PPT
... (T1,T2,…,Tn) is the type of n-tuples whose ith components have type Ti for any i in 1…n. Lecture 18 – Functional Programming, Spring 2008 ...
... (T1,T2,…,Tn) is the type of n-tuples whose ith components have type Ti for any i in 1…n. Lecture 18 – Functional Programming, Spring 2008 ...
scheme1 - Computer Science and Electrical Engineering
... (e.g., number, symbol) or a list of atoms or sublists • Functional Programming Style – computation done by applying functions to arguments, functions are first class objects, minimal use of side-effects • Uniform Representation of Data & Code – (A B C D) can be interpreted as data (i.e., a list of f ...
... (e.g., number, symbol) or a list of atoms or sublists • Functional Programming Style – computation done by applying functions to arguments, functions are first class objects, minimal use of side-effects • Uniform Representation of Data & Code – (A B C D) can be interpreted as data (i.e., a list of f ...
Week 1
... Features of functional languages • usually strongly typed (modern languages) • algebraic type definitions – mathematical based notation – no (implicit) pointers • higher-order functions – can accept functions as parameters – can return functions as results • recursion as a basic principle • applicat ...
... Features of functional languages • usually strongly typed (modern languages) • algebraic type definitions – mathematical based notation – no (implicit) pointers • higher-order functions – can accept functions as parameters – can return functions as results • recursion as a basic principle • applicat ...
Week 1
... Features of functional languages • usually strongly typed (modern languages) • algebraic type definitions – mathematical based notation – no (implicit) pointers • higher-order functions – can accept functions as parameters – can return functions as results • recursion as a basic principle • applicat ...
... Features of functional languages • usually strongly typed (modern languages) • algebraic type definitions – mathematical based notation – no (implicit) pointers • higher-order functions – can accept functions as parameters – can return functions as results • recursion as a basic principle • applicat ...
The Continuity of Monadic Stream Functions
... evil function has an input sequence as a parameter. But in Brouwer’s conception there is a clear distinction between sequences, that are non-computable, and functions, that must be effectively computable. Therefore we should not allow the definition of a function to depend on a sequence. However, in ...
... evil function has an input sequence as a parameter. But in Brouwer’s conception there is a clear distinction between sequences, that are non-computable, and functions, that must be effectively computable. Therefore we should not allow the definition of a function to depend on a sequence. However, in ...
The Lambda Calculus: a minimal ML?
... computation over lambda terms. We reduce terms until no more reductions can be applied, in a manner that’s similar to evaluation of a functional language’s expressions. The lambda terms that have a reduced form— this is analogous to them having a halting evaluation— have a unique reduced form. Befor ...
... computation over lambda terms. We reduce terms until no more reductions can be applied, in a manner that’s similar to evaluation of a functional language’s expressions. The lambda terms that have a reduced form— this is analogous to them having a halting evaluation— have a unique reduced form. Befor ...
Chapter 11 - Functional Programming, Part II: ML, Delayed
... A fun declaration is really just a val declaration: > val square = fn x => x * x; val square = fn : int -> int ...
... A fun declaration is really just a val declaration: > val square = fn x => x * x; val square = fn : int -> int ...
Abstract machine for a comonadic dataflow language
... structure for denotational semantics. However, its category theoretic dual, comonad, has not enjoyed nearly as much use. Monads are widely used to represent effectful computations and input/output in Haskell, but there is no well known practical use for its dual. While various context dependent comp ...
... structure for denotational semantics. However, its category theoretic dual, comonad, has not enjoyed nearly as much use. Monads are widely used to represent effectful computations and input/output in Haskell, but there is no well known practical use for its dual. While various context dependent comp ...
Foundations of Functional Programming
... Peter Landin used the λ-calculus to analyze Algol 60, and introduced ISWIM as a framework for future languages. His SECD machine, with extensions, was used to implement ML and other strict functional languages. Christopher Wadsworth developed graph reduction as a method for performing lazy evaluatio ...
... Peter Landin used the λ-calculus to analyze Algol 60, and introduced ISWIM as a framework for future languages. His SECD machine, with extensions, was used to implement ML and other strict functional languages. Christopher Wadsworth developed graph reduction as a method for performing lazy evaluatio ...
Functional Programming: Scheme
... • Scheme functions are first-class objects: – functions can be created dynamically, stored in data structures, returned as results of expressions or other functions. • functions are defined as lists ⇒ can be treated as data. Lecture 11 ...
... • Scheme functions are first-class objects: – functions can be created dynamically, stored in data structures, returned as results of expressions or other functions. • functions are defined as lists ⇒ can be treated as data. Lecture 11 ...
Why Functional Programming Matters
... All this can be achieved because functional languages allow functions which are indivisible in conventional programming languages to be expressed as a combination of parts - a general higher order function and some particular specialising functions. Once defined, such higher order functions allow ma ...
... All this can be achieved because functional languages allow functions which are indivisible in conventional programming languages to be expressed as a combination of parts - a general higher order function and some particular specialising functions. Once defined, such higher order functions allow ma ...
Lambda Calculus as a Programming Language
... "theoretically" we should. We forbid the use of the symbol as a free variable within the λexpression itself. This is in line with Lambda calculus where λ-expressions must be textually finite and where free variables have nothing to do with defining recursive functions. The notation E1 = E2 is used t ...
... "theoretically" we should. We forbid the use of the symbol as a free variable within the λexpression itself. This is in line with Lambda calculus where λ-expressions must be textually finite and where free variables have nothing to do with defining recursive functions. The notation E1 = E2 is used t ...
Untyped Lambda Calculus - Programming Systems Lab
... Untyped lambda calculus is a basic logical system everyone should know. It provides syntactic descriptions of computable functions and can express all computable functions. Untyped lambda calculus is a minimal system with only three primitives: variables, application, and functional abstraction. Unt ...
... Untyped lambda calculus is a basic logical system everyone should know. It provides syntactic descriptions of computable functions and can express all computable functions. Untyped lambda calculus is a minimal system with only three primitives: variables, application, and functional abstraction. Unt ...
Example
... arithmetic expressions the output is expected to be in a format suitable to direct evaluation. It is wellknown that an expression like 1+3*2 requires first the multiplication and then the addition and this should be achieved through a more proper format of this expression. Such a format derives from ...
... arithmetic expressions the output is expected to be in a format suitable to direct evaluation. It is wellknown that an expression like 1+3*2 requires first the multiplication and then the addition and this should be achieved through a more proper format of this expression. Such a format derives from ...
Chapter 15 - McMaster Computing and Software
... • A functional form that takes two functions as parameters and yields a function whose value is the first actual parameter function applied to the application of the second Form: h f ° g which means h (x) f ( g ( x)) For f (x) x + 2 and g (x) 3 * x, h f ° g yields (3 * x)+ 2 ...
... • A functional form that takes two functions as parameters and yields a function whose value is the first actual parameter function applied to the application of the second Form: h f ° g which means h (x) f ( g ( x)) For f (x) x + 2 and g (x) 3 * x, h f ° g yields (3 * x)+ 2 ...
Functional Languages
... mymax(x,y) = if x > y then x else y – Haskell infers factorial is an Ord function ...
... mymax(x,y) = if x > y then x else y – Haskell infers factorial is an Ord function ...
- Free Documents
... y Define a Scheme function named totalreverse that will take a list as the parameter and returns a list in which all elements are reversed including the nested lists. For example if the function totalreverse is applied on the list a b c d e the resulting list would be e d c b a. You may assume that ...
... y Define a Scheme function named totalreverse that will take a list as the parameter and returns a list in which all elements are reversed including the nested lists. For example if the function totalreverse is applied on the list a b c d e the resulting list would be e d c b a. You may assume that ...
Constructive logic and type theory (lecture notes 2009)
... calculus as a programming language. It has the unusual property that all programs terminate. To prove this formally is very complicated, see for instance (Hindley and Seldin 1986) for a proof concerning a simplified calculus. The fact that all programs terminate implies that a programming language i ...
... calculus as a programming language. It has the unusual property that all programs terminate. To prove this formally is very complicated, see for instance (Hindley and Seldin 1986) for a proof concerning a simplified calculus. The fact that all programs terminate implies that a programming language i ...
A retrospective on Haskell
... theory-into-practice (more the thought pattern than actual theorems) Hidden effects are like hire-purchase: pay nothing now, but it catches up with you in the end Enforced purity is like paying up front: painful on Day 1, but usually worth it But we made one big mistake... ...
... theory-into-practice (more the thought pattern than actual theorems) Hidden effects are like hire-purchase: pay nothing now, but it catches up with you in the end Enforced purity is like paying up front: painful on Day 1, but usually worth it But we made one big mistake... ...
Lambda
... (x. y. (+ x y)) 3 5 A 2-parameter function is simulated with two 1parameter functions. The result of applying the first function is another function. This new function accepts the second argument and produces the result of the simulated 2-parameter function. More parameters can be handled similarl ...
... (x. y. (+ x y)) 3 5 A 2-parameter function is simulated with two 1parameter functions. The result of applying the first function is another function. This new function accepts the second argument and produces the result of the simulated 2-parameter function. More parameters can be handled similarl ...
Chapter 15 slides - Erica Heitman-Ford
... • 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 ...
pl10ch15
... • 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 ...
functional form
... the greatest extent possible – In an functional language, the evaluation of a function always produces the same result given the same parameters – No side effect, a.k.a. referential transparency ...
... the greatest extent possible – In an functional language, the evaluation of a function always produces the same result given the same parameters – No side effect, a.k.a. referential transparency ...
A/x - LAMP | EPFL
... action, the function’s stack frame can be re-used. This is called “tail recursion”. ⇒ Tail-recursive functions are iterative processes. More generally, if the last action of a function is a call to another (possible the same) function, only a single stack frame is needed for both functions. Such ...
... action, the function’s stack frame can be re-used. This is called “tail recursion”. ⇒ Tail-recursive functions are iterative processes. More generally, if the last action of a function is a call to another (possible the same) function, only a single stack frame is needed for both functions. Such ...
Short Introduction to the Lambda
... Λ ::= X | (ΛΛ) | λX.Λ where Λ stands for the set of lambda-terms and X is a metavariable that ranges over the (numerable) set of variables (x, y, v, w, z, x2, x2,...) Variable and application are well-known concepts, but what is abstraction ? In our sense it is a notion tied to that of "abstracting ...
... Λ ::= X | (ΛΛ) | λX.Λ where Λ stands for the set of lambda-terms and X is a metavariable that ranges over the (numerable) set of variables (x, y, v, w, z, x2, x2,...) Variable and application are well-known concepts, but what is abstraction ? In our sense it is a notion tied to that of "abstracting ...