Higher-order functions
... Higher-order functions are heavily used in C# since version 3.0, because the Linq (Language Integrated Query) syntax simply is ‘syntactic sugar’ for calls to methods that take delegates as arguments. For instance, consider again the filter-square-sum processing of an integer list from Section 5.2. I ...
... Higher-order functions are heavily used in C# since version 3.0, because the Linq (Language Integrated Query) syntax simply is ‘syntactic sugar’ for calls to methods that take delegates as arguments. For instance, consider again the filter-square-sum processing of an integer list from Section 5.2. I ...
functional form
... 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 named A is applied to the two parameters, B and C • The first LISP interpreter appeared only as a demonstrat ...
... 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 named A is applied to the two parameters, B and C • The first LISP interpreter appeared only as a demonstrat ...
CSE 341 - Unit 4
... might be putting this code up on the internet for people to use. I want to be able to think about could I replace this function with this other function without any possible call to these functions ever being able to tell. That's what equivalence is all about. [00:02:30.65] Now, we need to define wh ...
... might be putting this code up on the internet for people to use. I want to be able to think about could I replace this function with this other function without any possible call to these functions ever being able to tell. That's what equivalence is all about. [00:02:30.65] Now, we need to define wh ...
Functional Programming
... 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 assignment but only a true mathematical equality. ...
... 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 assignment but only a true mathematical equality. ...
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. ...
slides
... – Arguments, results, parts of tuples, bound to variables, carried by datatype constructors or exceptions, … fun double x = 2*x fun incr x = x+1 val a_tuple = (double, incr, double(incr 7)) ...
... – Arguments, results, parts of tuples, bound to variables, carried by datatype constructors or exceptions, … fun double x = 2*x fun incr x = x+1 val a_tuple = (double, incr, double(incr 7)) ...
Chapter 7 Recursion
... -conversion permits the name of a bound variable to be changed, provided that no name clash is introduced. Compare with programming, where the name of a formal parameter can be changed provided that the new name does not clash with local or global variables. ...
... -conversion permits the name of a bound variable to be changed, provided that no name clash is introduced. Compare with programming, where the name of a formal parameter can be changed provided that the new name does not clash with local or global variables. ...
Lecture Slides
... An international committee of researchers initiates the development of Haskell, a standard lazy functional language. Partially in response to “Can programming be liberated from the Von Neuman style?”, by John Backus. (Named in honor of logician Haskell B. Curry.) ...
... An international committee of researchers initiates the development of Haskell, a standard lazy functional language. Partially in response to “Can programming be liberated from the Von Neuman style?”, by John Backus. (Named in honor of logician Haskell B. Curry.) ...
Functional PLs
... • Many kinds of functional forms, here are some: 1. Function Composition – A functional form that takes two functions as parameters and yields a function whose value is the first actual parameter function applied to the result of the second Form: h f ° g ...
... • Many kinds of functional forms, here are some: 1. Function Composition – A functional form that takes two functions as parameters and yields a function whose value is the first actual parameter function applied to the result of the second Form: h f ° g ...
Y in Practical Programs Extended Abstract
... As well as demonstrating the practical properties of this programming technique, we will see an interesting property relating to the theory of sequential realisability [Lon99]. ...
... As well as demonstrating the practical properties of this programming technique, we will see an interesting property relating to the theory of sequential realisability [Lon99]. ...
Hugs (Haskell)
... Variables begin with a lowercase letter Type names begin with an uppercase letter Braces and semicolons can be used, but it’s not common Tabs can really obscure the indentation; set your text editor to replace tabs with spaces ...
... Variables begin with a lowercase letter Type names begin with an uppercase letter Braces and semicolons can be used, but it’s not common Tabs can really obscure the indentation; set your text editor to replace tabs with spaces ...
4.6 Lisp - University of Hawaii
... pure functions to the greatest extent possible • Process of computation is fundamentally different – In an imperative language, operations are executed and the results are stored in variables for later use – Management of variables is a constant concern and source of complexity for imperative progra ...
... pure functions to the greatest extent possible • Process of computation is fundamentally different – In an imperative language, operations are executed and the results are stored in variables for later use – Management of variables is a constant concern and source of complexity for imperative progra ...
Chapter 2
... example a point in a graph is represented by two values i.e. of x-axis and y-axis. In order to model such requirements Haskell has introduced the concept of Tuples. Tuples in Haskell can be compared with “structures” in C/C++. Like structures Tuples are able to group together values of dissimilar ty ...
... example a point in a graph is represented by two values i.e. of x-axis and y-axis. In order to model such requirements Haskell has introduced the concept of Tuples. Tuples in Haskell can be compared with “structures” in C/C++. Like structures Tuples are able to group together values of dissimilar ty ...
Lecture Notes
... All type errors are found at compile time, which makes programs safer and faster by removing the need for type checks at run time. In GHCi, the :type command calculates the type of an expression, without evaluating it: ...
... All type errors are found at compile time, which makes programs safer and faster by removing the need for type checks at run time. In GHCi, the :type command calculates the type of an expression, without evaluating it: ...
PPT
... Calculation rule • Symbolic evaluation useful for discussing programs • Used in optimization (in-lining), macro expansion ...
... Calculation rule • Symbolic evaluation useful for discussing programs • Used in optimization (in-lining), macro expansion ...
Declarative Programming
... A lambda expression specifies the parameter(s) and the mapping of a function in the following form (x) x * x * x for the function cube (x) = x * x * x - Lambda expressions describe nameless functions - Lambda expressions are applied to parameter(s) by placing the parameter(s) after the expression ...
... A lambda expression specifies the parameter(s) and the mapping of a function in the following form (x) x * x * x for the function cube (x) = x * x * x - Lambda expressions describe nameless functions - Lambda expressions are applied to parameter(s) by placing the parameter(s) after the expression ...
Foundations of Programming Languages Seyed H. Roosta
... where the id’s are identifiers (parameters or variables) and expression (called the body of the lambda function) is some expression that may involve the identifiers. ...
... where the id’s are identifiers (parameters or variables) and expression (called the body of the lambda function) is some expression that may involve the identifiers. ...
Functional Programming
... An obvious solution is just to pass the function’s body (mapcar ‘(cons val x) L) It is ambiguous : we do not know which names are parameters and which ones are global “lambda expressions” come in hand (mapcar ‘(lambda (x) (cons val x)) L) ...
... An obvious solution is just to pass the function’s body (mapcar ‘(cons val x) L) It is ambiguous : we do not know which names are parameters and which ones are global “lambda expressions” come in hand (mapcar ‘(lambda (x) (cons val x)) L) ...
Functional Programming Languages
... 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 named A is applied to the two parameters, B and C • The first LISP interpreter appeared only as a demonstration of the uni ...
... 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 named A is applied to the two parameters, B and C • The first LISP interpreter appeared only as a demonstration of the uni ...
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
... So far we were concerned with models of computation based on machine models. In particular, we used the Turing machine model to define the boundary between computability and non-computability, feasibility and intractability. Machine models are often rather contrived and when using them one often has ...
... So far we were concerned with models of computation based on machine models. In particular, we used the Turing machine model to define the boundary between computability and non-computability, feasibility and intractability. Machine models are often rather contrived and when using them one often has ...
Lambda Calculus
... α-renaming 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 variab ...
... α-renaming 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 variab ...