Haskell, as implemented in the Glasgow Haskell Compiler (GHC), has been adding new
type-level programming features for some time. Many of these features—generalized …

In dependently-typed functional programming languages that allow general recursion,
programs used as proofs must be evaluated to retain type soundness. As a result …

Type family applications in Haskell must be fully saturated. This means that all type-level
functions have to be first-order, leading to code that is both messy and longwinded. In this …

Dependently typed languages are well known for having a problem with code reuse.
Traditional non-indexed algebraic datatypes (eg lists) appear alongside a plethora of …

Modern Haskell supports zero-cost coercions, a mechanism where types that share the
same run-time representation may be freely converted between. To make sure such …

Many fancy types (eg, generalized algebraic data types, type families) require a type
checker plugin. These fancy types have a type index (eg, type level natural numbers) with an …

Designing a language feature often requires a choice between several, similarly expressive
possibilities. Given that user studies are generally impractical, we propose using stability as …

A language supporting polymorphism is a boon to programmers: they can express complex
ideas once and reuse functions in a variety of situations. However, polymorphism is pain for …

Guided by Tarksi's fixpoint theorem in order theory, we show how to derive monotone
recursive types with constant-time roll and unroll operations within Cedille, an impredicative …

A classic example of the power of generalized algebraic datatypes (GADTs) to verify a
delicate implementation is the type-indexed expression AST. This functional pearl refreshes …