• Study Resource
  • Explore
    • Arts & Humanities
    • Business
    • Engineering & Technology
    • Foreign Language
    • History
    • Math
    • Science
    • Social Science

    Top subcategories

    • Advanced Math
    • Algebra
    • Basic Math
    • Calculus
    • Geometry
    • Linear Algebra
    • Pre-Algebra
    • Pre-Calculus
    • Statistics And Probability
    • Trigonometry
    • other →

    Top subcategories

    • Astronomy
    • Astrophysics
    • Biology
    • Chemistry
    • Earth Science
    • Environmental Science
    • Health Science
    • Physics
    • other →

    Top subcategories

    • Anthropology
    • Law
    • Political Science
    • Psychology
    • Sociology
    • other →

    Top subcategories

    • Accounting
    • Economics
    • Finance
    • Management
    • other →

    Top subcategories

    • Aerospace Engineering
    • Bioengineering
    • Chemical Engineering
    • Civil Engineering
    • Computer Science
    • Electrical Engineering
    • Industrial Engineering
    • Mechanical Engineering
    • Web Design
    • other →

    Top subcategories

    • Architecture
    • Communications
    • English
    • Gender Studies
    • Music
    • Performing Arts
    • Philosophy
    • Religious Studies
    • Writing
    • other →

    Top subcategories

    • Ancient History
    • European History
    • US History
    • World History
    • other →

    Top subcategories

    • Croatian
    • Czech
    • Finnish
    • Greek
    • Hindi
    • Japanese
    • Korean
    • Persian
    • Swedish
    • Turkish
    • other →
 
Profile Documents Logout
Upload
PPTX
PPTX

... – You are implementing an interpreter for the “Rube” language, which means understanding and implementing its operational semantics – AST definition (“expr”) on page 2 – Value definition (“value”) on page 5 ...
Functional Languages and Higher
Functional Languages and Higher

... • Local variables need to be stored on heap if they can escape and be accessed after the defining function returns • It happens only if – the variable is referenced from within some nested function – the nested function is returned or passed to some function that might store it in a data structure ...
funprog
funprog

... addition, various special forms such as quote and if must be handled separately. ...
Principles of Programming Languages Lecture 11: Paradigms
Principles of Programming Languages Lecture 11: Paradigms

... Syntax: I ...
Chapter 2
Chapter 2

... pure or not is to see that Given the same arguments, will this function always produce the same result. A concept that is the product of “no side effects” and “Pure Functions” is that of “Referential Transparency”. According to Daume, H (2006), there is no agreed-upon exact definition of Referential ...
Parametric Polymorphism and Abstract Models of Storage
Parametric Polymorphism and Abstract Models of Storage

... By generalising Plotkin’s logical relations theorem, we can argue that anything definable in a good typed language is parametric. All constructive mathematics is parametric. For example, natural deduction rules are parametric. So are all category-theoretic adjunctions. The rule of excluded middle an ...
Chapter 7: Functional Programming Languages
Chapter 7: Functional Programming Languages

... defined function symbol; in the functional language, it can be any expression (for instance, a lambda abstract or an application). Thus the evaluation of f is not simply a look-up in the function table. But we can just replace the look-up by a step of evaluating the expression f . This evaluation re ...
15. Functional Programming Languages.
15. Functional Programming Languages.

... A functional form that takes a list of functions as parameters and yields a list of the results of applying each of its parameter functions to a given parameter Form: [f, g] For f (x) ∫ x * x * x and g (x) ∫ x + 3, [f, g] (4) yields (64, 7) 3. Apply-to-all A functional form that takes a single funct ...
slides
slides

Chapter 14 Functional Programming Languages
Chapter 14 Functional Programming Languages

02/06
02/06

3. Functional Programming
3. Functional Programming

... represented as lists that resemble lambda expressions and are then interpreted or compiled. APL is a language for manipulating arrays and arrays of arrays. Programs are built up of functional operators applied to arrays. Later languages like Mathematica owe a great deal to APL. ...
Econ 231 / 232 Examples Using MAPLE
Econ 231 / 232 Examples Using MAPLE

Document
Document

FUNCTIONS TEST STUDY GUIDE Test covers
FUNCTIONS TEST STUDY GUIDE Test covers

Section 4 - Introduction Handout
Section 4 - Introduction Handout

Functional Programming
Functional Programming

... • cons: used to build lists – Requires two arguments: an element and a list; e.g., – (cons 8 ( )) ; gives the 1-element list (8) – (cons 6 (cons 8( ))) ; gives the list (6 8) – (cons 6 ‘(8)) ; also gives the list (6 8) – (cons 4(cons 8 9)) ; gives the dotted list ; (4 8 . 9 ) since 9 is not a ...
10~Chapter 10_Functi.. - Programming Assignment 0
10~Chapter 10_Functi.. - Programming Assignment 0

... • Church’s model of computing is called the lambda calculus – based on the notion of parameterized expressions (with each parameter introduced by an occurrence of the letter λ—hence the notation’s name. – Lambda calculus was the inspiration for functional programming – one uses it to compute by subs ...
A Typed Lambda Calculus with Categorical Type Constructors 1
A Typed Lambda Calculus with Categorical Type Constructors 1

Functional Programming Big Picture
Functional Programming Big Picture

... 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 ...
presentation - Queaso Systems nv
presentation - Queaso Systems nv

... How to return many values? • Imperative programs Return 1 value from function o And others as ‘out’ parameters (using call by reference) • OO programs using only call by value o Define a container class for each combination of types o Cumbersome… o ...
Functions
Functions

... Introduction to FP • The design of the imperative languages is based directly on the von Neumann architecture • Efficiency is the primary concern, rather than the suitability of the language for software development • The design of the functional languages is based on mathematical functions • A sol ...
Section 2.1 – The Definition of a Derivative 1 Section 2.1 The
Section 2.1 – The Definition of a Derivative 1 Section 2.1 The

A/x - LAMP | EPFL
A/x - LAMP | EPFL

...  Implementation note: If a function calls itself as its last action, the function’s stack frame can be re-used. This is called “tail recursion”.  ⇒ Tail-recursive functions are iterative processes.  More generally, if the last action of a function is a call to another (possible the same) function ...
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 ...
< 1 ... 5 6 7 8 9 10 11 12 13 ... 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.
  • studyres.com © 2025
  • DMCA
  • Privacy
  • Terms
  • Report