**
** NZNAT
**
**
** Copyright (c) 2000-2015, Toshimi Sawada. All rights reserved.
**
** Redistribution and use in source and binary forms, with or without
** modification, are permitted provided that the following conditions
** are met:
**
**   * Redistributions of source code must retain the above copyright
**     notice, this list of conditions and the following disclaimer.
**
**   * Redistributions in binary form must reproduce the above
**     copyright notice, this list of conditions and the following
**     disclaimer in the documentation and/or other materials
**     provided with the distribution.
**
** THIS SOFTWARE IS PROVIDED BY THE AUTHOR 'AS IS' AND ANY EXPRESSED
** OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
** WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
** ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
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** INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
** WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
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** SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
**

sys:mod! NZNAT
     principal-sort NzNat
{
  imports {
    protecting (NZNAT-VALUE)
    protecting (BOOL)
  }
  signature {
    op _ + _ : NzNat NzNat -> NzNat { assoc comm demod prec: 33 r-assoc }
    op d : NzNat NzNat -> NzNat { comm demod prec: 0 }
    op _ * _ : NzNat NzNat -> NzNat { assoc comm idr: 1 demod prec: 31 r-assoc }
    op _ quot _ : NzNat NzNat -> NzNat { demod prec: 31 l-assoc }
    pred _ < _ : NzNat NzNat  { demod prec: 51 }
    pred _ <= _ : NzNat NzNat  { demod prec: 51 }
    pred _ > _ : NzNat NzNat  { demod prec: 51 }
    pred _ >= _ : NzNat NzNat  { demod prec: 51 }
    op s _ : NzNat -> NzNat { demod prec: 15 }
  }
  axioms {
    var NN : NzNat
    var NM : NzNat
    eq [:BDEMOD]: (NN + NM) = #! (+ nn nm) .
    eq [:BDEMOD]: d(NN,NM) = #! (if (= nn nm) 1 (abs (- nn nm))) .
    eq [:BDEMOD]: (NN * NM) = #! (* nn nm) .
    eq [:BDEMOD]: (NN quot NM) = #! (if (> nn nm) (truncate nn nm) 1) .
    eq [:BDEMOD]: (NN < NM) = #! (< nn nm) .
    eq [:BDEMOD]: (NN <= NM) = #! (<= nn nm) .
    eq [:BDEMOD]: (NN > NM) = #! (> nn nm) .
    eq [:BDEMOD]: (NN >= NM) = #! (>= nn nm) .
    eq [:BDEMOD]: (s NN) = #! (1+ nn) .
  }
}

lispq
(defun chaos-nznat-tram-interface ()
  (setq *z-nznat* (get-z-module-or-panic "NZNAT"))
  (pushnew *z-nznat* *tram-builtin-modules*))

lispq
(eval-when (:execute :load-toplevel)
  (chaos-nznat-tram-interface))

protect NZNAT
provide nznat
--
eof
