Lambda Calculus

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 λ-calculus
  Intro.
  Examples
  Syntax
  Interp.(L)
  Interp.(S)

also see
 PFL (λ-CCS)
 Prolog
<Exp> ::= <identifier> |  
( <Exp> ) |  
<Exp> <Exp> |  --application
λ<identifier>.<Exp>    --abstraction
-- Syntax of the λ-calculus --
 
The syntax of the λ-calculus is very simple, comprising just four kinds of expression but surprisingly it is sufficient to define any computable function.
Constants including integers, booleans and so on can all be defined using just the syntax above, as demonstrated by examples. Because of this it is sometimes convenient to extend the syntax with a fifth option of constants (0, 1, 2, ..., true, false, ∧, ∨, ¬, +, ...) but, if that is done, it is only a convenience and does not increase the power of the language.
Note that an abstraction defines an anonymous function.
The pure λ calculus appears to lack recursion (or equivalently iteration) but recursive functions can in fact be defined, as also demonstrated by examples.
 

NB. The applet above needs Java on.
 
The introduction describes the semantics of λ calculus and programming techniques, and the interpreter shows how it can be made to work.
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