fp_in_scheme
... • Here’s compose for two functions in Scheme (define (compose2 f g) (lambda (x) (f (g x)))) • Note that compose calls lambda which returns a new function that applies f to the result of applying g to x • We’ll look at how the variable environments work to support this in the next topic, closures • B ...
... • Here’s compose for two functions in Scheme (define (compose2 f g) (lambda (x) (f (g x)))) • Note that compose calls lambda which returns a new function that applies f to the result of applying g to x • We’ll look at how the variable environments work to support this in the next topic, closures • B ...
worksheet - domains and ranges of relations
... Part 2 - Different Representations. Read each problem carefully and perform the indicated task. Also, for each problem, determine if the relation given. represents a function and record your answers in the appropriate spaces provided for each ...
... Part 2 - Different Representations. Read each problem carefully and perform the indicated task. Also, for each problem, determine if the relation given. represents a function and record your answers in the appropriate spaces provided for each ...
λ Calculus - Computer Science at RPI
... execution. In particular, if the arguments are evaluated right to left, execution would not be as expected. The applicative-order sequencing combinator can be written as follows: ASeq = λx.λy.(y x) where y is a lambda abstraction that wraps the original last expression to evaluate. The same example ...
... execution. In particular, if the arguments are evaluated right to left, execution would not be as expected. The applicative-order sequencing combinator can be written as follows: ASeq = λx.λy.(y x) where y is a lambda abstraction that wraps the original last expression to evaluate. The same example ...
LISP
... The execution of a function always produces the same result when given the same parameters. This is called referential transparency. ...
... The execution of a function always produces the same result when given the same parameters. This is called referential transparency. ...
Functional Programming
... that are often missing in imperative languages: – First-class function values: the ability of functions to return newly constructed functions – Higher-order functions : functions that take other functions as input parameters or return functions. – Polymorphism: the ability to write functions that op ...
... that are often missing in imperative languages: – First-class function values: the ability of functions to return newly constructed functions – Higher-order functions : functions that take other functions as input parameters or return functions. – Polymorphism: the ability to write functions that op ...
ppt - Rensselaer Polytechnic Institute: Computer Science
... Currying The lambda calculus can only represent functions of one variable. It turns out that one-variable functions are sufficient to represent multiple-variable functions, using a strategy called currying. E.g., given the mathematical function: of type ...
... Currying The lambda calculus can only represent functions of one variable. It turns out that one-variable functions are sufficient to represent multiple-variable functions, using a strategy called currying. E.g., given the mathematical function: of type ...
Functional Programming
... Functional programming languages are carefully designed to support problem solving. There are many features in these languages which help the user to design clear, concise, abstract, modular, correct and reusable solutions to problems. The functional Style of Programming allows the formulation of so ...
... Functional programming languages are carefully designed to support problem solving. There are many features in these languages which help the user to design clear, concise, abstract, modular, correct and reusable solutions to problems. The functional Style of Programming allows the formulation of so ...
Lecture Notes
... definition, but generally speaking: Functional programming is style of programming in which the basic method of computation is the application of functions to arguments; ...
... definition, but generally speaking: Functional programming is style of programming in which the basic method of computation is the application of functions to arguments; ...
Chapter 15 Functional Programming
... and bound in M. Then consistently replace the binding and corresponding bound occurrences of y in M by a new variable, say u. Repeat this renaming of bound variables in M until the condition in Step 1 applies, then proceed as in Step 1. Chapter 15: Functional Programming ...
... and bound in M. Then consistently replace the binding and corresponding bound occurrences of y in M by a new variable, say u. Repeat this renaming of bound variables in M until the condition in Step 1 applies, then proceed as in Step 1. Chapter 15: Functional Programming ...
pdf
... f = λ(x.F(f,x)) is another expression of it, and the CTT definition is: fi (λ(f λ( F(f ))) fix(λ(f. λ(x. F(f,x))) which reduces in one step to: λ(x.F(fix(λ(f. λ(x. F(f,x)))),x)) by substituting the fix term for f in λ(x.F(f,x)) . ...
... f = λ(x.F(f,x)) is another expression of it, and the CTT definition is: fi (λ(f λ( F(f ))) fix(λ(f. λ(x. F(f,x))) which reduces in one step to: λ(x.F(fix(λ(f. λ(x. F(f,x)))),x)) by substituting the fix term for f in λ(x.F(f,x)) . ...
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 ∧ ...
PPT
... C[[ while B do P ]] = the function f such that f(s) = s if E [[ B ]] s is false f(s) = f( C[[ P ]](s) ) if E [[ B ]] s is true Mathematics of denotational semantics: prove that there is such a function and that it is uniquely determined. “Beyond scope of this course.” ...
... C[[ while B do P ]] = the function f such that f(s) = s if E [[ B ]] s is false f(s) = f( C[[ P ]](s) ) if E [[ B ]] s is true Mathematics of denotational semantics: prove that there is such a function and that it is uniquely determined. “Beyond scope of this course.” ...
Lecture Slides
... definition, but generally speaking: Functional programming is style of programming in which the basic method of computation is the application of functions to arguments; ...
... definition, but generally speaking: Functional programming is style of programming in which the basic method of computation is the application of functions to arguments; ...
Higher Order Functions
... • If initializer is provided, initializer will stand as the first argument in the sum • Unfortunately in python 3 reduce() requires an import ...
... • If initializer is provided, initializer will stand as the first argument in the sum • Unfortunately in python 3 reduce() requires an import ...
Lect 1
... Functional programming languages are carefully designed to support problem solving. There are many features in these languages which help the user to design clear, concise, abstract, modular, correct and reusable solutions to problems. The functional Style of Programming allows the formulation of so ...
... Functional programming languages are carefully designed to support problem solving. There are many features in these languages which help the user to design clear, concise, abstract, modular, correct and reusable solutions to problems. The functional Style of Programming allows the formulation of so ...
Document
... Functional programming languages are carefully designed to support problem solving. There are many features in these languages which help the user to design clear, concise, abstract, modular, correct and reusable solutions to problems. The functional Style of Programming allows the formulation of so ...
... Functional programming languages are carefully designed to support problem solving. There are many features in these languages which help the user to design clear, concise, abstract, modular, correct and reusable solutions to problems. The functional Style of Programming allows the formulation of so ...
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 ...
Introduction to Racket
... (cons 1 2) is valid code but it does not produce a proper list. (list? x) tells if it is a proper list (in constant time). This is a difference between strongly typed code (such as SML) and Racket. ...
... (cons 1 2) is valid code but it does not produce a proper list. (list? x) tells if it is a proper list (in constant time). This is a difference between strongly typed code (such as SML) and Racket. ...