Lambda abstraction
A term in lambda-calculus denoting a function. A lambda abstraction begins with a lower-case lambda (represented as “\” in this document), followed by a variable name (the “bound variable”), a full stop and a lambda expression (the body). The body is taken to extend as far to the right as possible so, for example an expression,
\ x . \ y . x+y
is read as
\ x . (\ y . x+y).
A nested abstraction such as this is often abbreviated to:
\ x y . x + y
The lambda expression (\ v . E) denotes a function which takes an argument and returns the term E with all free occurrences of v replaced by the actual argument. Application is represented by juxtaposition so
(\ x . x) 42
represents the identity function applied to the constant 42.
A lambda abstraction in Lisp is written as the symbol lambda, a list of zero or more variable names and a list of zero or more terms, e.g.
(lambda (x y) (plus x y))
Lambda expressions in Haskell are written as a backslash, “\”, one or more patterns (e.g. variable names), “->” and an expression, e.g. \ x -> x.
(1995-01-24)
Read Also:
- Lambda-b baryon
[lam-duh-bee] /ˈlæm dəˈbi/ noun, Physics. 1. a protonlike baryon containing a b quark; a neutral baryon with a mass 11,000 times that of the electron and a mean lifetime of approximately 1.1 X 10 -12 seconds.
- Lambda-b particle
lambda-b particle (lām’də-bē’) An electrically neutral baryon having a mass 11,000 times that of the electron and a mean lifetime of approximately 1.1 × 10-12 seconds. See Table at subatomic particle.
- Lambda-calculus
mathematics (Normally written with a Greek letter lambda). A branch of mathematical logic developed by Alonzo Church in the late 1930s and early 1940s, dealing with the application of functions to their arguments. The pure lambda-calculus contains no constants – neither numbers nor mathematical functions such as plus – and is untyped. It consists only […]
- Lambda-c baryon
[lam-duh-see] /ˈlæm dəˈsi/ noun, Physics. 1. a positively charged baryon with a mean lifetime of approximately 2.1 X 10 -13 seconds.
- Lambdacism
[lam-duh-siz-uh m] /ˈlæm dəˌsɪz əm/ noun, Phonetics. 1. excessive use of the sound l, its misarticulation, or its substitution for the sound r. /ˈlæmdəˌsɪzəm/ noun (phonetics) 1. excessive use or idiosyncratic pronunciation of l 2. another word for lallation