       Re: Non-sequential composition of pure functions

• To: mathgroup at smc.vnet.net
• Subject: [mg127804] Re: Non-sequential composition of pure functions
• From: Earl Mitchell <earl.j.mitchell at gmail.com>
• Date: Thu, 23 Aug 2012 02:55:43 -0400 (EDT)
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```Thanks Ray,

This doesn't quite answer my question (though it is due to the lack of
clarity I had in my original example).  The exact problem I have is this:

I have the following list of functions:

list1={If[#1[] <= 6, 4.52] &, If[#1[] <= 0, 4.47] &, If[#1[] <= 0,
4.40] &,
If[#1[] <= 0, 4.02`] &, If[#1[] <= 0, 4.30] &}

I want to produce the following list of functions:

targetlist= {
If[#1[] <= 6, 4.52] &,
If[(#1[] <= 6) && (#1[] <= 0), 4.47] &,

If[(#1[] <= 6) && (#1[] <= 0) && (#1[] <= 0), 4.40] &,
If[(#1[] <= 6) && (#1[] <= 0) && (#1[] <= 0) && (#1[] <=
0), 4.02`] &,

If[(#1[] <= 6) && (#1[] <= 0) && (#1[] <= 0) && (#1[] <=0) &&
(#1[] <= 0), 4.30] &

}

Quick aside - I recognize that given the function in position two, the
function in position one is irrelevant (redundant). If the composition
algorithm could check for and discard any *sequential* irrelevancies that
would be even better. If, however, the third function were put sequentially
between functions one and two, then all three statements would be relevant.

Thanks!

Mitch
Mitch

On Wed, Aug 22, 2012 at 3:19 AM, Ray Koopman <koopman at sfu.ca> wrote:

> On Aug 21, 11:26 pm, Earl Mitchell <earl.j.mitch... at gmail.com> wrote:
> > Hi All,
> >
> > I have a list of pure functions (If[Conditional[#[]],Action]&
> > statements) and I want to compose them into one large pure function
> >
> If[FirstConditional[#[]]&&SecondConditional[#[]]&&ThirdConditional[#[[foo]]],Action]&.
> >  They are to be applied to a list of values, and the conditionals checked
> > for multiple columns for a given element of a list.
> >
> > I'm having problems joining these things together - to the point that
> I've
> > considered converting them all to strings and doing the tedious
> > (hackie) string manipulations to get the final function in the right
> form.
> >  Any recommendations on how to do this?  I found Composition[] but it
> nests
> > the functions - and I want to combine them.
> >
> > Thanks!
> >
> > Mitch
>
> In:= f1 = If[c1@#, a1]&;
>         f2 = If[c2@#, a2]&;
>         f3 = If[c3@#, a3]&;
>