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diff --git a/src/hyper/pages/MAPPKG1.ht b/src/hyper/pages/MAPPKG1.ht new file mode 100644 index 00000000..33553bc3 --- /dev/null +++ b/src/hyper/pages/MAPPKG1.ht @@ -0,0 +1,174 @@ +% Copyright The Numerical Algorithms Group Limited 1992-94. All rights reserved. +% !! DO NOT MODIFY THIS FILE BY HAND !! Created by ht.awk. +\newcommand{\MappingPackageOneXmpTitle}{MappingPackage1} +\newcommand{\MappingPackageOneXmpNumber}{9.51} +% +% ===================================================================== +\begin{page}{MappingPackageOneXmpPage}{9.51 MappingPackage1} +% ===================================================================== +\beginscroll + +Function are objects of type \pspadtype{Mapping}. +In this section we demonstrate some library operations from the +packages \spadtype{MappingPackage1}, \spadtype{MappingPackage2}, and +\spadtype{MappingPackage3} that manipulate and create functions. +Some terminology: a {\it nullary} function takes no arguments, +%-% \HDindex{function!nullary}{MappingPackageOneXmpPage}{9.51}{MappingPackage1} +a {\it unary} function takes one argument, and +%-% \HDindex{function!unary}{MappingPackageOneXmpPage}{9.51}{MappingPackage1} +a {\it binary} function takes two arguments. +%-% \HDindex{function!binary}{MappingPackageOneXmpPage}{9.51}{MappingPackage1} + +\xtc{ +We begin by creating an example function that raises a +rational number to an integer exponent. +}{ +\spadpaste{power(q: FRAC INT, n: INT): FRAC INT == q**n \bound{power}} +} +\xtc{ +}{ +\spadpaste{power(2,3) \free{power}} +} +\xtc{ +The \spadfunFrom{twist}{MappingPackage3} operation +transposes the arguments of a binary function. +Here \spad{rewop(a, b)} is \spad{power(b, a)}. +}{ +\spadpaste{rewop := twist power \free{power}\bound{rewop}} +} +\xtc{ +This is \texht{$2^3.$}{\spad{2**3.}} +}{ +\spadpaste{rewop(3, 2) \free{rewop}} +} +\xtc{ +Now we define \userfun{square} in terms of \userfun{power}. +}{ +\spadpaste{square: FRAC INT -> FRAC INT \bound{squaredec}} +} +\xtc{ +The \spadfunFrom{curryRight}{MappingPackage3} operation creates a unary +function from a binary one by providing a constant +argument on the right. +}{ +\spadpaste{square:= curryRight(power, 2) \free{squaredec poswer}\bound{square}} +} +\xtc{ +Likewise, the +\spadfunFrom{curryLeft}{MappingPackage3} operation provides a constant +argument on the left. +}{ +\spadpaste{square 4 \free{square}} +} +\xtc{ +The \spadfunFrom{constantRight}{MappingPackage3} operation creates +(in a trivial way) a binary function from a unary one: +\spad{constantRight(f)} is the function \spad{g} such that +\spad{g(a,b)= f(a).} +}{ +\spadpaste{squirrel:= constantRight(square)\$MAPPKG3(FRAC INT,FRAC INT,FRAC INT) \free{square}\bound{squirrel}} +} +\xtc{ +Likewise, +\spad{constantLeft(f)} is the function \spad{g} such that \spad{g(a,b)= f(b).} +}{ +\spadpaste{squirrel(1/2, 1/3) \free{squirrel}} +} +\xtc{ +The \spadfunFrom{curry}{MappingPackage2} operation makes a unary function nullary. +}{ +\spadpaste{sixteen := curry(square, 4/1) \free{square}\bound{sixteen}} +} +\xtc{ +}{ +\spadpaste{sixteen() \free{sixteen}} +} +\xtc{ +The \spadopFrom{*}{MappingPackage3} operation +constructs composed functions. +}{ +\spadpaste{square2:=square*square \free{square}\bound{square2}} +} +\xtc{ +}{ +\spadpaste{square2 3 \free{square2}} +} +\xtc{ +Use the \spadopFrom{**}{MappingPackage1} operation to create +functions that are \spad{n}-fold iterations of other functions. +}{ +\spadpaste{sc(x: FRAC INT): FRAC INT == x + 1 \bound{sc}} +} +\xtc{ +This is a list of \pspadtype{Mapping} objects. +}{ +\spadpaste{incfns := [sc**i for i in 0..10] \free{sc}\bound{incfns}} +} +\xtc{ +This is a list of applications of those functions. +}{ +\spadpaste{[f 4 for f in incfns] \free{incfns}} +} +\xtc{ +Use the \spadfunFrom{recur}{MappingPackage1} +operation for recursion: +\spad{g := recur f} means \spad{g(n,x) == f(n,f(n-1,...f(1,x))).} +}{ +\spadpaste{times(n:NNI, i:INT):INT == n*i \bound{rdec}} +} +\xtc{ +}{ +\spadpaste{r := recur(times) \free{rdec}\bound{r}} +} +\xtc{ +This is a factorial function. +%-% \HDindex{factorial}{MappingPackageOneXmpPage}{9.51}{MappingPackage1} +}{ +\spadpaste{fact := curryRight(r, 1) \free{r}\bound{fact}} +} +\xtc{ +}{ +\spadpaste{fact 4 \free{fact}} +} +\xtc{ +Constructed functions can be used within other functions. +}{ +\begin{spadsrc}[\free{square}\bound{mto2ton}] +mto2ton(m, n) == + raiser := square**n + raiser m +\end{spadsrc} +} +\xtc{ +This is \texht{$3^{2^3}.$}{\spad{3**(2**3).}} +}{ +\spadpaste{mto2ton(3, 3) \free{mto2ton}} +} +\xtc{ +Here \userfun{shiftfib} is a unary function that modifies its argument. +}{ +\begin{spadsrc}[\bound{shiftfib}] +shiftfib(r: List INT) : INT == + t := r.1 + r.1 := r.2 + r.2 := r.2 + t + t +\end{spadsrc} +} +\xtc{ +By currying over the argument we get a function with private state. +}{ +\spadpaste{fibinit: List INT := [0, 1] \bound{fibinitdec}} +} +\xtc{ +}{ +\spadpaste{fibs := curry(shiftfib, fibinit) \free{shiftfib fibinit}\bound{fibs}} +} +\xtc{ +}{ +\spadpaste{[fibs() for i in 0..30] \free{fibs}} +} +\endscroll +\autobuttons +\end{page} +% |