The Lambda Calculus: a minimal ML?
... λ x.M x is a bit “baroque” in a sense. Certainly, for any term a, since there are no free occurrences of x in M , the β-reduction rule gives us (λ x.M x) a →β M a . And so, depending on our purposes below, we sometimes view the terms λ x.M x and M as equivalent. Definition 21 (eta-conversion). For a ...
... λ x.M x is a bit “baroque” in a sense. Certainly, for any term a, since there are no free occurrences of x in M , the β-reduction rule gives us (λ x.M x) a →β M a . And so, depending on our purposes below, we sometimes view the terms λ x.M x and M as equivalent. Definition 21 (eta-conversion). For a ...
Chapter 15 Functional Programming
... Any identifier is a lambda expression. If M and N are lambda expressions, then the application of M to N , written (MN) is a lambda expression. An abstraction, written ( λx⋅M) where x is an identifier and M is a lambda expression, is also a lambda expression. Chapter 15: Functional Programming ...
... Any identifier is a lambda expression. If M and N are lambda expressions, then the application of M to N , written (MN) is a lambda expression. An abstraction, written ( λx⋅M) where x is an identifier and M is a lambda expression, is also a lambda expression. Chapter 15: Functional Programming ...
15. Functional Programming
... called the domain set, to another set, called the range set A lambda expression specifies the parameter(s) and the mapping of a function in the following form λ(x) x * x * x for the function cube (x) = x * x * x ...
... called the domain set, to another set, called the range set A lambda expression specifies the parameter(s) and the mapping of a function in the following form λ(x) x * x * x for the function cube (x) = x * x * x ...
PLD VII Haddad
... In the late 1970s, Gerald Sussman and Guy Steele developed a variant named Scheme. This is the version that had the most impact on university use of LISP. In 1992 a standard for Common LISP was finally written ...
... In the late 1970s, Gerald Sussman and Guy Steele developed a variant named Scheme. This is the version that had the most impact on university use of LISP. In 1992 a standard for Common LISP was finally written ...
curry
... A tasty dish? • Currying was named after the Mathematical logician Haskell Curry (1900-1982) • Curry worked on combinatory logic … • A technique that eliminates the need for variables in mathematical logic … • and hence computer programming! – at least in theory ...
... A tasty dish? • Currying was named after the Mathematical logician Haskell Curry (1900-1982) • Curry worked on combinatory logic … • A technique that eliminates the need for variables in mathematical logic … • and hence computer programming! – at least in theory ...
TILC: The Interactive Lambda-Calculus Tracer1
... Variables in lambda-terms may occur free when they are not bound by any λ-abstraction. Terms are considered identical modulo renaming of bound variables. By Λ1 [x 7→ Λ2 ] we denote the substitution of variable x occurring free in Λ1 by Λ2 ; this substitution can not capture variables occurring free ...
... Variables in lambda-terms may occur free when they are not bound by any λ-abstraction. Terms are considered identical modulo renaming of bound variables. By Λ1 [x 7→ Λ2 ] we denote the substitution of variable x occurring free in Λ1 by Λ2 ; this substitution can not capture variables occurring free ...
Functional Programming
... (member x xs) returns the sublist of xs that starts with x, or returns () (member 5 '(a b)) ⇒ () (member 5 '(1 2 3 4 5 6)) ⇒ (5 6) COP4020 Spring 2011 ...
... (member x xs) returns the sublist of xs that starts with x, or returns () (member 5 '(a b)) ⇒ () (member 5 '(1 2 3 4 5 6)) ⇒ (5 6) COP4020 Spring 2011 ...
COMP 356 Programming Language Structures Notes for Chapter 15
... • assigning one processor to f and one to each
• each processor evaluating an returns its result to the processor evaluating f
• f is evaluated
This works because each ei has no side effects, so the order they are evaluated in doesn’t matter. Additionally, all processors can share the sa ...
... • assigning one processor to f and one to each
Propositional Calculus
... • In the base case, there are self evaluating expressions (e.g. numbers and symbols). In addition, various special forms such as quote and if must be handled separately. ...
... • In the base case, there are self evaluating expressions (e.g. numbers and symbols). In addition, various special forms such as quote and if must be handled separately. ...
Lambda the Ultimate - Rice University Campus Wiki
... “Lambda expressions are especially useful when you want to perform operations on a list or other collection and want to avoid the extra work of defining a function. Many F# library functions take function values as arguments, and it can be especially convenient to use a lambda expression in those ca ...
... “Lambda expressions are especially useful when you want to perform operations on a list or other collection and want to avoid the extra work of defining a function. Many F# library functions take function values as arguments, and it can be especially convenient to use a lambda expression in those ca ...
Functional Programming
... ; also abbreviated as (cadr '(2 3 4)) ; also abbreviated as (cddr '(2 3 4)) ...
... ; also abbreviated as (cadr '(2 3 4)) ; also abbreviated as (cddr '(2 3 4)) ...
Higher-order functions
... and if properly done, this is even rather efficient. Lazy languages require a rather different programming style than eager ones. They are studied primarily at Chalmers University (Gothenburg), Oregon Graduate Institute, Yale University, University of Kent at Canterbury, and Microsoft Research Cambr ...
... and if properly done, this is even rather efficient. Lazy languages require a rather different programming style than eager ones. They are studied primarily at Chalmers University (Gothenburg), Oregon Graduate Institute, Yale University, University of Kent at Canterbury, and Microsoft Research Cambr ...
Variable Scoping Rules in Erlang
... These lookup tables can be used directly to implement the transformations ...
... These lookup tables can be used directly to implement the transformations ...
15. Functional Programming
... called the domain set, to another set, called the range set A lambda expression specifies the parameter(s) and the mapping of a function in the following form λ(x) x * x * x for the function cube (x) = x * x * x ...
... called the domain set, to another set, called the range set A lambda expression specifies the parameter(s) and the mapping of a function in the following form λ(x) x * x * x for the function cube (x) = x * x * x ...
ppt
... Can be returned as a value Can be passed as an argument Can be put into a data structure as a value Can be the value of an expression ...
... Can be returned as a value Can be passed as an argument Can be put into a data structure as a value Can be the value of an expression ...
7. Introduction to the Lambda Calculus
... work only under a license identical to this one. • For any reuse or distribution, you must make clear to others the license terms of this work. • Any of these conditions can be waived if you get permission from the copyright holder. Your fair use and other rights are in no way affected by the above. ...
... work only under a license identical to this one. • For any reuse or distribution, you must make clear to others the license terms of this work. • Any of these conditions can be waived if you get permission from the copyright holder. Your fair use and other rights are in no way affected by the above. ...
ppt
... Can be returned as a value Can be passed as an argument Can be put into a data structure as a value Can be the value of an expression ...
... Can be returned as a value Can be passed as an argument Can be put into a data structure as a value Can be the value of an expression ...
Functional Programming in Scheme Functional Programming
... Can be returned as a value Can be passed as an argument Can be put into a data structure as a value Can be the value of an expression ...
... Can be returned as a value Can be passed as an argument Can be put into a data structure as a value Can be the value of an expression ...
Lambda Calculus
... to Share — to copy, distribute and transmit the work to Remix — to adapt the work Under the following conditions: Attribution. You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work). Share Alike. ...
... to Share — to copy, distribute and transmit the work to Remix — to adapt the work Under the following conditions: Attribution. You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work). Share Alike. ...
Lambda
... x. y. z. ((x y) z) true apple pear x. y. z. ((x y) z) x.y.x apple pear y. z. ((x.y.x y) z) apple pear z. ((x.y.x apple ) z) pear ((x.y.x apple ) pear) (y. apple ) pear) ...
... x. y. z. ((x y) z) true apple pear x. y. z. ((x y) z) x.y.x apple pear y. z. ((x.y.x y) z) apple pear z. ((x.y.x apple ) z) pear ((x.y.x apple ) pear) (y. apple ) pear) ...
19. Introduction to evaluation order
... 20. Rewrite rules, reduction, and normal forms At this point in the material it will be assumed that the reader is motivated to study evaluation order in some detail. An evaluation of an expression can be understood as a transformation of the expressions which preserves its meaning. In this chapter ...
... 20. Rewrite rules, reduction, and normal forms At this point in the material it will be assumed that the reader is motivated to study evaluation order in some detail. An evaluation of an expression can be understood as a transformation of the expressions which preserves its meaning. In this chapter ...
Lambda expressions, functions and binding
... Here's a very simple Haskell program. If you're used to C or Java or Visual Basic, you might think that x, y, z are boxes that you put values in. Later you might change the value in the box using something like x = x + 1. Not in functional programming! This is BINDING, not ASSIGNMENT. We say "x is b ...
... Here's a very simple Haskell program. If you're used to C or Java or Visual Basic, you might think that x, y, z are boxes that you put values in. Later you might change the value in the box using something like x = x + 1. Not in functional programming! This is BINDING, not ASSIGNMENT. We say "x is b ...
Chapter 7 Recursion
... Alonzo Church in 1934. It's analogous to Turing machines, but it's both simpler and more practical. Where the Turing machine is something like a model of assembly language, the -calculus is a model of function application. Like Turing machines, it defines a simplified programming language that you ...
... Alonzo Church in 1934. It's analogous to Turing machines, but it's both simpler and more practical. Where the Turing machine is something like a model of assembly language, the -calculus is a model of function application. Like Turing machines, it defines a simplified programming language that you ...