Type Theory as a Language Workbench

Language Workbenches offer language designers an expressive environment in which to create their Domain Specific Languages (DSLs). Similarly, research into mechanised meta-theory has shown how dependently typed languages provide expressive environments to formalise and study DSLs and their meta-theoretical properties. But can we claim that dependently typed languages qualify as language workbenches? We argue yes! We have developed an exemplar DSL called Vélo that showcases not only dependently typed techniques to realise and manipulate Intermediate Representations (IRs), but that dependently typed languages make fine language workbenches. Vélo is a simple verified language with well-typed holes and comes with a complete compiler pipeline: parser, elaborator, REPL, evaluator, and compiler passes. Specifically, we describe our design choices for well-typed IR design that includes support for well-typed holes, how CSE is achieved in a well-typed setting, and how the mechanised type-soundness proof for Vélo is the source of the evaluator

Builtin types viewed as inductive families

This research was funded by the Engineering and Physical Sciences Research Council (grant number EP/T007265/1).State of the art optimisation passes for dependently typed languages can help erase the redundant information typical of invariant-rich data structures and programs. These automated processes do not dramatically change the structure of the data, even though more efficient representations could be available. Using Quantitative Type Theory, we demonstrate how to define an invariant-rich, typechecking time data structure packing an efficient runtime representation together with runtime irrelevant invariants. The compiler can then aggressively erase all such invariants during compilation. Unlike other approaches, the complexity of the resulting representation is entirely predictable, we do not require both representations to have the same structure, and yet we are able to seamlessly program as if we were using the high-level structure.Publisher PD

Builtin types viewed as inductive families

State of the art optimisation passes for dependently typed languages can help erase the redundant information typical of invariant-rich data structures and programs. These automated processes do not dramatically change the structure of the data, even though more efficient representations could be available. Using Quantitative Type Theory as implemented in Idris 2, we demonstrate how to define an invariant-rich, typechecking-time data structure packing an efficient runtime representation together with runtime irrelevant invariants. The compiler can then aggressively erase all such invariants during compilation. Unlike other approaches, the complexity of the resulting representation is entirely predictable, we do not require both representations to have the same structure, and yet we are able to seamlessly program as if we were using the high-level structure

A type-theoretic framework for software component synthesis

A language-agnostic approach for type-based component-oriented software synthesis is developed from the fundamental principles of abstract algebra and Combinatory Logic. It relies on an enumerative type inhabitation algorithm for Finite Combinatory Logic with Intersection Types (FCL) and a universal algebraic construction to translate terms of Combinatory Logic into any given target language. New insights are gained on the combination of semantic domains of discourse with intersection types. Long standing gaps in the algorithmic understanding of the type inhabitation question of FCL are closed. A practical implementation is developed and its applications by the author and other researchers are discussed. They include, but are not limited to, vast improvements in the context of synthesis of software product line members. An interactive theorem prover, Coq, is used to formalize and check all the theoretical results. This makes them more reusable for other developments and enhances confidence in their correctness.Es wird ein sprachunabhängiger Ansatz für die typbasierte und komponentenorientierte Synthese von Software entwickelt. Hierzu werden grundlegende Erkenntnisse über abstrakte Algebra und kombinatorische Logik verwendet. Der Ansatz beruht auf dem enumerativen Typinhabitationsproblem der endlichen kombinatorischen Logik mit Intersektionstypen, sowie einer universellen algebraischen Konstruktion, um Ergebnisterme in jede beliebe Zielsprache übersetzen zu können. Es werden neue Einblicke gewonnen, wie verschiedene semantische Domänen des Diskurses über Softwareeigenschaften miteinander verbunden werden können. Offene Fragestellungen im Zusammenhand mit der Algorithmik des Typinhabitationsproblems für Intersektionstypen werden beantwortet. Eine praktische Implementierung des Ansatzes wird entwickelt und ihre bisherigen Anwendungen durch den Autor und andere Wissenschaftler werden diskutiert. Diese beinhalten starke Verbesserungen im Zusammenhang mit der Synthese von Ausprägungen von Software Produktlinien. Ein interaktiver Theorembeweiser wir genutzt, um alle Ergebnisse der Arbeit zu formalisieren und mechanisch zu überprüfen. Dies trägt zum einen zur Wiederverwendbarkeit der theoretischen Ergebnisse in anderen Kontexten bei, und erhöht zum andern das Vertrauen in ihre Korrektheit

Foundations of Information-Flow Control and Effects

In programming language research, information-flow control (IFC) is a technique for enforcing a variety of security aspects, such as confidentiality of data,on programs. This Licenciate thesis makes novel contributions to the theory and foundations of IFC in the following ways: Chapter A presents a new proof method for showing the usual desired property of noninterference; Chapter B shows how to securely extend the concurrent IFC language MAC with asynchronous exceptions; and, Chapter C presents a new and simpler language for IFC with effects based on an explicit separation of pure and effectful computations

Programming Languages and Systems

This open access book constitutes the proceedings of the 30th European Symposium on Programming, ESOP 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 24 papers included in this volume were carefully reviewed and selected from 79 submissions. They deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems

Formal verification of the equivalence of system F and the pure type system L2

We develop a formal proof of the equivalence of two different variants of System F. The first is close to the original presentation where expressions are separated into distinct syntactic classes of types and terms. The second, L2 (also written as λ2), is a particular pure type system (PTS) where the notions of types and terms, and the associated expressions are unified in a single syntactic class. The employed notion of equivalence is a bidirectional reduction of the respective typing relations. A machine-verified proof of this result turns out to be surprisingly intricate, since the two variants noticeably differ in their expression languages, their type systems and the binding of local variables. Most of this work is executed in the Coq theorem prover and encompasses a general development of the PTS metatheory, an equivalence result for a stratified and a PTS variant of the simply typed λ-calculus as well as the subsequent extension to the full equivalence result for System F. We utilise nameless de Bruijn syntax with parallel substitutions for the representation of variable binding and develop an extended notion of context morphism lemmas as a structured proof method for this setting. We also provide two developments of the equivalence result in the proof systems Abella and Beluga, where we rely on higher-order abstract syntax (HOAS). This allows us to compare the three proof systems, as well as HOAS and de Bruijn for the purpose of developing formal metatheory.Wir präsentieren einen maschinell verifizierten Beweis der Äquivalenz zweier Darstellungen des Lambda-Kalküls System F. Die erste unterscheidet syntaktisch zwischen Termen und Typen und entspricht somit der geläufigen Form. Die zweite, L2 bzw. λ2, ist ein sog. Pure Type System (PTS), bei welchem alle Ausdrücke in einer syntaktischen Klasse zusammen fallen. Unser Äquivalenzbegriff ist eine bidirektionale Reduktion der jeweiligen Typrelationen. Ein formaler Beweis dieser Eigenschaft ist aufgrund der Unterschiede der Ausdruckssprachen, der Typrelationen und der Bindung lokaler Variablen überraschend anspruchsvoll. Der Hauptteil dieser Arbeit wurde in dem Beweisassistenten Coq entwickelt und umfasst eine Abhandlung der PTS Metatheorie, sowie einen Äquivalenzbeweis für das einfach getypte Lambda-Kalkül, welcher dann zu dem vollen Ergebnis für System F skaliert wird. Für die Darstellung lokaler Variablenbindung verwenden wir de Bruijn Syntax, gepaart mit parallelen Substitutionen. Außerdem entwickeln wir eine generalisierte Form von Kontext-Morphismen Lemmas, welche eine strukturierte Beweismethodik in diesem Umfeld liefern. Darüber hinaus betrachten wir zwei weitere Formalisierungen des Äquivalenzresultats in den Beweissystemen Abella und Beluga, welche beide höherstufige abstrakte Syntax (HOAS) zur Darstellung lokaler Bindung verwenden. Dies ermöglicht es uns, sowohl die drei Beweissysteme, als auch den HOAS und den de Bruijn Ansatz mit Hinblick auf die Entwicklung formaler Metatheorie zu vergleichen