3 ms·

The word "monoid" has been used with its current meaning since the 50s, maybe before. I think the authors of SICP didn't describe the picture language as such

• davexunit 9y ago
  It wasn't a term used in computer science then. Gerald Sussman himself said this about the term "monad" in one of his talks.
• kazinator 9y ago
  A monoid is just an algebraic group which is missing the concept of the inverse element. This has been gutted out of the group so that the category theorists can then see monoids in situations where they would otherwise have to rack their brains to come up with the inverse operation. https://en.wikipedia.org/wiki/Group_(mathematics)#Definition https://en.wikipedia.org/wiki/Group_(mathematics)#Definition For instance, the set of character strings and the catenate operation are almost a group. The identity element is the empty string. Closure holds: if a and b are strings, (cat a b) is a string. Associativity holds : (cat a (cat b c)) is (cat (cat a b) c). (Which is then just (cat a b c) to a Lisp programmer, (cat a) is a, and (cat) produces the empty string.) Identity element: empty string. (cat a "") -> a Inverse element: oops! We would have to postulate some sort of "negative string" so that (cat "abc" -"abc") produces "". Then we have the problem of what is (cat "abc" -"xyz"): the combination of a string and the inverse element of a different string. Let's not bother; just drop this axiom and call it a "monoid".