Complexity theory and lambda calculus

  • What are the fundamentals of lambda calculus?

    Lambda calculus is composed of 3 elements: variables, functions, and applications.
    The most basic function is the identity function: λx. x which is equivalent to f(x) = x .
    The first “x” is the function's argument, and the second is the body of the function..

  • What is the point of lambda calculus?

    Lambda calculus is a notation for describing mathematical functions and programs.
    It is a mathematical system for studying the interaction of functional abstraction and functional application.
    It captures some of the essential, common features of a wide variety of programming languages..

  • What is the relationship between lambda calculus and Turing machines?

    Alan Turing showed that lambda calculus calculations can be performed by a Turing machine and vice versa.
    Haskell Curry provided types for combinators, which was generalized by Church to a typing system for for lambda terms.
    Finally Dick de Bruijn used lambda terms to represent proofs..

  • What was the purpose of inventing lambda calculus?

    The λ-calculus was invented by Alonzo Church in the 1930s to study the interaction of functional abstraction and function application from an abstract, purely mathematical point of view..

  • Where is lambda calculus used?

    Lambda calculus has applications in many different areas in mathematics, philosophy, linguistics, and computer science.
    Lambda calculus has played an important role in the development of the theory of programming languages.
    Functional programming languages implement lambda calculus..

  • Which language whose syntax is based on lambda calculus?

    Functional programming languages are based on the lambda-calculus.
    The lambda-calculus grew out of an attempt by Alonzo Church and Stephen Kleene in the early 1930s to formalize the notion of computability (also known as constructibility and effective calculability)..

  • Why is lambda calculus important?

    Lambda calculus has played an important role in the development of the theory of programming languages.
    Functional programming languages implement lambda calculus.
    Lambda calculus is also a current research topic in category theory..

  • Functional programming languages are based on the lambda-calculus.
    The lambda-calculus grew out of an attempt by Alonzo Church and Stephen Kleene in the early 1930s to formalize the notion of computability (also known as constructibility and effective calculability).
  • Lambda calculus is a notation for describing mathematical functions and programs.
    It is a mathematical system for studying the interaction of functional abstraction and functional application.
    It captures some of the essential, common features of a wide variety of programming languages.
  • The Lambda calculus is an abstract mathematical theory of computation, involving λ functions.
    The lambda calculus can be thought of as the theoretical foundation of functional programming.
  • The λ calculus can be called the smallest universal programming language of the world.
    The λ calculus consists of a single transformation rule (variable substitution) and a single function definition scheme.
    It was introduced in the 1930s by Alonzo Church as a way of formalizing the concept of effective computability.
Oct 23, 2018My intuitive notion is that time complexity can be expressed as the number of β-reductions (we can define away α-conversion by using De Brujin  Can affine lambda calculus solve every problem in P?P and NP classes explanation through lambda-calculusUsing lambda calculus to derive time complexity?On the use of Turing machines for computational complexityMore results from cstheory.stackexchange.com
Oct 23, 2018My intuitive notion is that time complexity can be expressed as the number of β-reductions (we can define away α-conversion by using De Brujin  Can affine lambda calculus solve every problem in P?P and NP classes explanation through lambda-calculusUsing lambda calculus to derive time complexity?Can typed lambda calculi express *all* algorithms below a given More results from cstheory.stackexchange.com
Oct 23, 2018My intuitive notion is that time complexity can be expressed as the number of β-reductions (we can define away α-conversion by using De Brujin  Using lambda calculus to derive time complexity?Can affine lambda calculus solve every problem in P?P and NP classes explanation through lambda-calculusCan typed lambda calculi express *all* algorithms below a given More results from cstheory.stackexchange.com
Oct 23, 2018My intuitive notion is that time complexity can be expressed as the number of β-reductions (we can define away α-conversion by using De Brujin  Using lambda calculus to derive time complexity?Can affine lambda calculus solve every problem in P?P and NP classes explanation through lambda-calculusWhat is the contribution of lambda calculus to the field of theory of More results from cstheory.stackexchange.com

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