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Chapter 3
Chapter 3

... • In functional programming, functions are firstclass data values – Functions can be computed by other functions – Functions can be parameters to other functions ...
Functional Programming Basics
Functional Programming Basics

The Utility Frontier
The Utility Frontier

Haskell Summary Functions • A function takes 1 or more parameter
Haskell Summary Functions • A function takes 1 or more parameter

Group C
Group C

pl10ch15 - ODU Computer Science
pl10ch15 - ODU Computer Science

... • Usually not needed, because the interpreter always displays the result of a function evaluated at the top level (not nested) • Scheme has PRINTF, which is similar to the printf function of C • Note: explicit input and output are not part of the pure functional programming model, because input oper ...
Appendix B FUNCTIONAL PROGRAMMING WITH SCHEME
Appendix B FUNCTIONAL PROGRAMMING WITH SCHEME

... On the IBM 704, car stood for “contents of address register” and cdr for “contents of decrement register”. Some authors have suggested that “head” and “tail” or “first” and “rest” are more suggestive names for these functions, but most Lisp programmers still use the traditional names. The following ...
Discussion 07
Discussion 07

... Expressions that look like function calls (because they’re surrounded by parentheses!), but have special functionality in that they don’t follow normal order of evaluation define, if, and, or, not, lambda, let ...
Part 1
Part 1

... In functional programming, functions are viewed as values themselves, which can be computed by other functions and can be parameters to other functions  Functions are first-class values ...
Scheme: More function examples, higher
Scheme: More function examples, higher

Module 4
Module 4

AP Calculus - ceemrr.com
AP Calculus - ceemrr.com

Appendix B
Appendix B

... Appendix B ...
4.1 - Exponential Functions
4.1 - Exponential Functions

... research study is reflected in the bar graph to the right which can be modeled with the function f ( x)  42.2(1.56) x , where f ( x) is the average amount spent, in dollars, at a shopping mall after x hours. The above function is called an exponential function. Do you see what makes it different fr ...
review of haskell
review of haskell

... Why Are Lambda's Useful? Lambda expressions can be used to give a formal meaning to functions defined using currying. For example: add x y = x+y ...
Differentiation - DBS Applicant Gateway
Differentiation - DBS Applicant Gateway

... Data was collected on the depth of a dive of penguins and the duration of the dive. The following linear model is a fairly good summary of the data, where x is the duration of the dive in minutes and y is the depth of the dive in yards. The equation for the model is y = 2.915x + 0.015 This means tha ...
Predicate_calculus
Predicate_calculus

Y in Practical Programs Extended Abstract
Y in Practical Programs Extended Abstract

... an interesting property relating to the theory of sequential realisability [Lon99]. ...
Functional Programming
Functional Programming

... • We can formally model the process of evaluating an expression as the application of one or more reduction rules. • E.g., lambda-calculus includes the beta-reduction rule to evaluate the application of a lambda abstraction to an argument expression. – A copy of the body of the lambda abstraction is ...
Assessing Conceptual Understanding
Assessing Conceptual Understanding

Introduction
Introduction

...  Course organization  History of Lisp  Lisp syntax  Examples  Lisp IDE ...
4.2 Extreme Values Mon Dec 10
4.2 Extreme Values Mon Dec 10

... • Extreme values refer to the minimum or maximum value of a function • There are two types of extreme values: – Absolute extrema: the min or max value of the entire function or interval – Local extrema: the min or max value of a piece of a function ...
lesson 5 notebook.notebook
lesson 5 notebook.notebook

... An algebraic expression is just a mathematical sentence made up of….. ...
Lecture 3
Lecture 3

+ + 1
+ + 1

< 1 ... 6 7 8 9 10 11 12 13 14 ... 18 >

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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