The Universe of Discourse

Mon, 10 Sep 2018

Why hooks and forks in the J language?

I recently said:

I don't know why [Ken] Iverson thought the hook was the thing to embed in the [J] language.

And I think I now recall that the name of the language itself, J, is intended to showcase the hook, so he must have thought it was pretty wonderful.

A helpful Hacker News comment pointed me to the explanation. Here Iverson explains why the “hook” feature: it is actually the S combinator in disguise. Recall that $${\bf S} x y z = x z (y z).$$ This is exactly what J's hook computes when you write (x y) z. For instance, if I understand correctly, in J (+ !) means the one-place operation that takes an argument !!z!! to !!z + z! !!.

As McBride and Paterson point out, S is also the same as the <*> operator in the Reader instance of Applicative. Since in J the only possible inputs to a hook are functions, it is operating in the Reader idiom and in that context its hook is doing the same thing as Haskell's <*>. Similarly, J's “fork” feature can be understood as essentially the same as the Reader insance of Haskell's liftA2.

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