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1---
2sort: 5
3next: true
4title: Interpreter
5---
7# Interpreter: `nock`
9The Nock VM is a Turing-complete function that maps a cell
10`{subject formula}` to a noun `product`, where `subject` is the
11data, `formula` is the code, and `product` is the result.
13To program in Hoon, this is all you need to know about Nock.
14It's probably at least worth skimming this definition, though.
16(Also, the Hoon programmer should know that (a) tail call
17elimination in Nock is straightforward; and (b) tail calls in
18Hoon always become tail calls in Nock.)
20## Rules
22Nock is a combinator interpreter defined by the spec below.
24This pseudocode (any system of axioms is properly defined in
25pseudocode) is a system of problem reduction rules. Variables
26match any noun; the first rule from the top matches.
28A problem that reduces to itself is an infinite loop, hence a
29crash ("bottom" in formal logic). Obviously a real interpreter
30can detect this crash and produce an out-of-band value instead.
32```
33?[a b] 0
34?a 1
35+[a b] +[a b]
36+a 1 + a
37=[a a] 0
38=[a b] 1
39=a =a
41/[1 a] a
42/[2 a b] a
43/[3 a b] b
44/[(a + a) b] /[2 /[a b]]
45/[(a + a + 1) b] /[3 /[a b]]
46/a /a
48*[a [b c] d] [*[a b c] *[a d]]
50*[a 0 b] /[b a]
51*[a 1 b] b
52*[a 2 b c] *[*[a b] *[a c]]
53*[a 3 b] ?*[a b]
54*[a 4 b] +*[a b]
55*[a 5 b] =*[a b]
57*[a 6 b c d] *[a 2 [0 1] 2 [1 c d] [1 0]
58 2 [1 2 3] [1 0] 4 4 b]
59*[a 7 b c] *[a 2 b 1 c]
60*[a 8 b c] *[a 7 [[7 [0 1] b] 0 1] c]
61*[a 9 b c] *[a 7 c 2 [0 1] 0 b]
62*[a 10 [b c] d] *[a 8 c 7 [0 3] d]
63*[a 10 b c] *[a c]
65*a *a
66```
68## Operators
70The pseudocode notation defines five prefix operators: `?`, `+`,
71`=`, `/`, and `*`.
73`?[x]` produces `0` if `x` is a cell, `1` if an atom.
75`+[x]` produces the atom `x` plus `1`.
77`=[x y]` produces `0` if `x` and `y` are the same noun, `1`
78otherwise.
80`/` is a tree addressing operator. The root of the tree is `1`;
81the left child of any node `n` is `2n`; the right child is
82`2n+1`. `/[x y]` is the subtree of `y` at address `x`.
84(For instance, `/[1 [531 25 99]]` is `[531 25 99]`; `/[2 [531 25
8599]]` is `531`; `/[3 [531 25 99]]` is `[25 99]`; `/[6 [531 25
8699]]` is `25`; `/[12 [531 25 99]]` crashes.)
88`*[x y]` is the Nock interpreter function. `x` is the subject,
89`y` is the formula.
91An invalid use of any operator (eg, incrementing a cell) crashes.
92This is specified as an infinite loop, but it's not actually an
93infinite loop.
95## Instructions
97A valid formula is always a cell. If the head of the formula is a
98cell, Nock treats both head and tail as formulas, resolves each
99against the subject, and produces the cell of their products. In
100other words, the Lisp program `(cons x y)` becomes the Nock
101formula `[x y]`.
103If the head of the formula is an atom, it's an instruction from
104`0` to `10`.
106A formula `[0 b]` produces the noun at tree address `b`
107in the subject.
109A formula `[1 b]` produces the constant noun `b`.
111A formula `[2 b c]` treats `b` and `c` is formulas, resolves each
112against the subject, then computes Nock again with the product of
113`b` as the subject, `c` as the formula.
115In formulas `[3 b]`, `[4 b]`, and `[5 b]`, `b` is another
116formula, whose product against the subject becomes the input to
117an axiomatic operator. `3` is `?`, `4` is `+`, `5` is `=`.
119Instructions `6` through `10` are macros; deleting them
120from Nock would decrease compactness, but not expressiveness.
122`[6 b c d]` is *if* `b`, *then* `c`, *else* `d`. Each of `b`,
123`c`, `d` is a formula against the subject. Remember that `0` is
124true and `1` is false.
126`[7 b c]` composes the formulas `b` and `c`.
128`[8 b c]` produces the product of formula `c`, against
129a subject whose head is the product of formula `b` with the
130original subject, and whose tail is the original subject. (Think
131of `8` as a ``variable declaration'' or ``stack push.'')
133`[9 b c]` computes the product of formula `c` with the
134current subject; from that product `d` it extracts a formula
135`e` at tree address `b`, then computes `*[d e]`.
136(Think, very roughly, of `d` as an object and `e` as a
137method.)
139`[10 b c]` is a *hint* semantically equivalent to the formula
140`c`. If `b` is an atom, it's a *static hint*, which is just
141discarded. If `b` is a cell, it's a *dynamic* hint; the head of
142`b` is discarded, and the tail of `b` is executed as a formula
143against the current subject; the product of this is discarded.
145A practical interpreter can do anything with discarded data, so
146long as the result it computes complies with the semantics of
147Nock. For example, the simplest use of hints is the ordinary
148"debug printf." It is erroneous for an interpreter to skip
149computing dynamic hints; they might crash.
151## Implementation
153The reader might wonder how an interpreter whose only arithmetic
154operation is increment can ever be practical.
156The short answer is that a Nock interpreter doesn't have to use
157the algorithm above; it just has to get the same result as the
158algorithm above.
160The algorithm for decrementing an atom is to count up to it, an
161O(n) operation. But if we know we are running a decrement
162formula,