Monad and dyad
- A verb with only a right argument is called a monad.
- A verb with both right and left arguments is called a dyad.
Whether a verb is a monad or a dyad is its Valence.
A given verb's valence depends on the context it's being used in. It is not a property the verb keeps for life. When a given sentence containing the verb is executed, J decides from the syntax alone whether the verb is a monad or a dyad.
Often the same verb v behaves differently depending on whether it is called with one or two arguments.
- called with just a y-argument we talk of the monadic form of v, or that v is called monadically.
- called with both an x-argument and a y-argument we talk of the dyadic form of v, or that v is called dyadically.
Do all verbs have monadic and dyadic forms?
- Some verbs are monadic-only, e.g. Nub (~.). If you call them dyadically J signals a domain error.
- Some verbs are dyadic-only, e.g. Secant Slope (D:). If you call them monadically J signals a domain error.
A verb with both monadic and dyadic forms is called "dual-valence" or ambivalent.
All tacit verbs are ambivalent.
But it's possible to write a tacit verb having separate phrases to define the monadic form and the dyadic form of the verb. See Monad-Dyad (:) .
Example: the standard library verb: sort
sort is a
- Standard Library word(s) residing in the 'z'-locale.
- Defined in the factory script stdlib.ijs.
- View definition(s) by entering in the J session: open'stdlib'
sort /:~ :/:
The two phrases of sort lie either side of (:). They define respectively
- the monadic form: /:~
- the dyadic form: /:
- If both code blocks are present, the verb is ambivalent.
- If the 1st code block is absent, then the verb is dyadic-only, behaving as if defined using dyad define . See Explicit (:).
- If the 2nd code block is absent, then the verb is monadic-only, behaving as if defined using monad define . See Explicit (:).
Can monad and dyad have different names?
Yes. If v is a primitive, its monadic and dyadic forms may be known by different names.
The NuVoc portal shows different names for the same primitive in many cases.
Example: Let v be the primitive verb (<)
y-argument and x-argument
What's more, the names y and x are conventionally used for nouns which are intended to become the right and left arguments respectively of some given verb. NuVoc employs this convention throughout.
% y NB. monadic form of % x % y NB. dyadic form of %
Example: Let v be the primitive verb %
- called monadically - it returns the reciprocal of its right argument
- called dyadically - it divides the left argument by the right argument
% 4 NB. monadic % 0.25 4 % 2 NB. dyadic % 2
Can a verb be called with no arguments?
Some verbs don't need arguments.
Some languages, e.g. APL (the ancestor of J), allow a function to be executed with no arguments (niladic form). But J has no niladic form. If you type the name of a verb without any arguments into the session window, J does not execute the verb. Instead it displays its definition.
As we said above, J decides from the syntax alone whether the verb is a monad or a dyad. It can't do this without finding a noun to serve as the y-argument.
A verb that ignores its arguments is conventionally executed by giving it an empty y-argument. Such verbs include
- Several Foreigns (!:), e.g. 9!:14 (returns the J version)
- User-written verbs that get their data from global nouns or the machine environment.
Example: The Constant Function (0:) ignores its arguments and always returns the value 0 . If you call 0: monadically, it needs no y-argument and ignores whatever noun you give it. Nevertheless a y-argument must be given, so we choose to give it the empty string: '' .
0: '' 0
But if you give it no arguments at all, J computes a verb value, which it returns. The effect is to show you the verb's definition, i.e. itself, in this case.
Example: The Foreign (9!:14) returns the J version. It needs no argument to be able to do this. Nevertheless it needs a y-argument for the sake of sentence syntax, otherwise J won't execute it.
jver=: 9!:14 jver '' j602/2008-03-03/16:45
In this case the verb is so touchy that J signals an error if you give it any argument except an empty one.
jver 0 |rank error: jver | jver 0 jver 'the quick brown fox' |length error: jver | jver'the quick brown fox'
But if you give jver no arguments at all, J doesn't execute it. Instead J computes a verb value, which it displays in the session. The effect is to show you the verb's definition
Does your verb need more than 2 arguments?
Often we want to call a verb with more than 2 arguments.
There are a number of Strategies for dealing with Multiple Verb Arguments.