Logical Relations for Coherence of Effect Subtyping

A coercion semantics of a programming language with subtyping is typically defined on typing derivations rather than on typing judgments. To avoid semantic ambiguity, such a semantics is expected to be coherent, i.e., independent of the typing derivation for a given typing judgment. In this article we present heterogeneous, biorthogonal, step-indexed logical relations for establishing the coherence of coercion semantics of programming languages with subtyping. To illustrate the effectiveness of the proof method, we develop a proof of coherence of a type-directed, selective CPS translation from a typed call-by-value lambda calculus with delimited continuations and control-effect subtyping. The article is accompanied by a Coq formalization that relies on a novel shallow embedding of a logic for reasoning about step-indexing

Logical relations for coherence of effect subtyping

A coercion semantics of a programming language with subtyping is typically defined on typing derivations rather than on typing judgments. To avoid semantic ambiguity, such a semantics is expected to be coherent, i.e., independent of the typing derivation for a given typing judgment. In this article we present heterogeneous, biorthogonal, step-indexed logical relations for establishing the coherence of coercion semantics of programming languages with subtyping. To illustrate the effectiveness of the proof method, we develop a proof of coherence of a type-directed, selective CPS translation from a typed call-by-value lambda calculus with delimited continuations and control-effect subtyping. The article is accompanied by a Coq formalization that relies on a novel shallow embedding of a logic for reasoning about step-indexing

The Essence of Nested Composition

Calculi with disjoint intersection types support an introduction form for intersections called the merge operator, while retaining a coherent semantics. Disjoint intersections types have great potential to serve as a foundation for powerful, flexible and yet type-safe and easy to reason OO languages. This paper shows how to significantly increase the expressive power of disjoint intersection types by adding support for nested subtyping and composition, which enables simple forms of family polymorphism to be expressed in the calculus. The extension with nested subtyping and composition is challenging, for two different reasons. Firstly, the subtyping relation that supports these features is non-trivial, especially when it comes to obtaining an algorithmic version. Secondly, the syntactic method used to prove coherence for previous calculi with disjoint intersection types is too inflexible, making it hard to extend those calculi with new features (such as nested subtyping). We show how to address the first problem by adapting and extending the Barendregt, Coppo and Dezani (BCD) subtyping rules for intersections with records and coercions. A sound and complete algorithmic system is obtained by using an approach inspired by Pierce\u27s work. To address the second problem we replace the syntactic method to prove coherence, by a semantic proof method based on logical relations. Our work has been fully formalized in Coq, and we have an implementation of our calculus

Programming Languages and Systems

This open access book constitutes the proceedings of the 28th European Symposium on Programming, ESOP 2019, which took place in Prague, Czech Republic, in April 2019, held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2019