Functional Languages
... Lambda expressions describe nameless functions Lambda expressions are applied to parameter(s) by placing the parameter(s) after the expression e.g. ((x) x * x * x)(3) which evaluates to 27 Dr. Muhammed Al-Mulhem ...
... Lambda expressions describe nameless functions Lambda expressions are applied to parameter(s) by placing the parameter(s) after the expression e.g. ((x) x * x * x)(3) which evaluates to 27 Dr. Muhammed Al-Mulhem ...
Chapter 5 THE LAMBDA CALCULUS
... The notation E[v→E 1] refers to the lambda expression obtained by replacing each free occurrence of the variable v in E by the lambda expression E1. Such a substitution is called valid or safe if no free variable in E1 becomes bound as a result of the substitution E[v→E1]. An invalid substitution in ...
... The notation E[v→E 1] refers to the lambda expression obtained by replacing each free occurrence of the variable v in E by the lambda expression E1. Such a substitution is called valid or safe if no free variable in E1 becomes bound as a result of the substitution E[v→E1]. An invalid substitution in ...
ppt - Rensselaer Polytechnic Institute: Computer Science
... Furthermore, if there is a way for an expression evaluation to terminate, using normal order will cause termination. C. Varela ...
... Furthermore, if there is a way for an expression evaluation to terminate, using normal order will cause termination. C. Varela ...
Lambda Calculus Background, λ calculus Models of computation
... • Sometimes there are several redexes in a λ-expression => possible to choose different reduction orders • Normal order = reduce leftmost-outermost redex first = substitute the argumentet literally into the body of the function = call-by-name ≈ lazy evaluation • Applicative order = Leftmost-innermos ...
... • Sometimes there are several redexes in a λ-expression => possible to choose different reduction orders • Normal order = reduce leftmost-outermost redex first = substitute the argumentet literally into the body of the function = call-by-name ≈ lazy evaluation • Applicative order = Leftmost-innermos ...
ppt - Computer Science at RPI
... Furthermore, if there is a way for an expression evaluation to terminate, using normal order will cause termination. C. Varela ...
... Furthermore, if there is a way for an expression evaluation to terminate, using normal order will cause termination. C. Varela ...
Introduction, Scheme basics (expressions, values)
... Evaluation of Expressions The value of a numeral: number The value of a built-in operator: machine instructions to execute The value of any name: the associated value in the environment To Evaluate a combination: (as opposed to special form) a. Evaluate all of the sub-expressions in some order b. A ...
... Evaluation of Expressions The value of a numeral: number The value of a built-in operator: machine instructions to execute The value of any name: the associated value in the environment To Evaluate a combination: (as opposed to special form) a. Evaluate all of the sub-expressions in some order b. A ...
Chapter 14a - McGraw Hill Higher Education
... A function is total if it is defined for all values of its domain. Otherwise, it is partial. E.g., Square is total. A lambda expression is a particular way to define a function: LambdaExpression variable | ( M N) | ( variable . M ) M LambdaExpression N LambdaExpression E.g., ( x . x2 ) rep ...
... A function is total if it is defined for all values of its domain. Otherwise, it is partial. E.g., Square is total. A lambda expression is a particular way to define a function: LambdaExpression variable | ( M N) | ( variable . M ) M LambdaExpression N LambdaExpression E.g., ( x . x2 ) rep ...
Computer Science 203 Programming Languages Bindings
... Call-by-Value Evaluation • Don’t reduce under lambda. • Do evaluate the argument to a function call. • Most languages are primarily call-by-value. • But CBV is not normalizing – (λx. I) (D D) ...
... Call-by-Value Evaluation • Don’t reduce under lambda. • Do evaluate the argument to a function call. • Most languages are primarily call-by-value. • But CBV is not normalizing – (λx. I) (D D) ...
+ + 1
... When this function is applied to another λ-term N, as in the λ-term (λx.M) N , evaluation proceeds by replacing x with N in the body M. For example, ...
... When this function is applied to another λ-term N, as in the λ-term (λx.M) N , evaluation proceeds by replacing x with N in the body M. For example, ...
Chapter_4
... The symbol is the Greek letter lambda, and is typed at the keyboard as a backslash \. In mathematics, nameless functions are usually denoted using the symbol, as in x x+x. In Haskell, the use of the symbol for nameless functions comes from the lambda calculus, the theory of functions o ...
... The symbol is the Greek letter lambda, and is typed at the keyboard as a backslash \. In mathematics, nameless functions are usually denoted using the symbol, as in x x+x. In Haskell, the use of the symbol for nameless functions comes from the lambda calculus, the theory of functions o ...
Lecture 21 - FSU Computer Science
... • Pure functional programming languages only allow pure functions in a program. • A pure function can be counted on to return the same output each time we invoke it with the same input parameter values. • Can be emulated in traditional languages: expressions behave like pure functions; many routines ...
... • Pure functional programming languages only allow pure functions in a program. • A pure function can be counted on to return the same output each time we invoke it with the same input parameter values. • Can be emulated in traditional languages: expressions behave like pure functions; many routines ...
Scheme and functional programming
... (cons (car dfa) (if (null? input) (if (infinal? dfa) '(accept) '(reject)) (simulate (move dfa (car input)) (cdr input)))))) ...
... (cons (car dfa) (if (null? input) (if (infinal? dfa) '(accept) '(reject)) (simulate (move dfa (car input)) (cdr input)))))) ...
Slides - Chapter 10
... constructive proofs, but at a more abstract level: – the logic programmer writes a set of axioms that allow the computer to discover a constructive proof for each particular set of inputs Copyright © 2005 Elsevier ...
... constructive proofs, but at a more abstract level: – the logic programmer writes a set of axioms that allow the computer to discover a constructive proof for each particular set of inputs Copyright © 2005 Elsevier ...
Functional PLs
... 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 (x) x * x * x for the nameless function f(x) = x * x * x ...
... 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 (x) x * x * x for the nameless function f(x) = x * x * x ...
Defining Functions
... using the a symbol, as in x a x + x. z In Haskell, the use of the l symbol for nameless functions comes from the lambda calculus, the theory of functions on which Haskell is based. ...
... using the a symbol, as in x a x + x. z In Haskell, the use of the l symbol for nameless functions comes from the lambda calculus, the theory of functions on which Haskell is based. ...
Programming Least Squares Final
... concise code. A result of this, however, is that the code is literally “dense” with meaning, and it can be hard to read if you are not accustomed to functional programming. In our first example, “filter(is_even, q)” was fairly easy to understand (fortunately, we chose a descriptive function name), w ...
... concise code. A result of this, however, is that the code is literally “dense” with meaning, and it can be hard to read if you are not accustomed to functional programming. In our first example, “filter(is_even, q)” was fairly easy to understand (fortunately, we chose a descriptive function name), w ...
functional form
... named EVAL, always evaluates parameters to function applications before applying the function. QUOTE is used to avoid parameter evaluation when it is not appropriate QUOTE can be abbreviated with the apostrophe prefix operator ...
... named EVAL, always evaluates parameters to function applications before applying the function. QUOTE is used to avoid parameter evaluation when it is not appropriate QUOTE can be abbreviated with the apostrophe prefix operator ...
Lambda-calculus. - UT Computer Science
... Lambda Calculus Formal system with three parts • Notation for function expressions • Proof system for equations • Calculation rules called reduction ...
... Lambda Calculus Formal system with three parts • Notation for function expressions • Proof system for equations • Calculation rules called reduction ...
doc
... of the lambda calculus and Church’s goals is given including an explanation of how the letter ‘’ was chosen to denote function abstraction. The latter part of the introductory section is dedicated to giving a preliminary introduction into the lambda calculus for those not familiar with it. This cov ...
... of the lambda calculus and Church’s goals is given including an explanation of how the letter ‘’ was chosen to denote function abstraction. The latter part of the introductory section is dedicated to giving a preliminary introduction into the lambda calculus for those not familiar with it. This cov ...
A Tutorial Introduction to the Lambda Calculus
... are substituted by y in the expression to the right. The names of the arguments in function definitions do not carry any meaning by themselves. They are just “place holders”, that is, they are used to indicate how to rearrange the arguments of the function when it is evaluated. Therefore ...
... are substituted by y in the expression to the right. The names of the arguments in function definitions do not carry any meaning by themselves. They are just “place holders”, that is, they are used to indicate how to rearrange the arguments of the function when it is evaluated. Therefore ...