úÎ%Ó#Ð      Safe-Inferred<The class of Peano-like constructions (i.e. Nat and Whole). Test for zero. An unobservable infinity. #Converts the number to an Integer. 2Reduces the absolute value of the number by 1. If isZero n , then  decr n = n. Whole numbers (Z). Sign for whole numbers. <Lazy Peano numbers. Allow calculation with infinite values.  Negation of . Removes at most  k constructors from a Peano number. Outputs the number of removed constructors and the remaining number. rReturns the length of a list as Nat. Can handle infinite lists, provided that a finite lower bound is checked. Integral-instance for  -. Since negative numbers are not allowed,  quot = div and  rem = mod. The methods quot, rem, div, mod, quotRem and divModa will return as long as their first argument is finite. Infinities are handled as follows:  n  infinity = n  infinity = 0 n   infinity = n ! infinity = n Real-instance for  . Since " returns a  Ratio Integer*, it WILL NOT terminate on infinities. Ord-instance for  A. All methods work as long as at least one operand is finite. Eq-instance for 3. Positive and negative zero are considered equal. Eq-instance for  . # and $4 work as long as at least one operand is finite. Num-instance for  ÿ%. Addition, multiplication, and subtraction are lazy in both arguments, meaning that, in the case of infinite values, they can produce an infinite stream of S-constructors. As long as the callers of these functions only consume a finite amount of these, the program will not hang.  fromInteger is not injective in case of  5, since negative integers are all converted to Z. Enum-instance for . % and &A work according to the total order on the whole numbers, i.e.  succ n = n+1 and  pred n = n-1. Enum-instance for  . The & function is bounded at Zero. Bounded-instance for  1. The bounds are negative and positive infinity. Bounded-instance for  ;. The lower bound is zero, the upper bound is infinity.         '      ! " # $ %&'(&')*+*,-numericpeano-0.1.0.0 Numeric.PeanoPeanoisZeroinfinity fromPeanodecrWholeSignNegPosNatSZisSucctakeNat natLength $fIntegralNat $fRealNat $fOrdWhole$fOrdNat $fEqWhole$fEqNat $fNumWhole$fNumNat $fEnumWhole $fEnumNat$fBoundedWhole $fBoundedNat $fPeanoWhole $fPeanoNatbaseGHC.Realquotdivremmod toRationalghc-prim GHC.Classes==/=GHC.Enumsuccpred