Bidirectional ty** combines two modes of ty**: type checking, which checks that a
program satisfies a known type, and type synthesis, which determines a type from the …

When scripts in untyped languages grow into large programs, maintaining them becomes
difficult. A lack of types in typical scripting languages means that programmers must (re) …

Generalized algebraic data types (GADTs), sometimes known as" guarded recursive data
types" or" first-class phantom types", are a simple but powerful generalization of the data …

Bidirectional typechecking, in which terms either synthesize a type or are checked against a
known type, has become popular for its scalability (unlike Damas-Milner type inference …

In this paper we consider categories over a commutative ring provided either with a free
action or with a grading of a not necessarily finite group. We define the smash product …

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 …

Type inference for parametric polymorphism is wildly successful, but has always suffered
from an embarrassing flaw: polymorphic types are themselves not first class. We present …

We present a uniqueness type system that is simpler than both Clean's uniqueness system
and a system we proposed previously. The new type system is straightforward to implement …

Type inference in the presence of first-class or “impredicative” second-order polymorphism à
la System F has been an active research area for several decades, with original works …

HMF is a conservative extension of Hindley-Milner type inference with first-class
polymorphism. In contrast to other proposals, HML uses regular System F types and has a …