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- noun Plural form of
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An appropriate subrelation of reduction is the simultaneous contraction of a set of nonoverlapping redexes, which is denoted by sc.
˜Nonoverlapping™ means that there are no shared subterm occurrences between two redexes. sc includes because a one-step reduction of a redex may be viewed instead as sc of a singleton set of redexes. sc is, obviously, included in ¥ (i.e., in reduction).
A term that is either of the form SMNP or of the form KMN is a redex, and the leading combinators (S and K, respectively) are the heads of the redexes.
A term is in normal form (nf) when it contains no redexes.
Note that one-step reduction need not decrease the total number of redexes that a term contains, hence, is does not follow that every term can be turned into one in nf after finitely many one-step reductions.