shrub/pub/doc/hoon/library/2da.md

section 2dA, sets

++apt

Set verification

++  apt                                                 ::  set invariant
  |=  a=(tree)
  ?~  a
    &
  ?&  ?~(l.a & ?&((vor n.a n.l.a) (hor n.l.a n.a)))
      ?~(r.a & ?&((vor n.a n.r.a) (hor n.a n.r.a)))
  ==
::

Produces a loobean indicating whether a is a set or not.

a is a tree.

~zod/try=> =b (sa `(list ,@t)`['john' 'bonita' 'daniel' 'madeleine' ~])
~zod/try=> (apt b)
    %.y
~zod/try=> =m (mo `(list ,[@t *])`[['a' 1] ['b' [2 3]] ['c' 4] ['d' 5] ~])
~zod/try=> m
    {[p='d' q=5] [p='a' q=1] [p='c' q=4] [p='b' q=[2 3]]}
~zod/try=> (apt m)
    %.y

---

++in

Set operations

++  in                                                  ::  set engine
  ~/  %in
  |/  a=(set)

Input arm.

~zod/try=> ~(. in (sa "asd"))
<13.evb [nlr(^$1{@tD $1}) <414.fvk 101.jzo 1.ypj %164>]>

a is a set

+-all:in

Logical AND

  +-  all                                               ::  logical AND
    ~/  %all
    |*  b=$+(* ?)
    |-  ^-  ?
    ?~  a
      &
    ?&((b n.a) $(a l.a) $(a r.a))
  ::

Computes the logical AND on every element in a slammed with b, producing a loobean.

a is a set.

b is a wet gate that accepts a noun and produces a loobean.

~zod/try=> =b (sa `(list ,[@t *])`[['a' 1] ['b' [2 3]] ~])
~zod/try=> (~(all in b) |=(a=* ?@(+.a & |)))
    %.n
~zod/try=> =b (sa `(list ,@t)`['john' 'bonita' 'daniel' 'madeleine' ~])
~zod/try=> (~(all in b) |=(a=@t (gte a 100)))
    %.y

---

+-any:in

Logical OR

  +-  any                                               ::  logical OR
    ~/  %any
    |*  b=$+(* ?)
    |-  ^-  ?
    ?~  a
      |
    ?|((b n.a) $(a l.a) $(a r.a))
  ::

Computes the logical OR on every element of a slammed with b.

a is a set.

b is a gate that accepts a noun and produces a loobean.

~zod/try=> =b (sa `(list ,[@t *])`[['a' 1] ['b' [2 3]] ~])
~zod/try=> (~(any in b) |=(a=* ?@(+.a & |)))
    %.y
~zod/try=> =b (sa `(list ,@t)`['john' 'bonita' 'daniel' 'madeleine' ~])
~zod/try=> (~(any in b) |=(a=@t (lte a 100)))
    %.n

---

+-del:in

Remove noun

  +-  del                                               ::  b without any a
    ~/  %del
    |*  b=*
    |-  ^+  a
    ?~  a
      ~
    ?.  =(b n.a)
      ?:  (hor b n.a)
        [n.a $(a l.a) r.a]
      [n.a l.a $(a r.a)]
    |-  ^-  ?(~ _a)
    ?~  l.a  r.a
    ?~  r.a  l.a
    ?:  (vor n.l.a n.r.a)
      [n.l.a l.l.a $(l.a r.l.a)]
    [n.r.a $(r.a l.r.a) r.r.a]
  ::

Removes b from the set a.

a is a set.

b is a noun.

~zod/try=> =b (sa `(list ,@t)`['a' 'b' 'c' ~])
~zod/try=> (~(del in b) 'a')
{'c' 'b'}
~zod/try=> =b (sa `(list ,@t)`['john' 'bonita' 'daniel' 'madeleine' ~])
~zod/try=> (~(del in b) 'john')
{'bonita' 'madeleine' 'daniel'}
~zod/try=> (~(del in b) 'susan')
{'bonita' 'madeleine' 'daniel' 'john'}

---

+-dig:in

Axis a in b

  +-  dig                                               ::  axis of a in b
    |=  b=*
    =+  c=1
    |-  ^-  (unit ,@)
    ?~  a  ~
    ?:  =(b n.a)  [~ u=(peg c 2)]
    ?:  (gor b n.a)
      $(a l.a, c (peg c 6))
    $(a r.a, c (peg c 7))
  ::

Produce the axis of b within a.

a is a set.

b is a noun.

~zod/try=> =a (sa `(list ,@)`[1 2 3 4 5 6 7 ~])
~zod/try=> a
{5 4 7 6 1 3 2}
~zod/try=> -.a
n=6
~zod/try=> (~(dig in a) 7)
[~ 12]
~zod/try=> (~(dig in a) 2)
[~ 14]
~zod/try=> (~(dig in a) 6)
[~ 2]

---

+-gas:in

Concatenate

  +-  gas                                               ::  concatenate
    ~/  %gas
    |=  b=(list ,_?>(?=(^ a) n.a))
    |-  ^+  a
    ?~  b
      a
    $(b t.b, a (put(+< a) i.b))
  ::

Insert the elements of a list b into a set a.

a is a set.

b is a list.

~zod/try=> b
{'bonita' 'madeleine' 'rudolf' 'john'}
~zod/try=> (~(gas in b) `(list ,@t)`['14' 'things' 'number' '1.337' ~])
{'1.337' '14' 'number' 'things' 'bonita' 'madeleine' 'rudolf' 'john'}
~zod/try=> (~(gas in s) `(list ,@t)`['1' '2' '3' ~])
{'1' '3' '2' 'e' 'd' 'a' 'c' 'b'}

---

+-has:in

b in a?

  +-  has                                               ::  b exists in a check
    ~/  %has
    |*  b=*
    |-  ^-  ?
    ?~  a
      |
    ?:  =(b n.a)
      &
    ?:  (hor b n.a)
      $(a l.a)
    $(a r.a)
  ::

Checks if b is an element of a, producing a loobean.

a is a set.

b is a noun.

~zod/try=> =a (~(gas in `(set ,@t)`~) `(list ,@t)`[`a` `b` `c` ~])
~zod/try=> (~(has in a) `a`)
%.y
~zod/try=> (~(has in a) 'z')
%.n

---

+-int:in

Intersection

+-  int                                               ::  intersection
    ~/  %int
    |*  b=_a
    |-  ^+  a
    ?~  b
      ~
    ?~  a
      ~
    ?.  (vor n.a n.b)
      $(a b, b a)
    ?:  =(n.b n.a)
      [n.a $(a l.a, b l.b) $(a r.a, b r.b)]
    ?:  (hor n.b n.a)
      %-  uni(+< $(a l.a, b [n.b l.b ~]))  $(b r.b)
    %-  uni(+< $(a r.a, b [n.b ~ r.b]))  $(b l.b)

Produces a set of the intersection between two sets of the same type, a and b.

a is a set.

b is a set.

~zod/try=> (~(int in (sa "ac")) (sa "ha"))
{~~a}
~zod/try=> (~(int in (sa "acmo")) ~)
{}
~zod/try=> (~(int in (sa "acmo")) (sa "ham"))
{~~a ~~m}
~zod/try=> (~(int in (sa "acmo")) (sa "lep"))
{}

---

+-put:in

Put b in a

  +-  put                                               ::  puts b in a
    ~/  %put
    |*  b=*
    |-  ^+  a
    ?~  a
      [b ~ ~]
    ?:  =(b n.a)
      a
    ?:  (hor b n.a)
      =+  c=$(a l.a)
      ?>  ?=(^ c)
      ?:  (vor n.a n.c)
        [n.a c r.a]
      [n.c l.c [n.a r.c r.a]]
    =+  c=$(a r.a)
    ?>  ?=(^ c)
    ?:  (vor n.a n.c)
      [n.a l.a c]
    [n.c [n.a l.a l.c] r.c]
  ::

Add an element b to the set a.

a is a set.

b is a noun.

~zod/try=> =a (~(gas in `(set ,@t)`~) `(list ,@t)`[`a` `b` `c` ~])
~zod/try=> =b (~(put in a) `d`)
~zod/try=> b
{`d` `a` `c` `b`}
~zod/try=> -.l.+.b
n=`d`

---

+-rep:in

Accumulate

  +-  rep                                               ::  replace by tile
    |*  [b=* c=_,*]
    |-
    ?~  a  b
    $(a r.a, b $(a l.a, b (c n.a b)))
  ::

Accumulate the elements of a using a gate c and an accumulator b.

a is a set.

b is a noun that accepts a noun and produces a loobean.

c is a gate.

~zod/try=> =a (~(gas in *(set ,@)) [1 2 3 ~])
~zod/try=> a
{1 3 2}
~zod/try=> (~(rep in a) 0 |=([a=@ b=@] (add a b)))
6

---

+-tap:in

Set to list

  +-  tap                                               ::  list tiles a set
    ~/  %tap
    |=  b=(list ,_?>(?=(^ a) n.a))
    ^+  b
    ?~  a
      b
    $(a r.a, b [n.a $(a l.a)])
  ::

Flatten the set a into a list.

a is an set.

a is a set.

b is a list.

~zod/try=> =s (sa `(list ,@t)`['a' 'b' 'c' 'd' 'e' ~])
~zod/try=> s
{'e' 'd' 'a' 'c' 'b'}
~zod/try=> (~(tap in s) `(list ,@t)`['1' '2' '3' ~])
~['b' 'c' 'a' 'd' 'e' '1' '2' '3']
~zod/try=> b
{'bonita' 'madeleine' 'daniel' 'john'}
~zod/try=> (~(tap in b) `(list ,@t)`['david' 'people' ~])
~['john' 'daniel' 'madeleine' 'bonita' 'david' 'people']

---

+-uni:in

Union

  +-  uni                                               ::  union
    ~/  %uni
    |*  b=_a
    |-  ^+  a
    ?~  b
      a
    ?~  a
      b
    ?:  (vor n.a n.b)
      ?:  =(n.b n.a)
        [n.b $(a l.a, b l.b) $(a r.a, b r.b)]
      ?:  (hor n.b n.a)
        $(a [n.a $(a l.a, b [n.b l.b ~]) r.a], b r.b)
      $(a [n.a l.a $(a r.a, b [n.b ~ r.b])], b l.b)
    ?:  =(n.a n.b)
      [n.b $(b l.b, a l.a) $(b r.b, a r.a)]
    ?:  (hor n.a n.b)
      $(b [n.b $(b l.b, a [n.a l.a ~]) r.b], a r.a)
    $(b [n.b l.b $(b r.b, a [n.a ~ r.a])], a l.a)

Produces a set of the union between two sets of the same type, a and b.

a is a set.

b is a set.

~zod/try=> (~(uni in (sa "ac")) (sa "ha"))
{~~a ~~c ~~h}
 ~zod/try=> (~(uni in (sa "acmo")) ~)
{~~a ~~c ~~m ~~o}
~zod/try=> (~(uni in (sa "acmo")) (sa "ham"))
{~~a ~~c ~~m ~~o ~~h}
~zod/try=> (~(uni in (sa "acmo")) (sa "lep"))
{~~e ~~a ~~c ~~m ~~l ~~o ~~p}

---

+-wyt:in

Set size

  +-  wyt                                               ::  size of set
    |-  ^-  @
    ?~(a 0 +((add $(a l.a) $(a r.a))))

Produce the number of elements in set a as an atom.

a is an set.

~zod/try=> =a (~(put in (~(put in (sa)) 'a')) 'b')
~zod/try=> ~(wyt in a)
2
~zod/try=> b
{'bonita' 'madeleine' 'daniel' 'john'}
~zod/try=> ~(wyt in b)
4

---