CITS3211 FUNCTIONAL PROGRAMMING 5. Higherorder functions
... − e.g. by naming an explicit constant − this gives concise programs and reusable code − it’s better to write one program and use it ten times than it is to write ten slightlydifferent programs Consider asc’sort, which sorts a list into ascending order asc’sort :: Ord a => [a] > [a] ...
... − e.g. by naming an explicit constant − this gives concise programs and reusable code − it’s better to write one program and use it ten times than it is to write ten slightlydifferent programs Consider asc’sort, which sorts a list into ascending order asc’sort :: Ord a => [a] > [a] ...
Lect 1
... 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. ...
Document
... 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. ...
notes
... When we say a given term has a given type (for example, λx.x2 has type Z → Z), we are saying that the value of the term after evaluation at runtime, if it exists, will be a member of the class of similar values represented by the type. In the pure untyped λ-calculus, there are no types, and all term ...
... When we say a given term has a given type (for example, λx.x2 has type Z → Z), we are saying that the value of the term after evaluation at runtime, if it exists, will be a member of the class of similar values represented by the type. In the pure untyped λ-calculus, there are no types, and all term ...
Lecture10 - CIS @ UPenn
... Functional programming • Functions taking other functions as an argument are ...
... Functional programming • Functions taking other functions as an argument are ...
Functional Programming www.AssignmentPoint.com In computer
... and David Turner initially developed the language SASL at the University of St. Andrews and later the language Miranda at the University of Kent. Also in Edinburgh in the 1970s, Burstall and Darlington developed the functional language NPL. NPL was based on Kleene Recursion Equations and was first i ...
... and David Turner initially developed the language SASL at the University of St. Andrews and later the language Miranda at the University of Kent. Also in Edinburgh in the 1970s, Burstall and Darlington developed the functional language NPL. NPL was based on Kleene Recursion Equations and was first i ...
PROGRAMMING LANGUAGES 6.5 Higher Order Functions A
... Note again the difference in the inferred types of the functions. It is of course possible to define curried_fold by nesting occurrences of the explicit fn notation within the function’s body. The shorthand notation, however, is substantially more intuitive and convenient. Note also that Currying in ...
... Note again the difference in the inferred types of the functions. It is of course possible to define curried_fold by nesting occurrences of the explicit fn notation within the function’s body. The shorthand notation, however, is substantially more intuitive and convenient. Note also that Currying in ...
Fundamentals
... Describe meaning of programs by specifying the mathematical • Function • Function on functions • Value, such as natural numbers or strings ...
... Describe meaning of programs by specifying the mathematical • Function • Function on functions • Value, such as natural numbers or strings ...
A short introduction to the Lambda Calculus
... oriented features. The OCaml dialect of ML is one of the few attempts to combine the two paradigms. 2. Expressions in the λ-calculus. The λ-calculus is a notation for functions. It is extremely economical but at first sight perhaps somewhat cryptic, which stems from its origins in mathematical logic ...
... oriented features. The OCaml dialect of ML is one of the few attempts to combine the two paradigms. 2. Expressions in the λ-calculus. The λ-calculus is a notation for functions. It is extremely economical but at first sight perhaps somewhat cryptic, which stems from its origins in mathematical logic ...
Notes
... The type-checking rules for the lambda calculus are exactly what you’d expect from our study of ML: • A variable x has whatever type t is recorded in the current static environment for x. If the environment doesn’t have a type for x, then there is a type error (and x is free). • If e1 has type t → t ...
... The type-checking rules for the lambda calculus are exactly what you’d expect from our study of ML: • A variable x has whatever type t is recorded in the current static environment for x. If the environment doesn’t have a type for x, then there is a type error (and x is free). • If e1 has type t → t ...
Chapter 11 slides
... the letter λ—hence the notation’s name. – Lambda calculus was the inspiration for functional programming – one uses it to compute by substituting parameters into expressions, just as one computes in a high level functional program by passing arguments to functions ...
... the letter λ—hence the notation’s name. – Lambda calculus was the inspiration for functional programming – one uses it to compute by substituting parameters into expressions, just as one computes in a high level functional program by passing arguments to functions ...
Lect_8_9
... An operator written between its two arguments can be converted into a curried function written before its two arguments by using parentheses ...
... An operator written between its two arguments can be converted into a curried function written before its two arguments by using parentheses ...
Programming Least Squares Final
... concise code. A result of this, however, is that the code is literally “dense” with meaning, and it can be hard to read if you are not accustomed to functional programming. In our first example, “filter(is_even, q)” was fairly easy to understand (fortunately, we chose a descriptive function name), w ...
... concise code. A result of this, however, is that the code is literally “dense” with meaning, and it can be hard to read if you are not accustomed to functional programming. In our first example, “filter(is_even, q)” was fairly easy to understand (fortunately, we chose a descriptive function name), w ...
4.1 Characteristics of Functional Programming Languages Chapter
... Entities in a program that can be treated this way are called first-class values or first-class objects. Note that the term object in this definition does not necessarily imply an object in an object-oriented language. Although most imperative languages do not contain first class functions, they pr ...
... Entities in a program that can be treated this way are called first-class values or first-class objects. Note that the term object in this definition does not necessarily imply an object in an object-oriented language. Although most imperative languages do not contain first class functions, they pr ...
Lambda Calculus and Lisp
... First (12 14 16) is 12 Rest (12 14 16) is (14 16) First ( Rest (12 14 16) ) is? NOTE: Rest always returns a list! The empty list is written () or nil. So, rest of (12) is (). First and rest only work on lists ...
... First (12 14 16) is 12 Rest (12 14 16) is (14 16) First ( Rest (12 14 16) ) is? NOTE: Rest always returns a list! The empty list is written () or nil. So, rest of (12) is (). First and rest only work on lists ...
3. Functional Programming
... polymorphic, i.e., can take arguments of different types. In addition, Haskell supports (ML-style) type inference: (most) programs can be type-checked even without explicit type annotations. User-defined algebraic datatypes are abstract data types that bundle functions together with a hidden represe ...
... polymorphic, i.e., can take arguments of different types. In addition, Haskell supports (ML-style) type inference: (most) programs can be type-checked even without explicit type annotations. User-defined algebraic datatypes are abstract data types that bundle functions together with a hidden represe ...
review of haskell
... GHC is the leading implementation of Haskell, and comprises a compiler and interpreter; The interactive nature of the interpreter makes it well suited for teaching and prototyping; GHC is freely available from: ...
... GHC is the leading implementation of Haskell, and comprises a compiler and interpreter; The interactive nature of the interpreter makes it well suited for teaching and prototyping; GHC is freely available from: ...
The gist of side effects in pure functional languages
... Pure functional languages lack assignment constructs, an expression produces the same value independently of when it is evaluated—a property called referential transparency—, and side-effects like inputoutput are carefully controlled and separated at the type level by so-called monads and unique typ ...
... Pure functional languages lack assignment constructs, an expression produces the same value independently of when it is evaluated—a property called referential transparency—, and side-effects like inputoutput are carefully controlled and separated at the type level by so-called monads and unique typ ...
unit 8 - WordPress.com
... In our overview of Scheme we have differentiated on several occasions between special forms and functions. Arguments to functions are always passed by sharing and are evaluated before they are passed (i.e., in applicative order). Arguments to special forms are passed unevaluated¡ªin other words, by ...
... In our overview of Scheme we have differentiated on several occasions between special forms and functions. Arguments to functions are always passed by sharing and are evaluated before they are passed (i.e., in applicative order). Arguments to special forms are passed unevaluated¡ªin other words, by ...
Functional Languages
... obtained by applying the given function to each element of a list of parameters Form: For h (x) x * x * x ( h, (3, 2, 4)) yields (27, 8, 64) Dr. Muhammed Al-Mulhem ...
... obtained by applying the given function to each element of a list of parameters Form: For h (x) x * x * x ( h, (3, 2, 4)) yields (27, 8, 64) Dr. Muhammed Al-Mulhem ...
curried functions - Universitatea "Politehnica"
... An operator written between its two arguments can be converted into a curried function written before its two arguments by using parentheses ...
... An operator written between its two arguments can be converted into a curried function written before its two arguments by using parentheses ...
Chapter_4
... The symbol is the Greek letter lambda, and is typed at the keyboard as a backslash \. In mathematics, nameless functions are usually denoted using the symbol, as in x x+x. In Haskell, the use of the symbol for nameless functions comes from the lambda calculus, the theory of functions o ...
... The symbol is the Greek letter lambda, and is typed at the keyboard as a backslash \. In mathematics, nameless functions are usually denoted using the symbol, as in x x+x. In Haskell, the use of the symbol for nameless functions comes from the lambda calculus, the theory of functions o ...
Haskell Summary Functions • A function takes 1 or more parameter
... Also, functions have precedence over all other operators. Hence, we write f a (b+1) to mean f (a, b + 1); otherwise (f a b) + 1 is understood. Operator identifiers use only a set of special characters: !, #, $, %, &, *, +, ., /, <, =, >, ?, @, \, ^, |, -, ~ . Operators can also be used as functions: ...
... Also, functions have precedence over all other operators. Hence, we write f a (b+1) to mean f (a, b + 1); otherwise (f a b) + 1 is understood. Operator identifiers use only a set of special characters: !, #, $, %, &, *, +, ., /, <, =, >, ?, @, \, ^, |, -, ~ . Operators can also be used as functions: ...
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 ...