@@ -55,43 +55,41 @@ or `48.879`, whose parent is `~mun`, `0xef`, `239`. The parent of
5555- `noun`: an `atom` or a `cell`
5656- `atom`: any natural number
5757- `cell`: any ordered pair of `noun`s
58−- `subject`: a `noun` - the argument against which a `formula` is evaluated
59−- `formula`: a `noun` - any of the Hoon formula numbers (0-10), followed by *(TODO: ?)*
58+- `subject`: a `noun` - the data against which a `formula` is evaluated
59+- `formula`: a `cell` - any of the Nock formula numbers (0-10) or a pair of formulas that resolves to a cell.
6060- `product`: a `noun` - the result of evaluating a `formula` against a `subject`
6161
62−*See [Nock definition](../../nock/definition/)*
62+*See [Nock definition](/nock/definition/).*
6363
6464### Hoon
6565
66−> Hoon is a strict, higher-order typed functional language which compiles itself to Nock.
66+> Hoon is a strict, higher-order typed functional language that compiles itself to Nock.
6767
6868###### `span`: an inferred type
6969
7070A `span` defines a set (finite or infinite) of `noun`s and ascribes some semantics to it. There is no Hoon syntax for a `span`; it is always produced as the inferred range of an expression (`twig`).
7171
72−*See [basic types](../../hoon/basic/#-type-span-and-mold)*
72+*See [basic types](/hoon/basic/#-type-span-and-mold).*
7373
7474###### `mold`: a type constructor / validator
7575
7676A mold is an idempotent `gate` (function), accepting any `noun` and normalizing it to a range.
7777
78−- `icon`: the `span` of a `mold`
79−- `bunt`: *(TODO: ??)*
78+- `bunt`: the default value of a `mold`
79+- `icon`: the `span` of a `bunt`
8080
81−*See [`mold` `twig`s](../../hoon/twig/buc-mold/)*
81+*See [`mold` `twig`s](/hoon/twig/buc-mold/).*
8282
8383###### `gate`: a function, lambda or closure
8484
85−*TODO: simplify description*
86−
87−A `gate` is a specialized `core` with only one `arm` (whose name is the empty string (the symbol `$`). To call a `gate` on an argument, replace the `sample` (at tree address `6` in the `core`) with the argument, and then compute the `arm`.
85+A `gate` is a `core` with one `arm`. To call a `gate` on an argument, replace the `sample` (at tree address `6` in the `core`) with the argument, and then compute the `arm`.
8886
8987The `payload` of a `gate` has a shape of `{sample context}`.
9088
91−- `sample`: the argument *(TODO: or plural?)* of a `gate`
92−- `context`: the subject in *(TODO: against?)* which a `gate` was defined
89+- `sample`: the argument
90+- `context`: the subject in which a `gate` was defined
9391
94−+*See [basic types](../../hoon/basic/#-core-p-span-q-map-term-span), [`%-` or `:call`](../../hoon/twig/cen-call/hep-call/) (the `twig` for calling a `gate`)*
92+*See [basic types](/hoon/basic/#-core-p-span-q-map-term-span), [`%-` or `:call`](/hoon/twig/cen-call/hep-call/) (the `twig` for calling a `gate`).*
9593
9694###### `core`: a code-data `cell`
9795
@@ -104,92 +102,68 @@ The code (`battery`) is the head, the data (`payload`) is the tail. All code-dat
104102
105103- `wet`: polymorphic by means of *genericity*
106104
107−*TODO: simplify*
108−
109−> When we call a `wet` `arm`, we're essentially using the `twig` as a macro. We are not generating new code for every call site; we are creating a new type analysis path, which works as if we expanded the callee with the caller's context.
105+A `wet` `arm` uses the `twig` as a macro. We create a new type analysis path, which works as if we expanded the callee with the caller's context.
110106
111107- `dry`: polymorphic by means of *variance*
112108
113109For a `dry` `arm`, we ask, is the new `payload` compatible with the old `payload` (against which the `core` was compiled)?
114110
115−Every `dry` `core` has a `metal` *(TODO: check)* which defines its *variance* model (ie, the properties of the `span` of a compatible `core`).
116−
117−*TODO: is the core dry, the arm dry, or both?*
111+Every `core` has a `metal` which defines its *variance* model (ie, the properties of the `span` of a compatible `core`).
118112
119113- `gold`: *invariant*
120114- `lead`: *bivariant*
121115- `zync`: *covariant*
122116- `iron`: *contravariant*
123117
124−*See [advanced types](../../hoon/advanced)*
118+*See [advanced types](/hoon/advanced)*.
125119
126120###### `arm`: a named, functionally-computed attribute of a `core`
127121
128122The `twig` of each `arm` is compiled to a Nock formula, with the enclosing `core` itself as the subject.
129123
130−*See [basic types](../../hoon/basic)*
124+*See [basic types](/hoon/basic)*.
131125
132−###### `foot`: a `wet` or `dry` `twig`
133−
134−*TODO: any `twig`, or always an `arm` within a `battery`?*
126+###### `foot`: a `wet` or `dry` `arm`
135127
136128###### `atom`
137129
138−A Hoon `atom` is a Nock `atom`, with two additional pieces of metadata (TODO: ?): an `aura`, and a `unit`.
139−
140−- `unit`: a nullable pointer (TODO: ?), or a Maybe
130+A Hoon `atom` is a Nock `atom`, with two additional pieces of metadata: an `aura`, and an optional constant.
141131
142−`atom`s are said to be `warm` or `cold` based on their `unit`
132+`atom`s are `warm` or `cold` based on whether the constant exists.
143133
144−- `warm`: if the `unit` is `~` (null), any `atom` is in the `span`
145−- `cold`: if the `unit` is `[~ x]`, where `x` is any `atom`, its only legal value is the constant `x`. *(TODO: what does this actually mean? What is the consequence of illegality?)*
134+- `warm`: if the constant is `~` (null), any `atom` is in the `span`
135+- `cold`: if the constant is `[~ atom]`, its only legal value is `atom`.
146136
147137*See [basic types](../../hoon/basic/#-atom-p-term-q-unit-atom)*
148138
149139###### `aura`: a soft `atom` type
150140
151−*alternately `odor`*
141+`aura` is a name for an atom type. It represents the structure of an `atom` in a string beginning with `@`. Any `aura` may change into any other by casting it through `@`, which by itself is an empty `aura`: [nominal equivalence](https://en.wikipedia.org/wiki/Nominal_type_system), rather than [structural equivalence](https://en.wikipedia.org/wiki/Structural_type_system).
152142
153−*TODO: write a short summary*
154−
155−*TODO: are `aura`s always `mold`s? just the built-in `aura`s?*
156−
157−> Auras are a lightweight, advisory representation of the units, semantics, and/or syntax of an `atom`. An `aura` is an atomic string; two auras are compatible if one is a prefix of the other.
158−>
159−> For instance, @t means UTF-8 text (LSB low), @ta means ASCII text, and @tas means an ASCII symbol. @u means an unsigned integer, @ud an unsigned decimal, @ux an unsigned hexadecimal. You can use a @ud atom as a @u or vice versa, but not as a @tas.
160−>
161−> Auras are truly soft; you can turn any `aura` into any other, statically, by casting through the empty `aura` `@`. Hoon is not dependently typed and can't statically enforce data constraints (for example, it can't enforce that a `@tas` is really a symbol).
162−>
163−
164−- `term` (`@tas`): a symbol - an atomic ASCII string which obeys symbol rules: lowercase and digit only, infix hyphen ("worm-case"), first character must be lowercase *(TODO: alphabetic?)*.
143+- `term` (`@tas`): a symbol - an atomic ASCII string which obeys symbol rules: lowercase and digit only, infix hyphen ("kebab-case"), first character must be lowercase alphabetic.
165144
166145- `cord` (`@t`): UTF-8 text, least-significant-byte first
167146
168−- `char` (`@tD`): a character, a single unicode byte (for multi-byte characters and codepoints, see `@c`)
147+- `char` (`@td`): a character, a single unicode byte (for multi-byte characters and codepoints, see `@c`)
169148
170−- `tape` (`(list char)`): a `tape` is not an `aura`, but a `mold` for a collection where every item has an `aura` of `char` *(TODO: is this for easy indexing vs `@t`?)*
149+- `tape` (`(list char)`): a `tape` is not an `aura`, but a `mold` for a list where every item has an `aura` of `char`.
171150
172−*See [basic types](../../hoon/basic/#-atom-p-term-q-unit-atom)*
151+*See [basic types](../../hoon/basic/#-atom-p-term-q-unit-atom)*.
173152
174153###### `loobean`: a Hoon boolean
175154
176155`0` (`%.y`) is *true*, `1` (`%.n`) is *false*.
177156
178−>Why? It's fresh, it's different, it's new. And it's annoying. And it keeps you on your toes. And it's also just intuitively right.
157+> Why? It's fresh, it's different, it's new. And it's annoying. And it keeps you on your toes. And it's also just intuitively right.
179158
180159###### `twig`: a Hoon expression
181160
182−A `twig` is the name for any Hoon expression, and for the AST node representing the expression as compiled to a Nock formula *(TODO: seems to be used interchangeably in the docs)*. It is a `book` with the form `{stem bulb}`.
161+A `twig` is the name for any Hoon expression, and for the AST node representing the expression as compiled to a Nock formula. It is a `book` with the form `{stem bulb}`.
183162
184163- `book`: a tagged-union
185164- `page`: an item in a `book`
186−- `stem`: an atomic symbol (`@tas`) - uniquely identifies a `twig` *(TODO: ?)*
187−- `bulb`: The `bulb` for each `stem` has its own type, usually a tuple, sometimes a list or a map.
188−
189−A `twig` is either a `moss` ("mossy") or a `seed` ("woody"):
190−
191−- `moss`: a `twig` whose `product` is used as a `mold`
192−- `seed`: a `twig` whose `product` could be anything
165+- `stem`: an atomic symbol (`@tas`) - the name of a `twig`
166+- `bulb`: The `mold` of the `twig`'s arguments.
193167
194168The vast majority of `twig`s have a *regular form*, beginning with either a keyword `sigil` or a digraph `rune`. Some `twig`s also have a syntactic *irregular form*, a handful have *only* an *irregular form*.
195169
@@ -199,9 +173,9 @@ Hoon does not have reserved words, but `sigil`s (prefixed with `:`), which are e
199173
200174- `rune`: a pair of ASCII symbols used to begin a `twig` - the first symbol represents a family of related `twig`s. For example, the [`?` family](../../hoon/twig/wut-test/) are all conditionals.
201175
202−*regular forms* can alternate between *tall* and *wide* (or *flat*) syntax, *irregular formas* can use only the *wide*/*flat* syntax.
176+*regular forms* can alternate between *tall* and *wide* (or *flat*) syntax, *irregular forms* can use only the *wide*/*flat* syntax.
203177
204−*See [`twig` concept](../../hoon/concepts/#-twig-expression), [expressions](../../hoon/twig/), and [syntax](../../hoon/syntax/)*
178+*See [`twig` concept](../../hoon/concepts/#-twig-expression), [expressions](../../hoon/twig/), and [syntax](../../hoon/syntax/)*.
205179
206180###### `limb`: attribute or variable reference
207181
@@ -216,27 +190,10 @@ To resolve a `limb` named "foo", the `subject` is searched depth-first, head-fir
216190
217191Hoon has no scope or symbol-table; there is only the `subject`. To "declare" a "variable" is to construct a new `subject`: `[variable old-subject]`.
218192
219−A `face` is a `span` *(TODO: ?)* with a label (`@tas`) wrapped around it.
220−
221−- `taco`: a `symbol` (for a *type-inferred* `face`), or a `symbol` *with* a `mold` (for a *type-checked* `face`)
222−
223−*TODO: check these*
224−
225−- `tune`: advanced `face`s:
226− - `alias`: a `face` that is a lazy reference to another `face`
227− - `bridge`: a `face` that references a `twig`, against which the `face` label is resolved
193+A `face` wraps a name (`@tas`) around a `span`.
228194
229−*See [advanced types](../../hoon/advanced/#-face-aliases-and-bridges)*
195+*See [advanced types](../../hoon/advanced/#-face-aliases-and-bridges)*.
230196
231197###### `nest`: a type-casting operation
232198
233−*TODO:*
234−
235−### Arvo
236−
237−> Arvo is a nonpreemptive OS kernel, a single-threaded event interpreter.
238−
239−- `mark`
240−- `generator`
241−
242−*... TODO*
199+`nest` checks if the type of the second child is a subset of the type of the first chile. That's a short summary. To go in-depth, see [advanced types](../../hoon/advanced/).