Vocabulary/cou

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u : v

Monad-Dyad

Conjunction

Rank -- depends on the ranks of u and v -- WHY IS THIS IMPORTANT?

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Derives a dual-valence verb, which executes

• verb  u if called monadically
• verb  v if called dyadically.

The ranks of the derived verb (u : v) are as you'd expect:

• the monadic rank is the monadic rank of u
• the dyadic rank is the dyadic rank of v.

Conjunction Def (:) has several different uses, requiring several pages to document it

• Vocabulary/cor – A swatch (roadmap) of the different usages of (:) you'll encounter
• Vocabulary/com – the complete formal details of Explicit Definition
• Vocabulary/coa – anatomy of a sample explicit definition
• Vocabulary/cou [THIS PAGE] – how to use (:) to combine monad and dyad valences from separate definitions
• Vocabulary/NounExplicitDefinition – defining a noun as an explicit entity.

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Common uses

1. Define a single name with different monadic and dyadic forms

sort =: /:~ : /:  NB. monadic, sort y; dyadic, sort x in the order given by y

2. Provide a default value for argument x to let you call a given dyad monadically (i.e. with just a y-argument)

NB. Return the date x days in the future (default 0)
getdate =: (0&getdate) : (dyad define)
NB. body of dyadic verb here
)

3. Create a verb that can't be called with the wrong valence

Executes Cap ([:) in place of the bad valence to force  domain error

   mp =: +/ . *          NB. define a name for matrix product
   mtx =: i. 2 2         NB. a matrix
   mp mtx                NB. Oops, we called mp monadically, yielding an unexplainable result
2
   mp =: [: : (+/ . *)   NB. This'll fix it
   mp mtx
|domain error: mp
|       mp mtx

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