A type is usually understood to be a set of values. Hoon values are all nouns, so a Hoon type is a set of nouns.

Hoon's type system conducts various type-checks at compile time in order to ensure type safety. For example, one's program might have an integer squaring function, such that given some atom n the return value is n^2. The output value should be an unsigned integer (i.e., an atom). Hoon uses type inference on the expression that defines the squaring function in to determine what possible values it could produce. If the inferred type 'nests' under the desired type then the program compiles; otherwise the compile fails with a nest-fail crash.

(For an introduction on how to use Hoon's type system, see Chapter 2 of the Hoon tutorial.)

In this document we discuss the recursive data structure Hoon uses for type inference. Because the Hoon compiler is written in Hoon this structure is likewise defined in Hoon.

$type

Below is a simplified version the +$ type arm, which defines the data structure Hoon uses to keep track of types. But this data structure is used for more than simply type inference. It also handles the resolution of names, including both faces and arm names. (See Chapter 1 of the Hoon tutorial for an introduction to name resolution.)

As noted, this is a simplified version of type. We undo and explain the simplifications in the advanced types section.

+$  term  @tas
+$  type  $~  %noun
          $@  $?  %noun
                  %void
              ==
          $%  [%atom p=term q=(unit @)]
              [%cell p=type q=type]
              [%core p=type q=(map term hoon)]
              [%face p=term q=type]
              [%fork p=(set type)]
              [%hold p=type q=hoon]
          ==

Effectively this structure defines a set of nouns that Hoon uses to keep track track of (1) type information, and (2) name resolution information. This set of nouns is recursively defined.

?(%noun %void)

%noun is the label for a noun about which nothing else is known. Every piece of Hoon data is a noun, so everything nests under %noun.

%void is the label for the empty set.

[%cell p=type q=type]

[%cell p=type q=type] is for cells. The type of the head is labelled p and the tail type is q.

[%fork p=(set type)]

[%fork p=(set type)] is for the union of all types in the set p. That is, when the type of an expression is known to be a %fork, the expression must evaluate as one of the types in p.

Hoon uses branching (usually with conditional runes of the ? family) for type inference in order to rule out which of the types in p can apply.

[%hold p=type q=hoon]

A %hold type, with type p and hoon q, is a lazy reference to the type of (mint p q). In English, it means: "the type of the product when we compile Hoon expression q against a subject with type p."

[%face p=term q=type]

A [%face p=term q=type] wraps the label p around the type q. p is a term or @tas, an atomic ASCII string which obeys symbol rules: lowercase and digit only, infix hyphen, first character must be a lowercase letter.

[%atom p=term q=(unit atom))]

%atom is for an atom, with two twists. q is a unit, Hoon's equivalent of a nullable pointer or a Haskell Maybe. If q is ~, null, the type is warm; any atom is in the type. If q is [~ x], where x is any atom, the type is cold; its only legal value is the constant x.

p in the atom is a terminal used as an aura, or soft atom type. 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.

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.

Auras can also end with an optional, capitalized suffix, which defines the atom's bitwidth as a log starting from A. For example, @udD is an unsigned decimal byte; @uxG is an unsigned 64-bit hexadecimal.

You can make up your own auras and are encouraged to do so, but here are some conventions bound to constant syntax:

@c              UTF-32 codepoint
@d              date
  @da           absolute date
  @dr           relative date (ie, timespan)
@n              nil
@p              phonemic base (plot)
@r              IEEE floating-point
  @rd           double precision  (64 bits)
  @rh           half precision (16 bits)
  @rq           quad precision (128 bits)
  @rs           single precision (32 bits)
@s              signed integer, sign bit low
  @sb           signed binary
  @sd           signed decimal
  @sv           signed base32
  @sw           signed base64
  @sx           signed hexadecimal
@t              UTF-8 text (cord)
  @ta           ASCII text (knot)
    @tas        ASCII text symbol (term)
@u              unsigned integer
  @ub           unsigned binary
  @ud           unsigned decimal
  @uv           unsigned base32
  @uw           unsigned base64
  @ux           unsigned hexadecimal

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).

[%core p=type q=(map term hoon)]

%core is for a code-data cell. The data (or payload) is the tail; the code (or battery) is the head. p, a type, is the type of the payload. q is a mapping of arm names and Hoon expressions. It is the source code for the core battery.

(For an introduction to cores and arms, see Chapter 1 of the Hoon tutorial.)

Each expression in the battery source is compiled to a formula, with the core itself as the subject. The battery is a tree of these formulas, or arms. An arm is a computed attribute against its core.

All code-data structures in normal languages (functions, objects, modules, etc) become cores in Hoon. A Hoon battery looks a bit like a method table, but not every arm is a "method" in the OO sense. An arm is a computed attribute. A method is an arm whose product is a Hoon function (or gate).

A gate (function, lambda, etc) is a core with one arm, whose name is the empty symbol $, and a payload whose shape is [sample context]. The context is the subject in which the gate was defined; the sample is the argument.

To call this function on an argument x, replace the sample (at tree address 6 in the core) with x, then compute the arm. (Of course, we don't mutate the noun, we make a mutant copy.)