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Haskell's "that" operator

«Практика функционального программирования»

Translated as "Practice of functional programming" is the title of an introductory magazine. The magazine is free (free as in "free beer", not "free speech"); you can download it at (yes, it's in Russian). It contains a lot of interesting stuff and is a very fruitful source of references to [mostly English] articles and books about functional programming in general and particular languages.

The key is that it's focused on practical aspects of functional programming. This is useful as a reference to industrial success stories, which you may need to convince your boss to use such a powerful tool as functional programming.

I liked it so much that even donated 10$ to it. And I recommend this magazine with no hesitation.

I recently started reading a magazine called «Практика функционального программирования» ("Practice of functional programming") to learn more about the world of the functional programming languages. There I noticed a nice piece of Haskell's syntactic sugar; it is what I'd like to tell about.

They called it "infix version of function application". I call it "that" operator.

Here's how it works. In functional languages you usually write f(x,y) as f x y. Moreover, you pass a lot of functions as parameters, so f(x(y)) should be expressed differently. Here's where parentheses come into play: f (x y). Lisp, for example, requires these parentheses to wrap each application of a function. Instead, Haskell introduces syntactic sugar to avoid lots of parentheses in expressions like f (x (y (z (t v)))). Or, to be less abstract, in expressions like this (it's functional pseudocode):

In Haskell you can avoid these parentheses with functional application operator. (Or it's a function, not an operator? I'm still not much into this.) Its has different "handedness" from that of usual function application, and that's why it's convenient. Here's the example above with this operator.:

Or, we can use another operator, "dot", which expresses "function composition", and was chosen to resemble its symbol in math, ∘.

Now, why do I call $ "that" operator? Because "that" word in English language has the similar purpose: it frees the language from unnecessary parentheses. Compare these two versions of "This is the house that Jack built..." nursery lyrics by Mother Goose:

With "that" operator:

This is the farmer sowing his corn,
That kept the cock that crowed in the morn,
That waked the priest all shaven and shorn,
That married the man all tattered and torn,
That kissed the maiden all forlorn,
That milked the cow with the crumpled horn,
That tossed the dog,
That worried the cat,
That killed the rat,
That ate the malt
That lay in the house that Jack built. 

With parentheses:

This is the (farmer sowing his corn,
kept (the cock that crowed in the morn,
waked (the priest all shaven and shorn,
married (the man all tattered and torn,
kissed (the maiden all forlorn,
milked (the cow with the crumpled horn,
tossed (the dog,
worried (the cat,
killed (the rat,
ate (the malt
lay in (the house Jack built))))))))))). 


One of the most famous functional languages is LISP. Its name is an acronym for "Lots of Insignificant Stupid Parentheses" There are several LISP jokes involving parentheses. Here's good a joke about a soviet spy and LISP.

Doesn't look too nice. And it finishes with this notorious tail of parentheses (see side note). But this natural language developed itself in such a way that it provided a nice notion of function application. Was it what inspired Haskell authors? Hardly. But still, I think that there is a lot of similarity, between these concepts.

"That" operator is a very helpful thing, and it's sad that some functional languages (namely, OCaml, which I use at work) don't have such a nice feature.

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