<s>
Tacit	B-Application
programming	I-Application
,	O
also	O
called	O
point-free	B-Application
style	I-Application
,	O
is	O
a	O
programming	O
paradigm	O
in	O
which	O
function	O
definitions	O
do	O
not	O
identify	O
the	O
arguments	O
(	O
or	O
"	O
points	O
"	O
)	O
on	O
which	O
they	O
operate	O
.	O
</s>
<s>
Instead	O
the	O
definitions	O
merely	O
compose	B-Application
other	O
functions	O
,	O
among	O
which	O
are	O
combinators	B-Application
that	O
manipulate	O
the	O
arguments	O
.	O
</s>
<s>
Tacit	B-Application
programming	I-Application
is	O
of	O
theoretical	O
interest	O
,	O
because	O
the	O
strict	O
use	O
of	O
composition	O
results	O
in	O
programs	O
that	O
are	O
well	O
adapted	O
for	O
equational	O
reasoning	O
.	O
</s>
<s>
It	O
is	O
also	O
the	O
natural	O
style	O
of	O
certain	O
programming	O
languages	O
,	O
including	O
APL	B-Language
and	O
its	O
derivatives	O
,	O
and	O
concatenative	B-Language
languages	I-Language
such	O
as	O
Forth	B-Application
.	O
</s>
<s>
The	O
lack	O
of	O
argument	O
naming	O
gives	O
point-free	B-Application
style	I-Application
a	O
reputation	O
of	O
being	O
unnecessarily	O
obscure	O
,	O
hence	O
the	O
epithet	O
"	O
pointless	O
style	O
"	O
.	O
</s>
<s>
Unix	B-Application
scripting	B-Application
uses	O
the	O
paradigm	O
with	O
pipes	B-Operating_System
.	O
</s>
<s>
The	O
key	O
idea	O
in	O
tacit	B-Application
programming	I-Application
is	O
to	O
assist	O
in	O
operating	O
at	O
the	O
appropriate	O
level	O
of	O
abstraction	O
.	O
</s>
<s>
Tacit	B-Application
programming	I-Application
can	O
be	O
illustrated	O
with	O
the	O
following	O
Python	B-Language
code	I-Language
.	O
</s>
<s>
...	O
is	O
written	O
in	O
point-free	B-Application
style	I-Application
as	O
the	O
composition	O
of	O
a	O
sequence	O
of	O
functions	O
,	O
without	O
parameters	O
:	O
</s>
<s>
For	O
a	O
more	O
complex	O
example	O
,	O
the	O
Haskell	B-Language
code	O
can	O
be	O
translated	O
as	O
:	O
</s>
<s>
A	O
simple	O
example	O
(	O
in	O
Haskell	B-Language
)	O
is	O
a	O
program	O
which	O
computes	O
the	O
sum	O
of	O
a	O
list	O
of	O
numbers	O
.	O
</s>
<s>
value-level	B-Application
programming	I-Application
)	O
as	O
:	O
</s>
<s>
However	O
,	O
using	O
a	O
fold	B-Application
we	O
can	O
replace	O
this	O
with	O
:	O
</s>
<s>
Another	O
example	O
uses	O
function	B-Application
composition	I-Application
:	O
</s>
<s>
The	O
following	O
Haskell-like	O
pseudo-code	O
exposes	O
how	O
to	O
reduce	O
a	O
function	O
definition	O
to	O
its	O
point-free	O
equivalent	O
:	O
</s>
<s>
A	O
few	O
programs	O
have	O
been	O
written	O
to	O
automatically	O
convert	O
a	O
Haskell	B-Language
expression	O
to	O
a	O
point-free	O
form	O
.	O
</s>
<s>
In	O
J	B-Language
,	O
the	O
same	O
sort	O
of	O
point-free	O
code	O
occurs	O
in	O
a	O
function	O
made	O
to	O
compute	O
the	O
average	O
of	O
a	O
list	O
(	O
array	O
)	O
of	O
numbers	O
:	O
</s>
<s>
(	O
j	B-Language
.	O
is	O
a	O
primitive	O
function	O
whose	O
monadic	O
definition	O
is	O
0j1	O
times	O
x	O
and	O
whose	O
dyadic	O
definition	O
is	O
x+0j1×y	O
.	O
)	O
</s>
<s>
The	O
same	O
tacit	O
computations	O
expressed	O
in	O
Dyalog	O
APL	B-Language
:	O
</s>
<s>
In	O
stack-oriented	B-Language
programming	I-Language
languages	I-Language
(	O
and	O
concatenative	B-Language
ones	I-Language
,	O
most	O
of	O
which	O
are	O
stack	O
based	O
)	O
,	O
point-free	O
methods	O
are	O
commonly	O
used	O
.	O
</s>
<s>
For	O
example	O
,	O
a	O
procedure	O
to	O
compute	O
the	O
Fibonacci	B-Algorithm
numbers	I-Algorithm
might	O
look	O
like	O
the	O
following	O
in	O
PostScript	B-Language
:	O
</s>
<s>
In	O
Unix	B-Application
scripting	B-Application
the	O
functions	O
are	O
computer	O
programs	O
which	O
receive	O
data	O
from	O
standard	B-Operating_System
input	I-Operating_System
and	O
send	O
the	O
results	O
to	O
standard	B-Operating_System
output	I-Operating_System
.	O
</s>
<s>
Due	O
to	O
the	O
way	O
pipelines	B-Operating_System
work	O
,	O
it	O
is	O
only	O
normally	O
possible	O
to	O
pass	O
one	O
"	O
argument	O
"	O
at	O
a	O
time	O
in	O
the	O
form	O
of	O
a	O
pair	O
of	O
standard	O
input/output	O
stream	O
.	O
</s>
<s>
Although	O
extra	O
file	B-Application
descriptors	I-Application
can	O
be	O
opened	O
from	O
named	B-Operating_System
pipes	I-Operating_System
,	O
this	O
no	O
longer	O
constitutes	O
a	O
point-free	B-Application
style	I-Application
.	O
</s>
<s>
(	O
Yes	O
,	O
the	O
JSON	O
array	O
is	O
a	O
jq	B-Language
filter	O
that	O
evaluates	O
to	O
an	O
array	O
.	O
)	O
</s>
<s>
A	O
tacit	O
jq	B-Language
program	O
for	O
generating	O
the	O
Fibonnaci	B-Algorithm
sequence	I-Algorithm
would	O
be	O
:	O
</s>
<s>
in	O
the	O
Fibonnaci	B-Algorithm
sequence	I-Algorithm
.	O
</s>
<s>
jq	B-Language
also	O
allows	O
new	O
filters	O
to	O
be	O
defined	O
in	O
a	O
tacit	O
style	O
,	O
e.g.	O
</s>
<s>
In	O
the	O
section	O
on	O
Python	B-Language
in	O
this	O
article	O
,	O
the	O
following	O
Python	B-Language
definition	O
is	O
considered	O
:	O
</s>
<s>
In	O
point-free	B-Application
style	I-Application
,	O
this	O
could	O
be	O
written	O
in	O
Python	B-Language
as	O
:	O
</s>
<s>
In	O
jq	B-Language
,	O
the	O
equivalent	O
point-free	O
definition	O
would	O
be	O
:	O
</s>
