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curry
curry

... A tasty dish? • Currying was named after the Mathematical logician Haskell Curry (1900-1982) • Curry worked on combinatory logic … • A technique that eliminates the need for variables in mathematical logic … • and hence computer programming! – at least in theory ...
First-Class Functions What is functional programming? First
First-Class Functions What is functional programming? First

... “Functional  programming”  can  mean  a  few  different  things: 1. Avoiding  mutation  in  most/all  cases  (done  and  ongoing) 2. Using  functions  as  values  (this  unit) ...
Higher-order functions
Higher-order functions

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Propositional Calculus

... involve function application. Programs may also produce function by returning functions as values. In pure functional programming, this is it, there are no variables, side effects, nor loops. This simplifies semantics but does not reduce computational power. • We will investigate the style of progra ...
Lambda Calculus and Functional Programming
Lambda Calculus and Functional Programming

The untyped Lambda Calculus
The untyped Lambda Calculus

... Note: there is no way to define identifiers for function - the numbers used above are no symbolic identifiers but only shorthands. In reality, a lambda expression is nothing more than a long sequence of variables, abstractions and applications - one has to replace each of this identiiers with the co ...
List
List

Lambda
Lambda

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Foundations of Programming Languages Seyed H. Roosta
Foundations of Programming Languages Seyed H. Roosta

... where the id’s are identifiers (parameters or variables) and expression (called the body of the lambda function) is some expression that may involve the identifiers. ...
Chapter 2 - Lambda Calculus - Rensselaer Polytechnic Institute
Chapter 2 - Lambda Calculus - Rensselaer Polytechnic Institute

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Scheme and functional programming

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80-310/610 Formal Logic Fall 2015 Homework 3
80-310/610 Formal Logic Fall 2015 Homework 3

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CS 170 * Intro to Programming for Scientists and Engineers

... definitions. Function applications and data have the same form. e.g., If the list (A B C) is interpreted as data it is a simple list of three atoms, A, B, and C If it is interpreted as a function application, it means that the function named A is applied to the two parameters, B and C • The first LI ...
fund
fund

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Functional Programming Languages

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Fundamentals

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Advanced Formal Methods

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SOLUTION OF PROBLEM 1/PAGE 158 Problem: Show that the

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slides 4-up

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Handout 10 from Models of Computation

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Functional Programming

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Lecture10

Lecture10 - CIS @ UPenn
Lecture10 - CIS @ UPenn

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Lambda calculus

Lambda calculus (also written as λ-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. First formulated by Alonzo Church to formalize the concept of effective computability, lambda calculus found early successes in the area of computability theory, such as a negative answer to Hilbert's Entscheidungsproblem. Lambda calculus is a conceptually simple universal model of computation (Turing showed in 1937 that Turing machines equaled the lambda calculus in expressiveness). The name derives from the Greek letter lambda (λ) used to denote binding a variable in a function. The letter itself is arbitrary and has no special meaning. Lambda calculus is taught and used in computer science because of its usefulness in showcasing functional thinking and iterative reduction.Because of the importance of the notion of variable binding and substitution, there is not just one system of lambda calculus, and in particular there are typed and untyped variants. Historically, the most important system was the untyped lambda calculus, in which function application has no restrictions (so the notion of the domain of a function is not built into the system). In the Church–Turing Thesis, the untyped lambda calculus is claimed to be capable of computing all effectively calculable functions. The typed lambda calculus is a variety that restricts function application, so that functions can be applied only if they are capable of accepting the given input's ""type"" of data.Today, the lambda calculus has applications in many different areas in mathematics, philosophy, linguistics, and computer science. It is still used in the area of computability theory, although Turing machines are also an important model for computation. Lambda calculus has played an important role in the development of the theory of programming languages. Counterparts to lambda calculus in computer science are functional programming languages, which essentially implement the lambda calculus (augmented with some constants and datatypes). Beyond programming languages, the lambda calculus also has many applications in proof theory. A major example of this is the Curry–Howard correspondence, which gives a correspondence between different systems of typed lambda calculus and systems of formal logic.
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