strangerRidingCaml

Higher-order Polymorphism Higher-order polymorphism extends polymorphism to higher-order functions, allowing functions to be polymorphic not only in their arguments but also in their return types. This enables more expressive programming constructs where functions can operate on other functions in a polymorphic manner. In higher-order polymorphism, type variables can be universally quantified..

System F: Introduction to Polymorphic Lambda Calculus System F, also known as the second-order lambda calculus or polymorphic lambda calculus, is an extension of the simply typed lambda calculus with support for polymorphism. In System F, functions can be polymorphic, meaning they can operate on values of any type. This is achieved through the introduction of type variables and type abstracti..

Dependent Types and Pi Types Dependent types are types that depend on values, allowing types to be parameterized by terms. They enable richer type systems where types can describe precise properties of values. One common form of dependent type is the Pi type, denoted as Π, which represents dependent function types. In Pi types, the type of the result can depend on the value of one or more ar..

Subtyping and Variance Subtyping is a relationship between types where one type is considered a subtype of another type. This relationship is often denoted as S , meaning that type S is a subtype of type T. Subtyping allows for more flexible type systems where a value of a subtype can be used wherever a value of its supertype is expected. Variance is a property of type constructors, such as ..

Polymorphism and Parametric Polymorphism Polymorphism is a programming language feature that allows a single function or data type to operate on different types. There are two main types of polymorphism: ad-hoc polymorphism and parametric polymorphism. Ad-hoc polymorphism, also known as overloading, refers to the ability to define multiple functions or methods with the same name but different..

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..