Lambda Calculus
... Most modern functional languages, on the other hand, use lazy evaluation, that is, expressions are only evaluated when they are needed. Consider: ...
... Most modern functional languages, on the other hand, use lazy evaluation, that is, expressions are only evaluated when they are needed. Consider: ...
Denotational design with type class morphisms
... in Haskell). Also, ∅ must be a left and right identity for (⊕), and (⊕) must be associative. Thus a type class determines part of the essence, as well as the form, of each of its instances. What about the rest of the meaning of a type class instance–the semantic freedom remaining after the types and ...
... in Haskell). Also, ∅ must be a left and right identity for (⊕), and (⊕) must be associative. Thus a type class determines part of the essence, as well as the form, of each of its instances. What about the rest of the meaning of a type class instance–the semantic freedom remaining after the types and ...
Declarative Programming in Escher
... solve. The problem is then formalized as an interpretation (called the intended interpretation) of an alphabet in the logic at hand. The intended interpretation speci es the various domains and the meaning of the symbols of the alphabet in these domains. In practice, the intended interpretation is r ...
... solve. The problem is then formalized as an interpretation (called the intended interpretation) of an alphabet in the logic at hand. The intended interpretation speci es the various domains and the meaning of the symbols of the alphabet in these domains. In practice, the intended interpretation is r ...
The Conception, Evolution, and Application of Functional
... The development of functional languages has been influenced from time to time by many sources, but none is as paramount nor as fundamental as the work of Alonzo Church on the lambda calculus [Chu33, Chu41]. Indeed the lambda calculus is usually regarded as the first functional language, although it wa ...
... The development of functional languages has been influenced from time to time by many sources, but none is as paramount nor as fundamental as the work of Alonzo Church on the lambda calculus [Chu33, Chu41]. Indeed the lambda calculus is usually regarded as the first functional language, although it wa ...
CS-Intro-AI-LISP - Geometric and Intelligent Computing Laboratory
... • EQ: tests for memory location exactly, therefore, atoms only! • LISP automatically makes sure that all refs to some symbol actually point to the UNIQUE point in mem that the symbol happens to be stored physically. This way, any info stored w/ it (e.g., its value) is accessible from every ref. • An ...
... • EQ: tests for memory location exactly, therefore, atoms only! • LISP automatically makes sure that all refs to some symbol actually point to the UNIQUE point in mem that the symbol happens to be stored physically. This way, any info stored w/ it (e.g., its value) is accessible from every ref. • An ...
Drexel-CS-Intro-AI-LISP
... • Best way to understand Lisp: Develop an intuitive understanding of its data structures (remember: programs and data stored the same way) – forget conventional programming languages w/ which you are familiar (else confusion). – Three notations for Lisp data structures: • paren/list (printed) • dot ...
... • Best way to understand Lisp: Develop an intuitive understanding of its data structures (remember: programs and data stored the same way) – forget conventional programming languages w/ which you are familiar (else confusion). – Three notations for Lisp data structures: • paren/list (printed) • dot ...
Pragmatic Functional Programming in Dyalog
... • Be pragmatic: Stay functional where you can • Use objects and mute state when you must • Languages like APL will be the solution to the next BIG problem after concurrency: ...
... • Be pragmatic: Stay functional where you can • Use objects and mute state when you must • Languages like APL will be the solution to the next BIG problem after concurrency: ...
Calculating Functional Programs - Research School of Computer
... One particularly appropriate framework for program calculation is functional programming, simply because the absence of side-effects ensures referential transparency — all that matters of any expression is the value it denotes, not any other characteristic such as the method by which it computed, the ...
... One particularly appropriate framework for program calculation is functional programming, simply because the absence of side-effects ensures referential transparency — all that matters of any expression is the value it denotes, not any other characteristic such as the method by which it computed, the ...
Lecture Notes
... This course is about computing. The notion of computing is much more fundamental than the notion of a computer, because computing can be done even without one. In fact, we have been computing ever since we entered primary school, mainly using pencil and paper. Since then, we have been adding, subtra ...
... This course is about computing. The notion of computing is much more fundamental than the notion of a computer, because computing can be done even without one. In fact, we have been computing ever since we entered primary school, mainly using pencil and paper. Since then, we have been adding, subtra ...
Functional Programming in Scheme
... almost as in the Lambda calculus, where we are writing sum ≡def λx. λy.((+ λ (define sum ...
... almost as in the Lambda calculus, where we are writing sum ≡def λx. λy.((+ λ (define sum ...
funprog
... To evaluate (E1 E2 ... En), recursively evaluate E1, E2,...,En - E1 should evaluate to a function and then apply the function value of E1 to the arguments given by the values of E2,...,En. In the base case, there are self evaluating expressions (e.g. numbers and symbols). In addition, various spec ...
... To evaluate (E1 E2 ... En), recursively evaluate E1, E2,...,En - E1 should evaluate to a function and then apply the function value of E1 to the arguments given by the values of E2,...,En. In the base case, there are self evaluating expressions (e.g. numbers and symbols). In addition, various spec ...
Towards CNC Programming Using Haskell
... a specific movement each time a piece is under it. Thanks to laziness, we can define the behavior of the robot hand by this infinite movement since it will only be evaluated as much as needed. To the best of our knowledge, all languages used in CNC programming lack of lazy evaluation (i.e., they are ...
... a specific movement each time a piece is under it. Thanks to laziness, we can define the behavior of the robot hand by this infinite movement since it will only be evaluated as much as needed. To the best of our knowledge, all languages used in CNC programming lack of lazy evaluation (i.e., they are ...
ppt - TAMU Computer Science Faculty Pages
... form of a program: how expressions, commands, declarations etc. are put together to result in the final program. • The semantics of a language is concerned with the meaning of a program: how the programs behave when executed on computers • Syntax defines the set of valid programs, ...
... form of a program: how expressions, commands, declarations etc. are put together to result in the final program. • The semantics of a language is concerned with the meaning of a program: how the programs behave when executed on computers • Syntax defines the set of valid programs, ...
lec4
... To evaluate (E1 E2 ... En), recursively evaluate E1, E2,...,En - E1 should evaluate to a function and then apply the function value of E1 to the arguments given by the values of E2,...,En. In the base case, there are self evaluating expressions (e.g. numbers and symbols). In addition, various spec ...
... To evaluate (E1 E2 ... En), recursively evaluate E1, E2,...,En - E1 should evaluate to a function and then apply the function value of E1 to the arguments given by the values of E2,...,En. In the base case, there are self evaluating expressions (e.g. numbers and symbols). In addition, various spec ...
A Typed Lambda Calculus with Categorical Type Constructors 1
... calculus may not be normalizing. Of course, it depends on the choice of terms and reduction rules in the calculus, but we would like to have a fixed point operator or something which enables us to write terms for addition, multiplication and so on. If we have a fixed point operator, reductions may not ...
... calculus may not be normalizing. Of course, it depends on the choice of terms and reduction rules in the calculus, but we would like to have a fixed point operator or something which enables us to write terms for addition, multiplication and so on. If we have a fixed point operator, reductions may not ...
Slide 1
... exists : ('a -> bool) -> 'a list -> bool for_all : ('a -> bool) -> 'a list -> bool map : ('a -> 'b) -> 'a list -> 'b list filter : ('a -> bool) -> 'a list -> 'a list iter : ('a -> unit) -> 'a list -> unit ...
... exists : ('a -> bool) -> 'a list -> bool for_all : ('a -> bool) -> 'a list -> bool map : ('a -> 'b) -> 'a list -> 'b list filter : ('a -> bool) -> 'a list -> 'a list iter : ('a -> unit) -> 'a list -> unit ...
Unit 11 — Functional Programming with Haskell
... Lists/1 Haskell also supports lists with the standard square bracket notation ...
... Lists/1 Haskell also supports lists with the standard square bracket notation ...
INTEGRATION OF FUNCTIONAL PROGRAMMING AND
... specification into a programming language. Ideally, the resulting code should as expressive and generic as the original algebraic specification. In practice, limits of the chosen programming language interfere in the translation. For example, the Java programming language is unable to express gener ...
... specification into a programming language. Ideally, the resulting code should as expressive and generic as the original algebraic specification. In practice, limits of the chosen programming language interfere in the translation. For example, the Java programming language is unable to express gener ...
Lecture 9
... This is more - readable - amenable to reuse. Type classes are the mechanism which allow us to define functions like elem with type requirements. ...
... This is more - readable - amenable to reuse. Type classes are the mechanism which allow us to define functions like elem with type requirements. ...
Lambda Calculus Background, λ calculus Models of computation
... substitute the argumentet literally into the body of the function = call-by-name ≈ lazy evaluation • Applicative order = Leftmost-innermost = evaluate the argument first = call-by-value = eager evaluation • There are expressions with no normal form • If there is a normal form then normal order evalu ...
... substitute the argumentet literally into the body of the function = call-by-name ≈ lazy evaluation • Applicative order = Leftmost-innermost = evaluate the argument first = call-by-value = eager evaluation • There are expressions with no normal form • If there is a normal form then normal order evalu ...
A system of constructor classes
... original map and also satisfies the functor laws given above. With this in mind, it seems a shame that we have to use different names for each of these variants. A more attractive solution would allow the use of a single name map, relying on the types of the objects involved to determine which parti ...
... original map and also satisfies the functor laws given above. With this in mind, it seems a shame that we have to use different names for each of these variants. A more attractive solution would allow the use of a single name map, relying on the types of the objects involved to determine which parti ...
Functional Programming in Haskell
... 'The square of n is n*n, for every integer n.' Programs are equations. So we can write proofs using the definitions. square (double n) = square (2*n) = (2*n)*(2*n) = 2*2*n*n = double (double (square n)) CS7120 (Prasad) ...
... 'The square of n is n*n, for every integer n.' Programs are equations. So we can write proofs using the definitions. square (double n) = square (2*n) = (2*n)*(2*n) = 2*2*n*n = double (double (square n)) CS7120 (Prasad) ...
document
... (define mymap (lambda (f a b) (cond ((and (null? a) (null? b)) '()) (else (cons (f (first a) (first b)) (mymap f (rest a) (rest b))))))) Haskell mymap :: (Int -> Int-> Int) -> [Int] -> [Int] ->[Int] mymap f [] [] = [] mymap f (x:xs) (y:ys) = f x y : mymap f xs ys add :: Int -> Int -> Int add x y = x ...
... (define mymap (lambda (f a b) (cond ((and (null? a) (null? b)) '()) (else (cons (f (first a) (first b)) (mymap f (rest a) (rest b))))))) Haskell mymap :: (Int -> Int-> Int) -> [Int] -> [Int] ->[Int] mymap f [] [] = [] mymap f (x:xs) (y:ys) = f x y : mymap f xs ys add :: Int -> Int -> Int add x y = x ...
- Starter tutorials
... called as S-expressions or symbolic expressions. • An S-expression can be either an atom or a list. • McCarthy developed a universal function capable of evaluating any other function. It was named EVAL. Vishnu Institute of technology – Website: www.vishnu.edu.in ...
... called as S-expressions or symbolic expressions. • An S-expression can be either an atom or a list. • McCarthy developed a universal function capable of evaluating any other function. It was named EVAL. Vishnu Institute of technology – Website: www.vishnu.edu.in ...