typable

The correspondence between implicational theorems of intuitionistic logic (and their proofs) and typable closed λ-terms

Combinatory Logic Bimbó, Katalin 2008

If the term M is typable, then M has a principal type and a principal type schema.

Combinatory Logic Bimbó, Katalin 2008

The aim to extend the set of typable terms led to the introduction of ˆ§ into types.

Combinatory Logic Bimbó, Katalin 2008

A term M is strongly normalizable whenever M is typable and the proof does not contain

Combinatory Logic Bimbó, Katalin 2008

It is decidable if a term M can be assigned a type, that is, if M is typable.

Combinatory Logic Bimbó, Katalin 2008

First, a correspondence between formulas that are provable in the implicational fragment of intuitionistic logic and the typable combinatory terms was discovered.

Combinatory Logic Bimbó, Katalin 2008

If a combinatory term M is typable (with simple types) then M strongly normalizes, that is, all reduction sequences of M are finite (i.e., terminate).

Combinatory Logic Bimbó, Katalin 2008

A combinator that can be assigned a type is said to be typable, and a type that can be assigned to a combinator is said to be inhabited.

Combinatory Logic Bimbó, Katalin 2008

In particular, no self-application is typable in a Church-style typing system, whereas some of those terms can be assigned a type in a Curry-style typing system.

Combinatory Logic Bimbó, Katalin 2008

Indeed, there is an algorithm that given a combinator decides if the combinator is typable, and for a typable combinator produces a type too.

Combinatory Logic Bimbó, Katalin 2008