Quantcast
Channel: Luke Palmer » ixi
Browsing latest articles
Browse All 6 View Live

Image may be NSFW.
Clik here to view.

Dependent types are ridiculously easy

After an inquiry about a combinatory calculus for dependent types, somebody in #haskell — unfortunately I don’t remember who — recommended I look at Illative Combinatory Logic. After studying the paper...

View Article



Image may be NSFW.
Clik here to view.

System IG Semantics

I don’t have much time, so here’s just a quick jot. I don’t think System IG can prove this rather obvious proposition: |- GL(\a. Ga(Ka)) (\a x. x) Or translated to more conventional notation: (\a x. x)...

View Article

Image may be NSFW.
Clik here to view.

Might as well face it, I’m addicted to logic

I’m trying really hard not to become a logician. Like my obsession with FRP, it would be very interesting and educational. But my FRP fancy came from a desire to make games more easily, and I have...

View Article

Image may be NSFW.
Clik here to view.

Some Constructions in IΞ

Over the past couple months, I have been attempting to find a language to use as a core calculus for Dana, as anyone who follows this blog knows. I have been slowly converging on IΞ for its elegance...

View Article

Image may be NSFW.
Clik here to view.

Dana (actual) progress

I have some very exciting news! I wrote some actual code in the Dana repository. It is the IΞ Certificate module. That is, it’s an abstract data type Proof, such that only valid proofs in IΞ can be...

View Article


Image may be NSFW.
Clik here to view.

Recursive Types in IΞ

In the last IΞ post, I introduced the calculus and sketched the construction of some standard mathematical objects. In this post, I will dive a little deeper and construct of all the positive recursive...

View Article
Browsing latest articles
Browse All 6 View Live




Latest Images