strangerRidingCaml

Type Safety: Progress and Preservation Theorems Type safety is a property of programming languages and type systems that ensures certain guarantees about the behavior of programs. Two key theorems in type safety are the Progress theorem and the Preservation theorem. The Progress theorem states that well-typed programs will never get stuck during evaluation. This means that if a program can t..

Introduction to Inference Rules and Typing Rules Inference rules and typing rules are fundamental components of formal systems used to derive conclusions about the behavior and properties of expressions. Inference rules are logical rules that specify how new knowledge or conclusions can be derived from existing premises or assumptions. They are typically expressed as a set of premises leading..

Simply Typed Lambda Calculus (STLC) The Simply Typed Lambda Calculus (STLC) is a foundational formal system in lambda calculus with typed expressions. In STLC, each lambda abstraction is annotated with a specific type, and the application of functions is type-checked to ensure type compatibility. The syntax of STLC includes terms, types, and typing judgments. Terms are represented as lambda ..

Basic Concepts of Type Theory In Type Theory, types are fundamental constructs that classify various entities in a formal system. Each entity, known as a term, is assigned a type, indicating its nature or category. Terms represent objects, values, or expressions within the system, while types categorize these terms based on their properties. For example, in a simple type system, we might hav..

Overview of Type Theory: Historical Context and Motivation Type Theory is a foundational framework in mathematics and computer science for formalizing the notion of computation and reasoning about types of data. The roots of Type Theory can be traced back to the early 20th century, with the work of David Hilbert and Alonzo Church. In the 1930s, Church introduced the concept of the lambda calc..