nock.js

Nock is a combinator interpreter on nouns. A noun is an atom or a cell. An atom is an unsigned integer of any size; a cell is an ordered pair of nouns.

Nock is the foundational layer of Urbit.

nock.js is a toy interpreter, built for the fun of it.

usage

• install from npm: npm install nock.js

var nock = require('nock.js')
nock.nock(1, [0, 1])
// => 1

• or, clone and run

git clone https://github.com/joemfb/nock.js.git
cd nock.js
node example.js

• run unit tests

npm install
npm test

• load it in the browser (nock.js is a UMD module):

<script src="./nock.js"></script>
<script>
  nock.nock(1, [0, 1])
  // => 1
</script>

methods

See urbit.org/docs/nock/definition/ for an explanation of the pseudocode reduction rules that make up the Nock spec.

nock

nock(a)          *a
[a b c]          [a [b c]]
*[a [b c] d]     [*[a b c] *[a d]]
*a               *a

nock() recursively applies formulas (tail of its argument) to the subject (head of its argument).

nock.nock(1, [0, 1])
// 1

Nock nouns are always atoms (unsigned integers) or cells (a pair of nouns). The JS analogue to a cell is Array(2), so nock() converts Array arguments into nouns, associating right:

nock.nock([1, 2, 3], [0, 1])
// [1,[2,3]]

The subject can be omitted if the formula doesn't reference it:

nock.nock([1, 1])
// 1

Formulas without a subject are evaluated against [1, 0], which is Hoon null (~).

For convenience in evaluating generated formulas, arguments can be passed as strings (see generating formulas below):

nock.nock("[1 2 3]", "[0 1]")
// [1,[2,3]]

operators

Nock defines four operators:

?[a b]           0
?a               1
+[a b]           +[a b]
+a               1 + a
=[a a]           0
=[a b]           1
=a               =a

/[1 a]           a
/[2 a b]         a
/[3 a b]         b
/[(a + a) b]     /[2 /[a b]]
/[(a + a + 1) b] /[3 /[a b]]
/a               /a

• wut (?): test for an atom (1) or cell (0)
• lus (+): increment an atom
• tis (=): test equality
• fas (/): resolve a tree address

See urbit.org/docs/hoon/syntax for an explanation of the the method names

Operators are exported in the nock.operators namespace:

nock.operators.fas(2, [5, 9])
// 5

Unlike nock(), operators require both arguments to be present and valid nouns.

formulas

Nock defines 6 primitive formulas:

*[a 0 b]         /[b a]
*[a 1 b]         b
*[a 2 b c]       *[*[a b] *[a c]]
*[a 3 b]         ?*[a b]
*[a 4 b]         +*[a b]
*[a 5 b]         =*[a b]

• slot (0): resolve a tree address
• constant (1): return the formula regardless of subject
• evaluate (2): evaluate the product of second formula against the product of the first
• cell (3): test if the product is a cell
• incr (4): increment the product
• eq (5): test for equality between nouns in the product

And five additional formulas, reducible to the 6 above:

*[a 6 b c d]     *[a 2 [0 1] 2 [1 c d] [1 0] 2 [1 2 3] [1 0] 4 4 b]
*[a 7 b c]       *[a 2 b 1 c]
*[a 8 b c]       *[a 7 [[7 [0 1] b] 0 1] c]
*[a 9 b c]       *[a 7 c 2 [0 1] 0 b]
*[a 10 [b c] d]  *[a 8 c 7 [0 3] d]
*[a 10 b c]      *[a c]

• ife (6): if/then/else
• compose (7): evaluate formulas composed left-to-right
• extend (8): evaluate the second formula against [product of first, subject]
• invoke (9): construct a core and evaluate one of it's arms against it
• hint (10): skip first formula, evaluate second

Formulas are exported in the nock.formulas namespace:

nock.nock(2, [8, [[4, [1, 1]], [0, 1]]])
// [2, 2]
nock.formulas.eq(2, [8, [[4, [1, 1]], [0, 1]]])
// 0

As in the case of nock.operators, formulas require both arguments to be present and valid nouns.

Formulas 6-10 are implemented in two ways: directly by the interpreter, and as evaluated macro expansions:

nock.formulas.extend(42, [[4, [0, 1]], [0, 1]])
// [43, 42]
nock.formulas.macroExtend(42, [[4, [0, 1]], [0, 1]])
// [43, 42]

By default, the direct implementations are used. To use the macro expansions instead:

nock.useMacros()
nock.nock(42, [8, [[4, [0, 1]], [0, 1]]])
// [43, 42]

generating formulas

Hoon, the native language of Urbit, is also the language of dojo, the Urbit shell. Hoon expressions are compiled into Nock formulas, which are interpreted.

~novlen-hanweb:dojo> 1
1

Hoon -> Nock compilation is a first class primitive in Hoon (:code or !=):

~novlen-hanweb:dojo> !=(1)
[1 1]

as is the Nock formula itself (:nock or .*):

~novlen-hanweb:dojo> .*(. [1 1])
1
~novlen-hanweb:dojo> .*(. !=(1))
1

As previously noted, nock() can evaluate formulas passed as strings:

nock.nock('[1 1]')
// => 1

For convenience, convert your Nock formula to a string directly in dojo (technically, print your noun to a tape):

~novlen-hanweb:dojo> <!=(1)>
"[1 1]"

generating decrement

Hoon provides a decrement function in it's standard library:

~novlen-hanweb:dojo> (dec 10)
9

The implemention for dec is in a core - compiling it to Nock results in a formula that references that core, not a standalone decrement implementation:

~novlen-hanweb:dojo> !=((dec 10))
[8 [9 24.834.031 0 31] 9 2 [0 4] [7 [0 3] 1 10] 0 11]

There's probably a way to de-reference that core address (24.834.031) and compile the implementation - but I don't know it... Instead, we can evaluate the standard-library decrement implementation directly:

++  dec                                                 ::  decrement
  ~/  %dec
  |=  a/@
  ~|  %decrement-underflow
  ?<  =(0 a)
  =+  b=0
  |-  ^-  @
  ?:  =(a +(b))  b
  $(b +(b))

from urbit.org/docs/hoon/library/1a/#-dec

Converting the linked implementation from tall-form to flat-form (and removing the hint instructions) results in this expression:

|=(a/@ ?<(=(0 a) =+(b=0 |-(^-(@ ?:(=(a +(b)) b $(b +(b))))))))

which we can evaluate:

~novlen-hanweb:dojo> (|=(a/@ ?<(=(0 a) =+(b=0 |-(^-(@ ?:(=(a +(b)) b $(b +(b)))))))) 10)
9

compile to Nock (with !=):

~novlen-hanweb:dojo> !=((|=(a/@ ?<(=(0 a) =+(b=0 |-(^-(@ ?:(=(a +(b)) b $(b +(b)))))))) 10))
[ 8
  [8 [1 0] [1 6 [5 [1 0] 0 6] [0 0] 8 [1 0] 8 [1 6 [5 [0 30] 4 0 6] [0 6] 9 2 [0 2] [4 0 6] 0 7] 9 2 0 1] 0 1]
  9
  2
  [0 4]
  [7 [0 3] 1 10]
  0
  11
]

evaluate the compiled Nock (with .*):

~novlen-hanweb:dojo> .*(~ !=((|=(a/@ ?<(=(0 a) =+(b=0 |-(^-(@ ?:(=(a +(b)) b $(b +(b)))))))) 10)))
9

print to a tape (with <...>):

~novlen-hanweb:dojo> <!=((|=(a/@ ?<(=(0 a) =+(b=0 |-(^-(@ ?:(=(a +(b)) b $(b +(b)))))))) 10))>
"[8 [8 [1 0] [1 6 [5 [1 0] 0 6] [0 0] 8 [1 0] 8 [1 6 [5 [0 30] 4 0 6] [0 6] 9 2 [0 2] [4 0 6] 0 7] 9 2 0 1] 0 1] 9 2 [0 4] [7 [0 3] 1 10] 0 11]"

and, finally, evaluate in nock.js:

nock.nock("[8 [8 [1 0] [1 6 [5 [1 0] 0 6] [0 0] 8 [1 0] 8 [1 6 [5 [0 30] 4 0 6] [0 6] 9 2 [0 2] [4 0 6] 0 7] 9 2 0 1] 0 1] 9 2 [0 4] [7 [0 3] 1 10] 0 11]")
// 9

To get up and and running with an urbit, see github.com/urbit/urbit and urbit.org/docs/using/install/.