Lectures in course CS-452: Foundations of software

Pen-and-paper session: Lambda Calculus Proofs

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

Coq Workshop: Inductive Data Types and Proofs

Covers the definition of an inductive data type in Coq and how to build proofs interactively using tactics.

Foundations of Software: Modeling Programming Languages

Covers the mathematical study of program behaviors, parsing, domain-specific languages, and powerful tools for language design.

Object-Oriented Parser Combinators

Covers object-oriented parser combinators in Scala for building parsers, including JSON parsing and testing.

Designing Calculi: Strong Normalization and Error Handling

Covers strong normalization, error handling, and typing rules for Calculi design.

Foundations of Software

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

Subtyping and Type Calculus

Explores subtyping, type calculus, and type bounds calculation in a system with subtyping, guiding through exercises and proofs step by step.

Lambda Calculus: Syntax and Abstractions

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

Lambda Calculus: Operational Semantics and Evaluation Strategies

Covers operational semantics and evaluation strategies in lambda calculus, including redex, alternative evaluation strategies, and Church Booleans.

Logical Formulas and Types: Understanding the Kerry Howard Isomorphism

Explores the Kerry Howard Isomorphism, translating logical propositions into types and terms, with a focus on proof by induction and exam preparation.

Lambda Calculus: Church Numerals

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

Types in Lambda Calculus

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

Type Systems: Preservation and Typing Rules

Covers preservation, substitution, weakening, and sequencing in type systems.

Records and Variants

Introduces records, variants, evaluation rules, typing rules, aliasing challenges, and benefits in programming languages.

Syntax and Typing Rules

Covers syntax and typing rules in programming languages, discussing aliasing, mutability, and store locations.

Propositions as Types: Logic and Programming Correspondence

Explores the relationship between logic proofs and programming evidence through the Curry-Howard Correspondence.

Type Checking and Reconstruction: Equations and Unification

Delves into type checking, reconstruction, equations, unification, Hindley/Milner system, polymorphism, and principal types.

Dependent Types in Programming Languages

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

Subtyping and Polymorphism

Explores subtyping rules, challenges, and its connection to various forms of polymorphism in programming languages.

Object-Oriented Programming: Core Features Analysis

Explores the core features of object-oriented programming, including dynamic dispatch, encapsulation, inheritance, and subtyping, using Java examples and practical insights.