An Operational Semantics for Declarative Multi
... “f t1 . . . tn = e” where f is a function, t1 , . . . , tn are data terms (i.e., without occurrences of defined functions), the left-hand side f t1 . . . tn is linear (i.e., without multiple occurrences of variables), and e is a well-formed expression. A rule is applicable if its left-hand side matc ...
... “f t1 . . . tn = e” where f is a function, t1 , . . . , tn are data terms (i.e., without occurrences of defined functions), the left-hand side f t1 . . . tn is linear (i.e., without multiple occurrences of variables), and e is a well-formed expression. A rule is applicable if its left-hand side matc ...
Python - ACE home page
... • The else branch is optional. • “Elif “ is short for “else if” and helps in reducing indentation. Lecture 12 ...
... • The else branch is optional. • “Elif “ is short for “else if” and helps in reducing indentation. Lecture 12 ...
recursive functions
... is some use of v in E that is bound by a decleration λv of v in E . A variable v is called f ree in an expression E if there is some use of v in E that is not bound by any decleration λv of v in E . Recursive Functions of Symbolic Expressions and Their Application, Part I – p. 20/43 ...
... is some use of v in E that is bound by a decleration λv of v in E . A variable v is called f ree in an expression E if there is some use of v in E that is not bound by any decleration λv of v in E . Recursive Functions of Symbolic Expressions and Their Application, Part I – p. 20/43 ...
Programming Languages and Compilers (CS 421)
... - The type could be attached to return value, as in fun cube (x) : int = x * x * x; - With no type specified, it would default to int (the default for numeric values) - User-defined overloaded functions are not allowed, so if we wanted a cube function for real parameters, it would need to have a dif ...
... - The type could be attached to return value, as in fun cube (x) : int = x * x * x; - With no type specified, it would default to int (the default for numeric values) - User-defined overloaded functions are not allowed, so if we wanted a cube function for real parameters, it would need to have a dif ...
A/x - LAMP | EPFL
... Anonymous functions Parameterisation by functions tends to create many small functions. Sometimes it is cumbersome to have to define the functions using def. A shorter notation makes use of anonymous functions, defined as follows: (x1 : T1 , ..., xn : Tn ) ⇒ E defines a function which maps it ...
... Anonymous functions Parameterisation by functions tends to create many small functions. Sometimes it is cumbersome to have to define the functions using def. A shorter notation makes use of anonymous functions, defined as follows: (x1 : T1 , ..., xn : Tn ) ⇒ E defines a function which maps it ...
val a = 15
... • Types are "latent" • Types of values are irrelevant (unchecked) until you use them. • Typing is still strong: attempting to perform an invalid operation will raise a runtime type error ...
... • Types are "latent" • Types of values are irrelevant (unchecked) until you use them. • Typing is still strong: attempting to perform an invalid operation will raise a runtime type error ...
λ-definition of Function(al)s by Normal Forms
... the idea of universal iterator, a finite object that can iterate functions an infinite number of times. Scott, Wadsworth and others were then able to construct the denotational semantics of programming languages based on fixed point theory and λ-calculus. Simultaneously Wadsworth, Welch and others ...
... the idea of universal iterator, a finite object that can iterate functions an infinite number of times. Scott, Wadsworth and others were then able to construct the denotational semantics of programming languages based on fixed point theory and λ-calculus. Simultaneously Wadsworth, Welch and others ...
Lecture 11 - Nipissing University Word
... function-body ) In other words, a lambda expression is somewhat like defun, except that it defines an unnamed function, or it allows the user to define a function with no name. For example, ((lambda (x y) (+ x y)) 2 3) binds x and y to 2 and 3, respectively, and applies +, giving 5 as the returned ...
... function-body ) In other words, a lambda expression is somewhat like defun, except that it defines an unnamed function, or it allows the user to define a function with no name. For example, ((lambda (x y) (+ x y)) 2 3) binds x and y to 2 and 3, respectively, and applies +, giving 5 as the returned ...
LISP
... are bound variables, and all the other variables that appear in the body of the function are free variables. When a function is called any bindings that a bound variable may have in the global environment are saved and the variable is rebound to the calling parameter. After the function has complete ...
... are bound variables, and all the other variables that appear in the body of the function are free variables. When a function is called any bindings that a bound variable may have in the global environment are saved and the variable is rebound to the calling parameter. After the function has complete ...
Short Introduction to the Lambda
... We can specify the square function by saying that it associates 1 to 1*1, 2 to 2*2, 3 to 3*3, ecc. In the specification of the function the actual values of the possible particular inputs are not needed, that is we can abstract from the actual values of the input by simply saying that the function s ...
... We can specify the square function by saying that it associates 1 to 1*1, 2 to 2*2, 3 to 3*3, ecc. In the specification of the function the actual values of the possible particular inputs are not needed, that is we can abstract from the actual values of the input by simply saying that the function s ...
Foundations of Functional Programming
... Proof See Barendregt [1] or Hindley and Seldin [6]. For instance, (λx.ax)((λy.by)c) has two different reduction sequences, both leading to the same normal form. The affected subterm is underlined at each step: (λx.ax)((λy.by)c) → a((λy.by)c) → a(bc) (λx.ax)((λy.by)c) → (λx.ax)(bc) → a(bc) The theore ...
... Proof See Barendregt [1] or Hindley and Seldin [6]. For instance, (λx.ax)((λy.by)c) has two different reduction sequences, both leading to the same normal form. The affected subterm is underlined at each step: (λx.ax)((λy.by)c) → a((λy.by)c) → a(bc) (λx.ax)((λy.by)c) → (λx.ax)(bc) → a(bc) The theore ...
ppt - Dave Reed
... clean, simple subset of LISP static scoping, first-class functions, efficient tail-recursion, … ...
... clean, simple subset of LISP static scoping, first-class functions, efficient tail-recursion, … ...
functional form
... Apply-to-all A functional form that takes a single function as a parameter and yields a list of values obtained by applying the given function to each element of a list of parameters ...
... Apply-to-all A functional form that takes a single function as a parameter and yields a list of values obtained by applying the given function to each element of a list of parameters ...
02/06
... that transforms Lisp into a code representation. Then macro calls are expanded into the code representation. A reader macro is a special kind of macro that is expanded during the reader phase A reader macro is a definition of a single character, which is expanded into its Lisp definition An ex ...
... that transforms Lisp into a code representation. Then macro calls are expanded into the code representation. A reader macro is a special kind of macro that is expanded during the reader phase A reader macro is a definition of a single character, which is expanded into its Lisp definition An ex ...
PowerPoint
... • The basic process of computation is fundamentally different in a FPL than in an imperative language – In an imperative language, operations are done and the results are stored in variables for later use – Management of variables is a constant concern and source of complexity for imperative program ...
... • The basic process of computation is fundamentally different in a FPL than in an imperative language – In an imperative language, operations are done and the results are stored in variables for later use – Management of variables is a constant concern and source of complexity for imperative program ...
Computational lambda calculus: A combination of functional and
... Functional programming languages, cf Lisp, have their roots in the lambda calculus and are widely known for their expressive power and simple semantics. Because of their mathematical simplicity are considered to be a great tool for formal analysis and program verification. Functional programs do not ...
... Functional programming languages, cf Lisp, have their roots in the lambda calculus and are widely known for their expressive power and simple semantics. Because of their mathematical simplicity are considered to be a great tool for formal analysis and program verification. Functional programs do not ...
Haskell Summary Functions • A function takes 1 or more parameter
... A binary operator can be converted into a curried function by enclosing the name of the operator in Useful functions can sometimes be constructed in a simple way using parentheses. For example: sections. Examples: 1+2 can be written as (+) 1 2 (1+) - successor function This convention also allows on ...
... A binary operator can be converted into a curried function by enclosing the name of the operator in Useful functions can sometimes be constructed in a simple way using parentheses. For example: sections. Examples: 1+2 can be written as (+) 1 2 (1+) - successor function This convention also allows on ...
Joy: Forth`s Functional Cousin
... where "Lx" is sometimes written "\x" or "lambda x" of "fn x". The expression on the right side of the definition then is to be read as "the function of one argument x which yields the value x * x". An expression like that is known as a lambda abstraction. Almost all programming languages use such a ...
... where "Lx" is sometimes written "\x" or "lambda x" of "fn x". The expression on the right side of the definition then is to be read as "the function of one argument x which yields the value x * x". An expression like that is known as a lambda abstraction. Almost all programming languages use such a ...
