This paper explores a principled approach to calculating abstract machines and associated compilers, starting from an intrinsically typed interpreter. After deriving a compiler for a simple expression language in some detail, the first steps of this calculation are repeated to derive an optimizing evaluator for the simply typed lambda calculus.

This pearl defines a translation from well-typed lambda terms to combinatory logic, where both the preservation of types and the correctness of the translation are enforced statically.

Vectors—or length-indexed lists—are classic example of a dependent type. Yet, most tutorials stay clear of any function on vectors whose definition requires non-trivial equalities between natural numbers to type check. This pearl shows how to write functions, such as vector reverse, that rely on monoidal equalities to be type correct without having to write any additional proofs. These techniques can be applied to many other functions over types indexed by a monoid, written using an accumulating parameter, and even be used to decide arbitrary equalities over monoids ‘for free.’

There has been sustained interest in functional programming languages with dependent types in recent years. The foundations of dependently typed programming can be traced back to Martin–Löf's work in the 1970s. In the past decades, this vision has given rise to the development of proof assistants and functional programming languages based on dependent types. The increased popularity of systems such as Agda, Coq, Idris, and many others, reflects the growing momentum in this research area. After sending out our first call for papers in October 2015, we are happy to accept six articles in this special issue covering a wide spectrum of topics.

This paper presents a library for programming with polymorphic dynamic types in the dependently typed programming language Agda. The resulting library allows dynamically typed values with a polymorphic type to be instantiated to a less general (possibly monomorphic) type without compromising type soundness.

The problem of the Dutch national flag was formulated by Dijkstra (1976) as follows:

The minicomputer in question should perform this rearrangement using two commands:

• • swapi j for 1≤i≤n and 1≤j≤n exchanges the pebbles stored in the buckets numbered i and j;

• • read (i) for 1≤i≤n returns the colour of the pebble currently lying in bucket number i. Dijkstra originally named this operation buck.

This paper describes a technique for assembling both data types and functions from isolated individual components. We also explore how the same technology can be used to combine free monads and, as a result, structure Haskell's monolithic IO monad.