Wednesday, December 14, 2005

Theorem Proving and Code Generation

According to the Curry-Howard isomorphism a type in a programming language is essentially the same thing as a proposition and an object or program of the type is a(n intuitionist) proof of the proposition. So an automatic proof generator should also be usable to generate objects or programs of a given type. This is exactly what Djinn does. It seems pretty neat.

(I only learned about the Curry-Howard isomorphism in the last couple of years but it's probably of general interest. So I recommend reading the Wikipedia article I link to if you haven't met it before. It's also probably not what you're currently guessing it is. It's not about program correctness but type correctness and it doesn't prove programs to be correct but shows how programs themselves are proofs of type correctness. In the language of the article, Djinn solves the "Type Inhabitation Problem".)

Wednesday, December 07, 2005

Rant: Just for kids?

Search Google News for stories about mathematics and you'll find that they are dominated by a particular subsection of our society: kids. It seems that the only people in the world doing mathematics are children. Very occasionally
you'll see a story about an adult, but then it's usually about an adult teaching children. Do a search on history and you'll see some actual history. Search on physics and you'll get stories about kids mixed in with stories about people doing actual physics. So why are there so few stories about adults doing mathematics?

It's not just in news stories. Look at Texas Instruments' and Hewlett Packard's web sites and you'll see that calculators are largely marketed towards kids. TI are much worse on this front. They have powerful calculators that can solve all kinds of real world problems and yet they're not being marketed as devices for solving such problems, they're about getting kids through exams. HP at least have a section for professionals. Even so, in the old days if an HP calculator had exchangeable faceplates it was so that you could label the keys with new functions, but now it's to change the colour to make it look cool. The only people working with numbers are clearly children.

On closer inspection I see that I was wrong. I missed a story. It's about an adult. No mention of children or education.'s about an adult who can't do mathematics.

So clearly no adults use mathematics. So why do we bother teaching children a skill they'll never use in adulthood?


Friday, December 02, 2005

Bees can fly after all!

According to this article it seems that bees can fly after all.

PS I'm wondering about the field of 'human aviation' that the article mentions. Am I lacking a superpower that normally comes standard with being human?