Hoon type that doesn't include hoon ASTs -- untested

type-no-hoons.hoon

::  $type: a hoon type, represented in noun form
::
::    Instead of lazily evaluating the type of a hoon when compiled against a
::    subject type, use the special value %loop to recurse back up to the
::    nearest %hold.
::
+$  type
  $@  ?(%noun %void %loop)
  $%  [%atom p=term q=(unit @)]
      [%cell p=type q=type]
      [%core p=type q=coil]
      [%face p=$@(term tune) q=type]
      [%fork p=(set type)]
      [%hint p=(pair type note) q=type]
      [%hold p=type]
  ==
+$  coil  $:  p=[p=(unit term) q=poly r=vair]
              q=type
              r=[p=seminoun q=(map term tomo)]
          ==
::  $tomo: type of a core chapter
::
::    Arm types are stored as a map from the arm's name
::    to its product type, which might contain a %loop
::    if it produces the whole core.
::
+$  tome  (pair what (map term type))
::
::  -:!>(*(list @))
::
::  ->
::
:-  %hold
:-  %fork
%-  sy  :~
  [%atom %n ~]
  [%cell [%face %i [%atom %$ ~]] [%face %t %loop]]
==
::
::  -:!>(*(tree @))
::
::  ->

:-  %hold
:-  %fork
%-  sy  :~
  [%atom %n ~]
  :+  %cell
    [%face %n [%atom %$ ~]]
  [%cell [%face %l %loop] [%face %r %loop]]
==
::
::  -:!>(*(list (tree @)))
::
::  ->
::
:-  %hold
:-  %fork
%-  sy  :~
  [%atom %n ~]
::
  :+  %cell
    :+  %face  %i
    :-  %hold
    :-  %fork
    %-  sy  :~
      [%atom %n ~]
      :+  %cell
        [%face %n [%atom %$ ~]]
      [%cell [%face %l %loop] [%face %r %loop]]
    ==
  [%face %t %loop]
==
::
++  unit
  |=  item=type
  ^-  type
  ::
  (fork [%atom %n ~] [%cell [%atom %n ~] [%face %u type]] ~)
::
++  list
  |=  item=type
  ^-  type
  ::
  :-  %hold
  %-  fork  :~
    [%atom %n ~]
  ::
    :+  %cell
      [%face %i item]
    [%face %t %loop]
  ==
::
++  lest
  |=  item=type
  ^-  type
  ::
  [%cell [%face %i item] [%face %t (list item)]]
::
++  tree
  |=  item=type
  ^-  type
  ::
  :-  %hold
  %-  fork  :~
    [%atom %n ~]
  ::
    :+  %cell
      [%face %n item]
    :+  %cell
      [%face %l %loop]
    [%face %r %loop]
  ==