Higher-Order Subtyping with Type Intervals

Modern, statically typed programming languages provide various abstraction facilities at both the term- and type-level. Common abstraction mechanisms for types include parametric polymorphism -- a hallmark of functional languages -- and subtyping -- which is pervasive in object-oriented languages. Additionally, both kinds of languages may allow parametrized (or generic) datatype definitions in modules or classes. When several of these features are present in the same language, new and more expressive combinations arise, such as (1) bounded quantification, (2) bounded operator abstractions and (3) translucent type definitions. An example of such a language is Scala, which features all three of the aforementioned type-level constructs. This increases the expressivity of the language, but also the complexity of its type system. From a theoretical point of view, the various abstraction mechanisms have been studied through different extensions of Girard's higher-order polymorphic lambda-calculus F-omega. Higher-order subtyping and bounded polymorphism (1 and 2) have been formalized in F-omega-sub and its many variants; type definitions of various degrees of opacity (3) have been formalized through extensions of F-omega with singleton types. In this dissertation, I propose type intervals as a unifying concept for expressing (1--3) and other related constructs. In particular, I develop an extension of F-omega with interval kinds as a formal theory of higher-order subtyping with type intervals, and show how the familiar concepts of higher-order bounded quantification, bounded operator abstraction and singleton kinds can all be encoded in a semantics-preserving way using interval kinds. Going beyond the status quo, the theory is expressive enough to also cover less familiar constructs, such as lower-bounded operator abstractions and first-class, higher-order inequality constraints. I establish basic metatheoretic properties of the theory: I prove that subject reduction holds for well-kinded types w.r.t. full beta-reduction, that types and kinds are weakly normalizing, and that the theory is type safe w.r.t. its call-by-value operational reduction semantics. Key to this metatheoretic development is the use of hereditary substitution and the definition of an equivalent, canonical presentation of subtyping, which involves only normal types and kinds. The resulting metatheory is entirely syntactic, i.e. does not involve any model constructions, and has been fully mechanized in Agda. The extension of F-omega with interval kinds constitutes a stepping stone to the development of a higher-order version of the calculus of Dependent Object Types (DOT) -- the theoretical foundation of Scala's type system. In the last part of this dissertation, I briefly sketch a possible extension of the theory toward this goal and discuss some of the challenges involved in adapting the existing metatheory to that extension.

Dependent Object Types

Nada Amin

A scalable programming language is one in which the same concepts can describe small as well as large parts. Towards this goal, Scala unifies concepts from object and module systems. In particular, objects can contain type members, which can be selected as types, called path-dependent types. Focusing on path-dependent types, we develop a type-theoretic foundation for Scala: the calculus of Dependent Object Types (DOT). We derive DOT from System F

EPFL2016

Object-oriented pattern matching

Burak Emir

Pattern matching is a programming language construct considered essential in functional programming. Its purpose is to inspect and decompose data. Instead, object-oriented programming languages do not have a dedicated construct for this purpose. A possible reason for this is that pattern matching is useful when data is defined separately from operations on the data – a scenario that clashes with the object-oriented motto of grouping data and operations. However, programmers are frequently confronted with situations where there is no alternative to expressing data and operations separately – because most data is neither stored in nor does it originate from an object-oriented context. Consequently, object-oriented programmers, too, are in need for elegant and concise solutions to the problem of decomposing data. To this end, we propose a built-in pattern matching construct compatible with object-oriented programming. We claim that it leads to more concise and readable code than standard object-oriented approaches. A pattern in our approach is any computable way of testing and deconstructing an object and binding relevant parts to local names. We introduce pattern matching in two variants, case classes and extractors. We compare the readability, extensibility and performance of built-in pattern matching in these two variants with standard decomposition techniques. It turns out that standard object-oriented approaches to decomposing data are not extensible. Case classes, which have been studied before, require a low notational overhead, but expose their representation, making them hard to change later. The novel extractor mechanism offers loose coupling and extensibility, but comes with a performance overhead. We present a formalization of object-oriented pattern matching with extractors. This is done by giving definitions and proving standard properties for a calculus that provides pattern matching as described before. We then give a formal, optimizing translation from the calculus including pattern matching to its fragment without pattern matching, and prove it correct. Finally, we consider non-obvious interactions between the pattern matching and parametric polymorphism. We review the technique of generalized algebraic data types from functional programming, and show how it can be carried over to the object-oriented style. The main tool is the extension of the type system with subtype constraints, which leads to a very expressive metatheory. Through this theory, we are able to express patterns that operate on existentially quantified types purely by universally quantified extractors.

EPFL2007

Programming language abstractions for mobile code

Stéphane Micheloud

Scala is a general-purpose programming language developed at EPFL. It combines the most important concepts found in object-oriented and functional languages. Scala is a statically typed language; in particular it features an advanced type system and supports local type inference. Furthermore it integrates well with the Java and .net platforms: their libraries are accessible without glue code and the Scala compiler generates code for both execution environments. The Scala programming language has several features that make it desirable as a language for distributed application programming. In particular, it supports first-class functions which are useful in relation with the notions of distributed scope and code mobility. In that context, the missing support for run-time types is one important drawback of the Java run-time environment as a target platform. This thesis focuses on the realisation of a new concept combining essential notions from the functional and distributed programming and implying the extension of the notion of lexical scoping to the distributed context. In short, we claim that the notion of lambda abstraction provides an elegant way for dealing with the dynamic rebinding of local references in a distributed execution environment. The key ideas exposed in this research work have been implemented in our Scala compiler. This helped us to evaluate the used techniques, in particular their impact on the reliability and the performance of distributed programs. So far, most research works related to the present subject have focused on functional programming languages, in particular on the ML language family.

EPFL2009

Object-oriented pattern matching

Burak Emir

EPFL2007