This content originally appeared on DEV Community and was authored by Jethro Larson
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.
This content originally appeared on DEV Community and was authored by Jethro Larson
Jethro Larson | Sciencx (2022-01-07T20:27:57+00:00) Beautiful Functions: Psi. Retrieved from https://www.scien.cx/2022/01/07/beautiful-functions-psi/
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