ppt - Computer Science at RPI
... Given the mathematical functions: f(x) = x2 , g(x) = x+1 f g is the composition of f and g: f g (x) = f(g(x)) f g (x) = f(g(x)) = f(x+1) = (x+1)2 = x2 + 2x + 1 g f (x) = g(f(x)) = g(x2) = x2 + 1 Function composition is therefore not commutative. Function composition can be regarded as a (highe ...
... Given the mathematical functions: f(x) = x2 , g(x) = x+1 f g is the composition of f and g: f g (x) = f(g(x)) f g (x) = f(g(x)) = f(x+1) = (x+1)2 = x2 + 2x + 1 g f (x) = g(f(x)) = g(x2) = x2 + 1 Function composition is therefore not commutative. Function composition can be regarded as a (highe ...
Elements of Functional Programming
... Functional programming languages are characterized by allowing functions as first class citizens. This means that functions are manipulated like any other values in the language, so in particular they can be passed as arguments to functions, can be returned by functions, and so on. The syntax of func ...
... Functional programming languages are characterized by allowing functions as first class citizens. This means that functions are manipulated like any other values in the language, so in particular they can be passed as arguments to functions, can be returned by functions, and so on. The syntax of func ...
Functional Pearls - Probabilistic Functional Programming in Haskell
... At the heart of functional programming rests the principle of referential transparency, which in particular means that a function f applied to a value x always yields one and the same value y = f (x). This principle seems to be violated when contemplating the use of functions to describe probabilist ...
... At the heart of functional programming rests the principle of referential transparency, which in particular means that a function f applied to a value x always yields one and the same value y = f (x). This principle seems to be violated when contemplating the use of functions to describe probabilist ...
What is a Program?
... to Share — to copy, distribute and transmit the work to Remix — to adapt the work Under the following conditions: Attribution. You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work). Share Alike. ...
... to Share — to copy, distribute and transmit the work to Remix — to adapt the work Under the following conditions: Attribution. You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work). Share Alike. ...
ppt
... variables when beta-reducing a lambda calculus expression. In the following, we rename x to z, (or any other fresh variable): (x.(y x) x) ...
... variables when beta-reducing a lambda calculus expression. In the following, we rename x to z, (or any other fresh variable): (x.(y x) x) ...
Beginning with the Haskell Programming Language About the Tutorial
... Unfortunately, in an introductory tutorial, many of Haskell's most powerful--but complex--features cannot be covered. In particular, the whole area of type classes and algebraic types (including abstract data types) is a bit too much for a first introduction. For readers whose interest is piqued, it ...
... Unfortunately, in an introductory tutorial, many of Haskell's most powerful--but complex--features cannot be covered. In particular, the whole area of type classes and algebraic types (including abstract data types) is a bit too much for a first introduction. For readers whose interest is piqued, it ...
Lecture 3
... • The closer you can get to mathematics the more elegant your programs become • In addition to the def statement, Python provides an expression which in-lines a function – similar to LISP • Instead of assigning a name to a function, lambda just returns the function itself – anonymous functions ...
... • The closer you can get to mathematics the more elegant your programs become • In addition to the def statement, Python provides an expression which in-lines a function – similar to LISP • Instead of assigning a name to a function, lambda just returns the function itself – anonymous functions ...
CA320 - Computability & Complexity
... that evaluates to the same values given the same arguments, it will have no effect on the rest of the program. This is called referential transparency. ...
... that evaluates to the same values given the same arguments, it will have no effect on the rest of the program. This is called referential transparency. ...
val
... • A functional form that takes two functions as parameters and yields a function whose value is the first actual parameter function applied to the application of the second Form: h f ° g which means h (x) f ( g ( x)) For f (x) x + 2 and g (x) 3 * x, h f ° g yields (3 * x)+ 2 ...
... • A functional form that takes two functions as parameters and yields a function whose value is the first actual parameter function applied to the application of the second Form: h f ° g which means h (x) f ( g ( x)) For f (x) x + 2 and g (x) 3 * x, h f ° g yields (3 * x)+ 2 ...
Lisp - University of Connecticut
... as parameters and yields a function whose value is the first actual parameter function applied to the application of the second Form: h f ° g which means h (x) f ( g ( x)) For f (x) x + 2 and g (x) 3 * x, h f ° g yields (3 * x)+ 2 ...
... as parameters and yields a function whose value is the first actual parameter function applied to the application of the second Form: h f ° g which means h (x) f ( g ( x)) For f (x) x + 2 and g (x) 3 * x, h f ° g yields (3 * x)+ 2 ...
This article discusses the programming language LISP. The
... n, f (x1 ; x2 ; : : : ; xn ). Here, x1; : : : ; xn are called the formal arguments and when we actually wish to evaluate the function f we provide the `actual arguments' (like 3 and 4 for + above) and evaluate the function to get the resulting answer. These kind of functions are part of most program ...
... n, f (x1 ; x2 ; : : : ; xn ). Here, x1; : : : ; xn are called the formal arguments and when we actually wish to evaluate the function f we provide the `actual arguments' (like 3 and 4 for + above) and evaluate the function to get the resulting answer. These kind of functions are part of most program ...
Chapter 7: Functional Programming Languages
... But since f is the variable bound by the first lambda, we also have f : a and hence, a = d -> e Thus the result of applying f must have type e. But it must also have type c, because f (f x) : c. What is more, it must also have type d, because f can be applied to its own result. Hence c = e = d The ...
... But since f is the variable bound by the first lambda, we also have f : a and hence, a = d -> e Thus the result of applying f must have type e. But it must also have type c, because f (f x) : c. What is more, it must also have type d, because f can be applied to its own result. Hence c = e = d The ...
Theorems for free! - Computing Science
... extent by Sheeran [She89]. So there is reason to believe that further research will further extend the applicability of this method. Many functional languages, including Standard ML [Mil84, Mil87], Miranda1 [Tur85], and Haskell [HW88], are based on the Hindley/Milner type system [Hin69, Mil78, DM82] ...
... extent by Sheeran [She89]. So there is reason to believe that further research will further extend the applicability of this method. Many functional languages, including Standard ML [Mil84, Mil87], Miranda1 [Tur85], and Haskell [HW88], are based on the Hindley/Milner type system [Hin69, Mil78, DM82] ...
CMSC330 Summer 2010—Midterm #2
... binding in the runtime call stack. Lexical scoping binds non-local variables to the nearest binding in the source code. ...
... binding in the runtime call stack. Lexical scoping binds non-local variables to the nearest binding in the source code. ...
presentation - Queaso Systems nv
... Strongly typed programs can’t go wrong • Type inference tries to find the most general type of function o Depending on the functions that are being used ...
... Strongly typed programs can’t go wrong • Type inference tries to find the most general type of function o Depending on the functions that are being used ...
pl10ch15 - ODU Computer Science
... mathematical functions to the greatest extent possible • The basic process of computation is fundamentally different in a FPL than in an imperative language – In an imperative language, operations are done and the results are stored in variables for later use – Management of variables is a constant ...
... mathematical functions to the greatest extent possible • The basic process of computation is fundamentally different in a FPL than in an imperative language – In an imperative language, operations are done and the results are stored in variables for later use – Management of variables is a constant ...
Concepts of Programming Languages A Brief Intro to Programming
... Monad and contextual information • The behaviour of functions in a pure functional language does not depend on a global state ...
... Monad and contextual information • The behaviour of functions in a pure functional language does not depend on a global state ...
19th Century Logic and 21st Century Computing
... the more motivated reader to puzzle out. But, remarkably, from modus ponens and the second and third axioms one can derive every truth about implication, including the first axiom. In addition to A implies B, written A → B, logicians considered other logical connectives, such as A and B written A ∧ ...
... the more motivated reader to puzzle out. But, remarkably, from modus ponens and the second and third axioms one can derive every truth about implication, including the first axiom. In addition to A implies B, written A → B, logicians considered other logical connectives, such as A and B written A ∧ ...
Document
... - List form: parenthesized collections of sublists and/or atoms e.g., (A B (C D) E) - Originally, LISP was a typeless language - LISP lists are stored internally as single-linked lists - Lambda notation is used to specify functions and function definitions, function applications, and data all have t ...
... - List form: parenthesized collections of sublists and/or atoms e.g., (A B (C D) E) - Originally, LISP was a typeless language - LISP lists are stored internally as single-linked lists - Lambda notation is used to specify functions and function definitions, function applications, and data all have t ...
Slides - Chapter 10
... the letter λ—hence the notation’s name. – Lambda calculus was the inspiration for functional programming – one uses it to compute by substituting parameters into expressions, just as one computes in a high level functional program by passing arguments to functions Copyright © 2005 Elsevier ...
... the letter λ—hence the notation’s name. – Lambda calculus was the inspiration for functional programming – one uses it to compute by substituting parameters into expressions, just as one computes in a high level functional program by passing arguments to functions Copyright © 2005 Elsevier ...
Functional Programming Big Picture
... A lambda expression provides a method for defining nameless functions ?(x) x * x * x ? Nameless functions are useful, e.g., functions that are produced for intermediate application to a parameter list do not need a name, for it is applied only at the point of its construction ...
... A lambda expression provides a method for defining nameless functions ?(x) x * x * x ? Nameless functions are useful, e.g., functions that are produced for intermediate application to a parameter list do not need a name, for it is applied only at the point of its construction ...
Functional Programming
... can discard the current activation record, push record for new recursive call thus, no limit on recursion depth (each recursive call reuses the same memory) Scheme interpreters are required to perform this tail-recursion optimization ...
... can discard the current activation record, push record for new recursive call thus, no limit on recursion depth (each recursive call reuses the same memory) Scheme interpreters are required to perform this tail-recursion optimization ...
CSC 533: Programming Languages Spring 2017
... note: an if-expression is a special form § is not considered a functional expression, doesn’t follow standard evaluation rules test expression is evaluated • if value is anything but #f, first expression is evaluated & returned • if value is #f, second expression is ...
... note: an if-expression is a special form § is not considered a functional expression, doesn’t follow standard evaluation rules test expression is evaluated • if value is anything but #f, first expression is evaluated & returned • if value is #f, second expression is ...