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
~/ %in
|_ a=(set)
Examples
> ~(. in (sy "asd"))
<13.evb [nlr(^$1{@tD $1}) <414.fvk 101.jzo 1.ypj %164>]>
+-all:in
Logical AND
Computes the logical AND on every element in a slammed with b, producing a
flag.
Accepts
a is a set.
b is a wet gate that accepts a noun and produces a flag.
Produces
A flag.
Source
+- all
~/ %all
|* b=$-(* ?)
|- ^- ?
?~ a
&
?&((b n.a) $(a l.a) $(a r.a))
Examples
> =b (sy `(list [@t *])`[['a' 1] ['b' [2 3]] ~])
> (~(all in b) |=(a=* ?@(+.a & |)))
%.n
> =b (sy `(list @t)`['john' 'bonita' 'daniel' 'madeleine' ~])
> (~(all in b) |=(a=@t (gte a 100)))
%.y
+-any:in
Logical OR
Computes the logical OR on every element of a slammed with b, producing a
flag.
Accepts
a is a set.
b is a gate that accepts a noun and produces a flag.
Produces
A flag.
Source
+- any
~/ %any
|* b=$-(* ?)
|- ^- ?
?~ a
|
?|((b n.a) $(a l.a) $(a r.a))
Examples
> =b (sy `(list [@t *])`[['a' 1] ['b' [2 3]] ~])
> (~(any in b) |=(a/* ?@(+.a & |)))
%.y
> =b (sy `(list @t)`['john' 'bonita' 'daniel' 'madeleine' ~])
> (~(any in b) |=(a=@t (lte a 100)))
%.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
=| [l=(unit) r=(unit)]
|- ^- ?
?~ a &
?& ?~(l & (hor n.a u.l))
?~(r & (hor u.r n.a))
?~(l.a & ?&((vor n.a n.l.a) $(a l.a, l `n.a)))
?~(r.a & ?&((vor n.a n.r.a) $(a r.a, r `n.a)))
==
Examples
> ~(apt in ~)
%.y
> =a (sy [1 2 3 4 5 6 ~])
> a
[n=6 l={5 4} r={1 3 2}]
> ~(apt in a)
%.y
> =z ?~ a ~ a(n 7)
> z
[n=7 l={5 4} r={1 3 2}]
> ~(apt in z)
%.n
Discussion
See section 2f for more information on noun ordering.
+-bif:in
Bifurcate
Splits set a into two sets l and r, with any noun b removed.
Accepts
a is a set.
b is a noun.
Produces
A cell of two sets.
Source
+- bif
~/ %bif
|* b=*
^+ [l=a r=a]
=< [+< +>]
|- ^+ a
?~ a
[b ~ ~]
?: =(b n.a)
a
?: (hor b n.a)
=+ c=$(a l.a)
?> ?=(^ c)
[n.c l.c [n.a r.c r.a]]
=+ c=$(a r.a)
?> ?=(^ c)
[n.c [n.a l.a l.c] r.c]
Examples
> =a (sy `(list @)`[1 2 3 4 5 6 ~])
> a
[n=6 l={5 4} r={1 3 2}]
> (~(bif in a) 6)
[l=[n=4 l=[n=5 l={} r={}] r=~] r=[n=2 l=[n=1 l={} r={3}] r=~]]
> (~(bif in a) 100)
[l=[n=6 l=[n=4 l={5} r={}] r=[n=2 l={1 3} r={}]] r=~]
+-del:in
Remove noun
Removes b from the set a.
Accepts
a is a set.
b is a noun.
Produces
A set.
Source
+- del
~/ %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 $(r.a l.r.a) r.r.a]
Examples
> =b (sy `(list @t)`['a' 'b' 'c' ~])
> (~(del in b) 'a')
[n='b' l=[n='c' l={} r={}] r=~]
> =b (sy `(list @t)`['john' 'bonita' 'daniel' 'madeleine' ~])
> (~(del in b) 'john')
[n='madeleine' l=[n='daniel' l={} r={'bonita'}] r=~]
> (~(del in b) 'susan')
[n='madeleine' l=[n='daniel' l={} r={'bonita'}] r=[n='john' l={} r={}]]
+-dif:in
Difference
Computes the difference between a and b, producing the set of items in a
that are not in b.
Accepts
a is a set.
b is a set.
Produces
A set.
Source
+- dif
~/ %dif
|* b=_a
|- ^+ a
?~ b
a
=+ c=(bif n.b)
?> ?=(^ c)
=+ d=$(a l.c, b l.b)
=+ e=$(a r.c, b r.b)
|- ^- {$?($~ _a)}
?~ e d
?: (vor n.d n.e)
[n.d l.d $(d r.d)]
[n.e $(e l.e) r.e]
Examples
> =c (sy 1 2 3 ~)
> =d (sy 2 3 4 ~)
> (~(dif in c) d)
[n=1 l=~ r=~]
> (~(dif in d) c)
[n=4 l=~ r=~]
> `(set @ud)`(~(dif in c) d)
{1}
> `(set @ud)`(~(dif in d) c)
{4}
+-dig:in
Address b in a
Produce the tree address of b within a.
Accepts
a is a set.
b is a noun.
Produces
The unit of an atom.
Source
+- dig
|= b=*
=+ c=1
|- ^- (unit @)
?~ a ~
?: =(b n.a) [~ u=(peg c 2)]
?: (hor b n.a)
$(a l.a, c (peg c 6))
$(a r.a, c (peg c 7))
Examples
> =a (sy `(list @)`[1 2 3 4 5 6 7 ~])
> `(set @)`a
{5 4 7 6 1 3 2}
> -.a
n=6
> (~(dig in a) 7)
[~ u=12]
> (~(dig in a) 2)
[~ u=14]
> (~(dig in a) 6)
[~ u=2]
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.
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
> =b `(set @t)`(sy `(list @t)`['bonita' 'madeleine' 'rudolf' 'john' ~])
> b
{'bonita' 'madeleine' 'rudolf' 'john'}
> (~(gas in b) `(list @t)`['14' 'things' 'number' '1.337' ~])
[n='number' l={'1.337' '14'} r={'things' 'bonita' 'madeleine' 'rudolf' 'john'}]
> =s (sy `(list @t)`['a' 'b' 'c' 'd' 'e' ~])
> (~(gas in s) `(list @t)`['1' '2' '3' ~])
[n='e' l=[n='1' l={} r={'3' '2'}] r=[n='b' l={'d' 'a' 'c'} r={}]]
+-has:in
b in a?
Checks if b is an element of a, producing a flag.
Accepts
a is a set.
b is a noun.
Produces
A flag.
Source
+- has
~/ %has
|* b=*
|- ^- ?
?~ a
|
?: =(b n.a)
&
?: (hor b n.a)
$(a l.a)
$(a r.a)
Examples
> =a (~(gas in `(set @t)`~) `(list @t)`['a' 'b' 'c' ~])
> (~(has in a) 'a')
%.y
> (~(has in a) 'z')
%.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.
b is a set.
Produces
A set.
Source
+- int
~/ %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 $(a l.a, b [n.b l.b ~])) $(b r.b)
%- uni(a $(a r.a, b [n.b ~ r.b])) $(b l.b)
Examples
> (~(int in `(set @t)`(sy "acmo")) `(set @t)`(sy "ham"))
[n='m' l={'a'} r={}]
> (~(int in (sy "acmo")) ~)
~
> (~(int in `(set @t)`(sy "ac")) `(set @t)`(sy "ha"))
[n='a' l={} r={}]
+-put:in
Put b in a
Add an element b to the set a, producing a set.
Accepts
a is a set.
b is a noun.
Produces
A set.
Source
+- put
~/ %put
|* b=*
|- ^+ a
?~ a
[b ~ ~]
?: =(b n.a)
a
?: (hor b n.a)
=+ c=$(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]
Examples
> =a (~(gas in `(set @t)`~) `(list @t)`['a' 'b' 'c' ~])
> =b (~(put in a) 'd')
> `(set @t)`b
{'d' 'a' 'c' 'b'}
> -.l.+.b
n='d'
+-rep:in
Accumulate
Accumulate the elements of a using a gate b.
Accepts
a is a set.
b is a gate.
Produces
A noun.
Source
+- rep :: replace by product
|* b=_|=([* *] +<+)
|-
?~ a +<+.b
$(a r.a, +<+.b $(a l.a, +<+.b (b n.a +<+.b)))
Examples
> =a (~(gas in *(set @)) [1 2 3 ~])
> `(set @)`a
{1 3 2}
> (~(rep in a) |=([a=@ b=@] (add a b)))
b=6
+-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 (sy ~["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
> =s (sy `(list @t)`['a' 'b' 'c' 'd' 'e' ~])
> s
[n='e' l={} r={'d' 'a' 'c' 'b'}]
> ~(tap in s)
~['b' 'c' 'a' 'd' 'e']
+-uni:in
Union
Produces a set of the union between two sets of the same type, a and
b.
Accepts
a is a set.
b is a set.
Produces
A set.
Source
+- uni
~/ %uni
|* b=_a
?: =(a 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)
::
Examples
> (~(uni in `(set @t)`(sy "ac")) `(set @)`(sy "ha"))
[n='c' l={'a'} r={'h'}]
> (~(uni in `(set @t)`(sy "acmo")) ~)
[n='c' l={'a'} r={'m' 'o'}]
> (~(uni in `(set @t)`(sy "acmo")) `(set @t)`(sy "ham"))
[n='c' l={'a'} r={'m' 'o' 'h'}]
> (~(uni in `(set @t)`(sy "acmo")) `(set @t)`(sy "lep"))
[n='e' l={} r={'a' 'c' 'm' 'l' 'o' 'p'}]
+-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 :: size of set
|- ^- @
?~(a 0 +((add $(a l.a) $(a r.a))))
--
Examples
> =a (~(put in (~(put in (sy)) 'a')) 'b')
> ~(wyt in a)
2
> =b (sy `(list @t)`['john' 'bonita' 'daniel' 'madeleine' ~])
> ~(wyt in b)
4