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Abstract

Various formal systems based on that invented by Church to formalise the properties of functions acting on arguments and being combined to form other functions. This involves “lambda-abstraction”. The function f given by
$$ f(x)\; = \;x\; + \;1 $$
can be written using lambda-abstraction as
$$ f\; = \;{\rm{\lambda }}x.x\; + \;1 $$
so that
$$ f(1)\; = \;({\rm{\lambda }}x.x\; + \;1)(1)\; = \;2 $$
Application is written as juxtaposition, eg. fx for f(x). Terms made up using application and lambda abstraction can be manipulated in various ways, eg. rename bound variables (alpha conversion), and rewrite (λx.fx)a as fa (beta reduction).

Keywords

Logic Program Logic Programming Lexical Access Vocal Tract Solution Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Alan Bundy
    • 1
  1. 1.Department of Artificial IntelligenceUniversity of EdinburghEdinburghScotland, UK

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