The F# Computation Expression Zoo

Many computations can be structured using abstract computation types such as monoids, monad transformers or applicative functors. Functional programmers use those abstractions directly while mainstream 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 computations, depending on what operations are available. They also provide greater syntactic flexibility leading to a more intuitive syntax, without resorting to full macro-based meta-programming. We show that computation expressions can structure well-known computations including monoidal list comprehensions, monadic parsers, applicative formlets and asynchronous sequences based on the list monad transformer. We also present typing rules for computation expressions that are capable of capturing all these applications.