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# 2B. Ambivalent Functions

The phrase`h=: f : g` defines`h` as the function whose monadic case is`f` and whose dyadic case is`g` .`` The components`f` and`g` may be functions already defined and named, or they may be tacit or explicit phrases. Moreover, either (but not both) may be defined in terms of the other by using`$:` for self-reference in a tacit definition.

`v0=: 10&^. : ^.` | Base 10 log for monadic case
`v1=: 10&$: : ^.` | Same using self-reference to dyad
`v2=: 10&^. :($:*^.@(10"0)%^.@[)` | Same using self-reference to monad
`d3=: res=: [: : |` | Domain of monad is empty (dyadic only)
`m4=: abs=: | : [:` | Domain of dyad is empty (monadic only)

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