Bibliography: ???

- [Hindley and Meredith, 1990]
- [Chidgey, 1973]

This axiom is also called B,
since it corresponds to Curry and Fey's "B" combinator.
[Hindley and Meredith,
1990, pg 91]
In terms of combinators, B is:

B x y z => X (Y Z)

This axiom is also called "T pre", and like its relative (p>q) > ((q>r)>(p>r)) ("T suf") in the presence of Uniform Substitution and detachment (for >) they yield the rule if |- p>q and |- q>r infer |- p>r . [Chidgey, 1973, page 273]

In the presence of either of the rules:

- From |- p > (q>r) infer |- q > (p>r)
- From |- p > ((q>r)>s) infer |- (q>r) > (r>s)

Or the axiom:

- p > ((p>q) > q)

then T pre and T suf are equivalent. (And not in a whole of other cases -JH) [Chidgey, 1973, page 273]

© Copyright 2007 by John Halleck, All Rights Reserved. This page is http://www.cc.utah.edu/~nahaj/logic/structures/axioms/CCpqCCrpCrq.html This page was last modified on January 22nd, 2007.