Re: Non-sequential composition of pure functions

• To: mathgroup at smc.vnet.net
• Subject: [mg127805] Re: Non-sequential composition of pure functions
• From: Earl Mitchell <earl.j.mitchell at gmail.com>
• Date: Thu, 23 Aug 2012 20:48:34 -0400 (EDT)
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• References: <20120822062720.4DD8A6850@smc.vnet.net>

```Thanks again - I think I got it.  The solution - slightly modified from
what Albert sent - was this (and if there are obvious improvements to what
I do here I'd love to hear them, learning a lot even though I program in M
every day!):

originalconds = {If[#1[[4]] <= 6, 4.52] &,
If[(#1[[4]] <= 6) && (#1[[4]] <= 0), 4.47] &,
If[(#1[[4]] <= 6) && (#1[[4]] <= 0) && (#1[[5]] <= 0), 4.40] &,
If[(#1[[4]] <= 6) && (#1[[4]] <= 0) && (#1[[5]] <= 0) && (#1[[1]] <= 0),
4.02] &,
If[(#1[[4]] <= 6) && (#1[[4]] <= 0) && (#1[[5]] <= 0) && (#1[[1]] <=
0) && (#1[[3]] <= 0), 4.30] &}

out472:= Join[{originalconds[[1]]},
Table[
With[{
condlist = Take[originalconds, i]
},
With[{
action = First@Last[condlist /. If[c_, a_] :> (a) /. Function -> List]
},
If @@@ (Function @@ {Join[
And @@@
Hold @@ {Flatten[
Hold @@ Cases[condlist, Function[If[c_, a_]] :> Hold[c],
{1}]]},
Hold[action]]})]], {i, 2, Length[originalconds]}]]

out472= {If[#1[[4]] <= 6, 4.52] &,
If[#1[[4]] <= 6 && (#1[[4]] <= 6 && #1[[4]] <= 0), 4.47] &,
If[#1[[4]] <= 6 && (#1[[4]] <= 6 && #1[[4]] <= 0) && (#1[[4]] <= 6 &&
#1[[4]] <= 0 && #1[[5]] <= 0), 4.4] &,

If[#1[[4]] <=
6 && (#1[[4]] <= 6 && #1[[4]] <= 0) && (#1[[4]] <= 6 && #1[[4]] <=
0 && #1[[5]] <= 0) && (#1[[4]] <= 6 && #1[[4]] <= 0 && #1[[5]] <=
0 && #1[[1]] <= 0), 4.02] &,
If[#1[[4]] <=
6 && (#1[[4]] <= 6 && #1[[4]] <= 0) && (#1[[4]] <= 6 && #1[[4]] <=
0 && #1[[5]] <= 0) && (#1[[4]] <= 6 && #1[[4]] <= 0 && #1[[5]] <=
0 && #1[[1]] <= 0) && (#1[[4]] <= 6 && #1[[4]] <= 0 && #1[[5]] <=
0 && #1[[1]] <= 0 && #1[[3]] <= 0), 4.3] &}

Thanks again!

Mitch
On Wed, Aug 22, 2012 at 9:05 AM, Sseziwa Mukasa <mukasa at gmail.com> wrote:

> On approach:
>
> Extract the list of conditions from the functions:
>
> (Debug) In[49]:=
> list = {(If[cond1[#[[1]]], action]) &, (If[cond2[#[[2]]],
>       action]) &, (If[cond3[#[[3]]], action]) &};
>
> (Debug) In[50]:= list /. (If[cond_, action_] &) -> (cond &)
>
> (Debug) Out[50]= {cond1[#1[[1]]] &, cond2[#1[[2]]] &,
>  cond3[#1[[3]]] &}
>
> Then you can use Through and And to evaluate all the conditions:
>
> (Debug) In[53]:= And @@
>  Through[(list /. (If[cond_, action_] &) -> (cond &))[{arg1, arg2,
>     arg3}]]
>
> (Debug) Out[53]= cond1[arg1] && cond2[arg2] && cond3[arg3]
>
> At this point all you need to do is extract the action from one of the
> functions, or all of them if they are different, and perform based on the
> result of the conditional.  Putting it all together:
>
> (Debug) In[55]:=
> combineConditionalFunctions[functions_ {If[_, _] & ..},
>   arguments_ {__}] :=
>  Module[{performAction =
>     And @@ Through[(functions /. (If[cond_, action_] &) -> (cond &))[
>        arguments]],
>    action = functions[[1]] /. (If[_, action_]) & -> action},
>   If[performAction, action]]
>
> (Debug) In[56]:= combineConditionalFunctions[list, {arg1, arg2, arg3}]
>
> (Debug) Out[56]= If[
>  cond1[arg1] && cond2[arg2] && cond3[arg3], action\$900]
>
>
> On Wed, Aug 22, 2012 at 2:27 AM, Earl Mitchell <earl.j.mitchell at gmail.com>wrote:
>
>>
>> Hi All,
>>
>> I have a list of pure functions (If[Conditional[#[[1]]],Action]&
>> statements) and I want to compose them into one large pure function
>>
>> If[FirstConditional[#[[1]]]&&SecondConditional[#[[6]]]&&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
>>
>
>

```

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