Haskell High Performance Programming

Trivia at type-level

The more expressive the types are, the more safety we can ensure at compile-time. What's more, expressive types serve as documentation that is always up-to-date.

Phantom types

A type that has type variables on the left-hand side that do not appear on the right-hand-side at all is called a phantom type. Such type variables are a cheap, in fact free, technique to guarantee correctness in multiple situations. An example from base is Data.Fixed, in which the precision of fixed-precision arithmetic is encoded in a phantom type.

An extremely useful class of phantom types is obtained in conjunction with Generalized Algebraic Data Types (GADT). As a little silly example, consider:

-- file: gadts.hs {-# LANGUAGE GADTs #-}data Value a where ...