a way of studying computable func­tions

lambda calculus Invented by Alonzo Church in the 1930s, the lambda calculus is a way of studying computable func­tions.

a formal system designed to investigate functions and recursion

In mathematical logic and computer science, the lambda calculus (also λ-calculus) is a formal system designed to investigate functions and recursion.

a formal system for expressing computation with functions

The lambda calculus, invented in the 30s, is a formal system for expressing computation with functions and can also been seen as a programming language.

a minimal programming language that only uses function definitions and function applications

The Lambda calculus, developed by Alonzo Church is a minimal programming language that uses only function definitions and function applications.

a system of functional programming

The lambda calculus is a system of functional programming.

a formal system in mathematical logic

People who have been formally trained in computer science will of course know of the lambda calculus, introduced by Alonso Church in the nineteen thirties; the lambda calculus is a formal system in mathematical logic based on function abstraction and application.

of a language of lambda terms, which is defined by a certain formal syntax, and a set of transformation rules, which allow manipulation of the lambda terms

The lambda calculus consists of a language of lambda terms, which is defined by a certain formal syntax, and a set of transformation rules, which allow manipulation of the lambda terms.

the basis of functional programming and higher order proof assistants

Lambda calculus is the basis of functional programming and higher order proof assistants.

a formal mathematical system for the notation and analysis of mathematical algorithms

The lambda calculus (or λ-calculus) is a formal mathematical system for the notation and analysis of mathematical algorithms.

a universal model of computation

As an universal model of computation, lambda calculus is important in programming language theory, and especially programming language theory is the foundation of functional programming.

a branch of logic and mathematics that deals with functions

Lambda calculus is basically a branch of logic and mathematics that deals with functions, and is the basis of functional programming languages.