Overview. This chapter provides a gentle introduction to type systems, functional languages,
and type error messages. We give examples of reported type error messages to illustrate the …

Type error messages that are reported for incorrect functional programs can be difficult to
understand. The reason for this is that most type inference algorithms proceed in a …

In the functional programming world, it is common to embed a domain specific language
(DSL) in a general purpose language. Unfortunately, the extra abstraction layer provided by …

Type classes have found a wide variety of uses in Haskell programs, from simple
overloading of operators (such as equality or ordering) to complex invariants used to …

Code generation is the leading approach to making high-performance software reusable.
Effects are indispensable in code generators, whether to report failures or to insert let …

Abstract Types and formal type systems have proven invaluable in the design and use of
modern declarative languages. The Hindley/Milner type system forms the basis of many type …

1. Introduction complexity and simplicity by describing features individually, as separate
aspects of a more complex whole. In the following section we first give an overview of our …

Some type systems are first described formally, to be sometimes followed by an
implementation. Other type systems are first implemented as language extensions, to be …

Herbrand constraint solving or unification has long been understood as an efficient
mechanism for type checking and inference for programs using Hindley/Milner types. If we …

In almost all languages all arguments to functions are to be given explicitly. The Haskell
class system however is an exception: functions can have class predicates as part of their …