# From lambda to mu: Functions as algebraic types

### Michael D. Adams

## Abstract

While the lambda-calculus and its descendents have dominated the foundational theories of functional languages, a new family of calculi has started to gain attention. These calculi focus on the mu operator rather than lambda. This talk presents one such mu-calculus and shows how it resolves irregularities in the lambda-calculus as well as provides additional symmetries. In addition, this mu-calculus provides a novel perspective on linear logic and intuitions for the more unusual operators in linear logics.