Compiler intermediate representations have to strike a balance between being high-level enough to allow for easy translation of surface languages into them and being low-level enough to make code generation easy. An intermediate representation based on a logical system typically has the former property and additionally satisfies several meta-theoretical properties which are valuable when optimizing code. Recently, classical sequent calculus, which is widely recognized and impactful within the fields of logic and proof theory, has been proposed as a natural candidate in this regard, due to its symmetric treatment of data and control flow. For such a language to be useful, however, it must eventually be compiled to machine code. In this paper, we introduce an intermediate representation that is based on classical sequent calculus and demonstrate that this language can be directly translated to conventional hardware. We provide both a formal description and an implementation. Preliminary performance evaluations indicate that our approach is viable.

Monomorphization is a common implementation technique for parametric type-polymorphism, which avoids the potential runtime overhead of uniform representations at the cost of code duplication. While important as a folklore implementation technique, there is a lack of general formal treatments in the published literature. Moreover, it is commonly believed to be incompatible with higher-rank polymorphism. In this paper, we formally present a simple monomorphization technique based on a type-based flow analysis that generalizes to programs with higher-rank types, existential types, and arbitrary combinations. Inspired by algebraic subtyping, we track the flow of type instantiations through the program. Our approach only supports monomorphization up to polymorphic recursion, which we uniformly detect as cyclic flow. Treating universal and existential quantification uniformly, we identify a novel form of polymorphic recursion in the presence of existential types, which we coin polymorphic packing. We study the meta-theory of our approach, showing that our translation is type-preserving and preserves semantics step-wise.

Type qualifiers offer a lightweight mechanism for enriching existing type systems to enforce additional, desirable, program invariants. They do so by offering a restricted but effective form of subtyping. While the theory of type qualifiers is well understood and present in many programming languages today, polymorphism over type qualifiers remains an area less well examined. We explore how such a polymorphic system could arise by constructing a calculus, System F-sub-Q, which combines the higher-rank bounded polymorphism of System F-sub with the theory of type qualifiers. We explore how the ideas used to construct System F-sub-Q can be reused in situations where type qualifiers naturally arise---in reference immutability, function colouring, and capture checking. Finally, we re-examine other qualifier systems in the literature in light of the observations presented while developing System F-sub-Q.

Creating good type error messages for constraint-based type inference systems is difficult. Typical type error messages reflect implementation details of the underlying constraint-solving algorithms rather than the specific factors leading to type mismatches. We propose using subtyping constraints that capture data flow to classify and explain type errors. Our algorithm explains type errors as faulty data flows, which programmers are already used to reasoning about, and illustrates these data flows as sequences of relevant program locations. We show that our ideas and algorithm are not limited to languages with subtyping, as they can be readily integrated with Hindley-Milner type inference. In addition to these core contributions, we present the results of a user study to evaluate the quality of our messages compared to other implementations. While the quantitative evaluation does not show that flow-based messages improve the localization or understanding of the causes of type errors, the qualitative evaluation suggests a real need and demand for flow-based messages.

Translating programs into continuation-passing style is a well-studied tool to explicitly deal with the control structure of programs. This is useful, for example, for compilation. In a typed setting, there also is a logical interpretation of such a translation as an embedding of classical logic into intuitionistic logic. A naturally arising question is whether there is an inverse translation back to direct style. The answer to this question depends on how the continuation-passing translation is defined and on the domain of the inverse translation. In general, translating programs from continuation-passing style back to direct style requires the use of control operators to account for the use of continuations in non-trivial ways. We present two languages, one in direct style and one in continuation-passing style. Both languages are typed and equipped with an abstract machine semantics. Moreover, both languages allow for non-trivial control flow. We further present a translation to continuation-passing style and a translation back to direct style. We show that both translations are type-preserving and also preserve semantics in a very precise way giving an operational correspondence between the two languages. Moreover, we show that the compositions of the translations are well-behaved. In particular, they are syntactic one-sided inverses on the full language and full syntactic inverses when restricted to trivial control flow.

Type and effect systems have been successfully used to statically reason about effects in many different domains, including region-based memory management, exceptions, and algebraic effects and handlers. Such systems’ soundness is often stated in terms of the absence of effects. Yet, existing systems only admit indirect reasoning about the absence of effects. This is further complicated by effect polymorphism which allows function signatures to abstract over arbitrary, unknown sets of effects. We present a new type and effect system with effect polymorphism as well as union, intersection, and complement effects. The effect system allows us to express effect exclusion as a new class of effect polymorphic functions: those that permit any effects except those in a specific set. This way, we equip programmers with the means to directly reason about the absence of effects. Our type and effect system builds on the Hindley-Milner type system, supports effect polymorphism, and preserves principal types modulo Boolean equivalence. In addition, a suitable extension of Algorithm W with Boolean unification on the algebra of sets enables complete type and effect inference. We formalize these notions in the λ ∁ calculus. We prove the standard progress and preservation theorems as well as a non-standard effect safety theorem: no excluded effect is ever performed. We implement the type and effect system as an extension of the Flix programming language. We conduct a case study of open source projects identifying 59 program fragments that require effect exclusion for correctness. To demonstrate the usefulness of the proposed type and effect system, we recast these program fragments into our extension of Flix.

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.

Type qualifiers offer a lightweight mechanism for enriching existing type systems to enforce additional, desirable, program invariants. They do so by offering a restricted but effective form of subtyping. While the theory of type qualifiers is well understood and present in many programming languages today, polymorphism over type qualifiers is an area that is less examined. We explore how such a polymorphic system could arise by constructing a calculus System F<:Q which combines the higher-rank bounded polymorphism of System F<: with the theory of type qualifiers. We explore how the ideas used to construct System F<:Q can be reused in situations where type qualifiers naturally arise – in reference immutability, function colouring, and capture checking. Finally, we re-examine other qualifier systems in the literature in light of the observations presented while developing System F<:Q.

Regions are a useful tool for the safe and automatic management of resources. Due to their scarcity, resources are often limited in their lifetime which is associated with a certain scope. When control flow leaves the scope, the resources are released. Exceptions can non-locally exit such scopes and it is important that resources are also released in this case. Continuation-passing style is a useful compiler intermediate language that makes control flow explicit. All calls are tail calls and the runtime stack is not used. It can also serve as an implementation technique for control effects like exceptions. In this case throwing an exception means jumping to a continuation which is not the current one. How is it possible to offer region-based resource management and exceptions in the same language and translate both to continuation-passing style? In this paper, we answer this question. We present a typed language with resources and exceptions, and its translation to continuation-passing style. The translation can be defined modularly for resources and exceptions – the correct interaction between the two automatically arises from simple composition. We prove that the translation preserves well-typedness and semantics.

Reasoning about the use of external resources is an important aspect of many practical applications. Effect systems enable tracking such information in types, but at the cost of complicating signatures of common functions. Capabilities coupled with escape analysis offer safety and natural signatures, but are often overly coarse grained and restrictive. We present System C, which builds on and generalizes ideas from type-based escape analysis and demonstrates that capabilities and effects can be reconciled harmoniously. By assuming that all functions are second class, we can admit natural signatures for many common programs. By introducing a notion of boxed values, we can lift the restrictions of second-class values at the cost of needing to track degree-of-impurity information in types. The system we present is expressive enough to support effect handlers in full capacity. We practically evaluate System C in an implementation and prove its soundness.

Type systems usually characterize the shape of values but not their free variables. However, many desirable safety properties could be guaranteed if one knew the free variables captured by values. We describe CCsubBox, a calculus where such captured variables are succinctly represented in types, and show it can be used to safely implement effects and effect polymorphism via scoped capabilities. We discuss how the decision to track captured variables guides key aspects of the calculus, and show that CCsubBox admits simple and intuitive types for common data structures and their typical usage patterns. We demonstrate how these ideas can be used to guide the implementation of capture checking in a practical programming language.

Type-level programming is becoming more and more popular in the realm of functional programming. However, the combination of type-level programming and subtyping remains largely unexplored in practical programming languages. This paper presents match types, a type-level equivalent of pattern matching. Match types integrate seamlessly into programming languages with subtyping and, despite their simplicity, offer significant additional expressiveness. We formalize the feature of match types in a calculus based on System F sub and prove its soundness. We practically evaluate our system by implementing match types in the Scala 3 reference compiler, thus making type-level programming readily available to a broad audience of programmers.

Effect handlers are a language feature which enjoys popularity in academia and is also gaining traction in industry. Programs use abstract effect operations and handlers provide meaning to them in a delimited scope. Each effect operation is handled by the dynamically closest handler. Using an effect operation outside of a matching handler is meaningless and results in an error. A type-and-effect system prevents such errors from happening. Lexical effect handlers are a recent variant of effect handlers with a number of attractive properties. Just as with traditional effect handlers, programs use effect operations and handlers give meaning to them. But unlike with traditional effect handlers, the connection between effect operations and their handler is lexical. Consequently, they typically have different type-and-effect systems. The semantics of lexical effect handlers as well as their implementations use multi-prompt delimited control. They rely on the generation of fresh labels at runtime, which associate effect operations with their handlers. This use of labels and multi-prompt delimited control is theoretically and practically unsatisfactory. Our main result is that typed lexical effect handlers do not need the full power of multi-prompt delimited control. We present the first CPS translation for lexical effect handlers to pure System F. It preserves well-typedness and simulates the traditional operational semantics. Importantly, it does so without requiring runtime labels. The CPS translation can be used to study the semantics of lexical effect handlers as well as as an implementation technique.

In metaprogramming, code generation and code analysis are complementary. Traditionally, principled metaprogramming extensions for programming languages, like MetaML and BER MetaOCaml, offer strong foundations for code generation but lack equivalent support for code analysis. Similarly, existing macro systems are biased towards the code generation aspect. In this work, we present a calculus for macros featuring both code generation and code analysis. The calculus directly models separate compilation of macros, internalizing a commonly neglected aspect of macros. The system ensures that the generated code is well-typed and hygienic. We implement our system in Scala 3, provide a formalization, and prove its soundness.

We describe a scheme for reflecting exceptions as capabilities in the Scala type system that keeps notational overhead to a minimum and avoids well-known problems with Java's checked exceptions framework. The scheme makes exceptions safer but not fully safe since the capability for throwing an exception may still yet escape its enclosing try block. To address this limitation, we also propose a type system which prevents capabilities from escaping.

Scala 3 provides a metaprogramming interface that represents the abstract syntax tree definitions using algebraic data types. To allow the compiler to freely evolve without breaking the metaprogramming interface, we present virtual algebraic data types (or Virtual ADTs) -- a programming pattern, which allows programmers to describe mutually recursive hierarchies of types without coupling to a particular runtime representation.

Type systems usually characterize the shape of values but not their free variables. However, there are many desirable safety properties one could guarantee if one could track how references can escape. For example, one may implement algebraic effect handlers using capabilities – a value which permits one to perform the effect – safely if one can guarantee that the capability itself does not escape the scope bound by the effect handler. To this end, we study the CF_<: calculus, a conservative and lightweight extension of System F_<:, to track how values and their references can be captured and escape. We show that existing terms in System F_<: embed naturally in our calculus, and that many natural problems can be expressed in a system that tracks variable references like we do in CF_<:. We also give mechanized proofs of the soundness properties of CF_<: in Coq. The type system presented in CF_<: is powerful enough to reason about safety in the context of many natural extensions of CF_<: such as region-based memory-management, non-local returns, and effect handlers.

Effect handlers have recently gained popularity amongst programming language researchers. Existing typeand effect systems for effect handlers are often complicated and potentially hinder a wide-spread adoption. We present the language Effekt with the goal to close the gap between research languages with effect handlers and languages for working programmers. The design of Effekt revolves around a different view of effects and effect types. Traditionally, effect types express which side effects a computation might have. In Effekt, effect types express which capabilities a computation requires from its context. While this new point in the design space of effect systems impedes reasoning about purity, we demonstrate that it simplifies the treatment of effect polymorphism and the related issues of effect parametricity and effect encapsulation. To guarantee effect safety, we separate functions from values and treat all functions as second-class. We define the semantics of Effekt as a translation to System Ξ, a calculus in explicit capability-passing style.

Effect handlers have recently gained popularity amongst programming language researchers. Existing type- and effect systems for effect handlers are often complicated and potentially hinder a wide-spread adoption. We present the language Effekt with the goal to close the gap between research languages with effect handlers and languages for working programmers. The design of Effekt revolves around a different view of effects and effect types. Traditionally, effect types express which side effects a computation might have. In Effekt, effect types express which capabilities a computation requires from its context. While this new point in the design space of effect systems impedes reasoning about purity, we demonstrate that it simplifies the treatment of effect polymorphism and the related issues of effect parametricity and effect encapsulation. To guarantee effect safety, we separate functions from values and treat all functions as second-class. We define the semantics of Effekt as a translation to System Xi, a calculus in explicit capability-passing style.