COMP 302 Lecture Notes - Lecture 10: Higher-Order Function, Composition Operator, Monoid

• School: McGill University
• Department: Computer Science (Sci)
• Course: COMP 302
• Professor: Prakash Panangaden

Document Summary

Algebra: studying the ways in which sets relate to eachother. Suppose we have a function f, mapping set s to set s, and a function g mapping set s to set s. then, we can also have a composite function . : s s g g f. It is good to find the identity for binary operations. For example, for addition it is 0 and for multiplication it is 1. If you multiply anything by 1, it doesn"t change, and if you add 0 to anything it doesn"t change. f g is a binary operation on functions. A binary function involves applying the first function first and then the second function after that. It take an element and does nothing to it. fun x x. , f composed with the identity function gives you back f. f g g f. As input, feed in f (which itself takes inputs and outputs; it is a function).