A term in ef="module.php?name=Lexikon&file=search&eid=1&query=lambda-calculus">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 ef="module.php?name=Lexikon&file=search&eid=1&query=lambda expression">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 ef="module.php?name=Lexikon&file=search&eid=1&query=free">free occurrences of v replaced by the ef="module.php?name=Lexikon&file=search&eid=1&query=actual argument">actual argument. Application is represented by ef="module.php?name=Lexikon&file=search&eid=1&query=juxtaposition">juxtaposition so ( x . x) 42 represents the identity function applied to the constant 42. A ef="module.php?name=Lexikon&file=search&eid=1&query=lambda abstraction">lambda abstraction in ef="module.php?name=Lexikon&file=search&eid=1&query=Lisp">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 ef="module.php?name=Lexikon&file=search&eid=1&query=Haskell">Haskell are written as a backslash, "", one or more patterns (e.g. variable names), "->" and an expression, e.g. x -> x. (1995-01-24)

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