A static semantics for Haskell

Abstract

This paper gives a static semantics for Haskell 98, a non-strict purely functional programming language. The semantics formally specifies nearly all the details of the Haskell 98 type system, including the resolution of overloading, kind inference (including defaulting) and polymorphic recursion, the only major omission being a proper treatment of ambiguous overloading and its resolution. Overloading is translated into explicit dictionary passing, as in all current implementations of Haskell. The target language of this translation is a variant of the Girard–Reynolds polymorphic lambda calculus featuring higher order polymorphism and explicit type abstraction and application in the term language. Translated programs can thus still be type checked, although the implicit version of this system is impredicative. A surprising result of this formalization effort is that the monomorphism restriction, when rendered in a system of inference rules, compromises the principal type property.

Promoting functions to type families in Haskell

“…We are unaware of a simple formulation of surface Haskell's type system and so have written this ourselves. There is other work in this area (Faxén 2002;Jones 1999), but the nature of the existing formulations makes them hard to adapt for our purposes. Note that the typing judgements presented here are different than that in work on GHC's core language FC (for example, Sulzmann et al (2007)), because we are working solely in surface Haskell.…”

The architecture of the Utrecht Haskell compiler

“…Think of the Eq class, having mutually circular definitions of eq and ne, leaving it to the instance declaration to implement either one of them (or both). A clever scheme was designed by Faxén to generate the dictionary from a generator function that is parameterized by the dictionary containing the default implementations, while the default dictionary is generated from a generator function parameterized by the instance dictionary [13]. Lazy evaluation and black holes make this all work, and we employ this scheme in UHC too.…”

ML Modules and Haskell Type Classes: A Constructive Comparison

“…Dictionary translation [2,23,24,25] is a technique frequently used to eliminate overloading introduced by type classes. Using this technique, type-class constraints are turned into extra parameters, so that evidence for these constraints can be passed explicitly at runtime.…”