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Computing (FOLDOC) dictionary
lambda abstraction
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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.