# lambda calculus

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## lambda calculus

[′lam·də ‚kal·kyə·ləs]
(mathematics)
A mathematical formalism to model the mathematical notion of substitution of values for bound variables.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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This illustrates that the syntactic structures of B and C alone provide insufficient information for a satisfactory control of polyvariance and that a refined abstraction operator should also take the associated SLDNF-trees into consideration.
So an abstraction operator should focus on the "essential" structure of an SLDNF-tree and for instance disregard the particular substitutions and goals within the tree.
2.4 An Abstraction Operator Using Characteristic Trees
The following abstraction operator represents a first attempt at using characteristic trees for the control of polyvariance.
The abstraction operator [chabs.sub.P, U] is then defined as [chabs.sub.P, U](A) = {msg([A.sub.[Tau]]) [where] [Tau] is a characteristic tree}.
We first define an abstraction operator which, by definition, preserves the characteristic trees.
The overall tree is kept finite through ensuring monotonicity of the measure functions, and termination of the algorithm follows, provided the abstraction operator (on atoms) is similarly well-founded.
Alternatively, one could try to use an altogether more accurate abstraction operator than taking an msg on characteristic atoms.

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