for the few of us.

Anton Setzer argued in his letter to the Agda mailing list that we should go back to a category theoretical view of codata, and Dan Doel soon successfully experimented the ideas.

It would be nice to if we could write the program and prove its termination separately. Adam Megacz published an interesting paper: A Coinductive Monad for Prop-Bounded Recursion. As a practice, I tried to port his code to Agda.

In a recent meeting I talked to my assistants about using dependent type to guarantee that, in an evaluator for λ calculus using de Bruin indices, that variable look-up always succeeds.

How can I introduce accumulating parameters to derive the linear-time, tail recursive implementation of fib.

Prove the following property in point-free style:

$S\; \subseteq \; C\; .\; S\; \; \Leftarrow \; \; R\; \subseteq \; C\; .\; R\; \; \wedge \; \; S\; \subseteq \; R$

It seems that reductivity of Doornbos and Backhouse is in fact accessibility, which is often taken by type theorists to be an alternative definition of well-foundedness.

Given a relation < that has been shown to be well-founded, we know that a recursively defined function is terminating if its arguments becomes “smaller” with respect to < at each recursive call. We can encode such well-founded recursion in Agda’s style of structural recusion.

After seeing our code, Nils Anders Danielsson suggested two improvements. Firstly, to wrap the bound in the seed. Secondly, to define unfoldT↓ using well-founded recursion.

I hope to come up with a variation of unfoldr which, given a proof of well-foundedness, somehow passes the termination check.

Back in 2003, my colleagues there were discussing about the third homomorphism theorem — if a function f can be expressed both as a foldr and a foldl, there exists some associative binary operator ⊚ such that f can be computed from the middle. The aim was to automatically construct ⊚.