A comprehensive introduction to type systems and programming languages. A type system
is a syntactic method for automatically checking the absence of certain erroneous behaviors …

We introduce System FC, which extends System F with support for non-syntactic type
equality. There are two main extensions:(i) explicit witnesses for type equalities, and (ii) …

Haskell programmers often use a multi-parameter type class in which one or more type
parameters are functionally dependent on the first. Although such functional dependencies …

The implementation and semantics of dependent type theories can be studied in a syntax-
independent way: the objective metatheory of dependent type theories exploits the universal …

Haskell's type classes allow ad-hoc overloading, or type-indexing, of functions. A natural
generalisation is to allow type-indexing of data types as well. It turns out that this idea …

Mitchell's notion of representation independence is a particularly useful application of
Reynolds' relational parametricity--two different implementations of an abstract data type can …

We present an internal language with equivalent expressive power to Standard ML, and
discuss its formalization in LF and the machine-checked verification of its type safety in …

The theory of program modules is of interest to language designers not only for its practical
importance to programming, but also because it lies at the nexus of three fundamental …

We describe support for modularity in Newspeak, a programming language descended from
Smalltalk [33] and Self [69]. Like Self, all computation—even an object's own access to its …

ML modules are a powerful language mechanism for decomposing programs into reusable
components. Unfortunately, they also have a reputation for being “complex” and requiring …