Lambda calculus - Formal definition - Article Index

Encyclopedia - Lambda Calculus: Encyclopedia Ii - Lambda Calculus - Formal Definition
Formally, we start with a countably infinite set of identifiers, say {a, b, c, ..., x, y, z, x1, x2, ...}. The set of all lambda expressi...   » Read the article

Encyclopedia - Lambda Calculus: Encyclopedia Ii - Lambda Calculus - Undecidability Of Equivalence
There is no algorithm which takes as input two lambda expressions and outputs TRUE or FALSE depending on whether or not the two expressio...   » Read the article

Encyclopedia - Lambda Calculus: Encyclopedia Ii - Lambda Calculus - Lambda Calculus And Programming Languages
Most programming languages are equivalent to the lambda calculus extended with some additional programming language constructs. The class...   » Read the article

Encyclopedia - Lambda Calculus: Encyclopedia Ii - Lambda Calculus - Recursion
Recursion is the definition of a function using the function itself; on the face of it, lambda calculus does not allow this. However, thi...   » Read the article

Encyclopedia - Lambda Calculus: Encyclopedia Ii - Lambda Calculus - Logic And Predicates
By convention, the following two definitions (known as Church booleans) are used for the boolean values TRUE and FALSE: TRUE := λ ...   » Read the article

Encyclopedia - Lambda Calculus: Encyclopedia Ii - Lambda Calculus - Arithmetic In Lambda Calculus
There are several possible ways to define the natural numbers in lambda calculus, but by far the most common are the Church numerals, whi...   » Read the article

Encyclopedia - Lambda Calculus: Encyclopedia Ii - Lambda Calculus - Informal Description
In lambda calculus, every expression stands for a function with a single argument; the argument of the function is in turn a function wit...   » Read the article