Expansion: the Crucial Mechanism for Type Inference with Intersection Types: A Survey and Explanation

Expansion: the Crucial Mechanism for Type Inference with Intersection Types: A Survey and Explanation

The operation of expansion on typings was introduced at the end of the 1970s by Coppo, Dezani, and Venneri for reasoning about the possible typings of a term when using intersection types. Until recently, it has remained somewhat mysterious and unfamiliar, even though it is essential for carrying out compositional type inference. The fundamental idea of expansion is to be able to calculate the ...

Expansion: the Crucial Mechanism for Type Inference with Intersection Types: Survey and Explanation

The operation of expansion on typings was introduced at the end of the 1970s by Coppo, Dezani, and Venneri for reasoning about the possible typings of a term when using intersection types. Until recently, it has remained somewhat mysterious and unfamiliar, even though it is essential for carrying out compositional type inference. The fundamental idea of expansion is to be able to calculate the ...

Principality and type inference for intersection types using expansion variables

Principality of typings is the property that for each typable term, there is a typing from which all other typings are obtained via some set of operations. Type inference is the problem of finding a typing for a given term, if possible. We define an intersection type system which has principal typings and types exactly the strongly normalizable λ-terms. More interestingly, every finite-rank res...

Polar Type Inference with Intersection Types and ω

We present a type system featuring intersection types and ω, a type constant which is assigned to unused terms. We exploit and extend the technology of expansion variables from the recently developed System I, with which we believe our system shares many interesting properties, such as strong normalization, principal typings, and compositional analysis. Our presentation emphasizes a polarity di...

Polar Type Inference with Intersection Types and ω