CSP 506 Comparative Programming Languages
... • Lambda notation is used to specify functions and function definitions. Function applications and data have the same form. e.g., If the list (A B C) is interpreted as data it is a simple list of three atoms, A, B, and C If it is interpreted as a function application, it means that the function name ...
... • Lambda notation is used to specify functions and function definitions. Function applications and data have the same form. e.g., If the list (A B C) is interpreted as data it is a simple list of three atoms, A, B, and C If it is interpreted as a function application, it means that the function name ...
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 ...
Lect 1
... Programs are easy to understand because functional programs have nice mathematical properties (unlike imperative programs) . Functional programs are referentially transparent , that is, if a variable is set to be a certain value in a program; this value cannot be changed again. That is, there is no ...
... Programs are easy to understand because functional programs have nice mathematical properties (unlike imperative programs) . Functional programs are referentially transparent , that is, if a variable is set to be a certain value in a program; this value cannot be changed again. That is, there is no ...
Document
... Programs are easy to understand because functional programs have nice mathematical properties (unlike imperative programs) . Functional programs are referentially transparent , that is, if a variable is set to be a certain value in a program; this value cannot be changed again. That is, there is no ...
... Programs are easy to understand because functional programs have nice mathematical properties (unlike imperative programs) . Functional programs are referentially transparent , that is, if a variable is set to be a certain value in a program; this value cannot be changed again. That is, there is no ...
Functional Programming
... ; i runs from 1 updated by 1 ; f from 1, multiplied by i ; until i > n, return f ...
... ; i runs from 1 updated by 1 ; f from 1, multiplied by i ; until i > n, return f ...
Chapter 2 - Lambda Calculus - Rensselaer Polytechnic Institute
... 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 followi ...
... 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 followi ...
Lambda Calculus and Functional Programming
... the fact that functional programming avoids side effects, which are used in imperative programming to implement state and I/O. Pure functional programming disallows side effects completely. Disallowing side effects provides for referential transparency, which makes it easier to verify, optimize, and ...
... the fact that functional programming avoids side effects, which are used in imperative programming to implement state and I/O. Pure functional programming disallows side effects completely. Disallowing side effects provides for referential transparency, which makes it easier to verify, optimize, and ...
curry
... Note on lambda syntax • (lambda X (foo X)) is a way to define a lambda expression that takes any number of arguments • In this case X is bound to the list of the argument values, e.g.: > (define f (lambda x (print x))) ...
... Note on lambda syntax • (lambda X (foo X)) is a way to define a lambda expression that takes any number of arguments • In this case X is bound to the list of the argument values, e.g.: > (define f (lambda x (print x))) ...
Declarative Programming
... parameters and yields a function whose result is a function whose value is the first actual parameter function applied to the result of the application of the second Form: hf ° g which means h (x) f ( g ( x)) ...
... parameters and yields a function whose result is a function whose value is the first actual parameter function applied to the result of the application of the second Form: hf ° g which means h (x) f ( g ( x)) ...
Functional Programming
... ; i runs from 1 updated by 1 ; f from 1, multiplied by i ; until i > n, return f ...
... ; i runs from 1 updated by 1 ; f from 1, multiplied by i ; until i > n, return f ...
COMP 356 Programming Language Structures Notes for Chapter 15
... • no assignment statements • no loops • all parameters are passed by value • referential transparency – the same expression always evaluates to the same value. Note that this is not true in imperative languages such as C: int x = 2; int add(int y) { x++; return (x + y); ...
... • no assignment statements • no loops • all parameters are passed by value • referential transparency – the same expression always evaluates to the same value. Note that this is not true in imperative languages such as C: int x = 2; int add(int y) { x++; return (x + y); ...
Compiling Functional Programming Languages (FPLs) λ
... Combinators: A lambda expression with no occcurences of a free variable. Combinators have by convention names, such as B , S , K , I , C , T etc. Less than a handful is enough to write ANY lambda expression (assuming no free variables) WITHOUT VARIABLES, as Curry and Feys showed in 1958. Amazingly, ...
... Combinators: A lambda expression with no occcurences of a free variable. Combinators have by convention names, such as B , S , K , I , C , T etc. Less than a handful is enough to write ANY lambda expression (assuming no free variables) WITHOUT VARIABLES, as Curry and Feys showed in 1958. Amazingly, ...
Propositional Calculus
... 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 power. • We will investigate the style of progra ...
... 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 power. • We will investigate the style of progra ...
Functional Languages
... 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 Dr. Muhammed Al-Mulhem ...
... 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 Dr. Muhammed Al-Mulhem ...
Higher-order functions
... In a function call such as f(e), one may evaluate the argument expression e eagerly, to obtain a value v before evaluating the function body. That is what we are used to in Java, C#, F# and languages in the ML family. Alternatively, one might evaluate e lazily, that is, postpone evaluation of e unti ...
... In a function call such as f(e), one may evaluate the argument expression e eagerly, to obtain a value v before evaluating the function body. That is what we are used to in Java, C#, F# and languages in the ML family. Alternatively, one might evaluate e lazily, that is, postpone evaluation of e unti ...
First-Class Functions What is functional programming? First
... – Function bodies can use bindings from outside the function definition (in scope where function is defined) – Distinct concept from first-class functions. – Back to this powerful idea soon! ...
... – Function bodies can use bindings from outside the function definition (in scope where function is defined) – Distinct concept from first-class functions. – Back to this powerful idea soon! ...
Functions, recursion and lists
... No side effects or modification to variables No concept of control-flow or statements A function can be used everywhere a regular value is used Functions can take other functions as parameters and return other functions as results (higher-order functions) ...
... No side effects or modification to variables No concept of control-flow or statements A function can be used everywhere a regular value is used Functions can take other functions as parameters and return other functions as results (higher-order functions) ...
List
... • A substitution of an expression N for a variable x in M is written as M[xN] • If free variables of N have no bound occurrence in M, M[xN] is formed by replacing all free occurrences of x in M by N ...
... • A substitution of an expression N for a variable x in M is written as M[xN] • If free variables of N have no bound occurrence in M, M[xN] is formed by replacing all free occurrences of x in M by N ...
Scheme and functional programming
... (define x 3) (define y (list '+ x 5)) (eval y user-initial-environment) • The top level of the Scheme interpreter is a read-eval-print loop: read in an expression, evaluate it, and print the result. ...
... (define x 3) (define y (list '+ x 5)) (eval y user-initial-environment) • The top level of the Scheme interpreter is a read-eval-print loop: read in an expression, evaluate it, and print the result. ...
Handout 10 from Models of Computation
... foundation for Mathematics but in the end mathematicians preferred (axiomatic) set theory. The λcalculus was re-discovered as a versatile tool in Computer Science by people like McCarthy, Strachey, Landin, and Scott in the 1960s. Incidentally, the history of programming languages mirrors that of mat ...
... foundation for Mathematics but in the end mathematicians preferred (axiomatic) set theory. The λcalculus was re-discovered as a versatile tool in Computer Science by people like McCarthy, Strachey, Landin, and Scott in the 1960s. Incidentally, the history of programming languages mirrors that of mat ...
fund
... 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.” ...
Fundamentals
... Mathematics of denotational semantics: prove that there is such a function and that it is uniquely determined. “Beyond scope of this course.” ...
... Mathematics of denotational semantics: prove that there is such a function and that it is uniquely determined. “Beyond scope of this course.” ...
Foundations of Programming Languages Seyed H. Roosta
... parameters, not on any previous computations, the order of evaluation, or the execution path that led to the call. . Dynamic Memory Environment, which is allocation and deallocation of memory during program execution. As a consequence, a fully dynamic environment must perform some kind of automatic ...
... parameters, not on any previous computations, the order of evaluation, or the execution path that led to the call. . Dynamic Memory Environment, which is allocation and deallocation of memory during program execution. As a consequence, a fully dynamic environment must perform some kind of automatic ...
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 ...