redexes love

# redexes

## Definitions

• noun Plural form of redex.

## Etymologies

Sorry, no etymologies found.

## Examples

• An appropriate subrelation of reduction is the simultaneous contraction of a set of nonoverlapping redexes, which is denoted by sc.

Combinatory Logic

• ˜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).

Combinatory Logic

• 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.

Combinatory Logic

• A term is in normal form (nf) when it contains no redexes.

Combinatory Logic

• 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.

Combinatory Logic