See also PositiveInteger

)abbrev domain NNI NonNegativeInteger
++ Author:
++ Date Created:
++ Change History:
++ Basic Operations:
++ Related Constructors:
++ Keywords: integer
++ Description: \spadtype{NonNegativeInteger} provides functions for non
++   negative integers.
NonNegativeInteger: Join(OrderedAbelianMonoidSup,Monoid) with
            _quo : (%,%) -> %
              ++ a quo b returns the quotient of \spad{a} and b, forgetting
              ++ the remainder.
            _rem : (%,%) -> %
              ++ a rem b returns the remainder of \spad{a} and b.
            gcd  : (%,%) -> %
              ++ gcd(a,b) computes the greatest common divisor of two
              ++ non negative integers \spad{a} and b.
            divide: (%,%) -> Record(quotient:%,remainder:%)
              ++ divide(a,b) returns a record containing both
              ++ remainder and quotient.
            _exquo: (%,%) -> Union(%,"failed")
              ++ exquo(a,b) returns the quotient of \spad{a} and b, or "failed"
              ++ if b is zero or \spad{a} rem b is zero.
            shift: (%, Integer) -> %
              ++ shift(a,i) shift \spad{a} by i bits.
            random   : % -> %
              ++ random(n) returns a random integer from 0 to \spad{n-1}.
            commutative("*")
              ++ commutative("*") means multiplication is commutative : \spad{x*y = y*x}.

  == SubDomain(Integer,x+->(x >= 0)) add
      x,y:%
      sup(x,y) == MAX(x,y)$Lisp
      shift(x:%, n:Integer):% == ASH(x,n)$Lisp
      subtractIfCan(x, y) ==
        c:Integer := (x pretend Integer) - (y pretend Integer)
        c < 0 => "failed"
        c pretend %

   Compiling FriCAS source code from file 
      /var/zope2/var/LatexWiki/5780123711064895556-25px001.spad using 
      old system compiler.
   NNI abbreviates domain NonNegativeInteger 
------------------------------------------------------------------------
   initializing NRLIB NNI for NonNegativeInteger 
   compiling into NRLIB NNI 
****** comp fails at level 1 with expression: ******
((+-> |x|
  (IF (< |x| 0)
      |false|
      |true|)))
****** level 1  ******
$x:= (+-> x (IF (< x (Zero)) false true))
$m:= (Boolean)
$f:=
((((|#1| #) (* #) (+ #) (- #) ...)))

   >> Apparent user error:
   compLambda: signature needed
   (+-> x (IF (< x (Zero)) false true))

)show NonNegativeInteger

 NonNegativeInteger  is a domain constructor
 Abbreviation for NonNegativeInteger is NNI
 This constructor is exposed in this frame.
------------------------------- Operations --------------------------------
 ?*? : (%,%) -> %                      ?*? : (PositiveInteger,%) -> %
 ?+? : (%,%) -> %                      ?<? : (%,%) -> Boolean
 ?<=? : (%,%) -> Boolean               ?=? : (%,%) -> Boolean
 ?>? : (%,%) -> Boolean                ?>=? : (%,%) -> Boolean
 1 : () -> %                           0 : () -> %
 ?^? : (%,PositiveInteger) -> %        coerce : % -> OutputForm
 gcd : (%,%) -> %                      hash : % -> SingleInteger
 latex : % -> String                   max : (%,%) -> %
 min : (%,%) -> %                      one? : % -> Boolean
 ?quo? : (%,%) -> %                    random : % -> %
 recip : % -> Union(%,"failed")        ?rem? : (%,%) -> %
 sample : () -> %                      shift : (%,Integer) -> %
 smaller? : (%,%) -> Boolean           sup : (%,%) -> %
 zero? : % -> Boolean                  ?~=? : (%,%) -> Boolean
 ?*? : (NonNegativeInteger,%) -> %
 ?^? : (%,NonNegativeInteger) -> %
 divide : (%,%) -> Record(quotient: %,remainder: %)
 exquo : (%,%) -> Union(%,"failed")
 subtractIfCan : (%,%) -> Union(%,"failed")