++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|@++ $|- ^+ a?~ ba=+ c=(bif n.b)?> ?=(^ c)=+ d=$(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))$(a r.a, c (peg c 7))
Examples
> =a (silt ~[1 2 3 4 5 6 7])> -.an=6> (~(dig in a) 7)[~ 12]> (~(dig in a) 2)[~ 60]> (~(dig in a) 6)[~ 2]> (~(dig in a) 10)~
Discussion
For more on the tree addressing system, see section 1b.
++gas:in
Concatenate
Insert the elements of a list b into a set a.
Accepts
a is a set, and is the sample of +in.
b is a list.
Produces
A set.
Source
++ gas~/ %gas|= b=(list _?>(?=(^ a) n.a))|- ^+ a?~ ba$(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=< $~/ %tap=+ b=`(list _?>(?=(^ a) n.a))`~|. ^+ b?~ ab$(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?~ ba?~ ab?: =(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