# Vocabulary/dollarco

 [x] \$: y Self-Reference

Rank Infinity -- operates on [x and] y as a whole -- WHY IS THIS IMPORTANT?

Lets a verb call itself, even if the verb is anonymous.

In a tacit recursive verb, \$: indicates a point of recursion. Executing \$: reexecutes the recursive verb.

### Common Uses

1. To provide a default for the monadic valence of a verb.

```   NB. create string to use for the sign of y
NB. x is (string to use for 0);(string to use for +);(string to use for -)
NB. result is the correct string for y
selsign =: ({::~ *)"1 0
('';'<CR>';'<DR>') selsign _4
<DR>
selsign =: (' +-'&\$:) : ({::~ *)"0 1 0  NB. Provide default signs for monadic use
selsign 4
+
('';'<CR>';'<DR>') selsign 4  NB. Dyadic use is unaffected
<CR>
```

This kind of default can also be used when the dyadic valence is defined explicitly:

```   NB. Get digits of y using radix x (default 10)
digits =: (10&\$:) : (4 : 0)
x #.^:_1 y
)
digits 64  NB. default base 10...
6 4
4 digits 64   NB. ...or use base given as x
1 0 0 0
```

Here the overall verb is tacit, because it is defined by u : v. The dyadic valence is explicit, but it doesn't enter the picture until after the recursion.

2. To create a tacit recursive verb.

```   NB. factorial(0 or 1)=1; otherwise factorial(n) = n * factorial(n-1)
factorial =: 1: ` (* \$:@<:) @. *
factorial 6
720
```

1. When used in the definition of a tacit recursive verb, (\$:) means the same as the name of the recursive verb.

```   factorial =: 1: ` (* factorial@<:) @. *  NB. Identical to definition above
```

The advantage of using \$: is that the name of the verb can change without requiring any change to the definition of the verb.

2. When used in any other context, \$: refers to a portion of the sentence in which it is found: the executing verb-phrase that contains the (\$:).

In the following sentences the portion referred to by \$: is underlined:
1: ` (* \$:@<:) @. * 6
720
Here we copied the definition of factorial. The entire sequence 1: ` (* \$:@<:) @. * is one derived verb, so \$: refers to it.
1 + 1: ` (* \$:@<:) @. * 6
721
Here 1: ` (* \$:@<:) @. * is still one derived verb. The leading 1 + is not part of this verb. When 1: ` (* \$:@<:) @. * is executed (monadically), \$: still refers only to it.

3. In no case does \$: refer to a larger unit than the sentence it appears in, for example an explicit definition in which it appears.

4. Another way to think of the limit of recursion is by recursion startpoints. A recursion starts executing at the most recent recursion startpoint. Recursion startpoints are:

• the execution by the parser of a verb on noun arguments
• the execution of any named entity
• the start of a task (i. e. execution of u in u t. v

### Details

1. Because \$: stands in for the name of the verb containing it, you must be wary of using u f. when u refers to a tacit recursive verb.

Since f. replaces names with their values,  \$: inside replaced names will change its meaning.

CategoryVoc CategoryVocRecursion