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Breck, Hartline
Breck, Hartline

... We have developed a number of tools for describing programming languages, but so far we have only applied the toolbox to IMP. IMP has no functions, (procedures, routines, methods). It has no way to write a functional abstraction. This makes it pretty uninteresting as a programming language. So we wi ...
Handout 10 from Models of Computation
Handout 10 from Models of Computation

... Example: We rename (λx.y x x) to (λz.y z z). We say that two λ-terms are α-equivalent if one can be gained from the other by α renaming. For pure λ-terms α-equivalence can be very easily seen by comparing their abstract syntax trees. Example: Obviously (λx.y x x) and (λz.y z z) are α-equivalent. How ...
arguments (an upper and lower bound (integers) and a function
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. ) ...
Haskell: Lambda Expressions
Haskell: Lambda Expressions

... Finally, λ-calculus allows one to clearly designate in every expression the variables that can be instantiated, by using a λ operator (which gave the calculus its name, in the first place). For example, if we want to express that in f x, the x is a parameter that can be instantiated, we write λx.f x ...
PowerPoint - School of Computing Science
PowerPoint - School of Computing Science

... Do we have a Better Functional Language? We have functions, e.g. x.x+2 is a function, but can we really do functional programming? It’s essential to be able to define recursive functions, but our language has no direct support for recursive definitions. We have no way of associating a name with a ...
Functional Programming
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 ...
Lambda-calculus. - UT Computer Science
Lambda-calculus. - UT Computer Science

... Case Study [Hudak and Jones, Yale TR, 1994] ...
Functional Programming Languages
Functional Programming Languages

... These symbols are not variables – they are like the names bound by Java’s final declarations ...
CS 170 * Intro to Programming for Scientists and Engineers
CS 170 * Intro to Programming for Scientists and Engineers

... is like EQ?, except that it works for both symbolic and numeric atoms; it is a value comparison, not a pointer ...
Introduction to Lambda Calculus - CSE IITK
Introduction to Lambda Calculus - CSE IITK

... [source: http://www.cs.nott.ac.uk/~gmh/chapter1.ppt] ...
pptx
pptx

... • Skipping parsing by writing language B programs directly in terms of language A constructors • An interpreter written in A recursively evaluates What we know about macros: • Extend the syntax of a language • Use of a macro expands into language syntax before the program is run, i.e., before callin ...
Lambda calculus
Lambda calculus

PPT
PPT

Notes
Notes

15. Functional Programming
15. Functional Programming

... A mathematical function is a mapping of members of one set, 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 ...
The λ – Calculus
The λ – Calculus

... said to be bound in the sub-expression M 2. A bound variable is one whose name is the same as the parameter. Otherwise the variable is said to be free 3. Any variable not bound in M is said to be free Note: bound variables are placeholders just like function parameters in the imperative and OOP para ...
First-Class Functions What is functional programming? First
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 ...
15. Functional Programming
15. Functional Programming

... In an FPL, variables are not necessary, as is the case in mathematics ...
Advanced Formal Methods
Advanced Formal Methods

... Intended as foundation for mathematics Discovered to be inconsistent, so interest faded (see later) Foundational importance in programming languages Lisp, McCarthy 1959 Programming languages and denotational semantics • Landin, Scott, Strachey 60’s and 70’s ...
Functional Programming
Functional Programming

SLam Calculus (Bradley Herrup)
SLam Calculus (Bradley Herrup)

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Closure (computer programming)

In programming languages, closures (also lexical closures or function closures) are a technique for implementing lexically scoped name binding in languages with first-class functions. Operationally, a closure is a record storing a function together with an environment: a mapping associating each free variable of the function (variables that are used locally, but defined in an enclosing scope) with the value or storage location to which the name was bound when the closure was created. A closure—unlike a plain function—allows the function to access those captured variables through the closure's reference to them, even when the function is invoked outside their scope.Example. The following program fragment defines a higher-order function startAt with a parameter x and a nested function incrementBy. The nested function incrementBy has access to x, because incrementBy is in the lexical scope of x, even though x is not local to incrementBy. The function startAt returns a closure containing the function incrementBy, which adds the y value to the x value, and a reference to the variable x from this invocation of startAt, so incrementBy will know where to find it once invoked:function startAt(x) function incrementBy(y) return x + y return incrementByvariable closure1 = startAt(1)variable closure2 = startAt(5)Note that, as startAt returns a function, the variables closure1 and closure2 are of function type. Invoking closure1(3) will return 4, while invoking closure2(3) will return 8. While closure1 and closure2 refer to the same function incrementBy, the associated environments differ, and invoking the closures will bind the name x to two distinct variables with different values in the two invocations, thus evaluating the function to different results.
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