This book is an introduction to programming language theory using the proof assistant Agda.
Practical Foundations for Programming Languages
GATlab: Modeling and Programming with Generalized Algebraic Theories
Categories and categorical structures are increasingly recognized as useful abstractions for modeling in science and engineering. To uniformly implement category-theoretic mathematical models in software, we introduce GATlab, a domain-specific language for algebraic specification embedded in a technical programming language. GATlab is based on generalized algebraic theories (GATs), a logical system extending algebraic theories with dependent types so as to encompass category theory. Using GATlab, the programmer can specify generalized algebraic theories and their models, including both free models, based on symbolic expressions, and computational models, defined by arbitrary code in the host language. Moreover, the programmer can define maps between theories and use them to declaratively migrate models of one theory to models of another. In short, GATlab aims to provide a unified environment for both computer algebra and software interface design with generalized algebraic theories. In this paper, we describe the design, implementation, and applications of GATlab.
Foundations of Algebraic Specification and Formal Software Development
This book provides foundations for software specification and formal software development from the perspective of work on algebraic specification, concentrating on developing basic concepts and studying their fundamental properties. These foundations are built on a solid mathematical basis, using elements of universal algebra, category theory and logic, and this mathematical toolbox provides a convenient language for precisely formulating the concepts involved in software specification and development. Once formally defined, these notions become subject to mathematical investigation, and this interplay between mathematics and software engineering yields results that are mathematically interesting, conceptually revealing, and practically useful. The theory presented by the authors has its origins in work on algebraic specifications that started in the early 1970s, and their treatment is comprehensive. This book contains five kinds of material: the requisite mathematicalfoundations; traditional algebraic specifications; elements of the theory of institutions; formal specification and development; and proof methods. While the book is self-contained, mathematical maturity and familiarity with the problems of software engineering is required; and in the examples that directly relate to programming, the authors assume acquaintance with the concepts of functional programming. The book will be of value to researchers and advanced graduate students in the areas of programming and theoretical computer science.
Resugaring | Proceedings of the 35th ACM SIGPLAN Conference on Programming Language Design and Implementation
Syntactic sugar plays a crucial role in engineering programming languages. It offers convenient syntax and higher-level of abstractions, as witnessed by its pervasive use in both general-purpose and domain-specific contexts. Unfortunately, the ...
The mythical matched modules | Proceedings of the 24th ACM SIGPLAN conference companion on Object oriented programming systems languages and applications
Certified compilers are complex software systems. Like other large systems, they demand modular, extensible designs. While there has been progress in extensible metatheory mechanization, scaling extensibility and reuse to meet the demands of full ...
Boomerang | Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Bidirectional programming languages are a practical approach to the view update problem. Programs in these languages, called lenses, define both a view and an update policy - i.e., every program can be read as a function mapping sources to views as well ...
Principal type-schemes for functional programs | Proceedings of the 9th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
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Integrating functional and imperative programming | Proceedings of the 1986 ACM conference on LISP and functional programming
We present a new model, based on monads, for performing input/output in a non-strict, purely functional language. It is composable, extensible, efficient, requires no extensions to the type system, and extends smoothly to incorporate mixed-language ...
Algebra of programming
Algebra of programming by Bird, Richard, 1997, Prentice Hall edition, in English
Finite-Choice Logic Programming | Proceedings of the ACM on Programming Languages
Logic programming, as exemplified by datalog, defines the meaning of a program as its unique smallest model: the deductive closure of its inference rules. However, many problems call for an enumeration of models that vary along some set of choices while ...
A modal analysis of staged computation | Journal of the ACM
We show that a type system based on the intuitionistic modal logic S4 provides an expressive framework for specifying and analyzing computation stages in the context of typed λ-calculi and functional languages. We directly demonstrate the sense in which ...
LLMs as Collaborators in Language Specification and Design (PLSS 2026) - SPLASH/ISSTA 2026
Workshop on Programming Language Standardization and Specification This workshop aims to foster cross-pollination between researchers and industry professionals with experience in programming language specification and standardization. It provides a forum where participants can share insights, case studies, and best practices, and collaboratively explore solutions to current challenges. The goal of the workshop is to improve the collective understanding of how programming languages are specified, standardized, and evolved in practice. The workshop examines specifications as the foundation ...
Satisfiability Modulo Theories: A Beginner’s Tutorial — Satisfiability Modulo Theories: A Beginner's Tutorial documentation
Great minds have long dreamed of creating machines that can function as general-purpose problem solvers. Satisfiability modulo theories (SMT) has emerged as one pragmatic realization of this dream, providing significant expressive power and automation. This tutorial is a beginner’s guide to SMT. It includes an overview of SMT and its formal foundations, a catalog of the main theories used in SMT solvers, and illustrations of how to obtain models and proofs. Throughout the tutorial, examples and exercises are provided as hands-on activities for the reader. They can be run using either Python or the SMT-LIB language, using either the cvc5 or the z3 SMT solver.
The Spoofax language workbench | Proceedings of the ACM international conference companion on Object oriented programming systems languages and applications companion
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The Topos of Programming | Yon
A topos-oriented programming language. Native via MLIR and LLVM, with a content-addressed heap on the Leech lattice.
