(muse:
Programmer Dvorak http://www.kaufmann.no/roland/dvorak
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┌────┬────┬────┬────┬────┬────┬────┬────┬────┬────┬────┬────┬────┬─────────┐
│~ │% │7 │5 │3 │1 │9 │0 │2 │4 │6 │8 │` │Backspace│
│$ │& │[ │{ │} │( │= │* │) │+ │] │! │# │ │
├────┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬──────┤
│Tab │: │< │> │P │Y │F │G │C │R │L │? │∧ │Enter │
│ │; │, │. │p │y │f │g │c │r │l │/ │@ │ │
├───────┴┬───┴┬───┴┬───┴┬───┴┬───┴┬───┴┬───┴┬───┴┬───┴┬───┴┬───┴┬───┴┐ │
│Caps │A │O │E │U │I │D │H │T │N │S │_ │| │ │
│Lock │a │o │e │u │i │d │h │t │n │s │- │\ │ │
├──────┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴────┴─────┤
│Shift │ │" │Q │J │K │X │B │M │W │V │Z │Shift │
│ │ │' │q │j │k │x │b │m │w │v │z │ │
├──────┴┬───┴─┬──┴───┬┴────┴────┴────┴────┴────┴┬───┴──┬─┴────┼─────┬──────┤
│ctrl │Win │Alt │ │Alt Gr│Win │Menu │Ctrl │
│ │ │ │ │ │ │ │ │
└───────┴─────┴──────┴──────────────────────────┴──────┴──────┴─────┴──────┘
Where should we allocate APL symbols on a Dvorak keyboard? The spirit of the
layout is to ignore mnemonic association in favour of arranging keys with
respect to the frequency of occurrence of key-sequences. Among other consid-
erations, the keys are placed so as to minimise the total distance that our
fingers travel from their home positions in the centre of the keyboard.
The guiding assumption is that, while mnemonic associations (⍴ on R, ⍳ on I,
and so forth) are handy while we're learning the keyboard, with a little
practice, our _fingers_ soon remember where the characters are located with-
out resort to the mnemonic. This "muscle memory" phenomenon can be seen in
action when we drive a stick-shift or dance the quickstep; we delegate the
changes to our hands and feet without having to think consciously about
them.
If we accept this, then mnemonic placement of keys soon becomes counter-
productive compared with schemes that try to minimise hand movements. The
(arguably) most mnemonic keyboard of all: ABCDEF..., doesn't seem to have
given QWERTY much of a run for its money even though such keyboards are,
these days, no more expensive to produce.
(muse:
For what it's worth, this typist finds it significantly easier spell
BRAM(ley) on those ticket machines in Reading Railway Station that sport
QWERTY touch-screens, than on the few that offer ABCDEF.
)
http://mkweb.bcgsc.ca/carpalx/?home is an excellent website, which addresses
many of the issues of efficient keyboard layout. In particular, see the
section on "typing effort".
Frequency of Characters in this Workspace
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Here is a frequency sample (as of 2009-03-22) of _single_ APL characters in
source code in this workspace. It excludes workspace notes and test-scripts
but includes APL characters in function comments:
apl←'⍫⍒⍋⌽⍉⊖⍟⍱⍲⌹⋄¨¯≤≥≠∨×÷⍣⍞⍬⊣⍵∊⍴↑↓⍳○←→⊢≡⍪⍺⌈⌊∇∆∘⎕⍎⍕⍷⍙⍨⊂⊃∩∪⊥⊤⍝⍀⌿⌷'
code←↑,/,∘⎕cr¨↓⎕nl 3 4 ⍝ source code chars.
freq ← {(∪⍵){⍺{(↓⍉↑⍺⍵)[⍒⍵]}+/⍺∘.=⍵}⍵}
4 40 cols freq code∩apl ⍝ apl char-frequency.
⍝ 4468 ∇ 426 → 111 ≥ 44 ∩ 14
⍵ 4011 ∘ 402 ⌈ 99 ⍋ 42 ⍒ 13
← 3159 ¯ 336 ⍉ 99 ∪ 42 ⊣ 7
⍺ 2705 ∊ 323 ⌊ 97 ⍪ 41 ⌹ 5
⍴ 811 × 318 ⍕ 81 ⊥ 40 ⍱ 4
⎕ 799 ⌽ 297 ∆ 81 ⊖ 38 ⌷ 3
¨ 717 ⍳ 279 ⌿ 70 ⊤ 36 ⍲ 3
↑ 623 ⋄ 268 ⍙ 68 ⍟ 32 ⊢ 1
⊂ 563 ⍬ 150 ⍎ 64 ≤ 25 ⍣ 1
↓ 532 ÷ 140 ⍷ 60 ⍫ 25
⊃ 523 ≠ 128 ⍨ 57 ⍞ 16
≡ 444 ∨ 127 ○ 54 ⍀ 15
It _could_ be argued that we should also reassign non-APL, non-alphameric
chars:
other←'~%`$&[{}(=*)+]!#:<>?∧;,./@_|-\"'''
4 40 cols freq code∩apl∪other ⍝ non-alphameric frequency.
⍝ 4468 = 618 \ 259 # 71 ⍫ 25
⍵ 4011 + 592 < 233 ⌿ 70 ! 22
. 3936 ⊂ 563 > 227 ? 69 ⍞ 16
' 3411 ↓ 532 | 206 ⍙ 68 ⍀ 15
← 3159 ⊃ 523 ∧ 193 ⍎ 64 ∩ 14
⍺ 2705 ≡ 444 ⍬ 150 ⍷ 60 ⍒ 13
) 1988 ∇ 426 " 142 ⍨ 57 ⊣ 7
: 1985 ∘ 402 ÷ 140 ○ 54 % 6
( 1981 ¯ 336 ≠ 128 ≥ 44 ⌹ 5
, 1859 [ 324 ∨ 127 ⍋ 42 ⍱ 4
{ 1779 ] 324 * 116 ∪ 42 ⌷ 3
} 1771 ∊ 323 → 111 ⍪ 41 ⍲ 3
- 1178 × 318 ⌈ 99 ⊥ 40 @ 3
/ 954 _ 307 ⍉ 99 ⊖ 38 $ 1
⍴ 811 ~ 298 ⌊ 97 ⊤ 36 ⊢ 1
⎕ 799 ⌽ 297 ⍕ 81 ⍟ 32 ` 1
¨ 717 ⍳ 279 ∆ 81 & 30 ⍣ 1
↑ 623 ⋄ 268 ; 75 ≤ 25
but doing so would win us few friends among (any) existing Programmer Dvorak
users.
Character sequences
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The incidence of character _sequences_ is as important as that of individual
characters. For example, it is beneficial to allocate frequently occurring
sequences so that, where possible, the characters are typed with alternating
hands or, failing that, single-hand "finger runs" from the outer (pinky) to
the inner (index) side with the same hand. Regarding this last point,
http://en.wikipedia.org/wiki/Dvorak_Simplified_Keyboard notes that we gener-
ally drum our fingers on the table in this direction.
(muse:
In the same Wikipedia article, Dvorak also recommends: "Digraphs should
not be typed with adjacent fingers.". This seems a bit rich, given that
he allocates one of the most frequent digraphs in English: "th" to the
second and index finger of the right hand. Presumably this was as the
result of a compromise, which avoided an even worse combination.
)
The following function returns a list, for each APL character, of the most
frequent non-alphameric characters that (a) precede and (b) follow it. The
list is returned in order of individual APL character frequency, as above.
cseqs←{ ⍝ ⍵-char-sequence table.
code←{(⍵≠1⌽⍵)/⍵}↑,/,∘⎕CR¨↓⎕NL 3 4 ⍝ source code chars.
atab←{+/⍵⍷code}¨∘.,⍨⍺,⍵ ⍝ adjacency count table.
pops←{{⍵⍳⌈/⍵}¨↓⍵⍉atab} ⍝ indices of popular pairs.
pqx←pops¨(2 1)(1 2) ⍝ popular ⍺⍵ and ⍵⍺ indices.
chars←⍺,⍵ ⍝ apl and other chars.
achar←{⍺⊃¨¨(⊂chars){⍺ ⍵}¨↓⍵⍉atab} ⍝ popular adjacent char and count.
pqvex←pqx achar¨(2 1)(1 2) ⍝ preceding and following counts.
fmt←{ ⍝ format:
(pc pn)(qc qn)←⍵ ⍝ preceding count and char,
pn pc(,⍺)qc(⍕qn) ⍝ - char -
} ⍝ following char and count.
list←⍺ fmt¨(⍴⍺)↑↓⍉↑pqvex ⍝ list of char adjacencies.
sort←{⍺{⍺[⍒⍵]}+/⍺∘.=⍵} ⍝ sorted in order of frequency.
freq←{(∪⍵)sort ⍵}code∩⍺ ⍝ char frequency.
↓⍕↑list[⍺⍳freq] ⍝ list by frequency.
}
For example, in the output below (arranged in four columns, so as to be easy
on the eye), the _third_ item in the first column: "129 ⍺ ← { 1015" indicat-
es that '←', the _third_ most popular APL character, is preceded most often
(128) by an '⍺' and followed most often (1015) by a '{'.
┌───────── ←, the third-most frequently occurring APL character,
129 ⍺ ← { 1015
└───┤ └────┴── is followed most (1015) frequently by {.
└─────────── and preceded most (129) frequently by ⍺.
This suggests that it might be (1015)-attractive to site the '←' key so that
Programmer-Dvorak '{' may easily follow it.
Of course, an analysis of a more traditional workspace, where D-function us-
age was less prevalent, might yield quite different results! ;-)
NB: Take care not to infer from the above item, anything about the frequency
of occurrence of the sequence '⍺←{'. In fact, it occurs only 21 times, while
'⍺←' occurs 129 times and '←{' occurs 1015 times.
Note also that, in the first line of cseqs, function {(⍵≠1⌽⍵)/⍵} deliberate-
ly removes adjacent identical characters from the analysis. A frequent oc-
currence of, say, double-each ¨¨ wouldn't help us to locate the ¨ symbol on
the keyboard.
Here are the results for the code in this workspace (as of 2009-03-22):
4 60 cols apl cseqs other ⍝ adjacent char frequencies.
28 ' ⍝ ' 34 51 ⍵ ∊ ' 47 19 + ⌿ ⍵ 18 5 ⍺ ⍫ ← 4
302 ⍴ ⍵ } 619 22 . × ⍵ 43 9 ' ⍙ _ 61 8 } ⍞ ← 10
129 ⍺ ← { 1015 42 ⊃ ⌽ ⍵ 53 14 ( ⍎ ⍵ 17 3 ' ⍀ . 4
193 ← ⍺ ) 243 34 ( ⍳ ⍴ 82 17 ' ⍷ ⍵ 30 7 [ ⍒ ⍵ 5
112 { ⎕ ← 14 5 ' ⋄ ' 9 5 ∊ ⍨ ∘ 8 6 ⍵ ∩ ' 4
111 ( ⍴ ⍵ 302 22 ← ⍬ ⍴ 22 2 × ○ ⍵ 36 3 ⍺ ⊣ ⍵ 3
137 } ¨ ⍵ 111 27 ) ÷ ⍵ 10 6 ⍺ ≥ ⍴ 13 2 ' ⌹ ' 2
71 ) ↑ ⍵ 101 24 ⍵ ≠ ' 21 13 ← ∪ , 10 2 ) ⍱ ⌽ 2
165 , ⊂ ' 145 21 ( ∨ \ 34 8 ) ⍪ ( 9 2 ) ⌷ ¨ 1
70 ) ↓ ⍵ 129 12 ' → ' 11 2 ' ⊥ ⍉ 5 1 ⍱ ⍲ ⍒ 1
62 ) ⊃ ⍵ 112 45 ↓ ⍉ ↑ 46 10 [ ⍋ ↑ 16 1 { ⊢ } 1
137 ' ≡ ⍺ 85 10 ← ⌈ / 25 8 { ⊖ ⍵ 9 1 ⍞ ⍣ ⍫ 0
85 ) ∇ ¨ 60 21 ← ⌊ / 19 13 ) ⊤ ⍵ 15
78 } ∘ { 75 14 ( ⍕ ¨ 15 3 × ⍟ ⍵ 6
37 ( ¯ ' 14 15 ' ∆ ← 5 4 < ≤ = 4
Happily, many of the above rankings confirm our expectations:
← is often followed by {, for function definition,
¨ is most often preceded by }, as in "dfn-each",
⍵ is often followed by },
⍵ often follows a primitive function,
) often precedes a primitive function,
⍋ and ⍒ are often preceded by [,
⍉ is often preceded by ↓ and often followed by ↑ (as in ↓⍉↑),
⊥ is often followed by ⍉,
... and so on.
NB: Before attempting to use the above results to design an APL/Dvorak key-
board, it might be better to adjust function cseqs to report not just the
single highest-frequency predecessor and successor character. Perhaps we
should consider a "top ten" popular neighbour chart for each character. This
would permit us a little "wiggle room" when trying to optimise the allocat-
ion of APL symbols to keys.
With the advent of Input Method Editors (IMEs), it is relatively easy to ex-
periment with alternative keyboard layouts. Here is one that has attracted a
modest following:
"Colemak" http://colemak.com
┌───┬───┬───┬───┬───┬───┬───┬───┬───┬───┬───┬───┬───┬───────┐
│ ` │ 1 │ 2 │ 3 │ 4 │ 5 │ 6 │ 7 │ 8 │ 9 │ 0 │ - │ = │Backspc│
├───┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─────┤
│Tab │ Q │ W │ F │ P │ G │ J │ L │ U │ Y │ ; │ [ │ ] │ \ │
├─────┴┬──┴┬──┴┬──┴┬──┴┬──┴┬──┴┬──┴┬──┴┬──┴┬──┴┬──┴┬──┴─────┤
│Caps │ A │ R │ S │ T │ D │ H │ N │ E │ I │ O │ ' │ Enter │
├──────┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴────────┤
│Shift │ Z │ X │ C │ V │ B │ K │ M │ , │ . │ / │ Shift │
├────┬───┴┬──┴──┬┴───┴───┴───┴───┴───┴┬──┴─┬─┴───┼────┬─────┤
│Ctrl│Win │Alt │ │AltG│Win │Menu│Ctrl │
└────┴────┴─────┴─────────────────────┴────┴─────┴────┴─────┘
Finally, here is the physical layout of a pretty little keyboard: the Happy
Hacking Professional JP, from PFU-Fujitsu. Notice that the narrow space bar
leaves room for some additional mode keys, which is just the ticket for APL.
For example, the keys adjacent to the space bar, which are pressed with the
thumbs, could be used for APL and APL+Shift.
Happy Hacking Professional2 JP (PD-KB420B)
┌───┬───┬───┬───┬───┬───┬───┬───┬───┬───┬───┬───┬───┬───┬───┐
│esc│ │ │ │ │ │ │ │ │ │ │ │ │ │bs │
├───┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴───┤
│tab │ │ │ │ │ │ │ │ │ │ │ │ │enter│
├─────┴┬──┴┬──┴┬──┴┬──┴┬──┴┬──┴┬──┴┬──┴┬──┴┬──┴┬──┴┬──┴┐ │
│ctrl │ │ │ │ │ │ │ │ │ │ │ │ │ │
├──────┴┬──┴┬──┴┬──┴┬──┴┬──┴┬──┴┬──┴┬──┴┬──┴┬──┴┬──┴┬──┴┬───┤
│shift │ │ │ │ │ │ │ │ │ │ │ │ ↑ │sft│
├───┬┬──┴┬──┴┬──┴┬──┴┬──┴───┴──┬┴──┬┴──┬┴──┬┴──┬┼───┼───┼───┤
│fn ││ │ │alt│ │ space │ │ │alt│fn ││ ← │ ↓ │ → │
└───┴┴───┴───┴───┴───┴─────────┴───┴───┴───┴───┴┴───┴───┴───┘
http://www.pfu.fujitsu.com/hhkeyboard
http://www.youtube.com/watch?v=kWGsxxV1k0A
See also: forum posting Space Bar as APL Key.
https://forums.dyalog.com/viewtopic.php?f=30&t=1063&p=4304
)
See also: http://en.wikipedia.org/wiki/Keyboard_layout
See also: cols
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