       Re: Non-sequential composition of pure functions

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• Subject: [mg127791] Re: Non-sequential composition of pure functions
• From: awnl <awnl at gmx-topmail.de>
• Date: Thu, 23 Aug 2012 02:51:22 -0400 (EDT)
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• References: <k11u1r\$t8m\$1@smc.vnet.net> <20120822091941.291ED6852@smc.vnet.net> <CAFAKiUS=A9Qyj_ReXSqKUC+TvOA5MGYb1TeNYapFwaCw3OZ53g@mail.gmail.com>

```Hi Earl,
>
> This is very close to what I need. ... 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.

The following should do what you want. I decided to store the
intermediate results as I think it is somewhat easier to follow what
happens. This is just what I came up with at first try, as usual there
are plenty possibilities to achieve the same thing, some of which might
be much more elegant. The code is also not bullet proof, but I didn't
want to introduce additional complexity for making it more safe or
general. Anyway I hope it is good enough to get you started:

(*extract the held conditions and bodies (in this case just values) *)
heldConditions=Cases[list1,Function[If[c_,_]]:>Hold[c]]
heldBodies=Cases[list1,Function[If[_,b_]]:>Hold[b]]

(* create the "accumulated" conditions, still wrapped with Hold *)
accumulatedConditions=ReplaceAll[
Hold/@Rest[FoldList[And,True,heldConditions]],
Hold[LessEqual[x___]]:>LessEqual[x]
]

(* finally compose the resulting functions from the accumulated
conditions and the stored "bodies" *)
targetList=Function/@Flatten/@Hold@@@Transpose[{accumulatedConditions,heldBodies}]/.Hold->If

hth,

albert

```

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