Function inside a function?

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I have been experimenting with writing a few little programs to perform
numerical integration, in which I have been running into difficulties.  I
can do all the operations I need from the command line, but I run into
problems when I try to bundle those commands into a program.

As a simple example, suppose I wanted a program to implement the two-point
Gaussian rule, which approximates the integral of f(x) between -1 and 1 by
f(-1/sqrt(3))+f(1/sqrt(3)).

On an interval other than [-1,1], we need a scaling transformation.  So I
might have a file called "gauss2.input" which contains one function:

gauss2(f,a,b)==
  xs:LIST Float := [-1/sqrt(3),1/sqrt(3)]
  g := (x:Float):Float +-> f((b-a)/2*x+(b+a)/2)
  int2 := (b-a)/2*(g(xs.1) + g(xs.2))
  return(int2)

However, the system clams up on the use of the scaling function g(x), and
this gives no results.

I have two questions here: first, how do I get round this?  and second, if
I'm writing programs, should I be writing them in Aldor (that's the
language of ".input" files, isn't it?), or SPAD?

For that matter, how do all the languages Aldor, SPAD, Lisp, Boot link up -
which is used for which purpose, and why?

Thanks,
Alasdair

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<div dir=3D"ltr"><div><div><div><div><div><div>I have been experimenting wi=
th writing a few little programs to perform numerical integration, in which=
 I have been running into difficulties.=C2=A0 I can do all the operations I=
 need from the command line, but I run into problems when I try to bundle t=
hose commands into a program.<br><br></div>As a simple example, suppose I w=
anted a program to implement the two-point Gaussian rule, which approximate=
s the integral of f(x) between -1 and 1 by f(-1/sqrt(3))+f(1/sqrt(3)).<br><=
br></div>On an interval other than [-1,1], we need a scaling transformation=
.=C2=A0 So I might have a file called &quot;gauss2.input&quot; which contai=
ns one function:<br><br></div>gauss2(f,a,b)=3D=3D<br>=C2=A0 xs:LIST Float :=
=3D [-1/sqrt(3),1/sqrt(3)]<br>=C2=A0 g :=3D (x:Float):Float +-&gt; f((b-a)/=
2*x+(b+a)/2)<br>=C2=A0 int2 :=3D (b-a)/2*(g(xs.1) + g(xs.2))<br>=C2=A0 retu=
rn(int2)<br><br></div><div>However, the system clams up on the use of the s=
caling function g(x), and this gives no results.<br><br></div><div>I have t=
wo questions here: first, how do I get round this?=C2=A0 and second, if I&#=
39;m writing programs, should I be writing them in Aldor (that&#39;s the la=
nguage of &quot;.input&quot; files, isn&#39;t it?), or SPAD?<br><br></div><=
div>For that matter, how do all the languages Aldor, SPAD, Lisp, Boot link =
up - which is used for which purpose, and why?<br><br></div><div>Thanks,<br=
></div><div>Alasdair<br></div><div><br>-- <br><div class=3D"gmail_signature=
"><div dir=3D"ltr"><a href=3D"http://www.facebook.com/alasdair.mcandrew" ta=
rget=3D"_blank"><img alt=3D"http://www.facebook.com/alasdair.mcandrew" src=
=3D"https://dl.dropboxusercontent.com/u/2796170/facebook.png"></a> <a href=
=3D"https://plus.google.com/+AlasdairMcAndrew/posts" target=3D"_blank"><img=
 alt=3D"https://plus.google.com/+AlasdairMcAndrew/posts" src=3D"https://dl.=
dropboxusercontent.com/u/2796170/f-gplus_256-48.png"></a> <a href=3D"https:=
//www.linkedin.com/pub/alasdair-mcandrew/a/178/108" target=3D"_blank"><img =
alt=3D"https://www.linkedin.com/pub/alasdair-mcandrew/a/178/108" src=3D"htt=
ps://dl.dropboxusercontent.com/u/2796170/linkedin.png"></a> <a href=3D"http=
s://twitter.com/amca01" target=3D"_blank"><img alt=3D"https://twitter.com/a=
mca01" src=3D"https://dl.dropboxusercontent.com/u/2796170/twitter.png"></a>=
 <a href=3D"http://numbersandshapes.net" target=3D"_blank"><img alt=3D"http=
://numbersandshapes.net" src=3D"https://dl.dropboxusercontent.com/u/2796170=
/wordpress.png"></a><br></div></div>
</div></div></div></div>

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