There is a population explosion among the logical systems used in computing science. Examples include first-order logic, equational logic, Horn-clause logic, higher-order logic, infinitary logic, dynamic logic, intuitionistic logic, order-sorted logic, ...
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 ...
Introduction to Higher-Order Categorical Logic (Cambridge Studies in Advanced Mathematics)
Introduction to higher order catagorical logic by J. Lambek, March 25, 1988, Cambridge University Press edition, Paperback in English
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 ...
The semantics of clear, a specification language
This paper gives a semantics for the Clear language for specifying problems and programs, described by Burstall and Goguen in 1977. A blend of denotational semantics with categorical ideas is used.
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.
Programming Language Foundations in Agda – Table of Contents
This book is an introduction to programming language theory using the proof assistant Agda.
Compiling Higher-Order Specifications to SMT Solvers: How to Deal with Rejection Constructively | Proceedings of the 12th ACM SIGPLAN International Conference on Certified Programs and Proofs
We present a decision procedure that combines reasoning about datatypes and codatatypes. The dual of the acyclicity rule for datatypes is a uniqueness rule that identifies observationally equal codatatype values, including cyclic values. The procedure ...
When Does a Specification Become a Program? - The Phoenix Architecture
A spec can contain prose, tests, schemas, formal models, even executable code. The useful boundary is not the syntax but, rather, what survives: if you throw the implementation away, what has to remain so you can build the next one?
When Does a Specification Become a Program? - The Phoenix Architecture
A spec can contain prose, tests, schemas, formal models, even executable code. The useful boundary is not the syntax but, rather, what survives: if you throw the implementation away, what has to remain so you can build the next one?
Abstract syntax and variable binding
We develop a theory of abstract syntax with variable binding. To every binding signature we associate a category of models consisting of variable sets endowed with compatible algebra and substitution structures. The syntax generated by the signature is the initial model. This gives a notion of initial algebra semantics encompassing the traditional one; besides compositionality, it automatically verifies the semantic substitution lemma.
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 ...
When Does a Specification Become a Program? · The Phoenix Architecture
A spec can contain prose, tests, schemas, formal models, even executable code. The useful boundary is not the syntax but, rather, what survives: if you throw the implementation away, what has to remain so you can build the next one?
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.
The Principal Type-Scheme of an Object in Combinatory Logic
R. Hindley, The Principal Type-Scheme of an Object in Combinatory Logic, Transactions of the American Mathematical Society, Vol. 146 (Dec., 1969), pp. 29-60
A taxonomy for next-generation reasoning models
Where we've been and where we're going with RLVR.
