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 […]

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 […]

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, […]

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 […]

Intereting Posts

Is every group a Galois group?
Compact operators on an infinite dimensional Banach space cannot be surjective
Area of hyperbolic triangle definition
Open maps which are not continuous
Show that an inverse of a bijective linear map is a linear map.
Product of positve definite matrix and seminegative definite matrix
Is there a garden of derivatives?
What is the ratio of rational to irrational real numbers?
Binary quadratic forms – Equivalence and repressentation of integers
Find the all possible real solutions of $x^y=y^x$
Evaluation of $\int_0^1 \frac{\log^2(1+x)}{x} \ dx$
Are derivatives defined at boundaries?
Stirling number
If $0<a<1, 0<b<1$, $a+b=1$, then prove that $a^{2b}+ b^{2a} \le 1$
Why is $f(x) = x\phi(x)$ one-to-one?