λ-definition of Function(al)s by Normal Forms
... the idea of universal iterator, a finite object that can iterate functions an infinite number of times. Scott, Wadsworth and others were then able to construct the denotational semantics of programming languages based on fixed point theory and λ-calculus. Simultaneously Wadsworth, Welch and others ...
... the idea of universal iterator, a finite object that can iterate functions an infinite number of times. Scott, Wadsworth and others were then able to construct the denotational semantics of programming languages based on fixed point theory and λ-calculus. Simultaneously Wadsworth, Welch and others ...
10~Chapter 10_Functi.. - Programming Assignment 0
... • Church’s model of computing is called the lambda calculus – based on the notion of parameterized expressions (with each parameter introduced by an occurrence of the letter λ—hence the notation’s name. – Lambda calculus was the inspiration for functional programming – one uses it to compute by subs ...
... • Church’s model of computing is called the lambda calculus – based on the notion of parameterized expressions (with each parameter introduced by an occurrence of the letter λ—hence the notation’s name. – Lambda calculus was the inspiration for functional programming – one uses it to compute by subs ...
Modeling Data With Functional Programming In R
... features. Many of these concepts originate from the lambda calculus, a mathematical framework for describing computation via functions. While each functional language supports a slightly di↵erent set of features, there is a minimal set of overlapping concepts that we can consider to form the basis o ...
... features. Many of these concepts originate from the lambda calculus, a mathematical framework for describing computation via functions. While each functional language supports a slightly di↵erent set of features, there is a minimal set of overlapping concepts that we can consider to form the basis o ...
Lecture 11: Functional Programming Concepts
... • If two expressions are defined to have equal values, then one can be substituted for the other in any expression without affecting the result of the computation. • For example, in s = sqrt(2); z = f(s,s); we can write z = f(sqrt(2), sqrt(2)); ...
... • If two expressions are defined to have equal values, then one can be substituted for the other in any expression without affecting the result of the computation. • For example, in s = sqrt(2); z = f(s,s); we can write z = f(sqrt(2), sqrt(2)); ...
Lambda-Lifting in Quadratic Time
... free variables of a function formal parameters of this function. All callers of the function must thus be passed these variables as arguments as well. A set of solutions is built by traversing the program. A solution pairs each function with a least set of additional parameters. Each block of locall ...
... free variables of a function formal parameters of this function. All callers of the function must thus be passed these variables as arguments as well. A set of solutions is built by traversing the program. A solution pairs each function with a least set of additional parameters. Each block of locall ...
Functional Programming
... Immutable data: Instead of altering existing values, altered copies are created and the original is preserved, thus, there’s no destructive assignment: a = 1; a = 2; -- illegal Referential transparency: Expressions yield the same value each time they are invoked; helps reasoning. Such expression ...
... Immutable data: Instead of altering existing values, altered copies are created and the original is preserved, thus, there’s no destructive assignment: a = 1; a = 2; -- illegal Referential transparency: Expressions yield the same value each time they are invoked; helps reasoning. Such expression ...
CS321 Functional Programming 2
... f == g = f False == g False && f True == g True It is possible to have instances for both Eq (a->b) and Eq (Bool->a) as long as both are not required at the same time in type checking some expression. ...
... f == g = f False == g False && f True == g True It is possible to have instances for both Eq (a->b) and Eq (Bool->a) as long as both are not required at the same time in type checking some expression. ...
PolyP | a polytypic programming language extension
... PolyP is an extension of a functional language that allows the programmer to de ne and use polytypic functions. The underlying language in this article is a subset of Haskell and hence lazy, but this is not essential for the polytypic extension. The extension introduces a new kind of (top level) de ...
... PolyP is an extension of a functional language that allows the programmer to de ne and use polytypic functions. The underlying language in this article is a subset of Haskell and hence lazy, but this is not essential for the polytypic extension. The extension introduces a new kind of (top level) de ...
An introduction to Python
... - range(N,M): return list of integers from N to M-1 - eval(string): evaluate a string as a Python expression ‣ eval(’C*x**n’, {’C’:10.,‘x’:2.0, ‘n’:3}) - str(object): convert obj to its string representation - zip(seq1, seq2, ...): return “zipped” list of tuples ...
... - range(N,M): return list of integers from N to M-1 - eval(string): evaluate a string as a Python expression ‣ eval(’C*x**n’, {’C’:10.,‘x’:2.0, ‘n’:3}) - str(object): convert obj to its string representation - zip(seq1, seq2, ...): return “zipped” list of tuples ...
Lisp, Then and Now
... For a function: The arguments are evaluated and their values passed to the function ...
... For a function: The arguments are evaluated and their values passed to the function ...
A static analysis for Bulk Synchronous Parallel ML to avoid
... (resp. hi− ) is the number of words transmitted (resp. received) by processor i during super-step s. The execution time of a BSP program composed of S super-steps is thus s Time(s). In general this execution time is a function of p and of the size of data n, or of more complex parameters like data ...
... (resp. hi− ) is the number of words transmitted (resp. received) by processor i during super-step s. The execution time of a BSP program composed of S super-steps is thus s Time(s). In general this execution time is a function of p and of the size of data n, or of more complex parameters like data ...
Proof for functional programming - University of Kent School of
... (where `_' is a wildcard pattern, matching anything), and also to allow access to the components of a compound object tail :: [a] -> [a] tail [] ...
... (where `_' is a wildcard pattern, matching anything), and also to allow access to the components of a compound object tail :: [a] -> [a] tail [] ...
Executing Higher Order Logic
... Execution What exactly do we mean by execution of specifications? Essentially, execution means finding solutions to queries. A solution σ is a mapping of variables to closed solution terms. A term t is called a solution term iff • t is of function type, or • t = c t1 . . . tn , where the ti are solu ...
... Execution What exactly do we mean by execution of specifications? Essentially, execution means finding solutions to queries. A solution σ is a mapping of variables to closed solution terms. A term t is called a solution term iff • t is of function type, or • t = c t1 . . . tn , where the ti are solu ...
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 ...
Common Lisp - cse.sc.edu
... Cons and Implicit Typing • Lisp uses lists as its primary data structure. • Lists are constructed similarly to other functional languages, using cons, append, etc. • Data is implicitly typed in list and can therefore be mixed in a given list. • For example, (cons ‘a (2 3)) evaluates to (a 2 3). ...
... Cons and Implicit Typing • Lisp uses lists as its primary data structure. • Lists are constructed similarly to other functional languages, using cons, append, etc. • Data is implicitly typed in list and can therefore be mixed in a given list. • For example, (cons ‘a (2 3)) evaluates to (a 2 3). ...
Functional Programming - TAMU Computer Science Faculty Pages
... Immutable data: Instead of altering existing values, altered copies are created and the original is preserved, thus, there’s no destructive assignment: a = 1; a = 2; -- illegal Referential transparency: Expressions yield the same value each time they are invoked; helps reasoning. Such expression ...
... Immutable data: Instead of altering existing values, altered copies are created and the original is preserved, thus, there’s no destructive assignment: a = 1; a = 2; -- illegal Referential transparency: Expressions yield the same value each time they are invoked; helps reasoning. Such expression ...
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 ...
Compiling Functional Programming Languages (FPLs) λ
... If we don’t want ANY variables, including those in the abstractions, we can use the universal combinators S and K . Note that, Supercombinator Method’s overhead for keeping environment is minimal but NOT ZERO: there are only local variables, values of which are all supplied at the same time. ...
... If we don’t want ANY variables, including those in the abstractions, we can use the universal combinators S and K . Note that, Supercombinator Method’s overhead for keeping environment is minimal but NOT ZERO: there are only local variables, values of which are all supplied at the same time. ...