Function composition using common argument

[JP]

Hi,

Newbie question I guess. To simplify, say I have 2 functions f1 & f2:

q) f1: {1-x%y}
q) f2: {mavg[x;y]}			/This is voluntary

which actually in this case, have a common argument when a composition <g> is applied, eg. :

q) a: til 10
q) g: f1 . (f2 . (3;a); a)
0n 0.5 0.5 0.3333333 0.25 0.2 0.1666667 0.1428571 0.125 0.1111111

I can't figure a compact/elegant way to specify <g> without repeating twice argument <a>.

A wrapper function can obviously do the job, though complexity grows with the number of compositions. So the question is basically: Is there an iterative (or other) way to pass an identical argument to any number of multivalent functions composed successively? 

Thx

[cillianreilly · Accepted solution]

You can do this using iteration over a list of the functions to apply.

q){z .(y;x)}[a]/[3;(f2;f1)]
0n 0.5 0.5 0.3333333 0.25 0.2 0.1666667 0.1428571 0.125 0.1111111

 Adding another function:

q)f3:+
q){z .(y;x)}[a]/[3;(f2;f1;f3)]
0n 1.5 2.5 3.333333 4.25 5.2 6.166667 7.142857 8.125 9.111111

[cillianreilly · Accepted solution]

You can do this using iteration over a list of the functions to apply.

q){z .(y;x)}[a]/[3;(f2;f1)]
0n 0.5 0.5 0.3333333 0.25 0.2 0.1666667 0.1428571 0.125 0.1111111

 Adding another function:

q)f3:+
q){z .(y;x)}[a]/[3;(f2;f1;f3)]
0n 1.5 2.5 3.333333 4.25 5.2 6.166667 7.142857 8.125 9.111111

[SJT · Accepted solution]

Q doesn’t really offer built-in combinators as liberally as its ancestor language APL does. An elegant way to compose the projections of f1 and f2? You can lose the parens…

q)c: f1[;a] f2[;a]@
q)c 3
0n 0.5 0.5 0.3333333 0.25 0.2 0.1666667 0.1428571 0.125 0.1111111

Of course, if you have to do this often, you can write your own combinator. Call it cr for curry right:

q)cr:{x[;y]}
q)c:('[;])over(f1;f2)cr\:a  / Compose over (f1[;a];f2[;a])
q)c 3
0n 0.5 0.5 0.3333333 0.25 0.2 0.1666667 0.1428571 0.125 0.1111111

Compose over a list of functions – as many as you need.

[JP]

Many thanks to you both for your inputs, very useful illustrations of projection/iteration/composition functionalities.

The function approaches work well in their current incarnation, with the small caveat (at least from my understanding) that functions to be composed must have the same rank. Relatively easy to implement argument condition handling should allow for a more generic multivalent case.  Again, thank you,

Best,

JP