Articles of lambda calculus

Meaning of variables and applications in lambda calculus

The wikipedia definition of lambda terms is: The following three rules give an inductive definition that can be applied to build all syntactically valid lambda terms: a variable, $x$, is itself a valid lambda term if $t$ is a lambda term, and $x$ is a variable, then $(\lambda x.t)$ is a lambda term (called a […]

Fixed point combinator (Y) and fixed point equation

In Hindley (Lambda-Calculus and Combinators, an Introduction), Corollary 3.3.1 to the fixed-point theorem states: In $\lambda$ and CL: for every $Z$ and $n \ge 0$ the equation $$xy_1..y_n = Z$$ can be solved for $x$. That is, there is a term $X$ such that $$Xy_1..y_n =_{\beta,w} [X/x]Z$$ I dont understand how to even think about […]

What's the point of eta-conversion in lambda calculus?

I think I’m not understanding it, but eta-conversion looks to me as a beta-conversion that does nothing, a special case of beta-conversion where the result is just the term in the lambda abstraction because there is nothing to do, kind of a pointless beta-conversion. So maybe eta-conversion is something really deep and different from this, […]

Learning Lambda Calculus

What are some good online/free resources (tutorials, guides, exercises, and the like) for learning Lambda Calculus? Specifically, I am interested in the following areas: Untyped lambda calculus Simply-typed lambda calculus Other typed lambda calculi Church’s Theory of Types (I’m not sure where this fits in). (As I understand, this should provide a solid basis for […]