non-termination

> Types and functions (ignoring non-termination) form a category Even including non-termination they form a category.

In a very real sense, we can treat potential non-termination as yet another effect and manage it accordingly.

Generally, monads would work more or less just fine even without non-termination though.

I'm not trying to prove anything, just to not that non-termination leads to suspicious looking logics.

This is already possible sometimes in Haskell so long as we restrict ourselves from pathological values like exceptions and non-termination.

This just drives home that non-termination is an effect itself!

There's no way to construct a value of an arbitrary type -- outside of non-termination[1] (which doesn't really produce any values) or abuses of unsafeXXX functions.

The function type given does not preclude non-termination in Haskell.

He just stated non-termination is not an option, therefore...

[1] As stated in [0], non-termination is an effect, so Haskell monads are impure in that sense.

Also, (lambda x: x(x))(lambda x: x(x)) already gives you an infinite loop, so why do you need a Y combinator to show non-termination?

Types and functions (ignoring non-termination) form a category.

It's well known that non-termination is an effect and it's a little slippery to define Haskell's notion of "observability" so as to no longer observe non-termination.

[0] And of course "pure and total" just means "pure" since non-termination is an effect.

The first shares this property (modulo non-termination, see [0]) and is where most "programming" occurs---here we use monads as a system for constructing terms of the second semantics, IO.

Non-termination is a fundamental property of turing machines; after all, if all programs terminate, a halting problem decider is trivial to write.