Affiliation:
1. University of Hong Kong, China
Abstract
Dunfield showed that a simply typed core calculus with intersection types and a merge operator is able to capture various programming language features. While his calculus is type-safe, it is not
coherent
: different derivations for the same expression can elaborate to expressions that evaluate to different values. The lack of coherence is an important disadvantage for adoption of his core calculus in implementations of programming languages, as the semantics of the programming language becomes implementation-dependent.
This paper presents λ_i: a coherent and type-safe calculus with a form of
intersection types
and a
merge operator
. Coherence is achieved by ensuring that intersection types are
disjoint
and programs are sufficiently annotated to avoid
type ambiguity
. We propose a definition of disjointness where two types A and B are disjoint only if certain set of types are common supertypes of A and B. We investigate three different variants of λ_i, with three variants of disjointness. In the simplest variant, which does not allow ⊤ types, two types are disjoint if they do not share any common supertypes at all. The other two variants introduce ⊤ types and refine the notion of disjointness to allow two types to be disjoint when the only the set of common supertypes are
top-like
. The difference between the two variants with ⊤ types is on the definition of top-like types, which has an impact on which types are allowed on intersections. We present a type system that prevents intersection types that are not disjoint, as well as an algorithmic specifications to determine whether two types are disjoint for all three variants.
Publisher
Association for Computing Machinery (ACM)
Subject
Computer Graphics and Computer-Aided Design,Software
Cited by
12 articles.
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