I've recently started casually reading into combinatorial logic, and I noticed that a higher-order function that I regularly use is a combinator. This combinator is actually pretty useful (you can use it to define addition on polynomial equations, for example), but I never gave it a decent name. Does anyone recognise this combinator? (ignoring differences in function currying)
unknown = function (h, f, g) function (x) h( f(x), g(x) ) }
In lambda calculus, the fully curried implementation would be $\lambda h. \lambda f. \lambda g. \lambda x. h (f x) (g x)$. In other words, if $M$ is this mystery combinator, then its defining equation is $M \, h \, f \, g \, x = h \, (f \, x) \, (g \, x)$.
If more information is needed, or my question is lacking key information please leave a comment and I will edit my question.