The $ family of runes is used for defining custom types. Strictly speaking, these runes are used to produce specs, which we call 'structures'.
Overview
Structures are abstract syntax trees for types (see the documentation on basic and advanced types for the precise definition of type). Structures are compile-time values of type which at runtime may be used to produce a 'mold'.
A mold is a function from nouns to nouns used to validate values of the type to which the structure defines. A mold can do two things at runtime. First, it may 'clam' a noun, which validates the shape of the noun to be one that fits the abstract syntax tree given by the spec that produced the mold. Failing this validation results in a crash. Secondly, a mold may also be used to produce an example value of the type to which is corresponds, called the 'bunt value'. The bunt value is used as a placeholder for sample values that may be passed to a gate that accepts the corresponding type.
A correct mold is a normalizer: an idempotent function across all nouns. If the sample of a gate has type %noun, and its body obeys the constraint that for any x, =((mold x) (mold (mold x))), it's a normalizer and can be used as a mold. Hoon is not dependently typed and so can't check idempotence statically, so we can't actually tell if a mold matches this definition perfectly. This is not actually a problem.
In any case, since molds are just functions, we can use functional programming to assemble interesting molds. For instance, (map foo bar) is a table from mold foo to mold bar. map is not a mold; it's a function that makes a mold. Molds and mold builders are generally described together.
specs contain more information and draw finer distinctions than types, which is to say that a given type may have more than one valid spec defining it, and thus downconversion from spec to type is lossy. Thus structure validation (done with $|, which is a more restrictive validation than that performed by molds, is a rare use case. Except for direct raw input, it's generally a faux pas to validate structure at runtime -- or even in userspace. Nonetheless they are sometimes utilized for types that will be more performant if they satisfy some validating gate.
$| "bucbar"
Structure that satisfies a validator.
Syntax
Two arguments, fixed.
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AST
[%bcbr p=spec q=hoon]
Discussion
$| is used for validation of values at a finer level than that of types. Recall that a given value of type can be equivalently defined by more than one spec. For performance reasons, it may be beneficial to restrict oneself to values of a given type that adhere to an abstract syntax tree specified by some subset of those specs that may be used to define a given type.
$| takes two arguments: a structure a and a gate b that produces a flag that is used to validate values produced by the mold generated by a at runtime. $|(a b) is a gate that takes in a noun x and first pins the product of clamming a with x, call this foo. Then it calls b on foo. It asserts that the product of (b foo) is &, and then produces foo. This is equivalent to the following (which is not how $| is actually defined but has the same behavior):
|= x=*=/ foo ;;(a x)?> (b foo)foo
For example, the elements of a set are treated as being unordered, but the values will necessarily possess an order by where they are in the memory. Thus if every set is stored using the same order scheme then faster algorithms involving sets may be written. Furthermore, if you just place elements in the set randomly, it may be mistreated by algorithms already in place that are expecting a certain order. This is not the same thing as casting - it is forcing a type to have a more specific set of values than its mold would suggest. This rune should rarely be used, but it is extremely important when it is.
Examples
> =foo $| (list @)|=(a=(list) (lth (lent a) 4))
This creates a structure foo whose values are lists with length less than 4.
> (foo ~[1 2 3])~[1 2 3]> (foo ~[1 2 3 4])ford: %ride failed to execute:
The definition of +set in hoon.hoon is the following:
++ set|$ [item]$| (tree item)|=(a=(tree) ?:(=(~ a) & ~(apt in a)))
Here |$ is used to define a mold builder that takes in a mold (given the face item) and creates a structure consisting of a tree of items with $| that is validated with the gate |=(a=(tree) ?:(=(~ a) & ~(apt in a))). in is a door in hoon.hoon with functions for handling sets, and apt is an arm in that door that checks that the values in the tree are arranged in the particular way that sets are arranged in Hoon, namely 'ascending +mug hash order'.
$_ "buccab"
Structure that normalizes to an example.
Syntax
One argument, fixed.
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AST
[%bccb p=hoon]
Expands to
|=(* p)
Discussion
$_ discards the sample it's supposedly normalizing and produces its example instead.
Examples
> =foo $_([%foobaz %moobaz])> (foo %foo %baz)[%foobaz %moobaz]> `foo`[%foobaz %moobaz][%foobaz %moobaz]> $:foo[%foobaz %moobaz]
$% "buccen"
Structure which recognizes a union tagged by head atom.
Syntax
A variable number of arguments.
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Each item may be an atom or (more commonly) a cell. The atom or head of the cell must be a constant (%foo, %1, %.y, etc).
AST
[%bccn p=(list spec)]
Defaults to
The default of the last item i in p. Crashes if p is empty.
Discussion
A $% is a tagged union, a common data model.
Make sure the last item in your $% terminates, or the default will be an infinite loop! Alteratively, you can use $~ to define a custom type default value.
Examples
> =foo $%([%foo [email protected] [email protected]] [%baz [email protected]])> (foo [%foo 4 2])[%foo p=4 q=2]> (foo [%baz 37])[%baz p=37]> $:foo[%baz p=0]
$: "buccol"
Form a cell type.
Syntax
A variable number of arguments.
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AST
[%bccl p=(list spec)]
Normalizes to
The tuple the length of p, normalizing each item.
Defaults to
The tuple the length of p.
Examples
> =foo $:([email protected] [email protected])> (foo 33 %foo)[p=33 q=%foo]> `foo`[33 %foo][p=33 q=%foo]> $:foo[p=0 q=%$]
$< "bucgal"
Filters a pre-existing mold to obtain a mold that excludes a particular structure.
Syntax
Two arguments, fixed.
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AST
[%bcgl p=spec q=spec]
Discussion
This can be used to obtain type(s) from a list of types q that do not satisfy a requirement given by p.
Examples
> =foo $%([%bar [email protected] [email protected]] [%baz [email protected]])> =m $<(%bar foo)> (m [%bar 2 4])ford: %ride failed to execute:> (m [%baz 2])[%baz p=2]> ;;($<(%foo [@tas *]) [%foo 1])ford: %ride failed to execute:> ;;($<(%foo [@tas *]) [%bar 1])[%bar 1]
$> "bucgar"
Filters a mold to obtain a new mold matching a particular structure.
Syntax
Two arguments, fixed.
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AST
[%bcgr p=spec q=spec]
Discussion
This can be used to obtain type(s) from a list of types q that satisfy a requirement given by p.
Examples
Examples with $%:
> =foo $%([%bar [email protected] [email protected]] [%baz [email protected]])> =m $>(%bar foo)> (m [%bar 2 4])[%bar p=2 q=4]> (m [%baz 2])ford: %ride failed to execute:
Examples with ;;:
> ;;([@tas *] [%foo 1])[%foo 1]> ;;([@tas *] [%bar 1])[%bar 1]> ;;($>(%foo [@tas *]) [%foo 1])[%foo 1]> ;;($>(%foo [@tas *]) [%bar 1])ford: %ride failed to execute:
$- "buchep"
Structure that normalizes to an example gate.
AST
[%bchp p=spec q=spec]
Expands to
$_ ^||=(p $:q)
Syntax
Two arguments, fixed.
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p is the type the gate takes and q is the type the gate produces.
Discussion
Since a $- reduces to a $_, it is not useful for normalizing, just for typechecking. In particular, the existence of $-s does not let us send gates or other cores over the network!
Examples
> =foo $-(%foo %baz)> ($:foo %foo)%baz
$^ "bucket"
Structure which normalizes a union tagged by head depth (cell).
Syntax
Two arguments, fixed.
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AST
[%bckt p=spec q=spec]
Normalizes to
Default, if the sample is an atom; p, if the head of the sample is an atom; q otherwise.
Defaults to
The default of p.
Examples
> =a $%([%foo [email protected] [email protected]] [%baz [email protected]])> =b $^([a a] a)> (b [[%baz 33] [%foo 19 22]])[[%baz p=33] [%foo p=19 q=22]]> (b [%foo 19 22])[%foo p=19 q=22]> $:b[%baz p=0]
$+ "buclus"
Specify a shorthand type name for use in prettyprinting.
Syntax
Two arguments, fixed.
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AST
[%bcls p=stud q=spec]
Examples
> =/ my-type $+(my-alias [@ @])> -:!>(*my-type)#t/#my-alias
$& "bucpam"
Repair a value of a tagged union type.
Syntax
Two arguments, fixed.
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$&(combined-mold=spec normalizing-gate=hoon)
Here combined-mold is a tagged union type (typically made with $%) and normalizing-gate is a gate which accepts values of combined-mold and normalizes them to be of one particular type in combined-mold.
AST
[%bcpm p=spec q=hoon]
Normalizes to
The product of the normalizing gate and sample.
Defaults to
The default of the last type listed in p, normalized with the normalizing gate.
Discussion
This rune is used to "upgrade" or "repair" values of a structure, typically from an old version to a new version. For example, this may happen when migrating state after updating an app.
Examples
+$ old [%0 @]+$ new [%1 ^]+$ combined $%(old new)+$ adapting $&(combined |=(?-(-.a %0 [%1 1 +.a], %1 a)))
Here adapting is a structure that bunts to [%1 ^] but also normalizes from [%0 @] if called on such a noun.
$~ "bucsig"
Define a custom type default value.
Syntax
Two arguments, fixed.
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p defines the default value, and q defines everything else about the structure.
AST
[%bcsg p=hoon q=spec]
Product
Creates a structure (custom type) just like q, except its default value is p.
Defaults to
The product of p.
Discussion
You should make sure that the product type of p nests under q. You can check the default value of some structure (custom type) r with *r. (See the ^* rune.)
Do not confuse the $~ rune with the constant type for null, $~. (The latter uses older Hoon syntax that is still accepted. Preferably it would be %~.)
Examples
First, let's define a type without using $~:
> =b [email protected](@tas $%([%two *] [%three *]))> `b`%hello%hello> `b`[%two %hello][%two 478.560.413.032]> *b%$> *@tas%$
Using $~:
> =c $~(%default-value [email protected](@tas $%([%two *] [%three *])))> `c`%hello%hello> `c`[%two %hello][%two 478.560.413.032]> *c%default-value
[email protected] "bucpat"
Structure which normalizes a union tagged by head depth (atom).
Syntax
Two arguments, fixed.
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AST
[%bcpt p=spec q=spec]
Normalizes to
p, if the sample is an atom; q, if the sample is a cell.
Defaults to
The default of p.
Produces
A structure which applies p if its sample is an atom, q if its sample is a cell.
Examples
> =a [email protected](%foo $:(p=%baz [email protected]))> (a %foo)%foo> `a`[%baz 99][p=%baz q=99]> $:a%foo
$= "buctis"
Structure which wraps a face around another structure.
Syntax
Two arguments, fixed.
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AST
[%bcts p=skin q=spec]
Expands to
|= *^=(p %-(q +6))
Discussion
Note that the Hoon compiler is at least slightly clever about compiling structures, and almost never has to actually put in a gate layer (as seen in the expansion above) to apply a $=.
Examples
> =a $=(p %foo)> (a %foo)p=%foo> (a %baz)ford: %ride failed to execute:
$? "bucwut"
Form a type from a union of other types.
Syntax
Variable number of arguments.
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AST
[%bcwt p=(list spec)]
Normalizes to
The last item in p which normalizes the sample to itself.
Void, if p is empty.
Defaults to
The last item in p.
Discussion
For a union of atoms, a $? is fine. For more complex nouns, always try to use a $%, [email protected] or $^, at least if you expect your structure to be used as a normalizer.
Examples
> =a ?(%foo %baz %baz)> (a %baz)%baz> (a [37 45])ford: %ride failed to execute:> $:a%baz