2f: Noun Ordering

+aor

Alphabetical order.

Computes whether .a and .b are in alphabetical order, producing a $flag. Orders $atoms before cells, and $atoms in ascending LSB order.

Accepts

.a is a $noun.

.b is a $noun.

Produces

A $flag.

Source

++  aor
  ~/  %aor
  |=  [a=* b=*]
  ^-  ?
  ?:  =(a b)  &
  ?.  ?=(@ a)
    ?:  ?=(@ b)  |
    ?:  =(-.a -.b)
      $(a +.a, b +.b)
    $(a -.a, b -.b)
  ?.  ?=(@ b)  &
  |-
  =+  [c=(end 3 a) d=(end 3 b)]
  ?:  =(c d)
    $(a (rsh 3 a), b (rsh 3 b))
  (lth c d)

Examples

> (aor 'a' 'b')

> (aor 'b' 'a')

> (aor 'a' 'a')
%.y

> (aor 1 2)
%.y

> (aor 2 1)
%.n

> (aor ['a' ~] 'b')
%.n

> (aor 'b' ['a' ~])
%.y

> (aor ['a' ~] ['b' ~])

> (aor ['b' ~] ['a' ~])
%.n

> (aor "abca" "abcz")
%.y

> (aor "abcz" "abca")
%.n

> (aor 0b1011 0b1010)
%.n

> (aor 0b1010 0b1011)
%.y

> (aor [1 2] [2 1])
%.y

> (aor [2 1] [1 2])
%.n

Note the possible differences with +dor due to comparing one byte at a time:

> (aor 0b1001.0000.0000 0b1000.1000.0000)
%.y

> (dor 0b1001.0000.0000 0b1000.1000.0000)
%.n

Discussion

This is different than +dor in that it compares $atoms one byte at a time, while +dor compares whole $atoms at once. Note that because it simply compares bytes, it doesn't account for multi-byte UTF-8 characters and the like.

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+dor

Depth order.

Computes whether .a and .b are in ascending tree depth order, producing a $flag. Orders $atoms before cells, and $atoms in ascending numerical order.

Accepts

.a is a $noun.

.b is a $noun.

Produces

A $flag.

Source

++  dor
  ~/  %dor
  |=  [a=* b=*]
  ^-  ?
  ?:  =(a b)  &
  ?.  ?=(@ a)
    ?:  ?=(@ b)  |
    ?:  =(-.a -.b)
      $(a +.a, b +.b)
    $(a -.a, b -.b)
  ?.  ?=(@ b)  &
  (lth a b)

Examples

> (dor 1 2)
%.y

> (dor 2 1)
%.n

> (dor ~[1 2 3] ~[1 2 4])
%.y

> (dor ~[1 2 4] ~[1 2 3])
%.n

> (dor `(list @)`~[99 100 10.000] ~[99 101 10.000])
%.y

> (dor ~[99 101 10.999] `(list @)`~[99 100 10.000])
%.n

Note the possible difference with +aor due to comparing whole $atoms rather than one byte at a time:

> (aor 0b1001.0000.0000 0b1000.1000.0000)
%.y

> (dor 0b1001.0000.0000 0b1000.1000.0000)
%.n

Discussion

If .a and .b are both $atoms, +dor is equivalent to +lte. If they're cells, +dor recurses on the heads, and then if the heads are the same it checks the tails.

If one sample is a cell and the other is an $atom, the cell sample is treated as "greater."

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+gor

Mug order.

Computes whether of (mug a) and (mug b) are in ascending numeric order, producing a $flag. If the +mug hashes are equal, .a and .b are compared by +dor instead.

+mug is the the 31-bit nonzero FNV-1a hash algorithm.

Accepts

.a is a $noun.

.b is a $noun.

Produces

A $flag.

Source

++  gor
  ~/  %gor
  |=  [a=* b=*]
  ^-  ?
  =+  [c=(mug a) d=(mug b)]
  ?:  =(c d)
    (dor a b)
  (lth c d)

Examples

> (gor 'd' 'c')
%.y

> 'd'
'd'

> 'c'
'c'

> `@ud`'d'
100

> `@ud`'c'
99

> (mug 'd')
1.628.185.714

> (mug 'c')
1.712.073.811

> (gor 'd' 'c')
%.y

> (gor 'c' 'd')
%.n

> (gor "foo" "bar")
%.n

> (gor (some 10) `(list @)`[1 2 3 ~])
%.n

Discussion

+maps use +gor on the key for horizontal ordering and +mor for vertical order. +maps only look at the keys (the head of the key-value pair elements) for ordering.

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+mor

(more) mug order.

Computes whether the double-hashes (mug (mug a)) and (mug (mug b)) are in ascending numeric order, producing a $flag. If the double-+mug hashes are equal, .a and .b are compared by +dor instead.

+mug is the the 31-bit nonzero FNV-1a hash algorithm.

Accepts

.a is a $noun

.b is a $noun

Produces

A $flag.

Source

++  mor
  ~/  %mor
  |=  [a=* b=*]
  ^-  ?
  =+  [c=(mug (mug a)) d=(mug (mug b))]
  ?:  =(c d)
    (dor a b)
  (lth c d)

Examples

> (mor 'f' 'g')
%.y

> [(mug 'f') (mug 'g')]
[1.661.740.952 1.644.963.335]

> [(mug (mug 'f')) (mug (mug 'g'))]
[261.421.509 1.861.258.547]

> (mor 'a' 'z')
%.n

> (mor 43.326 41.106)
%.n

Discussion

Maps, sets, and queues all use +mor to check for vertical ordering. Maps and sets also use +gor for horizontal order, but queues use vertical ordering alone.

Since hashing removes correlation, double-+mugging with +mor removes correlation with single-+mugged +gor. Vertical order becomes uncorrelated with horizontal order.

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