Following discussion in thread Peculiarity of Link I revised my
J approach to sets. Here are examples. Definitions are below.
] S =: set 4;2;3;2;1
+-+-+-+-++
|1|2|3|4||
+-+-+-+-++
] T =: set 3;4;5;6
+-+-+-+-++
|3|4|5|6||
+-+-+-+-++
S n T NB. intersection
+-+-++
|3|4||
+-+-++
E is (S n T) less S NB. empty set
1
1 get S n T
4
2 get S n T
|index error: get
| 2 get S n T
NB. Puzzle: what is the element of
]A =: set a:
+++
|||
+++
NB. ?
Here are the definitions.
NB. Proposal -- A "set" is a list of boxes, without duplicates,
NB. with tail <i.0 0 and curtail sorted. You can think of the
NB. tail as a "set marker" that permits the empty set to be a
NB. non-empty list. Sorting the curtail makes it easer to test
NB. whether a set is an element of another set and whether two
NB. sets have the same elements and so are regarded as the same
NB. set.
isset =: [: *./ (1 = #...@$),(0 < L.),(-: ~.),(<@empty -: {:),(-: /:~)@}:
NB. empty =: (i.0 0)"_ is standard in z locale, from stdlib.ijs
set =: <@empty ,~ [: /:~...@~. ] -. <@empty
NB. usage set box or set list-of-boxes creates a set
is =: -: NB. usage set is set
NB. An "element" is the array contained in a set box
NB. except that i.0 0 is not an element.
iselement =: (<@[ e. ])*.([: -. empty -: [) NB. array iselement set
in =: iselement NB. array in set
count =: <:@# NB. count set gives number of elements
index =: }:@[ i. <@] NB. set index array
get =: [:`({:: }:)@.(1 > l...@[) NB. index get set
u =: [: set -. , ] NB. union
less =: -. , <@empty NB. difference
n =: [ less less NB. intersection
subset =: [ is n NB. set subset set
]E =: , < i.0 0 NB. empty set
++
++
]V =: set 1 ; (set (set 3;4);8;<(set 8;9) ) ; 10 NB. Example of Butch Lakeshore
+-+--+------------------++
|1|10|+-+------+------++||
| | ||8|+-+-++|+-+-++||||
| | || ||3|4||||8|9||||||
| | || |+-+-++|+-+-++||||
| | |+-+------+------++||
+-+--+------------------++
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
