<s>
In	O
his	O
professional	O
career	O
he	O
was	O
devoted	O
to	O
the	O
development	O
of	O
the	O
programming	O
language	O
APL	B-Language
.	O
</s>
<s>
He	O
was	O
the	O
designer	O
and	O
implementer	O
of	O
direct	B-Application
functions	I-Application
.	O
</s>
<s>
Apart	O
from	O
APL	B-Language
,	O
he	O
also	O
found	O
beauty	O
in	O
nature	O
,	O
opera	O
,	O
the	O
music	O
of	O
Tom	O
Waits	O
,	O
the	O
literature	O
of	O
James	O
Joyce	O
,	O
the	O
poetry	O
of	O
W.B.	O
</s>
<s>
The	O
APL	B-Language
side	O
and	O
the	O
romantic	O
side	O
often	O
met	O
:	O
The	O
Depth-First	O
Search	O
video	O
(	O
below	O
)	O
was	O
recorded	O
at	O
dawn	O
on	O
the	O
summer	O
solstice	O
of	O
2014	O
,	O
with	O
birdsong	O
in	O
the	O
air	O
,	O
while	O
he	O
and	O
his	O
wife	O
were	O
on	O
a	O
21-day	O
Zen	O
retreat	O
in	O
France	O
led	O
by	O
Thích	O
Nhất	O
Hạnh	O
.	O
</s>
<s>
He	O
then	O
returned	O
to	O
ICL	O
Dataskil	O
working	O
on	O
APL	B-Language
for	O
the	O
VME/B	B-General_Concept
operating	O
system	O
(	O
1978	O
–	O
82	O
)	O
.	O
</s>
<s>
In	O
1982	O
,	O
he	O
started	O
the	O
Dyalog	O
APL	B-Language
project	O
for	O
Unix	B-Application
machines	O
,	O
and	O
in	O
1988	O
became	O
a	O
partner	O
and	O
director	O
of	O
the	O
Dyalog	O
Company	O
.	O
</s>
<s>
In	O
2004	O
,	O
Scholes	O
sold	O
his	O
shares	O
in	O
the	O
company	O
,	O
but	O
continued	O
as	O
a	O
consultant	O
and	O
,	O
in	O
his	O
words	O
,	O
pursued	O
his	O
passionate	O
interest	O
in	O
APL	B-Language
programming	O
on	O
various	O
mathematical	O
topics	O
in	O
general	O
and	O
functional	B-Language
programming	I-Language
and	O
dfns	B-Application
in	O
particular	O
.	O
</s>
<s>
Kenneth	O
E	O
.	O
Iverson	O
,	O
the	O
inventor	O
of	O
APL	B-Language
,	O
was	O
dissatisfied	O
with	O
the	O
way	O
user	O
functions	O
were	O
defined	O
.	O
</s>
<s>
Of	O
these	O
,	O
the	O
"	O
alternative	O
APL	B-Language
function	O
definition	O
"	O
of	O
Bunda	O
in	O
1987	O
came	O
closest	O
to	O
current	O
facilities	O
,	O
but	O
is	O
flawed	O
in	O
conflicts	O
with	O
existing	O
symbols	O
and	O
in	O
error	O
handling	O
which	O
would	O
have	O
caused	O
practical	O
difficulties	O
,	O
and	O
was	O
never	O
implemented	O
.	O
</s>
<s>
The	O
main	O
distillates	O
from	O
the	O
different	O
proposals	O
were	O
that	O
(	O
a	O
)	O
the	O
function	O
being	O
defined	O
is	O
anonymous	B-General_Concept
,	O
with	O
subsequent	O
naming	O
(	O
if	O
required	O
)	O
being	O
effected	O
by	O
assignment	O
;	O
(	O
b	O
)	O
the	O
function	O
is	O
denoted	O
by	O
a	O
symbol	O
and	O
thereby	O
enables	O
anonymous	B-Language
recursion	I-Language
.	O
</s>
<s>
In	O
1996	O
,	O
Scholes	O
invented	O
direct	B-Application
functions	I-Application
or	O
dfns	B-Application
(	O
pronounced	O
"	O
dee	O
funs	O
"	O
)	O
,	O
a	O
major	O
distinguishing	O
advance	O
of	O
early	O
21st	O
century	O
APL	B-Language
over	O
prior	O
versions	O
.	O
</s>
<s>
Dfns	B-Application
are	O
a	O
unique	O
combination	O
of	O
array	B-Application
programming	I-Application
,	O
higher-order	B-Language
functions	I-Language
,	O
and	O
functional	B-Language
programming	I-Language
.	O
</s>
<s>
The	O
ideas	O
originated	O
in	O
1989	O
when	O
he	O
read	O
a	O
special	O
issue	O
of	O
The	O
Computer	O
Journal	O
on	O
functional	B-Language
programming	I-Language
.	O
</s>
<s>
He	O
then	O
proceeded	O
to	O
study	O
functional	B-Language
programming	I-Language
and	O
became	O
strongly	O
motivated	O
(	O
"	O
sick	O
with	O
desire	O
"	O
,	O
like	O
Yeats	O
)	O
to	O
bring	O
these	O
ideas	O
to	O
APL	B-Language
.	O
</s>
<s>
Dfns	B-Application
were	O
first	O
presented	O
in	O
the	O
Dyalog	O
Vendor	O
Forum	O
at	O
the	O
APL	B-Language
'	O
96	O
Conference	O
and	O
released	O
in	O
Dyalog	O
APL	B-Language
in	O
early	O
1997	O
.	O
</s>
<s>
As	O
late	O
as	O
2008	O
,	O
in	O
Dyalog	O
at	O
25	O
,	O
a	O
publication	O
celebrating	O
the	O
25th	O
anniversary	O
of	O
Dyalog	O
Ltd	O
,	O
dfns	B-Application
were	O
barely	O
mentioned	O
(	O
mentioned	O
twice	O
as	O
"	O
dynamic	O
functions	O
"	O
and	O
without	O
elaboration	O
)	O
.	O
</s>
<s>
As	O
of	O
2019	O
,	O
dfns	B-Application
are	O
implemented	O
in	O
Dyalog	O
APL	B-Language
,	O
NARS2000	O
,	O
and	O
ngn/apl	O
.	O
</s>
<s>
They	O
also	O
play	O
a	O
key	O
role	O
in	O
efforts	O
to	O
exploit	O
the	O
computational	O
capabilities	O
of	O
a	O
GPU	B-Architecture
(	O
graphics	B-Architecture
processing	I-Architecture
unit	I-Architecture
)	O
.	O
</s>
<s>
Dfns	B-Application
are	O
illustrated	O
here	O
with	O
an	O
example	O
.	O
</s>
<s>
Much	O
more	O
extensive	O
explanation	O
and	O
examples	O
are	O
found	O
in	O
the	O
direct	B-Application
functions	I-Application
article	O
and	O
in	O
the	O
references	O
.	O
</s>
<s>
Quicksort	B-Algorithm
on	O
an	O
array	O
works	O
by	O
choosing	O
a	O
"	O
pivot	O
"	O
at	O
random	O
among	O
its	O
major	O
cells	O
,	O
then	O
catenating	O
the	O
sorted	O
major	O
cells	O
which	O
strictly	O
precede	O
the	O
pivot	O
,	O
the	O
major	O
cells	O
equal	O
to	O
the	O
pivot	O
,	O
and	O
the	O
sorted	O
major	O
cells	O
which	O
strictly	O
follow	O
the	O
pivot	O
,	O
as	O
determined	O
by	O
a	O
comparison	O
function	O
.	O
</s>
<s>
Defined	O
as	O
a	O
dop	O
(	O
direct	O
operator	B-Language
)	O
:	O
</s>
<s>
However	O
,	O
unlike	O
the	O
pidgin	B-Language
ALGOL	I-Language
program	O
in	O
Figure	O
3.7	O
,	O
and	O
are	O
executable	O
,	O
and	O
the	O
partial	O
order	O
used	O
in	O
the	O
sorting	O
is	O
an	O
operand	O
,	O
the	O
the	O
examples	O
above	O
.	O
</s>
<s>
2011	O
What	O
is	O
Functional	B-Language
Programming	I-Language
?	O
</s>
<s>
2011	O
What	O
is	O
Functional	B-Language
Programming	I-Language
?	O
</s>
