## Typability and Type Checking in System F Are Equivalent and Undecidable (1998)

Venue: | Annals of Pure and Applied Logic |

Citations: | 58 - 4 self |

### BibTeX

@ARTICLE{Wells98typabilityand,

author = {J. B. Wells},

title = {Typability and Type Checking in System F Are Equivalent and Undecidable},

journal = {Annals of Pure and Applied Logic},

year = {1998},

volume = {98},

pages = {111--156}

}

### Years of Citing Articles

### OpenURL

### Abstract

Girard and Reynolds independently invented System F (a.k.a. the second-order polymorphically typed lambda calculus) to handle problems in logic and computer programming language design, respectively. Viewing F in the Curry style, which associates types with untyped lambda terms, raises the questions of typability and type checking . Typability asks for a term whether there exists some type it can be given. Type checking asks, for a particular term and type, whether the term can be given that type. The decidability of these problems has been settled for restrictions and extensions of F and related systems and complexity lower-bounds have been determined for typability in F, but this report is the rst to resolve whether these problems are decidable for System F. This report proves that type checking in F is undecidable, by a reduction from semiuni cation, and that typability in F is undecidable, by a reduction from type checking. Because there is an easy reduction from typability to typ...