Lectures related to Second Order Logic: WS1S and HOL

Semantics in Computer Language Processing: Understanding Meaning

Covers the semantics of programming languages, focusing on the Add language and the role of rewriting rules and CK machines in understanding meaning.

Lambda Calculus and Type Safety: An Overview

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

Automating First-Order Logic Proofs Using Resolution

Covers first-order logic syntax, semantics, Skolemization, resolution, and normal form transformations.

Music Semantics: Problems and Prospects

Explores music semantics, discussing inferences triggered by different musical elements and proposing a framework for understanding music's meaning.

Foundations of Software

Covers the basics of induction, syntax, abstract vs. concrete syntax, and operational semantics for Booleans.

Hoare Logic: Foundations and Applications

Covers Hoare Logic, its foundations, applications, and significance in program verification.

Monotonicity and Semantics of Local Variables

Explores properties of relations, monotonicity, semantics of local variables, and translation in programs.

Lambda Calculus: Syntax and Abstractions

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

Big-step semantics: Defining arithmetic expressions and commands

Covers the definition of a simple programming language and its big-step semantics, including arithmetic expressions and imperative commands.

An Introduction to Iris: Higher-Order Concurrent Separation Logic

Introduces Iris, a logical framework for reasoning about safety and correctness of concurrent higher-order imperative programs, emphasizing its unique characteristics and applications.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Relational Semantics of Loops

Explores the relational semantics of loops in programs and the mathematical interpretation of loop structures.

Regular Expressions: Basics and Applications

Introduces regular expressions, covering language sets, syntax, semantics, and limitations.

Lambda Calculus: Church Numerals

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

Type Rules: Progress and Preservation

Covers Amyli, a tiny functional language, type rules, and soundness.

Polymorphism in Coq: Data Structures and Functions

Covers polymorphism in Coq, focusing on data structures and functions like lists, length, and append.

Operational Semantics: Amyli Language

Covers the Amyli language, including abstract syntax, program representation, and operational semantics.

Omega Continuity: Galois Connection and AI Recipe

Explores Tarski's fixed point theorem, omega continuity, Galois connection, and abstract interpretation concepts.

High-Level Synthesis: Formally Verified Elastic Circuits

Presents the development of a verified high-level synthesis compiler for elastic circuits.

Simply Typed Lambda Calculus: Foundations and Properties

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