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@abrudz abrudz/TAO.dyalog
Created Dec 7, 2017

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Sorting and grading any Dyalog APL array.
Sort{⎕ML1 Total array ordering (TAO) comparison.
acmp{ array comparison.
/:¯1 match: equal.
~/¨: xrnk ranks differ: reshape with 1-axes.
⊃⊃/:1 prefixes precede their continuations.
⊃⊃/:0 continuations follow their prefixes.
~/¨: xshp shapes differ: stretch with fills.
0=×/:¨ null: comparison of proto items.
~¨: halves,¨ non-atomic: item-wise comparison.
comparison of atomic items:
typestype¨ item types: char, number, ...
/types:/types types differ: compare.
3.=types: fixor¨ ⎕ORs: comparison of fixed items.
1.=types:ncmp simple numbs: comparison.
0.=types:/ simple chars: ⍋-style comparison.
comparison of refs:
/ot.⎕WG'Type': ot object-type mismatch: order on types
/¨⍺⍺: ⍺⍺¨⍺⍺ cycles in both: cycle lengths (NN).
unms.(~' '¨⎕NL10) user-supplied names.
ucls.⎕NC¨unms and their name-classes.
uvls valu¨¨unms value of each symbol in each space.
ucmpzip¨zip unms ucls uvls name/class/value triples.
scmp.(⎕CT ⎕DIV ⎕IO ⎕ML ⎕PP ⎕RL ⎕RTL) system variable values.
pcmp.(⎕WG¨⎕WG'PropList') property values.
(⍺⍺¨)∇∇ zip ucmp scmp pcmp cmp of user-vals; sysvars; props.
xshp{ stretch arrays of differing shape.
shp/¨ new shape
pad{@()0} padding of ref-array(s)
16::zip(shppad¨)(¨) nonce: can't over-take ref array <V>
newshp¨ extended arrays.
zip new(¨) (⍺ shp)(⍵ shp)
xrnk{ stretch arrays of differing rank.
rnk/¨ new rank.
onesrnk1 sufficient 1-padding.
shps(-rnk)¨ones,¨ new shapes.
ors{1 ()()}¨ must enclose ⎕or for reshape.
newshps¨ors{()}¨ extended arrays.
zip new(¨) (⍺ rnk)(⍵ rnk)
type{ types of depth-0 items:
1 0(),⍴⍴:3 ⎕OR: 3
9=⎕NC'':2 ref: 2
0=0 num: 1, char: 0
ncmp{ comparison of numbers.
0>(9 11-/)~0 real part trumps imaginary part.
fixor{ fix of ⎕OR item in tmp space.
11::⎕NS ⎕OR of namespace.
⎕NR(⎕NS'').⎕FX ⎕OR of fn/op.
valu{ referent value of name ⍺.⍵.
'':'' ignore null name.
3 4.=.⎕NC :.⎕NR fn/op: nested rep.
. var or ref: value.
zip{} items interleaved.
halves{ compare vector halves.
n()÷2 half-way point.
n=0:⍺⍺¨ compare single items
¯1c⍺⍺ n¨:c first halves differ: done.
⍺⍺ n¨ comparison of second halves.
| acmp ⍺≤⍵
}{ quicksort.
1: single item or null: done.
head tail(1)(1) first and remaining items.
le gt1 0=tail ⍺⍺¨head comparison with first item.
( le/tail),head, gt/tail sorted vector.
GradeUp{|/Sort { }¨}
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