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                                                                                              Reference/Hoon/Standard Library

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

                                                                                              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 an 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

                                                                                              <-

                                                                                              2g: Unsigned Powers

                                                                                              2i: Map Logic

                                                                                              ->

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                                                                                              Last modified March 17, 2023