functional form
... • Includes exception handling and a module facility for implementing abstract data types • Includes lists and list operations ...
... • Includes exception handling and a module facility for implementing abstract data types • Includes lists and list operations ...
Powerpoint ()
... • Like a mixin in Ruby • Think Java interfaces, but they can have methods defined on them ...
... • Like a mixin in Ruby • Think Java interfaces, but they can have methods defined on them ...
fund
... Can we implement list-update as assignment to cell? May not improve efficiency if there are multiple pointers to list, but should help if there is only one. ...
... Can we implement list-update as assignment to cell? May not improve efficiency if there are multiple pointers to list, but should help if there is only one. ...
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 ...
Handout 10 from Models of Computation
... with Lisp, has it led to some truly remarkable languages such as ML and Haskell. OCaml, a dialect of ML, that incorporates object oriented features, performs on many standard benchmarks better than C++. ...
... with Lisp, has it led to some truly remarkable languages such as ML and Haskell. OCaml, a dialect of ML, that incorporates object oriented features, performs on many standard benchmarks better than C++. ...
Propositional Calculus
... • Programs are functions and their semantics involve function application. Programs may also produce function by returning functions as values. In pure functional programming, this is it, there are no variables, side effects, nor loops. This simplifies semantics but does not reduce computational pow ...
... • Programs are functions and their semantics involve function application. Programs may also produce function by returning functions as values. In pure functional programming, this is it, there are no variables, side effects, nor loops. This simplifies semantics but does not reduce computational pow ...
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 ...
curry
... Functions in Haskell •All functions in Haskell are curried, i.e., all Haskell functions take just single arguments. •This is mostly hidden in notation, and is not apparent to a new Haskeller •Let's take the function div :: Int -> Int -> Int which performs integer division •The expression div 10 2 e ...
... Functions in Haskell •All functions in Haskell are curried, i.e., all Haskell functions take just single arguments. •This is mostly hidden in notation, and is not apparent to a new Haskeller •Let's take the function div :: Int -> Int -> Int which performs integer division •The expression div 10 2 e ...
Lecture10 - CIS @ UPenn
... Functional programming • Functions taking other functions as an argument are ...
... Functional programming • Functions taking other functions as an argument are ...
Advanced Formal Methods
... Exercise 4: Define ”Church lists”. A list [x,y,z] can be thought of as a function taking two arguments c (for cons) and n (for nil), and returns c x (c y (c z n)), similar to the Church numerals. Write a function nil representing the empty list, and a function cons that takes arguments h and (a func ...
... Exercise 4: Define ”Church lists”. A list [x,y,z] can be thought of as a function taking two arguments c (for cons) and n (for nil), and returns c x (c y (c z n)), similar to the Church numerals. Write a function nil representing the empty list, and a function cons that takes arguments h and (a func ...
Foundations of Programming Languages Seyed H. Roosta
... The functional form condition, denoted IF, takes three functions as arguments and, depending on the evaluation result of the first function as True or False, returns the second or third function, respectively. This function has the syntax (IF function1 function2 function3):x if function1:xT then ...
... The functional form condition, denoted IF, takes three functions as arguments and, depending on the evaluation result of the first function as True or False, returns the second or third function, respectively. This function has the syntax (IF function1 function2 function3):x if function1:xT then ...
Declarative Programming
... case in mathematics • In a FPL, the evaluation of a function always produces the same result given the same parameters This is called referential transparency ...
... case in mathematics • In a FPL, the evaluation of a function always produces the same result given the same parameters This is called referential transparency ...
Lambda Calculus
... 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 variable) e.g., (λ ...
... 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 variable) e.g., (λ ...
LambdaCalculus
... 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 (higher-order) function with the ...
... 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 (higher-order) function with the ...
Lambda calculus
... • Although the lambda-calculus is powerful enough to express any program, this doesn't mean that you'd actually want to do so. After all, the Turing Machine offers an equally powerful computational basis. Which lead us to Functional Programming… • Functional programming has its roots in lambda calcu ...
... • Although the lambda-calculus is powerful enough to express any program, this doesn't mean that you'd actually want to do so. After all, the Turing Machine offers an equally powerful computational basis. Which lead us to Functional Programming… • Functional programming has its roots in lambda calcu ...
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 ...
Higher-order functions
... evaluation. Some modern functional languages have lazy evaluation, most notably Clean and Haskell. This provides for concise programs, extreme modularization, and very powerful and general functions, especially when working with lazy data structures. For instance, one may define an infinite list of ...
... evaluation. Some modern functional languages have lazy evaluation, most notably Clean and Haskell. This provides for concise programs, extreme modularization, and very powerful and general functions, especially when working with lazy data structures. For instance, one may define an infinite list of ...
Scheme and functional programming
... (func reduced-x)))) Factorial is the classic example: (define (factorial n) (if (= n 0) 1 (* n (factorial (- n 1))))) ...
... (func reduced-x)))) Factorial is the classic example: (define (factorial n) (if (= n 0) 1 (* n (factorial (- n 1))))) ...
Lambda Calculus and Lisp
... think of. It has a simple syntax using prefix notation and parentheses. • Scheme is a dialect of Lisp. It has static scope rather than dynamic, uses meaningful identifiers, true and false are #T and #F, predicates end in ? ( so (atom? (x) ) returns #F because x is not an atom (it is a list). Also us ...
... think of. It has a simple syntax using prefix notation and parentheses. • Scheme is a dialect of Lisp. It has static scope rather than dynamic, uses meaningful identifiers, true and false are #T and #F, predicates end in ? ( so (atom? (x) ) returns #F because x is not an atom (it is a list). Also us ...
CITS 3242 Programming Paradigms
... This function does not use extra memory for longer lists even though it calls itself once for each element in the list. ...
... This function does not use extra memory for longer lists even though it calls itself once for each element in the list. ...
Functional Programming
... (defun times (x y) (* x y)) (times 3 FACT) the formal x will be bound to atom 3 and the formal y will be bound to the value of actual FACT ...
... (defun times (x y) (* x y)) (times 3 FACT) the formal x will be bound to atom 3 and the formal y will be bound to the value of actual FACT ...