Function composition composes from right to left:
const comp = f => g => x => f(g(x));
const inc = x => x + 1;
const dec = x => x - 1;
const sqr = x => x * x;
let seq = comp(dec)(comp(sqr)(inc));
seq(2); // 8
seq(2) is transformed to dec(sqr(inc(2))) and the application order is inc(2)...sqr...dec. Thus the functions are invoked in the reverse order in which they are passed to comp. This isn't intuitive for Javascript programmers, since they're used to method chaining, which goes from left to right:
o = {
x: 2,
inc() { return this.x + 1, this },
dec() { return this.x - 1, this },
sqr() { return this.x * this.x, this }
}
o.dec().sqr().inc(); // 2
I consider that confusing. Here's a reversed composition:
const flipped = f => g => x => g(f(x));
let seql = flipped(dec)(flipped(sqr)(inc));
seql(2); // 2
Are there any reasons why function composition goes from right to left?
Your question is actually about the order of arguments in a definition of the function composition operator rather than right- or left-associativity. In mathematics, we usually write "f o g" (equivalent to comp(f)(g) in your definition) to mean the function that takes x and returns f(g(x)). Thus "f o (g o h)" and "(f o g) o h" are equivalent and both mean the function that maps each argument x to f(g(h(x))).
That said, we sometimes write f;g (equivalent to compl(f)(g) in your code) to mean the function which maps x to g(f(x)). Thus, both (f;g);h and f;(g;h) mean the function mapping x to h(g(f(x))).
A reference: https://en.wikipedia.org/wiki/Function_composition#Alternative_notations