4.      NoneClass of vector spaces v with scalar s.  !"# !"# !"# Safe-InferedThe infinite natural number. $%&'()* $%&'()* Safe-Infered+,-./+,-./  Safe-Infered0123456789:;<=>?@ABCDEFG0123456789:;<=>?@ABCDEFG0123456789:;<=>?@ABCDEFGNone 50 decimals. Ten decimals. AA type construct that gives one more decimals than the argument. $An epsilon of 1, i.e., no decimals. The  < class contains the types that can be used to determine the  precision of a  number. 5Convert between two arbitrary fixed precision types.  HIJKLMNOPQRS       HIJKLMNOPQRS Safe-InferedDFloating point number where the precision is determined by the type e. TUVWXYZ  TUVWXYZNoneThe . type implements (constructive) real numbers. 'Note that the comparison operations on  may diverge < since it is (by necessity) impossible to implementent them # correctly and always terminating. *This implementation is really David Lester's ERA package. The  function connverts a  to a [. The number of decimals The real number The resulting string \]^_`abcdef \]^_`abcdef Safe-InferedThe - type is the type of differentiable numbers.  It'0s an instance of all the usual numeric classes. 5 The computed derivative of a function is is correct = except where the function is discontinuous, at these points 3 the derivative should be a Dirac pulse, but it isn't. The + numbers are printed with a trailing ~~ to  indicate that there is a "tail" of derivatives. The ' function turns a normal number into a  8 number with the same value. Not that numeric literals 6 do not need an explicit conversion due to the normal " Haskell overloading of literals. The ) function turns a number into a variable 8 number. This is the number with with respect to which  the derivaticve is computed. The  takes a  number and returns its first 5 derivative. The function can be iterated to to get  higher derivaties. The  function takes a  number back to a normal 4 number, thus forgetting about all the derivatives. The  takes a value and  value and makes  a / number that has the given value as its normal  value, and the  number as its derivatives. The * function is a simple utility to take the - derivative of a (single argument) function.  It is simply defined as  deriv f = val . df . f . dVar  Convert a # function to an ordinary function. ghijklmnopghijklmnop Safe-Infered7Symbolic numbers over some base type for the literals. Create a variable. 5Create a constant (useful when it is not a literal). The expression  subst x v e substitutes the expression v for each  occurence of the variable x in e. qrstuvwxyz{qrstuvwxyz{|     !"#$%&'()*+,-./0123456789 : ; < = > ? @ A B C D E F G H I J K L M N O P QRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~numbers-3000.0.0.0Data.Number.NaturalData.Number.IntervalData.Number.FixedData.Number.BigFloatData.Number.CRealData.Number.DifData.Number.SymbolicData.Number.VectorspaceData.Number.FixedFunctionsNaturalinfinityIntervalivalgetIvalFixed PrecPlus20Prec50Prec10EpsDiv10Eps1Epsilon precision convertFixed dynamicEpsBigFloatCReal showCRealDifdCondVardfvalmkDifderivunDifSymvarconsubstunSym Vectorspace*><+>vnegatevzero $fEnumNatural $fRealNatural$fIntegralNatural $fNumNatural $fOrdNatural $fEqNatural $fShowNatural$fFractionalInterval $fNumInterval$fShowInterval $fOrdInterval $fEqIntervalCFapproxfromCFtoCFapproxCFfromTaylorToCFfac integerRoot2pitansincosatanasinacossqrtexpcoshsinhtanhatanhasinhacoshlog$fRealFloatFixed$fFloatingFixed $fReadFixed $fShowFixed$fFractionalFixed $fNumFixed$fEpsilonPrecPlus20$fEpsilonPrec500$fEpsilonPrec50$fEpsilonPrec10$fEpsilonEpsDiv10 $fEpsilonEps1$fRealFloatBigFloat$fFloatingBigFloat$fRealFracBigFloat$fFractionalBigFloat$fRealBigFloat $fNumBigFloat$fShowBigFloatbaseGHC.BaseString $fShowCReal $fReadCReal$fRealFloatCReal$fRealFracCReal $fRealCReal $fEnumCReal$fFloatingCReal$fFractionalCReal $fNumCReal $fOrdCReal $fEqCReal$fRealFloatDif $fRealFracDif $fRealDif $fFloatingDif$fFractionalDif$fNumDif$fOrdDif$fEqDif $fReadDif $fShowDif$fRealFloatSym $fFloatingSym $fRealFracSym $fRealSym $fEnumSym $fIntegralSym$fFractionalSym$fNumSym $fShowSym$fOrdSym$fEqSym