Monads are one particular way of structuring and sequencing computations. The bind of a monad cannot magically restructure your computation so as to happen in a more efficient way. There are two problems with the way you structure your computation. When evaluating stepN 20 0, the result of step 0 will be computed 20 times. … Read more
The confusion arises from using similar terminology for the structure of a Σ type and for how its values look like. A value of Σ(x:A) B(x) is a pair (a,b) where a∈A and b∈B(a). The type of the second element depends on the value of the first one. If we look at the structure of … Read more
The Curry-Howard isomorphism simply states that types correspond to propositions, and values correspond to proofs. Int -> Int doesn’t really mean much interesting as a logical proposition. When interpreting something as a logical proposition, you’re only interested in whether the type is inhabited (has any values) or not. So, Int -> Int just means “given … Read more
Since you explicitly asked for the most interesting and obscure ones: You can extend C-H to many interesting logics and formulations of logics to obtain a really wide variety of correspondences. Here I’ve tried to focus on some of the more interesting ones rather than on the obscure, plus a couple of fundamental ones that … Read more
Life is a little bit hard, since Haskell is non strict. The general use case is to handle impossible paths. For example simple :: Either Void a -> a simple (Left x) = absurd x simple (Right y) = y This turns out to be somewhat useful. Consider a simple type for Pipes data Pipe … Read more