Programming Languages

Formalizing Computation Through Algebraic Theories Initial algebras provide a powerful denotational model for formalizing the meanings of computer programs. As mathematical constructs, initial algebras capture the essence of data types and recursion in a language-independent way. Programming languages such as Haskell and ML implement type systems based on initial algebras, enabling modular reasoning about programs….

Constructing Meaning in Mathematics Categorical foundations provide a semantic framework for constructing meaning and intuitionistic reasoning in topos theory. The category theory underpinning topos establishes powerful logics for formalizing mathematical concepts and structures. Internally, toposes host intuitionistic and constructive logical systems that align better with computational and constructive mathematics. Categorical Foundations of Topos Theory As…

Categorical Foundations of Quantum Programming Quantum programming languages allow the description and manipulation of quantum data and effects using classical control flow. To reason about and give semantics to these languages, the powerful mathematical framework of category theory is used. Categories provide objects and morphisms that can model quantum data and programs in an abstract…

Formalizing Computation with Category Theory Category theory provides a formal framework for modeling different computational models and relating them to each other. A category consists of objects and morphisms between those objects. Objects can represent computational models such as lambda calculus or Turing machines, while morphisms represent structure-preserving mappings between those models. Key aspects of…