notes
... The last of the six rules applies when y ∈ FV(e). In this case, we rename the bound variable y to z to avoid capture of the free occurrence of y. One might well ask: but what if y occurs free in the scope of a λz in e0 ? Wouldn’t the z then be captured? The answer is that it will be taken care of in ...
... The last of the six rules applies when y ∈ FV(e). In this case, we rename the bound variable y to z to avoid capture of the free occurrence of y. One might well ask: but what if y occurs free in the scope of a λz in e0 ? Wouldn’t the z then be captured? The answer is that it will be taken care of in ...
Scheme [PPT]
... • map – Takes as arguments a function and a sequence of lists – There must be as many lists as arguments of the function, and lists must have the same length – Applies the function on corresponding sets of elements from the lists – Returns all the results in a list f (E1 E2 ...... En) ((f E1) (f E ...
... • map – Takes as arguments a function and a sequence of lists – There must be as many lists as arguments of the function, and lists must have the same length – Applies the function on corresponding sets of elements from the lists – Returns all the results in a list f (E1 E2 ...... En) ((f E1) (f E ...
Functional Programming
... • Computation is more implicit (suggested but not communicated directly ) and functional call is the only form of explicit control • Many (commercial) applications exist for functional programming: ...
... • Computation is more implicit (suggested but not communicated directly ) and functional call is the only form of explicit control • Many (commercial) applications exist for functional programming: ...
functional form
... parameter and yields a list of values obtained by applying the given function to each element of a list of parameters ...
... parameter and yields a list of values obtained by applying the given function to each element of a list of parameters ...
Part 1
... a function application operation, some structure to represent data In functional programming, functions are viewed as values themselves, which can be computed by other functions and can be parameters to other functions Functions are first-class values ...
... a function application operation, some structure to represent data In functional programming, functions are viewed as values themselves, which can be computed by other functions and can be parameters to other functions Functions are first-class values ...
2. Functional Programming
... Automatic theorem proving and computer algebra Algorithmic optimization of programs written in pure functional languages ...
... Automatic theorem proving and computer algebra Algorithmic optimization of programs written in pure functional languages ...
Introduction, Scheme basics (expressions, values)
... Evaluation of Expressions The value of a numeral: number The value of a built-in operator: machine instructions to execute The value of any name: the associated value in the environment To Evaluate a combination: (as opposed to special form) a. Evaluate all of the sub-expressions in some order b. A ...
... Evaluation of Expressions The value of a numeral: number The value of a built-in operator: machine instructions to execute The value of any name: the associated value in the environment To Evaluate a combination: (as opposed to special form) a. Evaluate all of the sub-expressions in some order b. A ...
4on1 - FSU Computer Science
... Absence of side effects makes expressions referentially transparent: the value of an expression depends solely on the function return values in it and not on evaluation order and/or values of global variables A function can always be counted on to return the same results with the same input paramete ...
... Absence of side effects makes expressions referentially transparent: the value of an expression depends solely on the function return values in it and not on evaluation order and/or values of global variables A function can always be counted on to return the same results with the same input paramete ...
Example
... let val x = E1 in E2 end is called a binding of x. e.g., let val x = 2 in x + x end – All occurrences of x in E2 are said to be within the scope of this binding, but occurrences x in E1 are not in the scope of this binding of x. – For nested binding of the same variable, first applying renaming to t ...
... let val x = E1 in E2 end is called a binding of x. e.g., let val x = 2 in x + x end – All occurrences of x in E2 are said to be within the scope of this binding, but occurrences x in E1 are not in the scope of this binding of x. – For nested binding of the same variable, first applying renaming to t ...
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 prog. in scheme
... • Here’s compose for two functions in Scheme (define (compose2 f g) (lambda (x) (f (g x)))) • Note that compose calls lambda which returns a new function that applies f to the result of applying g to x • We’ll look at how the variable environments work to support this in the next topic, closures • B ...
... • Here’s compose for two functions in Scheme (define (compose2 f g) (lambda (x) (f (g x)))) • Note that compose calls lambda which returns a new function that applies f to the result of applying g to x • We’ll look at how the variable environments work to support this in the next topic, closures • B ...
Functional Programming
... • If M and N are lambda expressions, then the application of M to N, written (M N), is a lambda expression • An abstraction, written (x∙M), where x is an identifier and M is a lambda expression, is also a lambda expression. ...
... • If M and N are lambda expressions, then the application of M to N, written (M N), is a lambda expression • An abstraction, written (x∙M), where x is an identifier and M is a lambda expression, is also a lambda expression. ...
fp_in_scheme
... • Here’s compose for two functions in Scheme (define (compose2 f g) (lambda (x) (f (g x)))) • Note that compose calls lambda which returns a new function that applies f to the result of applying g to x • We’ll look at how the variable environments work to support this in the next topic, closures • B ...
... • Here’s compose for two functions in Scheme (define (compose2 f g) (lambda (x) (f (g x)))) • Note that compose calls lambda which returns a new function that applies f to the result of applying g to x • We’ll look at how the variable environments work to support this in the next topic, closures • B ...
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: ...
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 ...
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 Programming Basics
... • The only thing that matters about an expression is its value, and any subexpression can be replaced by any other expression equal in value. • The value of an expression is independent of its position only provided we remain within the scopes of the definitions which apply to the names occurring in ...
... • The only thing that matters about an expression is its value, and any subexpression can be replaced by any other expression equal in value. • The value of an expression is independent of its position only provided we remain within the scopes of the definitions which apply to the names occurring in ...
02/06
... Lisp implementations have a front end called the reader 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 cha ...
... Lisp implementations have a front end called the reader 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 cha ...
Scheme: More function examples, higher
... • Note that fib-help's parameter n keeps track of which Fibonacci number is currently being computed, and parameter last keeps track of which Fibonacci number that we ultimately want. f1 is the previous Fibonacci number, and f2 is the Fibonacci number that comes before f1. ...
... • Note that fib-help's parameter n keeps track of which Fibonacci number is currently being computed, and parameter last keeps track of which Fibonacci number that we ultimately want. f1 is the previous Fibonacci number, and f2 is the Fibonacci number that comes before f1. ...
notes
... depends on how they are interpreted. We must have a good understanding of this interpretation, otherwise it would be impossible to write programs that do what is intended. It may seem like a straightforward task to specify what a program is supposed to do when it executes. After all, basic instructi ...
... depends on how they are interpreted. We must have a good understanding of this interpretation, otherwise it would be impossible to write programs that do what is intended. It may seem like a straightforward task to specify what a program is supposed to do when it executes. After all, basic instructi ...
Advanced Formal Methods
... Exercise 4: Define ”Church lists”. A list [x,y,z] can be thought of as a function taking two arguments c (for cons) and n (for nil), and returns c x (c y (c z n)), similar to the Church numerals. Write a function nil representing the empty list, and a function cons that takes arguments h and (a func ...
... Exercise 4: Define ”Church lists”. A list [x,y,z] can be thought of as a function taking two arguments c (for cons) and n (for nil), and returns c x (c y (c z n)), similar to the Church numerals. Write a function nil representing the empty list, and a function cons that takes arguments h and (a func ...
PPT
... C[[ while B do P ]] = the function f such that f(s) = s if E [[ B ]] s is false f(s) = f( C[[ P ]](s) ) if E [[ B ]] s is true Mathematics of denotational semantics: prove that there is such a function and that it is uniquely determined. “Beyond scope of this course.” ...
... C[[ while B do P ]] = the function f such that f(s) = s if E [[ B ]] s is false f(s) = f( C[[ P ]](s) ) if E [[ B ]] s is true Mathematics of denotational semantics: prove that there is such a function and that it is uniquely determined. “Beyond scope of this course.” ...
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 ...
Chapter_4
... Hugs> prd 0 where prd (n+1) = n Program error: pattern match failure: v1618 0 Hugs> prd2 5 where prd2 (n+2) = n ...
... Hugs> prd 0 where prd (n+1) = n Program error: pattern match failure: v1618 0 Hugs> prd2 5 where prd2 (n+2) = n ...