Digits
Let's write a generator that takes a @ud
(unsigned decimal) and returns a list
of its digits.
!: : %say = [* [n=@ud ~] ~] : %noun = lis=(list @ud)  ^+ lis ?: (lte n 0) lis %= $ n (div n 10) lis (mod n 10)^lis ==
We're creating a %say
generator. That means we
need some "boilerplate" code in the format of [%say [%noun "data"]]
:
: %say = [* [n=@ud ~] ~] : %noun
The head of this cell is the literal %say
.
In the tail is the gate and its sample: = [* [n=@ud ~] ~]
. This is
where we describe any arguments we are expecting to be passed in when the
generator is called. We are expecting data of type @ud
. We give the data the
face n
so that we can easily reference it later.
Also in the tail is another cell
, its head indicating to the dojo
how to
print the value we are creating. In this case, we use the generic %noun
.
The tail of our second cell is the product of the rest of the program.
= lis=(list @ud)
We use the above code to construct a list
of @ud
by cutting up the @ud
we
got passed and so we add a face onto that type. This list is empty until we
manipulate it further.
 ^+ lis ?: (lte n 0) lis

creates a gate that functions as a recursion point.
We are actually able to reuse lis
for the type of output that we are going
to produce. A sibling of the ^
rune, ^+
is distinct because it is for
casting by example. It takes type information from an instance of that type.
It's useful when using a complicated type.
?: (lte n 0) lis
?:
checks if the statement that follows is true or false. In our case, if it's
true that n
is less than or equal to 0
, we simply return lis
. Otherwise,
we branch to the following operations:
%= $ n (div n 10) lis (mod n 10)^lis ==
%=
is the rune that takes a wing with any number changes, in the
form of a list. Our list has two elements that represent such changes, contained
in a $
expression to perform recursion. This is the tall form of an equivalent
syntax that you may be more familiar with:
$(n (div n 10), lis (mod n 10)^lis)
.
The first change divides n
by 10
, rounding down without a remainder, and
assigning that product as the new value for n
.
The second change prepends the remainder of n
divided 10
to lis
(x^y
is
an alternative syntax for [x y]
). mod
performs the modulo operation.
Together, these operations will pull each digit out of n
and put it into a
list
. That's because dividing n
by 10 will knock off one decimal place from
the value, and mod
will store the actual discarded digit. To visualize this
complementarity, let's run some operations in the dojo:
> (div 146 10) 14 > (mod 146 10) 6

TODO What if we do this with vases? Can we accept a vase, map it to whatever the correct value would be to extract each digit of the number in whatever base we are interpreting it in?

TODO from Rob: we need a few exercises here. Maybe asking the reader to make one that accepts a vase could be one?