Re: [Haskell-cafe] Musings on type systems

On 11/20/10 6:33 AM, Ketil Malde wrote:

Andrew Coppin writes:

...

Now here's an interesting thought. Haskell has "algebraic data types". "Algebraic" because they are sum types of product types (or, equivilently, product types of sum types). Now I don't actually know what those terms mean,

The quick rule to remember this that the size of the resulting types correspond to the arithmetic names. I.e.

data Sum a b = A a | B b -- values = values in a + values in b data Prod a b = P a b -- values = values in a * values in b

I guess this makes [X] an exponential type, although I don't remember seeing that term :-)

Nope. (a->b) is the exponential type, namely |a->b| = |b|^|a|. [_] is just a solution to the recursive equation [x] = 1 + x*[x]. -- Live well, ~wren