"(Bo's) 1986-article on ordinal fractions may be of interest."
https://www.academia.edu/10031088/ORDINAL_FRACTIONS_-_the_algebra_of_data
Has anyone got an implementation?
Is `=' synonymous with `compatible'? If so, the following seems to work,
replacing for the literals with a vector.
NB. ordinal fractions, represented by vectors
Dyad=: [: :
Monad=: :[:
Commutes=: adverb def 'assert@:(u -: u~) Dyad' NB. assertion failure if u
does not commute
ANY=: , 0
ERROR=: , __
error=: ERROR"_
NB. removes trailing zeros
simplify=: ([: ANY"_^:(0=#) ({.~ (1 i.~([email protected]&=)\.))^:(0={:))"1 Monad
intersect=: dyad define"1
'X Y'=. x ,:&, y NB. fill extends the shorter vector
X=. X + Y * X = 0
Y=. Y + X * Y = 0
simplify X error^:(-.@:-:) Y
)
difference=: simplify@:(([ * =)/)@:(,:&,)"1 Dyad
true=: ANY = simplify
eq=: equal=: -:"1 Dyad
incompatible=: (ERROR -: intersect)"1
compatible=: -.@:incompatible
le=: ([ -: intersect)&:,"1
ge=: le~
lt=: subordinate=: le > eq NB. x subordinate y proper subset
gt=: superordinate=: ge > eq NB. x superordinate y proper superset
,.(#~ (1 -.@e.&> ])) <@:(". ::]);._2]0 :0 NB. tests evaluate to 1
iff pass
(,3) -: simplify 3 0 0 0
ANY -: simplify ANY
ANY -: ANY intersect ANY
(,1) -: 1 intersect&:,1
ERROR -: 1 intersect&:,2
ERROR -: 1 2 3 intersect 1 2 1
2 3 -: ANY intersect 2 3 0
0 2 3 -: ANY intersect 0 2 3 0
2 3 -: 2 3 intersect 2 3 0
2 3 8 -: 2 3 intersect 2 3 8
2 3 compatible 2 3 0
0 2 3 incompatible 2 3 0
1 [ 2 1 1 1 difference Commutes 2 1 2 1
1 [ 2 1 0 3 intersect Commutes 0 1 8 3
)
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