Lambda-Calculus

• The Lambda Calculus and Combinatory Logic: The Minimalist Foundations of All Computation · 2025-05-06

  Rediscover the lambda calculus as the essence of computation: Church's elegant system of function definition and application, its equivalence to Turing machines, the fixed-point combinator, and its enduring influence on programming languages from Lisp to Haskell.

• The Curry-Howard Correspondence: How Type Theory Bridges Proof and Computation · 2025-03-18

  Explore the profound isomorphism between logical proofs and computer programs: how the Curry-Howard correspondence unifies propositional logic with typed lambda calculus, and how it enables modern proof assistants like Coq, Lean, and Agda.

• Domain Theory: Scott's D∞ Construction, Denotational Semantics, and the Mathematics of Recursive Types · 2022-01-15

  A rigorous exploration of domain theory—Scott's D∞ construction, continuous lattices, the fixpoint theorem, and how domains provide the mathematical foundation for denotational semantics of programming languages.

• Domain Theory: Scott's D∞ Construction, Solving Recursive Domain Equations, and the Foundations of Denotational Semantics · 2021-12-19

  An in-depth exploration of domain theory—Scott's construction of a universal domain D∞ isomorphic to its own function space, continuous lattices, and how these ideas gave birth to denotational semantics.