2h: Set Logic

+in

Set operations.

Core whose arms contain a variety of functions that operate on +sets. Its sample accepts the input +set to be manipulated.

Accepts

A +set.

Source

~/  %in
=|  a=(tree)
|@

Examples

> ~(. in (sy "asd"))
<16.ufw [a=?(%~ [?(n=@tD n=#1) l=nlr(?(@tD #1)) r=nlr(?(@tD ^#1.?(@tD #1)))]) <123.zao 46.hgz 1.pnw %140>]>

+all:in

Logical AND.

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

Accepts

.a is a +set, and is the sample of +in.

.b is a gate that accepts a $noun and produces a $flag.

Produces

A $flag.

Source

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

Examples

> (~(all in (silt ~[1 2 3 4])) |=(a=@ (lth a 5)))
%.y

> (~(all in (silt ~[1 2 3 4 5])) |=(a=@ (lth a 5)))
%.n

---

+any:in

Logical OR.

Computes the logical OR on every element of .a slammed with .b, producing a $flag.

Accepts

.a is a +set, and is the sample of +in.

.b is a gate that accepts a $noun and produces a $flag.

Produces

A $flag.

Source

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

Examples

> (~(any in (silt ~[2 3 4 5])) |=(a=@ (lth a 3)))
%.y

> (~(any in (silt ~[3 4 5])) |=(a=@ (lth a 3)))
%.n

---

+apt:in

Check correctness.

Computes whether .a has a correct horizontal order and a correct vertical order, producing a $flag.

Accepts

.a is a +set.

Produces

A $flag.

Source

++  apt
  =<  $
  ~/  %apt
  =|  [l=(unit) r=(unit)]
  |.  ^-  ?
  ?~  a   &
  ?&  ?~(l & (gor n.a u.l))
      ?~(r & (gor u.r n.a))
      ?~(l.a & ?&((mor n.a n.l.a) $(a l.a, l `n.a)))
      ?~(r.a & ?&((mor n.a n.r.a) $(a r.a, r `n.a)))
  ==

Examples

> ~(apt in ~)
%.y

> =a (silt ~[1 2 3])

> a
[n=2 l={1} r={3}]

> ~(apt in a)
%.y

> =z ?~(a ~ a(n 10))

> z
[n=10 l={1} r={3}]

> ~(apt in z)
%.n

Discussion

See section 2f for more information on $noun ordering.

---

+bif:in

Bifurcate.

Splits set .a into sets .l and .r, which contain the items either side of .b but not including .b.

Accepts

.a is a +set, and is the sample of +in.

.b is a $noun.

Produces

A cell of two +sets.

Source

++  bif
  ~/  %bif
  |*  b=*
  ^+  [l=a r=a]
  =<  +
  |-  ^+  a
  ?~  a
    [b ~ ~]
  ?:  =(b n.a)
    a
  ?:  (gor b n.a)
    =+  c=$(a l.a)
    ?>  ?=(^ c)
    c(r a(l r.c))
  =+  c=$(a r.a)
  ?>  ?=(^ c)
  c(l a(r l.c))

Examples

> =a `(set @)`(silt (gulf 1 20))
> a
{17 8 20 13 11 5 19 7 15 10 18 14 6 12 9 1 2 3 16 4}

> (~(bif in a) 10)
[l=[n=11 l={17 8 20 13} r={5 19 7 15}] r=[n=12 l={18 14 6} r={9 1 2 3 16 4}]]

> `[(set @) (set @)]`(~(bif in a) 10)
[{17 8 20 13 11 5 19 7 15} {18 14 6 12 9 1 2 3 16 4}]

Discussion

Note that +sets are horizontally ordered by the mug hash of their items and vertically ordered by the double-+mug hash of their items. This means bifurcating the set of numbers (silt ~[10 20 30 40 50]) at 30 will not produce [{10 20} {40 50}], but rather [{20} {10 40 50}] due to the tree structure resulting from their +mug hashes.

---

+del:in

Remove $noun.

Removes .b from the +set .a.

Accepts

.a is a +set, and is the sample of +in.

.b is a $noun.

Produces

A +set.

Source

++  del
  ~/  %del
  |*  b=*
  |-  ^+  a
  ?~  a
    ~
  ?.  =(b n.a)
    ?:  (gor b n.a)
      a(l $(a l.a))
    a(r $(a r.a))
  |-  ^-  [$?(~ _a)]
  ?~  l.a  r.a
  ?~  r.a  l.a
  ?:  (mor n.l.a n.r.a)
    l.a(r $(l.a r.l.a))
  r.a(l $(r.a l.r.a))

Examples

> `(set @)`(~(del in (silt ~[1 2 3 4 5])) 3)
{5 1 2 4}

> `(set @t)`(~(del in (silt ~['foo' 'bar' 'baz'])) 'bar')
{'baz' 'foo'}

> `(set @)`(~(del in (silt ~[1 2 3 4 5])) 10)
{5 1 2 3 4}

> `(set @)`(~(del in ~) 10)
{}

---

+dif:in

Difference.

Computes the difference between .a and .b, producing the set of items in .a that are not in .b.

Accepts

.a is a +set, and is the sample of +in.

.b is a +set.

Produces

A +set.

Source

++  dif
  ~/  %dif
  =+  b=a
  |@
  ++  $
    |-  ^+  a
    ?~  b
      a
    =+  c=(bif n.b)
    ?>  ?=(^ c)
    =+  d=$(a l.c, b l.b)
    =+  e=$(a r.c, b r.b)
    |-  ^-  [$?(~ _a)]
    ?~  d  e
    ?~  e  d
    ?:  (mor n.d n.e)
      d(r $(d r.d))
    e(l $(e l.e))
  --

Examples

> =a (silt ~[1 2 3 4 5])
> =b (silt ~[3 4])

> `(set @)`(~(dif in a) b)
{5 1 2}

---

+dig:in

Address .b in .a.

Produce the tree address of .b within .a.

Accepts

.a is a +set, and is the sample of +in.

.b is a $noun.

Produces

The +unit of an $atom.

Source

++  dig
  |=  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))

Examples

> =a (silt ~[1 2 3 4 5 6 7])

> -.a
n=6

> (~(dig in a) 7)
[~ 12]

> (~(dig in a) 2)
[~ 60]

> (~(dig in a) 6)
[~ 2]

> (~(dig in a) 10)
~

Discussion

For more on the tree addressing system, see section 1b.

---

+gas:in

Concatenate.

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

Accepts

.a is a +set, and is the sample of +in.

.b is a list.

Produces

A +set.

Source

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

Examples

> =a (silt ~['foo' 'bar' 'baz'])
> `(set @t)`a
{'bar' 'baz' 'foo'}

> `(set @t)`(~(gas in a) ~['foo' 'foo' 'foo' 'foo'])
{'bar' 'baz' 'foo'}

> `(set @t)`(~(gas in a) ~['abc' 'xyz' '123'])
{'xyz' 'bar' 'baz' 'foo' 'abc' '123'}

---

+has:in

Is .b in .a?

Checks if .b is an element of .a, producing a $flag.

Accepts

.a is a +set, and is the sample of +in.

.b is a $noun.

Produces

A $flag.

Source

++  has
  ~/  %has
  |*  b=*
  ^-  ?
  %.  [~ b]
  |=  b=(unit _?>(?=(^ a) n.a))
  =>  .(b ?>(?=(^ b) u.b))
  |-  ^-  ?
  ?~  a
    |
  ?:  =(b n.a)
    &
  ?:  (gor b n.a)
    $(a l.a)
  $(a r.a)

Examples

> =a (silt ~[1 2 3 4 5])

> (~(has in a) 2)
%.y

> (~(has in a) 6)
%.n

---

+int:in

Intersection.

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

Accepts

.a is a +set, and is the sample of +in.

.b is a +set.

Produces

A +set.

Source

++  int
  ~/  %int
  =+  b=a
  |@
  ++  $
    |-  ^+  a
    ?~  b
      ~
    ?~  a
      ~
    ?.  (mor n.a n.b)
      $(a b, b a)
    ?:  =(n.b n.a)
      a(l $(a l.a, b l.b), r $(a r.a, b r.b))
    ?:  (gor n.b n.a)
      %-  uni(a $(a l.a, r.b ~))  $(b r.b)
    %-  uni(a $(a r.a, l.b ~))  $(b l.b)
  --

Examples

> `(set @tD)`(~(int in (silt "foobar")) (silt "bar"))
{'r' 'b' 'a'}

> `(set @tD)`(~(int in (silt "foobar")) ~)
{}

> `(set @tD)`(~(int in (silt "foobar")) (silt "baz"))
{'b' 'a'}

---

+put:in

Put .b in .a.

Add an element .b to the set .a, producing a +set.

Accepts

.a is a +set, and is the sample of +in.

.b is a $noun.

Produces

A +set.

Source

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

Examples

> `(set @)`(~(put in (silt ~[1 2 3])) 4)
{1 2 3 4}

> `(set @)`(~(put in `(set @)`~) 42)
{42}

---

+rep:in

Accumulate.

Accumulate the elements of .a using binary gate .b.

Accepts

.a is a +set, and is the sample of +in.

.b is a gate.

Produces

A $noun.

Source

++  rep
  ~/  %rep
  |*  b=_=>(~ |=([* *] +<+))
  |-
  ?~  a  +<+.b
  $(a r.a, +<+.b $(a l.a, +<+.b (b n.a +<+.b)))

Examples

> (~(rep in (silt ~[1 2 3 4 5])) add)
b=15

> `@t`(~(rep in (silt ~['foo' 'bar' 'baz'])) |=(a=[@ @] (cat 3 a)))
'foobarbaz'

---

+run:in

Apply gate to set.

Produce a +set containing the products of gate .b applied to each element in .a.

Accepts

.a is a +set.

.b is a gate.

Produces

A +set.

Source

++  run
  ~/  %run
  |*  b=gate
  =+  c=`(set _?>(?=(^ a) (b n.a)))`~
  |-  ?~  a  c
  =.  c  (~(put in c) (b n.a))
  =.  c  $(a l.a, c c)
  $(a r.a, c c)

Examples

> =s (silt ~["a" "A" "b" "c"])

> `(set tape)`s
{"A" "a" "c" "b"}

> (~(run in s) cuss)
{"A" "C" "B"}

---

+tap:in

Set to list.

Flattens the +set .a into a +list.

Accepts

.a is an set.

Produces

A list.

Source

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

Examples

> ~(tap in (silt "foobar"))
"oafbr"

> ~(tap in (silt ~[1 2 3 4 5]))
~[4 3 2 1 5]

---

+uni:in

Union.

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

Accepts

.a is a +set, and is the sample of +in.

.b is a +set.

Produces

A +set.

Source

++  uni
  ~/  %uni
  =+  b=a
  |@
  ++  $
    ?:  =(a b)  a
    |-  ^+  a
    ?~  b
      a
    ?~  a
      b
    ?:  =(n.b n.a)
      b(l $(a l.a, b l.b), r $(a r.a, b r.b))
    ?:  (mor n.a n.b)
      ?:  (gor n.b n.a)
        $(l.a $(a l.a, r.b ~), b r.b)
      $(r.a $(a r.a, l.b ~), b l.b)
    ?:  (gor n.a n.b)
      $(l.b $(b l.b, r.a ~), a r.a)
    $(r.b $(b r.b, l.a ~), a l.a)
  --

Examples

> =a (silt ~[1 2 3 4 5])
> =b (silt ~[4 5 6 7 8])

> `(set @)`(~(uni in a) b)
{8 5 7 6 1 2 3 4}

> `(set @)`(~(uni in a) ~)
{5 1 2 3 4}

> `(set @)`(~(uni in `(set @)`~) b)
{8 5 7 6 4}

---

+wyt:in

Set size.

Produces the number of elements in set .a as an $atom.

Accepts

.a is a +set.

Produces

An $atom.

Source

++  wyt
  =<  $
  ~%  %wyt  +  ~
  |.  ^-  @
  ?~(a 0 +((add $(a l.a) $(a r.a))))
--

Examples

> ~(wyt in (silt ~[1 2 3 4]))
4

> ~(wyt in `(set @)`~)
0

---