We propose type qualifiers based on Boolean algebras. Traditional type systems with type qualifiers have been based on lattices, but lattices lack the ability to express exclusion . We argue that Boolean algebras, which permit exclusion, are a practical and useful choice of domain for qualifiers. In this paper, we present a calculus System F <:B that extends System F <: with type qualifiers over Boolean algebras and has support for negation, qualifier polymorphism, and subqualification. We illustrate how System F <:B can be used as a design recipe for a type and effect system, System F <:BE , with effect polymorphism, subeffecting, and polymorphic effect exclusion. We use System F <:BE to establish formal foundations of the type and effect system of the Flix programming language. We also pinpoint and implement a practical form of subeffecting: abstraction-site subeffecting. Experimental results show that abstraction-site subeffecting allows us to eliminate all effect upcasts present in the current Flix Standard Library.

We propose restrictable variants as a simple and practical alternative to extensible variants. Restrictable variants combine nominal and structural typing: a restrictable variant is an algebraic data type indexed by a type-level set formula that captures its set of active labels. We introduce new pattern-matching constructs that allows programmers to write functions that only match on a subset of variants, i.e., pattern-matches may be non-exhaustive. We then present a type system for restrictable variants which ensures that such non-exhaustive matches cannot get stuck at runtime. An essential feature of restrictable variants is that the type system can capture structure-preserving transformations: specifically the introduction and elimination of variants. This property is important for writing reusable functions, yet many row-based extensible variant systems lack it. In this paper, we present a calculus with restrictable variants, two partial pattern-matching constructs, and a type system that ensures progress and preservation. The type system extends Hindley-Milner with restrictable variants and supports type inference with an extension of Algorithm W with Boolean unification. We implement restrictable variants as an extension of the Flix programming language and conduct a few case studies to illustrate their practical usefulness.

The λ_Dat calculus brings together the power of functional and declarative logic programming in one language. In λ_Dat, Datalog constraints are first-class values that can be constructed, passed around as arguments, returned, composed with other constraints, and solved. A significant part of the expressive power of Datalog comes from the use of negation. Stratified negation is a particularly simple and practical form of negation accessible to ordinary programmers. Stratification requires that Datalog programs must not use recursion through negation. For a Datalog program, this requirement is straightforward to check, but for a λ_Dat program, it is not so simple: A λ_Dat program constructs, composes, and solves Datalog programs at runtime. Hence stratification cannot readily be determined at compile-time. In this paper, we explore the design space of stratification for λ_Dat. We investigate strategies to ensure, at compile-time, that programs constructed at runtime are guaranteed to be stratified, and we argue that previous design choices in the Flix programming language have been suboptimal.

Effect handlers are a high-level abstraction that enables programmers to use effects in a structured way. They have gained a lot of popularity within academia and subsequently also in industry. However, the abstraction often comes with a significant runtime cost and there has been intensive research recently on how to reduce this price. A promising approach in this regard is to implement effect handlers using a CPS translation and to provide sufficient information about the nesting of handlers. With this information the CPS translation can decide how effects have to be lifted through handlers, i.e., which handlers need to be skipped, in order to handle the effect at the correct place. A structured way to make this information available is to use a calculus with a region system and explicit subregion evidence. Such calculi, however, are quite verbose, which makes them impractical to use as a source-level language. We present a method to infer the lifting information for a calculus underlying a source-level language. This calculus uses second-class capabilities for the safe use of effects. To do so, we define a typed translation to a calculus with regions and evidence and we show that this lift-inference translation is typability- and semantics-preserving. On the one hand, this exposes the precise relation between the second-class property and the structure given by regions. On the other hand, it closes a gap in a compiler pipeline enabling efficient compilation of the source-level language. We have implemented lift inference in this compiler pipeline and conducted benchmarks which indicate that the approach is indeed working.