Skip to main content

Internet to the rescue

Once again the internet comes to the rescue with a Systematic Search for Lambda Expressions.  This is the answer to yesterdays question of whether we can iterate over isomorphic proofs exhaustively in order to extract all programs of a specification which in this case is realised as a "type".  Hooray for computer science!

Comments

Popular posts from this blog

Managing state in Prolog monadically, using DCGs.

Prolog is a beautiful language which makes a lot of irritating rudimentary rule application and search easy. I have found it is particularly nice when trying to deal with compilers which involve rule based transformation from a source language L to a target language L'. However, the management of these rules generally requires keeping track of a context, and this context has to be explicitly threaded through the entire application, which involves a lot of irritating and error prone sequence variables. This often leads to your code looking something a bit like this: compile(seq(a,b),(ResultA,ResultB),S0,S2) :- compile(a,ResultA,S0,S1), compile(b,ResultB,S1,S2). While not the worst thing, I've found it irritating and ugly, and I've made a lot of mistakes with incorrectly sequenced variables. It's much easier to see sequence made explicitly textually in the code. While they were not designed for this task, but rather for parsing, DCGs turn out to be a conveni

Decidable Equality in Agda

So I've been playing with typing various things in System-F which previously I had left with auxiliary well-formedness conditions. This includes substitutions and contexts, both of which are interesting to have well typed versions of. Since I've been learning Agda, it seemed sensible to carry out this work in that language, as there is nothing like a problem to help you learn a language. In the course of proving properties, I ran into the age old problem of showing that equivalence is decidable between two objects. In this particular case, I need to be able to show the decidability of equality over types in System F in order to have formation rules for variable contexts. We'd like a context Γ to have (x:A) only if (x:B) does not occur in Γ when (A ≠ B). For us to have statements about whether two types are equal or not, we're going to need to be able to decide if that's true using a terminating procedure. And so we arrive at our story. In Coq, equality is

Teagrey

I was ironing my shirt today, which I almost never do. Because of this I don't have an ironing board so I tried to make a make-shift ironing board on my floor using a towel and some books. I grabbed the heaviest books on the nearest shelf, which happened to be Organic Chemistry, Stalingrad and an annotated study bible containing the old and new testament. As I pulled out the bible, a flower fell out which had been there for over 17 years now. I know that because it was put there by my first wife, Daniel, who killed herself in April about 17 years ago. It fell from Thessalonians to which it had been opened partially. Highlighted was the passage: "Ye are all sons of the light and sons of the day." I guess the passage gave her solace. Daniel was a complicated woman. She had serious mental health issues which plagued her for her entire life. None of them were her fault. She was dealt an absolutely awful hand in life, some truly nasty cards. She had some considerable c