Combinatorial Problems, Combinator Equations and Normal Forms
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Some cases of solvability of the convertibility equation MX=N, where M,N and X are normal forms of the λ-K-β-calculus are considered and their relationship to pattern-matching problems is discussed. In particular, the solvability of such an equation is decided in the cases:
i)
N ≡ I and M = BF
ii)
N ≡ I and M = CBF where F is a normal form
iii)
N is an arbitrary normal form.
[1] Sören Stenlund. Combinators, λ-Terms and Proof Theory , 2011 .
[2] A. Church. The calculi of lambda-conversion , 1941 .