The F# Computation Expression Zoo

Abstract

Program logic can often be structured using abstract computation types such as monoids, monad transformers or applicative functors. Functional programmers use those abstractions directly while main-stream languages often integrate concrete instances as language features – e.g. generators in Python or asynchronous computations in C# 5.0. The question is, is there a sweet spot between convenient, hardwired language features, and an inconvenient but flexible libraries? F# computation expressions answer this question in the affirmative. Unlike the “do” notation in Haskell, computation expressions are not tied to a single kind of abstraction. They support a wide range of abstractions, depending on what operations are available. F# also provides greater syntactic flexibility leading to a more intuitive syntax, without resorting to full macro-based meta-programming. We present computation expressions in a principled way, developing a type system that captures the semantics of the calculus. We demonstrate how computation expressions structure well-known abstractions including monoidal list comprehensions, monadic parsers, applicative formlets and asynchronous sequences based on monad transformers.