
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      handle TERM _ => [t];
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fun find_first_numeral past (t::terms) =
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        ((snd (HOLogic.dest_number t), rev past @ terms)
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         handle TERM _ => find_first_numeral (t::past) terms)
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  | find_first_numeral past [] = raise TERM("find_first_numeral", []);
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(*DON'T do the obvious simplifications; that would create special cases*)
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fun mk_coeff (k, t) = mk_times (mk_number (Term.fastype_of t) k, t);
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(*Express t as a product of (possibly) a numeral with other sorted terms*)
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fun dest_coeff sign (Const (@{const_name HOL.uminus}, _) $ t) = dest_coeff (~sign) t
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  | dest_coeff sign t =
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    let val ts = sort TermOrd.term_ord (dest_prod t)
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        val (n, ts') = find_first_numeral [] ts
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                          handle TERM _ => (1, ts)
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    in (sign*n, mk_prod (Term.fastype_of t) ts') end;
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(*Find first coefficient-term THAT MATCHES u*)
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fun find_first_coeff past u [] = raise TERM("find_first_coeff", [])
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  | find_first_coeff past u (t::terms) =
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        let val (n,u') = dest_coeff 1 t
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        in if u aconv u' then (n, rev past @ terms)
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                         else find_first_coeff (t::past) u terms
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        end
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        handle TERM _ => find_first_coeff (t::past) u terms;
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(*Fractions as pairs of ints. Can't use Rat.rat because the representation
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  needs to preserve negative values in the denominator.*)
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fun mk_frac (p, q) = if q = 0 then raise Div else (p, q);
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(*Don't reduce fractions; sums must be proved by rule add_frac_eq.
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  Fractions are reduced later by the cancel_numeral_factor simproc.*)
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fun add_frac ((p1, q1), (p2, q2)) = (p1 * q2 + p2 * q1, q1 * q2);
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val mk_divide = HOLogic.mk_binop @{const_name HOL.divide};
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(*Build term (p / q) * t*)
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fun mk_fcoeff ((p, q), t) =
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  let val T = Term.fastype_of t
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  in mk_times (mk_divide (mk_number T p, mk_number T q), t) end;
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(*Express t as a product of a fraction with other sorted terms*)
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fun dest_fcoeff sign (Const (@{const_name HOL.uminus}, _) $ t) = dest_fcoeff (~sign) t
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  | dest_fcoeff sign (Const (@{const_name HOL.divide}, _) $ t $ u) =
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    let val (p, t') = dest_coeff sign t
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        val (q, u') = dest_coeff 1 u
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    in (mk_frac (p, q), mk_divide (t', u')) end
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  | dest_fcoeff sign t =
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    let val (p, t') = dest_coeff sign t
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        val T = Term.fastype_of t
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    in (mk_frac (p, 1), mk_divide (t', one_of T)) end;
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(** New term ordering so that AC-rewriting brings numerals to the front **)
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(*Order integers by absolute value and then by sign. The standard integer
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  ordering is not well-founded.*)
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fun num_ord (i,j) =
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  (case int_ord (abs i, abs j) of
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    EQUAL => int_ord (Int.sign i, Int.sign j) 
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  | ord => ord);
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(*This resembles TermOrd.term_ord, but it puts binary numerals before other
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  non-atomic terms.*)
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local open Term 
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in 
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fun numterm_ord (Abs (_, T, t), Abs(_, U, u)) =
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      (case numterm_ord (t, u) of EQUAL => TermOrd.typ_ord (T, U) | ord => ord)
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  | numterm_ord
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     (Const(@{const_name Int.number_of}, _) $ v, Const(@{const_name Int.number_of}, _) $ w) =
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     num_ord (HOLogic.dest_numeral v, HOLogic.dest_numeral w)
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  | numterm_ord (Const(@{const_name Int.number_of}, _) $ _, _) = LESS
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  | numterm_ord (_, Const(@{const_name Int.number_of}, _) $ _) = GREATER
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  | numterm_ord (t, u) =
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      (case int_ord (size_of_term t, size_of_term u) of
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        EQUAL =>
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          let val (f, ts) = strip_comb t and (g, us) = strip_comb u in
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            (case TermOrd.hd_ord (f, g) of EQUAL => numterms_ord (ts, us) | ord => ord)
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          end
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      | ord => ord)
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and numterms_ord (ts, us) = list_ord numterm_ord (ts, us)
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end;
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fun numtermless tu = (numterm_ord tu = LESS);
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val num_ss = HOL_ss settermless numtermless;
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(*Maps 0 to Numeral0 and 1 to Numeral1 so that arithmetic isn't complicated by the abstract 0 and 1.*)
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val numeral_syms = [@{thm numeral_0_eq_0} RS sym, @{thm numeral_1_eq_1} RS sym];
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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(*Simplify Numeral0+n, n+Numeral0, Numeral1*n, n*Numeral1, 1*x, x*1, x/1 *)
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val add_0s =  @{thms add_0s};
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val mult_1s = @{thms mult_1s mult_1_left mult_1_right divide_1};
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(*Simplify inverse Numeral1, a/Numeral1*)
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val inverse_1s = [@{thm inverse_numeral_1}];
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val divide_1s = [@{thm divide_numeral_1}];
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(*To perform binary arithmetic.  The "left" rewriting handles patterns
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  created by the Numeral_Simprocs, such as 3 * (5 * x). *)
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val simps = [@{thm numeral_0_eq_0} RS sym, @{thm numeral_1_eq_1} RS sym,
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                 @{thm add_number_of_left}, @{thm mult_number_of_left}] @
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                @{thms arith_simps} @ @{thms rel_simps};
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(*Binary arithmetic BUT NOT ADDITION since it may collapse adjacent terms
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  during re-arrangement*)
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val non_add_simps =
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  subtract Thm.eq_thm [@{thm add_number_of_left}, @{thm number_of_add} RS sym] simps;
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(*To evaluate binary negations of coefficients*)
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val minus_simps = [@{thm numeral_m1_eq_minus_1} RS sym, @{thm number_of_minus} RS sym] @
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                   @{thms minus_bin_simps} @ @{thms pred_bin_simps};
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(*To let us treat subtraction as addition*)
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val diff_simps = [@{thm diff_minus}, @{thm minus_add_distrib}, @{thm minus_minus}];
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(*To let us treat division as multiplication*)
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val divide_simps = [@{thm divide_inverse}, @{thm inverse_mult_distrib}, @{thm inverse_inverse_eq}];
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(*push the unary minus down: - x * y = x * - y *)
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val minus_mult_eq_1_to_2 =
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    [@{thm mult_minus_left}, @{thm minus_mult_right}] MRS trans |> Drule.standard;
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(*to extract again any uncancelled minuses*)
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val minus_from_mult_simps =
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    [@{thm minus_minus}, @{thm mult_minus_left}, @{thm mult_minus_right}];
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(*combine unary minus with numeric literals, however nested within a product*)
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val mult_minus_simps =
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    [@{thm mult_assoc}, @{thm minus_mult_left}, minus_mult_eq_1_to_2];
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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val norm_ss1 = num_ss addsimps numeral_syms @ add_0s @ mult_1s @
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  diff_simps @ minus_simps @ @{thms add_ac}
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val norm_ss2 = num_ss addsimps non_add_simps @ mult_minus_simps
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val norm_ss3 = num_ss addsimps minus_from_mult_simps @ @{thms add_ac} @ @{thms mult_ac}
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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structure CancelNumeralsCommon =
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  struct
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  val mk_sum            = mk_sum
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  val dest_sum          = dest_sum
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  val mk_coeff          = mk_coeff
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  val dest_coeff        = dest_coeff 1
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  val find_first_coeff  = find_first_coeff []
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  fun trans_tac _       = Arith_Data.trans_tac
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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  fun norm_tac ss =
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    ALLGOALS (simp_tac (Simplifier.inherit_context ss norm_ss1))
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    THEN ALLGOALS (simp_tac (Simplifier.inherit_context ss norm_ss2))
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    THEN ALLGOALS (simp_tac (Simplifier.inherit_context ss norm_ss3))
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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  val numeral_simp_ss = HOL_ss addsimps add_0s @ simps
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  fun numeral_simp_tac ss = ALLGOALS (simp_tac (Simplifier.inherit_context ss numeral_simp_ss))
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  val simplify_meta_eq = Arith_Data.simplify_meta_eq (add_0s @ mult_1s)
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  end;
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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structure EqCancelNumerals = CancelNumeralsFun
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 (open CancelNumeralsCommon
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  val prove_conv = Arith_Data.prove_conv
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  val mk_bal   = HOLogic.mk_eq
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  val dest_bal = HOLogic.dest_bin "op =" Term.dummyT
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  val bal_add1 = @{thm eq_add_iff1} RS trans
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  val bal_add2 = @{thm eq_add_iff2} RS trans
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);
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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structure LessCancelNumerals = CancelNumeralsFun
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 (open CancelNumeralsCommon
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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  val prove_conv = Arith_Data.prove_conv
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  val mk_bal   = HOLogic.mk_binrel @{const_name HOL.less}
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  val dest_bal = HOLogic.dest_bin @{const_name HOL.less} Term.dummyT
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  val bal_add1 = @{thm less_add_iff1} RS trans
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  val bal_add2 = @{thm less_add_iff2} RS trans
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);
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structure LeCancelNumerals = CancelNumeralsFun
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 (open CancelNumeralsCommon
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  val prove_conv = Arith_Data.prove_conv
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  val mk_bal   = HOLogic.mk_binrel @{const_name HOL.less_eq}
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  val dest_bal = HOLogic.dest_bin @{const_name HOL.less_eq} Term.dummyT
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  val bal_add1 = @{thm le_add_iff1} RS trans
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  val bal_add2 = @{thm le_add_iff2} RS trans
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);
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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val cancel_numerals =
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  map (Arith_Data.prep_simproc @{theory})
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   [("inteq_cancel_numerals",
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     ["(l::'a::number_ring) + m = n",
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      "(l::'a::number_ring) = m + n",
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      "(l::'a::number_ring) - m = n",
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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      "(l::'a::number_ring) = m - n",
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      "(l::'a::number_ring) * m = n",
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      "(l::'a::number_ring) = m * n"],
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     K EqCancelNumerals.proc),
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    ("intless_cancel_numerals",
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     ["(l::'a::{ordered_idom,number_ring}) + m < n",
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      "(l::'a::{ordered_idom,number_ring}) < m + n",
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      "(l::'a::{ordered_idom,number_ring}) - m < n",
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      "(l::'a::{ordered_idom,number_ring}) < m - n",
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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      "(l::'a::{ordered_idom,number_ring}) * m < n",
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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      "(l::'a::{ordered_idom,number_ring}) < m * n"],
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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     K LessCancelNumerals.proc),
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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    ("intle_cancel_numerals",
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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     ["(l::'a::{ordered_idom,number_ring}) + m <= n",
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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      "(l::'a::{ordered_idom,number_ring}) <= m + n",
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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      "(l::'a::{ordered_idom,number_ring}) - m <= n",
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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      "(l::'a::{ordered_idom,number_ring}) <= m - n",
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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      "(l::'a::{ordered_idom,number_ring}) * m <= n",
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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      "(l::'a::{ordered_idom,number_ring}) <= m * n"],
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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     K LeCancelNumerals.proc)];
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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structure CombineNumeralsData =
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  struct
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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  type coeff            = int
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  val iszero            = (fn x => x = 0)
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  val add               = op +
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  val mk_sum            = long_mk_sum    (*to work for e.g. 2*x + 3*x *)
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  val dest_sum          = dest_sum
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  val mk_coeff          = mk_coeff
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  val dest_coeff        = dest_coeff 1
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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  val left_distrib      = @{thm combine_common_factor} RS trans
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  val prove_conv        = Arith_Data.prove_conv_nohyps
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  fun trans_tac _       = Arith_Data.trans_tac
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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  fun norm_tac ss =
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    ALLGOALS (simp_tac (Simplifier.inherit_context ss norm_ss1))
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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    THEN ALLGOALS (simp_tac (Simplifier.inherit_context ss norm_ss2))
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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    THEN ALLGOALS (simp_tac (Simplifier.inherit_context ss norm_ss3))
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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  val numeral_simp_ss = HOL_ss addsimps add_0s @ simps
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  fun numeral_simp_tac ss = ALLGOALS (simp_tac (Simplifier.inherit_context ss numeral_simp_ss))
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  val simplify_meta_eq = Arith_Data.simplify_meta_eq (add_0s @ mult_1s)
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  end;
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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structure CombineNumerals = CombineNumeralsFun(CombineNumeralsData);
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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(*Version for fields, where coefficients can be fractions*)
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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structure FieldCombineNumeralsData =
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  struct
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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  type coeff            = int * int
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  val iszero            = (fn (p, q) => p = 0)
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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  val add               = add_frac
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   306
  val mk_sum            = long_mk_sum
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  val dest_sum          = dest_sum
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  val mk_coeff          = mk_fcoeff
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  val dest_coeff        = dest_fcoeff 1
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   310
  val left_distrib      = @{thm combine_common_factor} RS trans
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  val prove_conv        = Arith_Data.prove_conv_nohyps
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  fun trans_tac _       = Arith_Data.trans_tac
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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  val norm_ss1a = norm_ss1 addsimps inverse_1s @ divide_simps
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   315
  fun norm_tac ss =
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    ALLGOALS (simp_tac (Simplifier.inherit_context ss norm_ss1a))
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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    THEN ALLGOALS (simp_tac (Simplifier.inherit_context ss norm_ss2))
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   318
    THEN ALLGOALS (simp_tac (Simplifier.inherit_context ss norm_ss3))
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   320
  val numeral_simp_ss = HOL_ss addsimps add_0s @ simps @ [@{thm add_frac_eq}]
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   321
  fun numeral_simp_tac ss = ALLGOALS (simp_tac (Simplifier.inherit_context ss numeral_simp_ss))
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   322
  val simplify_meta_eq = Arith_Data.simplify_meta_eq (add_0s @ mult_1s @ divide_1s)
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   323
  end;
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   324
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   325
structure FieldCombineNumerals = CombineNumeralsFun(FieldCombineNumeralsData);
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   326
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   327
val combine_numerals =
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   328
  Arith_Data.prep_simproc @{theory}
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   329
    ("int_combine_numerals", 
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     ["(i::'a::number_ring) + j", "(i::'a::number_ring) - j"], 
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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     K CombineNumerals.proc);
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   332
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   333
val field_combine_numerals =
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   334
  Arith_Data.prep_simproc @{theory}
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   335
    ("field_combine_numerals", 
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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     ["(i::'a::{number_ring,field,division_by_zero}) + j",
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   337
      "(i::'a::{number_ring,field,division_by_zero}) - j"], 
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   338
     K FieldCombineNumerals.proc);
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   339
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   340
(** Constant folding for multiplication in semirings **)
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   341
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   342
(*We do not need folding for addition: combine_numerals does the same thing*)
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   343
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   344
structure Semiring_Times_Assoc_Data : ASSOC_FOLD_DATA =
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struct
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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  val assoc_ss = HOL_ss addsimps @{thms mult_ac}
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   347
  val eq_reflection = eq_reflection
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   348
  fun is_numeral (Const(@{const_name Int.number_of}, _) $ _) = true
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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    | is_numeral _ = false;
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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end;
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   351
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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structure Semiring_Times_Assoc = Assoc_Fold (Semiring_Times_Assoc_Data);
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   354
val assoc_fold_simproc =
32155
e2bf2f73b0c8 more @{theory} antiquotations;
wenzelm
parents: 31368
diff changeset
   355
  Arith_Data.prep_simproc @{theory}
31068
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   356
   ("semiring_assoc_fold", ["(a::'a::comm_semiring_1_cancel) * b"],
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   357
    K Semiring_Times_Assoc.proc);
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   358
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   359
structure CancelNumeralFactorCommon =
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   360
  struct
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   361
  val mk_coeff          = mk_coeff
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   362
  val dest_coeff        = dest_coeff 1
31368
763f4b0fd579 made SML/NJ happy;
wenzelm
parents: 31101
diff changeset
   363
  fun trans_tac _       = Arith_Data.trans_tac
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   364
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   365
  val norm_ss1 = HOL_ss addsimps minus_from_mult_simps @ mult_1s
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   366
  val norm_ss2 = HOL_ss addsimps simps @ mult_minus_simps
23881
851c74f1bb69 moved class ord from Orderings.thy to HOL.thy
haftmann
parents: 23413
diff changeset
   367
  val norm_ss3 = HOL_ss addsimps @{thms mult_ac}
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   368
  fun norm_tac ss =
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   369
    ALLGOALS (simp_tac (Simplifier.inherit_context ss norm_ss1))
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   370
    THEN ALLGOALS (simp_tac (Simplifier.inherit_context ss norm_ss2))
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   371
    THEN ALLGOALS (simp_tac (Simplifier.inherit_context ss norm_ss3))
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   372
31068
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   373
  val numeral_simp_ss = HOL_ss addsimps
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   374
    [@{thm eq_number_of_eq}, @{thm less_number_of}, @{thm le_number_of}] @ simps
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   375
  fun numeral_simp_tac ss = ALLGOALS (simp_tac (Simplifier.inherit_context ss numeral_simp_ss))
30518
07b45c1aa788 moved some generic nonsense to arith_data.ML
haftmann
parents: 30496
diff changeset
   376
  val simplify_meta_eq = Arith_Data.simplify_meta_eq
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   377
    [@{thm add_0}, @{thm add_0_right}, @{thm mult_zero_left},
26086
3c243098b64a New simpler representation of numerals, using Bit0 and Bit1 instead of BIT, B0, and B1
huffman
parents: 25481
diff changeset
   378
      @{thm mult_zero_right}, @{thm mult_Bit1}, @{thm mult_1_right}];
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   379
  end
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   380
30931
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   381
(*Version for semiring_div*)
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   382
structure DivCancelNumeralFactor = CancelNumeralFactorFun
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   383
 (open CancelNumeralFactorCommon
30496
7cdcc9dd95cb vague cleanup in arith proof tools setup: deleted dead code, more proper structures, clearer arrangement
haftmann
parents: 30242
diff changeset
   384
  val prove_conv = Arith_Data.prove_conv
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   385
  val mk_bal   = HOLogic.mk_binop @{const_name Divides.div}
30931
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   386
  val dest_bal = HOLogic.dest_bin @{const_name Divides.div} Term.dummyT
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   387
  val cancel = @{thm div_mult_mult1} RS trans
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   388
  val neg_exchanges = false
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   389
)
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   390
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   391
(*Version for fields*)
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   392
structure DivideCancelNumeralFactor = CancelNumeralFactorFun
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   393
 (open CancelNumeralFactorCommon
30496
7cdcc9dd95cb vague cleanup in arith proof tools setup: deleted dead code, more proper structures, clearer arrangement
haftmann
parents: 30242
diff changeset
   394
  val prove_conv = Arith_Data.prove_conv
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   395
  val mk_bal   = HOLogic.mk_binop @{const_name HOL.divide}
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   396
  val dest_bal = HOLogic.dest_bin @{const_name HOL.divide} Term.dummyT
23413
5caa2710dd5b tuned laws for cancellation in divisions for fields.
nipkow
parents: 23401
diff changeset
   397
  val cancel = @{thm mult_divide_mult_cancel_left} RS trans
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   398
  val neg_exchanges = false
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   399
)
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   400
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   401
structure EqCancelNumeralFactor = CancelNumeralFactorFun
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   402
 (open CancelNumeralFactorCommon
30496
7cdcc9dd95cb vague cleanup in arith proof tools setup: deleted dead code, more proper structures, clearer arrangement
haftmann
parents: 30242
diff changeset
   403
  val prove_conv = Arith_Data.prove_conv
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   404
  val mk_bal   = HOLogic.mk_eq
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   405
  val dest_bal = HOLogic.dest_bin "op =" Term.dummyT
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   406
  val cancel = @{thm mult_cancel_left} RS trans
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   407
  val neg_exchanges = false
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   408
)
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   409
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   410
structure LessCancelNumeralFactor = CancelNumeralFactorFun
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   411
 (open CancelNumeralFactorCommon
30496
7cdcc9dd95cb vague cleanup in arith proof tools setup: deleted dead code, more proper structures, clearer arrangement
haftmann
parents: 30242
diff changeset
   412
  val prove_conv = Arith_Data.prove_conv
23881
851c74f1bb69 moved class ord from Orderings.thy to HOL.thy
haftmann
parents: 23413
diff changeset
   413
  val mk_bal   = HOLogic.mk_binrel @{const_name HOL.less}
851c74f1bb69 moved class ord from Orderings.thy to HOL.thy
haftmann
parents: 23413
diff changeset
   414
  val dest_bal = HOLogic.dest_bin @{const_name HOL.less} Term.dummyT
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   415
  val cancel = @{thm mult_less_cancel_left} RS trans
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   416
  val neg_exchanges = true
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   417
)
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   418
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   419
structure LeCancelNumeralFactor = CancelNumeralFactorFun
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   420
 (open CancelNumeralFactorCommon
30496
7cdcc9dd95cb vague cleanup in arith proof tools setup: deleted dead code, more proper structures, clearer arrangement
haftmann
parents: 30242
diff changeset
   421
  val prove_conv = Arith_Data.prove_conv
23881
851c74f1bb69 moved class ord from Orderings.thy to HOL.thy
haftmann
parents: 23413
diff changeset
   422
  val mk_bal   = HOLogic.mk_binrel @{const_name HOL.less_eq}
851c74f1bb69 moved class ord from Orderings.thy to HOL.thy
haftmann
parents: 23413
diff changeset
   423
  val dest_bal = HOLogic.dest_bin @{const_name HOL.less_eq} Term.dummyT
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   424
  val cancel = @{thm mult_le_cancel_left} RS trans
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   425
  val neg_exchanges = true
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   426
)
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   427
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   428
val cancel_numeral_factors =
32155
e2bf2f73b0c8 more @{theory} antiquotations;
wenzelm
parents: 31368
diff changeset
   429
  map (Arith_Data.prep_simproc @{theory})
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   430
   [("ring_eq_cancel_numeral_factor",
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   431
     ["(l::'a::{idom,number_ring}) * m = n",
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   432
      "(l::'a::{idom,number_ring}) = m * n"],
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   433
     K EqCancelNumeralFactor.proc),
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   434
    ("ring_less_cancel_numeral_factor",
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   435
     ["(l::'a::{ordered_idom,number_ring}) * m < n",
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   436
      "(l::'a::{ordered_idom,number_ring}) < m * n"],
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   437
     K LessCancelNumeralFactor.proc),
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   438
    ("ring_le_cancel_numeral_factor",
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   439
     ["(l::'a::{ordered_idom,number_ring}) * m <= n",
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   440
      "(l::'a::{ordered_idom,number_ring}) <= m * n"],
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   441
     K LeCancelNumeralFactor.proc),
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   442
    ("int_div_cancel_numeral_factors",
30931
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   443
     ["((l::'a::{semiring_div,number_ring}) * m) div n",
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   444
      "(l::'a::{semiring_div,number_ring}) div (m * n)"],
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   445
     K DivCancelNumeralFactor.proc),
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   446
    ("divide_cancel_numeral_factor",
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   447
     ["((l::'a::{division_by_zero,field,number_ring}) * m) / n",
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   448
      "(l::'a::{division_by_zero,field,number_ring}) / (m * n)",
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   449
      "((number_of v)::'a::{division_by_zero,field,number_ring}) / (number_of w)"],
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   450
     K DivideCancelNumeralFactor.proc)];
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   451
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   452
val field_cancel_numeral_factors =
32155
e2bf2f73b0c8 more @{theory} antiquotations;
wenzelm
parents: 31368
diff changeset
   453
  map (Arith_Data.prep_simproc @{theory})
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   454
   [("field_eq_cancel_numeral_factor",
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   455
     ["(l::'a::{field,number_ring}) * m = n",
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   456
      "(l::'a::{field,number_ring}) = m * n"],
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   457
     K EqCancelNumeralFactor.proc),
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   458
    ("field_cancel_numeral_factor",
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   459
     ["((l::'a::{division_by_zero,field,number_ring}) * m) / n",
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   460
      "(l::'a::{division_by_zero,field,number_ring}) / (m * n)",
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   461
      "((number_of v)::'a::{division_by_zero,field,number_ring}) / (number_of w)"],
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   462
     K DivideCancelNumeralFactor.proc)]
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   463
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   464
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   465
(** Declarations for ExtractCommonTerm **)
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   466
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   467
(*Find first term that matches u*)
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   468
fun find_first_t past u []         = raise TERM ("find_first_t", [])
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   469
  | find_first_t past u (t::terms) =
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   470
        if u aconv t then (rev past @ terms)
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   471
        else find_first_t (t::past) u terms
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   472
        handle TERM _ => find_first_t (t::past) u terms;
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   473
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   474
(** Final simplification for the CancelFactor simprocs **)
30518
07b45c1aa788 moved some generic nonsense to arith_data.ML
haftmann
parents: 30496
diff changeset
   475
val simplify_one = Arith_Data.simplify_meta_eq  
30031
bd786c37af84 Removed redundant lemmas
nipkow
parents: 29981
diff changeset
   476
  [@{thm mult_1_left}, @{thm mult_1_right}, @{thm div_by_1}, @{thm numeral_1_eq_1}];
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   477
30649
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   478
fun cancel_simplify_meta_eq ss cancel_th th =
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   479
    simplify_one ss (([th, cancel_th]) MRS trans);
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   480
30649
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   481
local
31067
fd7ec31f850c generalized simproc for mod
haftmann
parents: 30931
diff changeset
   482
  val Tp_Eq = Thm.reflexive (Thm.cterm_of @{theory HOL} HOLogic.Trueprop)
30649
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   483
  fun Eq_True_elim Eq = 
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   484
    Thm.equal_elim (Thm.combination Tp_Eq (Thm.symmetric Eq)) @{thm TrueI}
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   485
in
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   486
fun sign_conv pos_th neg_th ss t =
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   487
  let val T = fastype_of t;
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   488
      val zero = Const(@{const_name HOL.zero}, T);
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   489
      val less = Const(@{const_name HOL.less}, [T,T] ---> HOLogic.boolT);
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   490
      val pos = less $ zero $ t and neg = less $ t $ zero
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   491
      fun prove p =
31101
26c7bb764a38 qualified names for Lin_Arith tactics and simprocs
haftmann
parents: 31068
diff changeset
   492
        Option.map Eq_True_elim (Lin_Arith.simproc ss p)
30649
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   493
        handle THM _ => NONE
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   494
    in case prove pos of
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   495
         SOME th => SOME(th RS pos_th)
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   496
       | NONE => (case prove neg of
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   497
                    SOME th => SOME(th RS neg_th)
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   498
                  | NONE => NONE)
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   499
    end;
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   500
end
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   501
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   502
structure CancelFactorCommon =
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   503
  struct
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   504
  val mk_sum            = long_mk_prod
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   505
  val dest_sum          = dest_prod
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   506
  val mk_coeff          = mk_coeff
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   507
  val dest_coeff        = dest_coeff
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   508
  val find_first        = find_first_t []
31368
763f4b0fd579 made SML/NJ happy;
wenzelm
parents: 31101
diff changeset
   509
  fun trans_tac _       = Arith_Data.trans_tac
23881
851c74f1bb69 moved class ord from Orderings.thy to HOL.thy
haftmann
parents: 23413
diff changeset
   510
  val norm_ss = HOL_ss addsimps mult_1s @ @{thms mult_ac}
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   511
  fun norm_tac ss = ALLGOALS (simp_tac (Simplifier.inherit_context ss norm_ss))
30649
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   512
  val simplify_meta_eq  = cancel_simplify_meta_eq 
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   513
  end;
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   514
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   515
(*mult_cancel_left requires a ring with no zero divisors.*)
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   516
structure EqCancelFactor = ExtractCommonTermFun
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   517
 (open CancelFactorCommon
30496
7cdcc9dd95cb vague cleanup in arith proof tools setup: deleted dead code, more proper structures, clearer arrangement
haftmann
parents: 30242
diff changeset
   518
  val prove_conv = Arith_Data.prove_conv
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   519
  val mk_bal   = HOLogic.mk_eq
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   520
  val dest_bal = HOLogic.dest_bin "op =" Term.dummyT
31368
763f4b0fd579 made SML/NJ happy;
wenzelm
parents: 31101
diff changeset
   521
  fun simp_conv _ _ = SOME @{thm mult_cancel_left}
30649
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   522
);
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   523
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   524
(*for ordered rings*)
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   525
structure LeCancelFactor = ExtractCommonTermFun
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   526
 (open CancelFactorCommon
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   527
  val prove_conv = Arith_Data.prove_conv
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   528
  val mk_bal   = HOLogic.mk_binrel @{const_name HOL.less_eq}
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   529
  val dest_bal = HOLogic.dest_bin @{const_name HOL.less_eq} Term.dummyT
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   530
  val simp_conv = sign_conv
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   531
    @{thm mult_le_cancel_left_pos} @{thm mult_le_cancel_left_neg}
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   532
);
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   533
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   534
(*for ordered rings*)
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   535
structure LessCancelFactor = ExtractCommonTermFun
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   536
 (open CancelFactorCommon
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   537
  val prove_conv = Arith_Data.prove_conv
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   538
  val mk_bal   = HOLogic.mk_binrel @{const_name HOL.less}
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   539
  val dest_bal = HOLogic.dest_bin @{const_name HOL.less} Term.dummyT
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   540
  val simp_conv = sign_conv
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   541
    @{thm mult_less_cancel_left_pos} @{thm mult_less_cancel_left_neg}
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   542
);
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   543
30931
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   544
(*for semirings with division*)
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   545
structure DivCancelFactor = ExtractCommonTermFun
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   546
 (open CancelFactorCommon
30496
7cdcc9dd95cb vague cleanup in arith proof tools setup: deleted dead code, more proper structures, clearer arrangement
haftmann
parents: 30242
diff changeset
   547
  val prove_conv = Arith_Data.prove_conv
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   548
  val mk_bal   = HOLogic.mk_binop @{const_name Divides.div}
30931
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   549
  val dest_bal = HOLogic.dest_bin @{const_name Divides.div} Term.dummyT
31368
763f4b0fd579 made SML/NJ happy;
wenzelm
parents: 31101
diff changeset
   550
  fun simp_conv _ _ = SOME @{thm div_mult_mult1_if}
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   551
);
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   552
30931
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   553
structure ModCancelFactor = ExtractCommonTermFun
24395
8df021f79e0b Added mod cancellation simproc
nipkow
parents: 23969
diff changeset
   554
 (open CancelFactorCommon
30496
7cdcc9dd95cb vague cleanup in arith proof tools setup: deleted dead code, more proper structures, clearer arrangement
haftmann
parents: 30242
diff changeset
   555
  val prove_conv = Arith_Data.prove_conv
24395
8df021f79e0b Added mod cancellation simproc
nipkow
parents: 23969
diff changeset
   556
  val mk_bal   = HOLogic.mk_binop @{const_name Divides.mod}
31067
fd7ec31f850c generalized simproc for mod
haftmann
parents: 30931
diff changeset
   557
  val dest_bal = HOLogic.dest_bin @{const_name Divides.mod} Term.dummyT
31368
763f4b0fd579 made SML/NJ happy;
wenzelm
parents: 31101
diff changeset
   558
  fun simp_conv _ _ = SOME @{thm mod_mult_mult1}
24395
8df021f79e0b Added mod cancellation simproc
nipkow
parents: 23969
diff changeset
   559
);
8df021f79e0b Added mod cancellation simproc
nipkow
parents: 23969
diff changeset
   560
30931
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   561
(*for idoms*)
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   562
structure DvdCancelFactor = ExtractCommonTermFun
23969
ef782bbf2d09 Added cancel simprocs for dvd on nat and int
nipkow
parents: 23881
diff changeset
   563
 (open CancelFactorCommon
30496
7cdcc9dd95cb vague cleanup in arith proof tools setup: deleted dead code, more proper structures, clearer arrangement
haftmann
parents: 30242
diff changeset
   564
  val prove_conv = Arith_Data.prove_conv
27651
16a26996c30e moved op dvd to theory Ring_and_Field; generalized a couple of lemmas
haftmann
parents: 26086
diff changeset
   565
  val mk_bal   = HOLogic.mk_binrel @{const_name Ring_and_Field.dvd}
29981
7d0ed261b712 generalize int_dvd_cancel_factor simproc to idom class
huffman
parents: 29038
diff changeset
   566
  val dest_bal = HOLogic.dest_bin @{const_name Ring_and_Field.dvd} Term.dummyT
31368
763f4b0fd579 made SML/NJ happy;
wenzelm
parents: 31101
diff changeset
   567
  fun simp_conv _ _ = SOME @{thm dvd_mult_cancel_left}
23969
ef782bbf2d09 Added cancel simprocs for dvd on nat and int
nipkow
parents: 23881
diff changeset
   568
);
ef782bbf2d09 Added cancel simprocs for dvd on nat and int
nipkow
parents: 23881
diff changeset
   569
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   570
(*Version for all fields, including unordered ones (type complex).*)
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   571
structure DivideCancelFactor = ExtractCommonTermFun
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   572
 (open CancelFactorCommon
30496
7cdcc9dd95cb vague cleanup in arith proof tools setup: deleted dead code, more proper structures, clearer arrangement
haftmann
parents: 30242
diff changeset
   573
  val prove_conv = Arith_Data.prove_conv
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   574
  val mk_bal   = HOLogic.mk_binop @{const_name HOL.divide}
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   575
  val dest_bal = HOLogic.dest_bin @{const_name HOL.divide} Term.dummyT
31368
763f4b0fd579 made SML/NJ happy;
wenzelm
parents: 31101
diff changeset
   576
  fun simp_conv _ _ = SOME @{thm mult_divide_mult_cancel_left_if}
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   577
);
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   578
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   579
val cancel_factors =
32155
e2bf2f73b0c8 more @{theory} antiquotations;
wenzelm
parents: 31368
diff changeset
   580
  map (Arith_Data.prep_simproc @{theory})
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   581
   [("ring_eq_cancel_factor",
30931
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   582
     ["(l::'a::idom) * m = n",
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   583
      "(l::'a::idom) = m * n"],
30649
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   584
     K EqCancelFactor.proc),
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   585
    ("ordered_ring_le_cancel_factor",
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   586
     ["(l::'a::ordered_ring) * m <= n",
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   587
      "(l::'a::ordered_ring) <= m * n"],
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   588
     K LeCancelFactor.proc),
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   589
    ("ordered_ring_less_cancel_factor",
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   590
     ["(l::'a::ordered_ring) * m < n",
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   591
      "(l::'a::ordered_ring) < m * n"],
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   592
     K LessCancelFactor.proc),
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   593
    ("int_div_cancel_factor",
30931
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   594
     ["((l::'a::semiring_div) * m) div n", "(l::'a::semiring_div) div (m * n)"],
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   595
     K DivCancelFactor.proc),
24395
8df021f79e0b Added mod cancellation simproc
nipkow
parents: 23969
diff changeset
   596
    ("int_mod_cancel_factor",
30931
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   597
     ["((l::'a::semiring_div) * m) mod n", "(l::'a::semiring_div) mod (m * n)"],
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   598
     K ModCancelFactor.proc),
29981
7d0ed261b712 generalize int_dvd_cancel_factor simproc to idom class
huffman
parents: 29038
diff changeset
   599
    ("dvd_cancel_factor",
7d0ed261b712 generalize int_dvd_cancel_factor simproc to idom class
huffman
parents: 29038
diff changeset
   600
     ["((l::'a::idom) * m) dvd n", "(l::'a::idom) dvd (m * n)"],
30931
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   601
     K DvdCancelFactor.proc),
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   602
    ("divide_cancel_factor",
23400
a64b39e5809b The simprocs "divide_cancel_factor" and "ring_eq_cancel_factor" no
nipkow
parents: 23398
diff changeset
   603
     ["((l::'a::{division_by_zero,field}) * m) / n",
a64b39e5809b The simprocs "divide_cancel_factor" and "ring_eq_cancel_factor" no
nipkow
parents: 23398
diff changeset
   604
      "(l::'a::{division_by_zero,field}) / (m * n)"],
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   605
     K DivideCancelFactor.proc)];
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   606
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   607
end;
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   608
31068
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   609
Addsimprocs Numeral_Simprocs.cancel_numerals;
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   610
Addsimprocs [Numeral_Simprocs.combine_numerals];
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   611
Addsimprocs [Numeral_Simprocs.field_combine_numerals];
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   612
Addsimprocs [Numeral_Simprocs.assoc_fold_simproc];
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   613
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   614
(*examples:
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   615
print_depth 22;
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   616
set timing;
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   617
set trace_simp;
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   618
fun test s = (Goal s, by (Simp_tac 1));
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   619
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   620
test "l + 2 + 2 + 2 + (l + 2) + (oo + 2) = (uu::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   621
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   622
test "2*u = (u::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   623
test "(i + j + 12 + (k::int)) - 15 = y";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   624
test "(i + j + 12 + (k::int)) - 5 = y";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   625
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   626
test "y - b < (b::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   627
test "y - (3*b + c) < (b::int) - 2*c";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   628
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   629
test "(2*x - (u*v) + y) - v*3*u = (w::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   630
test "(2*x*u*v + (u*v)*4 + y) - v*u*4 = (w::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   631
test "(2*x*u*v + (u*v)*4 + y) - v*u = (w::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   632
test "u*v - (x*u*v + (u*v)*4 + y) = (w::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   633
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   634
test "(i + j + 12 + (k::int)) = u + 15 + y";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   635
test "(i + j*2 + 12 + (k::int)) = j + 5 + y";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   636
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   637
test "2*y + 3*z + 6*w + 2*y + 3*z + 2*u = 2*y' + 3*z' + 6*w' + 2*y' + 3*z' + u + (vv::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   638
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   639
test "a + -(b+c) + b = (d::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   640
test "a + -(b+c) - b = (d::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   641
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   642
(*negative numerals*)
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   643
test "(i + j + -2 + (k::int)) - (u + 5 + y) = zz";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   644
test "(i + j + -3 + (k::int)) < u + 5 + y";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   645
test "(i + j + 3 + (k::int)) < u + -6 + y";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   646
test "(i + j + -12 + (k::int)) - 15 = y";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   647
test "(i + j + 12 + (k::int)) - -15 = y";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   648
test "(i + j + -12 + (k::int)) - -15 = y";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   649
*)
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   650
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   651
Addsimprocs Numeral_Simprocs.cancel_numeral_factors;
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   652
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   653
(*examples:
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   654
print_depth 22;
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   655
set timing;
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   656
set trace_simp;
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   657
fun test s = (Goal s; by (Simp_tac 1));
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   658
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   659
test "9*x = 12 * (y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   660
test "(9*x) div (12 * (y::int)) = z";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   661
test "9*x < 12 * (y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   662
test "9*x <= 12 * (y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   663
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   664
test "-99*x = 132 * (y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   665
test "(-99*x) div (132 * (y::int)) = z";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   666
test "-99*x < 132 * (y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   667
test "-99*x <= 132 * (y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   668
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   669
test "999*x = -396 * (y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   670
test "(999*x) div (-396 * (y::int)) = z";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   671
test "999*x < -396 * (y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   672
test "999*x <= -396 * (y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   673
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   674
test "-99*x = -81 * (y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   675
test "(-99*x) div (-81 * (y::int)) = z";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   676
test "-99*x <= -81 * (y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   677
test "-99*x < -81 * (y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   678
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   679
test "-2 * x = -1 * (y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   680
test "-2 * x = -(y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   681
test "(-2 * x) div (-1 * (y::int)) = z";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   682
test "-2 * x < -(y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   683
test "-2 * x <= -1 * (y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   684
test "-x < -23 * (y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   685
test "-x <= -23 * (y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   686
*)
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   687
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   688
(*And the same examples for fields such as rat or real:
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   689
test "0 <= (y::rat) * -2";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   690
test "9*x = 12 * (y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   691
test "(9*x) / (12 * (y::rat)) = z";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   692
test "9*x < 12 * (y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   693
test "9*x <= 12 * (y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   694
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   695
test "-99*x = 132 * (y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   696
test "(-99*x) / (132 * (y::rat)) = z";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   697
test "-99*x < 132 * (y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   698
test "-99*x <= 132 * (y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   699
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   700
test "999*x = -396 * (y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   701
test "(999*x) / (-396 * (y::rat)) = z";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   702
test "999*x < -396 * (y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   703
test "999*x <= -396 * (y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   704
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   705
test  "(- ((2::rat) * x) <= 2 * y)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   706
test "-99*x = -81 * (y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   707
test "(-99*x) / (-81 * (y::rat)) = z";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   708
test "-99*x <= -81 * (y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   709
test "-99*x < -81 * (y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   710
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   711
test "-2 * x = -1 * (y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   712
test "-2 * x = -(y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   713
test "(-2 * x) / (-1 * (y::rat)) = z";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   714
test "-2 * x < -(y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   715
test "-2 * x <= -1 * (y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   716
test "-x < -23 * (y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   717
test "-x <= -23 * (y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   718
*)
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   719
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   720
Addsimprocs Numeral_Simprocs.cancel_factors;
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   721
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   722
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   723
(*examples:
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   724
print_depth 22;
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   725
set timing;
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   726
set trace_simp;
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   727
fun test s = (Goal s; by (Asm_simp_tac 1));
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   728
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   729
test "x*k = k*(y::int)";
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   730
test "k = k*(y::int)";
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   731
test "a*(b*c) = (b::int)";
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   732
test "a*(b*c) = d*(b::int)*(x*a)";
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   733
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   734
test "(x*k) div (k*(y::int)) = (uu::int)";
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   735
test "(k) div (k*(y::int)) = (uu::int)";
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   736
test "(a*(b*c)) div ((b::int)) = (uu::int)";
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   737
test "(a*(b*c)) div (d*(b::int)*(x*a)) = (uu::int)";
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   738
*)
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   739
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   740
(*And the same examples for fields such as rat or real:
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   741
print_depth 22;
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   742
set timing;
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   743
set trace_simp;
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   744
fun test s = (Goal s; by (Asm_simp_tac 1));
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   745
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   746
test "x*k = k*(y::rat)";
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   747
test "k = k*(y::rat)";
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   748
test "a*(b*c) = (b::rat)";
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   749
test "a*(b*c) = d*(b::rat)*(x*a)";
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   750
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   751
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   752
test "(x*k) / (k*(y::rat)) = (uu::rat)";
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   753
test "(k) / (k*(y::rat)) = (uu::rat)";
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   754
test "(a*(b*c)) / ((b::rat)) = (uu::rat)";
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   755
test "(a*(b*c)) / (d*(b::rat)*(x*a)) = (uu::rat)";
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   756
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   757
(*FIXME: what do we do about this?*)
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   758
test "a*(b*c)/(y*z) = d*(b::rat)*(x*a)/z";
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   759
*)