Lectures related to Logical Formulas and Types: Understanding the Kerry Howard Isomorphism

Provides an overview of lambda calculus, type safety, and type inference in programming languages.

Introduces terms, abstractions, applications, and values in the lambda calculus.

Discusses inductive propositions, their definitions, and applications in reasoning and evaluation techniques in Coq.

Explores Church numerals, Booleans, pairs, recursion, and behavioral equivalence in Lambda Calculus.

Covers types in lambda calculus, including defining types, specifying rules, and proving soundness.

Explores maps, type operators, equivalence, first-class types, System Fw, Coq, and the challenges of type checking in programming languages.

Introduces logic, proofs, sets, functions, and algorithms in mathematics and computer science.

Explores the Cauchy-Schwarz inequality in integrals and functions, offering a comprehensive understanding of its applications.

Explores distribution and interpolation spaces, showcasing their importance in mathematical analysis and the computations involved.

Delves into Lambda Calculus proofs, emphasizing structural induction and variable manipulation.

Delves into the concept of proof in mathematics, emphasizing the importance of evidence and logical reasoning.

Explores differentiating under the integral sign and continuity of functions in integrals.

Covers the basics of formal logic, focusing on logical expressions and mathematical proofs.

Explores advanced Python programming concepts, focusing on list comprehensions and higher order functions.

Introduces Coq, an interactive theorem assistant based on the Curry-Howard isomorphism.

Covers the analysis of functions, composition, and mathematical induction.

Explores differentiating under the integral sign and conditions for differentiation, with examples and extensions to functions on open intervals.

Covers the extension and periodicity of Fourier series and the interpretation of coefficients.

Covers basic operations on arrays and functions in Matlab, including array creation, arithmetic operations, and function definitions.

Covers the simply typed lambda calculus, focusing on its syntax, semantics, and type system properties such as progress and preservation.