Functional Programming

... thing and the thing itself (e.g., call-by-value and call-by-reference are the same). • The order in which expressions are evaluated is not important; neither is the place of their occurrence in the source code. • The program will yield the same output on the same input in any evaluation order: deter ...

... thing and the thing itself (e.g., call-by-value and call-by-reference are the same). • The order in which expressions are evaluated is not important; neither is the place of their occurrence in the source code. • The program will yield the same output on the same input in any evaluation order: deter ...

curry

... two arguments of types a and b and returns a value of type c like this: – g :: (a, b) -> c • We can let f be the curried form of g by – f = curry g • The function f now has the signature – f :: a -> b -> c • f takes an arg of type a & returns a function that takes an arg of type b & returns a value ...

... two arguments of types a and b and returns a value of type c like this: – g :: (a, b) -> c • We can let f be the curried form of g by – f = curry g • The function f now has the signature – f :: a -> b -> c • f takes an arg of type a & returns a function that takes an arg of type b & returns a value ...

arguments (an upper and lower bound (integers) and a function

... Calculate the integrals of f(x)= sin(x) from 0 to pi, Calculate the integrals of f(x)= sin(x)* sin(x) from 0 to pi. (Note you may have to Google to find out how sin and pi work in Python. ) ...

... Calculate the integrals of f(x)= sin(x) from 0 to pi, Calculate the integrals of f(x)= sin(x)* sin(x) from 0 to pi. (Note you may have to Google to find out how sin and pi work in Python. ) ...

Haskell: Lambda Expressions

... Currying has been briefly discussed in the context of the Haskell functions curry and uncurry. The basic idea is that function application is only expressed in terms of applying a single function to a single argument. For example, the expression f x y is a function application of f to two arguments ...

... Currying has been briefly discussed in the context of the Haskell functions curry and uncurry. The basic idea is that function application is only expressed in terms of applying a single function to a single argument. For example, the expression f x y is a function application of f to two arguments ...

Breck, Hartline

... We would like to believe that the expression (λ x e0 ) e1 is ‘equal’ in some sense to the body of e0 where we have replaced x with e1 —we want to ’call’ or ’invoke’ the function e0 with e1 as its argument. The substitution is not as simple as it seems: not all xs should be replaced with e1 , just th ...

... We would like to believe that the expression (λ x e0 ) e1 is ‘equal’ in some sense to the body of e0 where we have replaced x with e1 —we want to ’call’ or ’invoke’ the function e0 with e1 as its argument. The substitution is not as simple as it seems: not all xs should be replaced with e1 , just th ...

First-Class Functions What is functional programming? First

... Our examples of first-class functions so far all: – Take one function as an argument to another function – Process a number or a list But first-class functions are useful anywhere for any kind of data ...

... Our examples of first-class functions so far all: – Take one function as an argument to another function – Process a number or a list But first-class functions are useful anywhere for any kind of data ...

CITS 3242 Programming Paradigms

... The F# libraries are specifically designed for functional programming. ◦ They avoid modifying data structures, and instead produce new ones that use sharing. ...

... The F# libraries are specifically designed for functional programming. ◦ They avoid modifying data structures, and instead produce new ones that use sharing. ...

Jun 2004 - University of Malta

... Define a function fromTo, which takes two integers and returns the list of integers starting from the first number and finishing with the second. For example, fromTo 2 5 would return [2,3,4,5]. Define a function dots which takes an integer parameter n and returns a string consisting of n dots. For e ...

... Define a function fromTo, which takes two integers and returns the list of integers starting from the first number and finishing with the second. For example, fromTo 2 5 would return [2,3,4,5]. Define a function dots which takes an integer parameter n and returns a string consisting of n dots. For e ...

15. Functional Programming

... called the domain set, to another set, called the range set A lambda expression specifies the parameter(s) and the mapping of a function in the following form λ(x) x * x * x for the function cube (x) = x * x * x ...

... called the domain set, to another set, called the range set A lambda expression specifies the parameter(s) and the mapping of a function in the following form λ(x) x * x * x for the function cube (x) = x * x * x ...

Lecture 10

... use LINQ • Scala, being taught in 591 uses it a lot! • It offers way more flexibility • Do not dismiss it the way I once did ...

... use LINQ • Scala, being taught in 591 uses it a lot! • It offers way more flexibility • Do not dismiss it the way I once did ...

Lecture 15: The Lambda Calculus

... • Homework: Assignment 10 in the workbook • Thu 3 Dec: tutorial on Assignment 10, general revision • Fri 4 Dec: Class Test 2, 10am, Assembly Hall ...

... • Homework: Assignment 10 in the workbook • Thu 3 Dec: tutorial on Assignment 10, general revision • Fri 4 Dec: Class Test 2, 10am, Assembly Hall ...

Introduction to Lambda Calculus - CSE IITK

... add x y = x + y inc = add 1 map f [] = [] map f (x:xs) = f x : map f xs • map is a higher order function. It takes a function as argument. • Functional programming treats functions as firstclass citizens. There is no discrimination between function and data. map inc [1, 2, 3] => ...

... add x y = x + y inc = add 1 map f [] = [] map f (x:xs) = f x : map f xs • map is a higher order function. It takes a function as argument. • Functional programming treats functions as firstclass citizens. There is no discrimination between function and data. map inc [1, 2, 3] => ...

Advanced Formal Methods

... Foundational importance in programming languages Lisp, McCarthy 1959 Programming languages and denotational semantics • Landin, Scott, Strachey 60’s and 70’s ...

... Foundational importance in programming languages Lisp, McCarthy 1959 Programming languages and denotational semantics • Landin, Scott, Strachey 60’s and 70’s ...

LN10

... Function type 18.1 The function type a->b (“Haskell is strongly typed” – PDG’s notes, p.7) Objects of type a->b are constructed by lambda abstraction \x->e and used in function application f e’. Lambda abstraction: if e has type b and x is a variable of type a then \x->e has type a->b Function appl ...

... Function type 18.1 The function type a->b (“Haskell is strongly typed” – PDG’s notes, p.7) Objects of type a->b are constructed by lambda abstraction \x->e and used in function application f e’. Lambda abstraction: if e has type b and x is a variable of type a then \x->e has type a->b Function appl ...

Functional Programming

... In informal mathematics, when talking about a function, one normally gives it a name, e.g., “define f(x) = E[x] … then … f …” Similarly, most programming languages will only let you define functions if you are prepared to give them a name. This approach is rather inconsistent, as we are not treating ...

... In informal mathematics, when talking about a function, one normally gives it a name, e.g., “define f(x) = E[x] … then … f …” Similarly, most programming languages will only let you define functions if you are prepared to give them a name. This approach is rather inconsistent, as we are not treating ...

... called the domain set, to another set, called the range set A lambda expression specifies the parameter(s) and the mapping of a function in the following form λ(x) x * x * x for the function cube (x) = x * x * x ...

notes

... The λ-calculus gives a convenient notation for describing functions built from these objects. We can incorporate them in the language by assuming there is a constant for each primitive value and each distinguished operation, and extending the definition of term accordingly. This allows us to write ...

... The λ-calculus gives a convenient notation for describing functions built from these objects. We can incorporate them in the language by assuming there is a constant for each primitive value and each distinguished operation, and extending the definition of term accordingly. This allows us to write ...

LambdaCalculus

... -renaming Alpha renaming is used to prevent capturing free occurrences of variables when reducing a lambda calculus expression, e.g., (x.y.(x y) (y w)) y.((y w) y) ...

... -renaming Alpha renaming is used to prevent capturing free occurrences of variables when reducing a lambda calculus expression, e.g., (x.y.(x y) (y w)) y.((y w) y) ...

Lambda Calculus

... α-renaming Alpha renaming is used to prevent capturing free occurrences of variables when reducing a lambda calculus expression, e.g., (λx.λy.(x y) (y w)) ⇒λy.((y w) y) This reduction erroneously captures the free occurrence of y. A correct reduction first renames y to z, (or any other fresh variab ...

... α-renaming Alpha renaming is used to prevent capturing free occurrences of variables when reducing a lambda calculus expression, e.g., (λx.λy.(x y) (y w)) ⇒λy.((y w) y) This reduction erroneously captures the free occurrence of y. A correct reduction first renames y to z, (or any other fresh variab ...

Handout 10 from Models of Computation

... So far we were concerned with models of computation based on machine models. In particular, we used the Turing machine model to define the boundary between computability and non-computability, feasibility and intractability. Machine models are often rather contrived and when using them one often has ...

... So far we were concerned with models of computation based on machine models. In particular, we used the Turing machine model to define the boundary between computability and non-computability, feasibility and intractability. Machine models are often rather contrived and when using them one often has ...