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# Beautiful Functions: Psi

Continuing on with my last post, I want to look at another function which I consider particularly elegant, the psi combinator:

`const psi = (f) => (g) => (x, y) => g(f(x), f(y));`

In TypeScript:

```
const psi = <A, B>(f: (x: A) => B) =>
<C>(g: (x: B, y: B) => C) =>
(x: A, y: A): C =>
g(f(x), f(y));
```

This is also called `on`

in Haskell.

What it does is map a function over both arguments of a binary(two-argument) function. This is similar to the `B`

combinator but changed to work on binary functions.

The quintessential usage is when sorting records:

```
// given a compare function
const localeCompare = (item1: string, item2: string): number =>
item1.localeCompare(item2);
// and some accessor function that drills into a data structure
const getName = (person) => person.name;
// compose that accessor with the compare function to drill both sides
const compareNames = psi(getName)(localeCompare);
// which can be passed to a sort method for an array of that structure
people.sort(compareNames)
```

Interestingly, this is equivalent to doing a map and then sort, but using psi is theoretically more memory efficient:

```
// generates an extra array
people.map(getName).sort(localeCompare)
```

Look out for other opportunities to use `psi`

and I'm sure you'll find them. Particularly if you're doing data aggregation or processing.

Pedantic Disclaimer: Psi is usually defined with the binary function as the first argument but I preferred the similarity to `B`

combinator when taking the mapping function as the first.

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