<s>
Inductive	B-Application
programming	I-Application
(	O
IP	O
)	O
is	O
a	O
special	O
area	O
of	O
automatic	B-Application
programming	I-Application
,	O
covering	O
research	O
from	O
artificial	B-Application
intelligence	I-Application
and	O
programming	B-General_Concept
,	O
which	O
addresses	O
learning	O
of	O
typically	O
declarative	B-Language
(	O
logic	B-Language
or	O
functional	B-Language
)	O
and	O
often	O
recursive	O
programs	O
from	O
incomplete	O
specifications	B-Application
,	O
such	O
as	O
input/output	O
examples	O
or	O
constraints	B-Application
.	O
</s>
<s>
Depending	O
on	O
the	O
programming	B-General_Concept
language	O
used	O
,	O
there	O
are	O
several	O
kinds	O
of	O
inductive	B-Application
programming	I-Application
.	O
</s>
<s>
Inductive	B-Application
functional	I-Application
programming	I-Application
,	O
which	O
uses	O
functional	B-Language
programming	I-Language
languages	I-Language
such	O
as	O
Lisp	B-Language
or	O
Haskell	B-Language
,	O
and	O
most	O
especially	O
inductive	B-Application
logic	I-Application
programming	I-Application
,	O
which	O
uses	O
logic	B-Language
programming	I-Language
languages	I-Language
such	O
as	O
Prolog	B-Language
and	O
other	O
logical	O
representations	O
such	O
as	O
description	B-Language
logics	I-Language
,	O
have	O
been	O
more	O
prominent	O
,	O
but	O
other	O
(	O
programming	B-General_Concept
)	O
language	O
paradigms	O
have	O
also	O
been	O
used	O
,	O
such	O
as	O
constraint	B-Application
programming	I-Application
or	O
probabilistic	O
programming	B-General_Concept
.	O
</s>
<s>
Inductive	B-Application
programming	I-Application
incorporates	O
all	O
approaches	O
which	O
are	O
concerned	O
with	O
learning	O
programs	O
or	O
algorithms	O
from	O
incomplete	O
(	O
formal	B-Application
)	O
specifications	B-Application
.	O
</s>
<s>
Possible	O
inputs	O
in	O
an	O
IP	O
system	O
are	O
a	O
set	O
of	O
training	O
inputs	O
and	O
corresponding	O
outputs	O
or	O
an	O
output	O
evaluation	O
function	O
,	O
describing	O
the	O
desired	O
behavior	O
of	O
the	O
intended	O
program	O
,	O
traces	O
or	O
action	O
sequences	O
which	O
describe	O
the	O
process	O
of	O
calculating	O
specific	O
outputs	O
,	O
constraints	B-Application
for	O
the	O
program	O
to	O
be	O
induced	O
concerning	O
its	O
time	O
efficiency	O
or	O
its	O
complexity	O
,	O
various	O
kinds	O
of	O
background	O
knowledge	O
such	O
as	O
standard	O
data	O
types	O
,	O
predefined	O
functions	O
to	O
be	O
used	O
,	O
program	O
schemes	O
or	O
templates	O
describing	O
the	O
data	O
flow	O
of	O
the	O
intended	O
program	O
,	O
heuristics	O
for	O
guiding	O
the	O
search	O
for	O
a	O
solution	O
or	O
other	O
biases	O
.	O
</s>
<s>
Output	O
of	O
an	O
IP	O
system	O
is	O
a	O
program	O
in	O
some	O
arbitrary	O
programming	B-General_Concept
language	O
containing	O
conditionals	O
and	O
loop	O
or	O
recursive	O
control	O
structures	O
,	O
or	O
any	O
other	O
kind	O
of	O
Turing-complete	B-Algorithm
representation	O
language	O
.	O
</s>
<s>
In	O
many	O
applications	O
the	O
output	O
program	O
must	O
be	O
correct	O
with	O
respect	O
to	O
the	O
examples	O
and	O
partial	O
specification	B-Application
,	O
and	O
this	O
leads	O
to	O
the	O
consideration	O
of	O
inductive	B-Application
programming	I-Application
as	O
a	O
special	O
area	O
inside	O
automatic	B-Application
programming	I-Application
or	O
program	B-Application
synthesis	I-Application
,	O
usually	O
opposed	O
to	O
'	O
deductive	O
 '	O
program	B-Application
synthesis	I-Application
,	O
where	O
the	O
specification	B-Application
is	O
usually	O
complete	O
.	O
</s>
<s>
In	O
other	O
cases	O
,	O
inductive	B-Application
programming	I-Application
is	O
seen	O
as	O
a	O
more	O
general	O
area	O
where	O
any	O
declarative	B-Language
programming	I-Language
or	O
representation	O
language	O
can	O
be	O
used	O
and	O
we	O
may	O
even	O
have	O
some	O
degree	O
of	O
error	O
in	O
the	O
examples	O
,	O
as	O
in	O
general	O
machine	O
learning	O
,	O
the	O
more	O
specific	O
area	O
of	O
structure	B-Algorithm
mining	I-Algorithm
or	O
the	O
area	O
of	O
symbolic	B-General_Concept
artificial	I-General_Concept
intelligence	I-General_Concept
.	O
</s>
<s>
A	O
distinctive	O
feature	O
is	O
the	O
number	O
of	O
examples	O
or	O
partial	O
specification	B-Application
needed	O
.	O
</s>
<s>
Typically	O
,	O
inductive	B-Application
programming	I-Application
techniques	O
can	O
learn	O
from	O
just	O
a	O
few	O
examples	O
.	O
</s>
<s>
The	O
diversity	O
of	O
inductive	B-Application
programming	I-Application
usually	O
comes	O
from	O
the	O
applications	O
and	O
the	O
languages	O
that	O
are	O
used	O
:	O
apart	O
from	O
logic	B-Language
programming	I-Language
and	O
functional	B-Language
programming	I-Language
,	O
other	O
programming	B-General_Concept
paradigms	O
and	O
representation	O
languages	O
have	O
been	O
used	O
or	O
suggested	O
in	O
inductive	B-Application
programming	I-Application
,	O
such	O
as	O
functional	B-Application
logic	I-Application
programming	I-Application
,	O
constraint	B-Application
programming	I-Application
,	O
probabilistic	O
programming	B-General_Concept
,	O
abductive	B-Application
logic	I-Application
programming	I-Application
,	O
modal	O
logic	B-Language
,	O
action	B-Application
languages	I-Application
,	O
agent	O
languages	O
and	O
many	O
types	O
of	O
imperative	B-Application
languages	I-Application
.	O
</s>
<s>
Research	O
on	O
the	O
inductive	O
synthesis	O
of	O
recursive	O
functional	B-Language
programs	I-Language
started	O
in	O
the	O
early	O
1970s	O
and	O
was	O
brought	O
onto	O
firm	O
theoretical	O
foundations	O
with	O
the	O
seminal	O
THESIS	O
system	O
of	O
Summers	O
and	O
work	O
of	O
Biermann	O
.	O
</s>
<s>
The	O
advent	O
of	O
logic	B-Language
programming	I-Language
brought	O
a	O
new	O
elan	O
but	O
also	O
a	O
new	O
direction	O
in	O
the	O
early	O
1980s	O
,	O
especially	O
due	O
to	O
the	O
MIS	O
system	O
of	O
Shapiro	O
eventually	O
spawning	O
the	O
new	O
field	O
of	O
inductive	B-Application
logic	I-Application
programming	I-Application
(	O
ILP	O
)	O
.	O
</s>
<s>
The	O
early	O
works	O
of	O
Plotkin	O
,	O
and	O
his	O
"	O
relative	O
least	O
general	O
generalization	O
(	O
rlgg	O
)	O
"	O
,	O
had	O
an	O
enormous	O
impact	O
in	O
inductive	B-Application
logic	I-Application
programming	I-Application
.	O
</s>
<s>
Most	O
of	O
ILP	O
work	O
addresses	O
a	O
wider	O
class	O
of	O
problems	O
,	O
as	O
the	O
focus	O
is	O
not	O
only	O
on	O
recursive	O
logic	B-Language
programs	I-Language
but	O
on	O
machine	O
learning	O
of	O
symbolic	O
hypotheses	O
from	O
logical	O
representations	O
.	O
</s>
<s>
However	O
,	O
there	O
were	O
some	O
encouraging	O
results	O
on	O
learning	O
recursive	O
Prolog	B-Language
programs	O
such	O
as	O
quicksort	O
from	O
examples	O
together	O
with	O
suitable	O
background	O
knowledge	O
,	O
for	O
example	O
with	O
GOLEM	O
.	O
</s>
<s>
But	O
again	O
,	O
after	O
initial	O
success	O
,	O
the	O
community	O
got	O
disappointed	O
by	O
limited	O
progress	O
about	O
the	O
induction	O
of	O
recursive	O
programs	O
with	O
ILP	O
less	O
and	O
less	O
focusing	O
on	O
recursive	O
programs	O
and	O
leaning	O
more	O
and	O
more	O
towards	O
a	O
machine	O
learning	O
setting	O
with	O
applications	O
in	O
relational	B-Application
data	I-Application
mining	I-Application
and	O
knowledge	O
discovery	O
.	O
</s>
<s>
In	O
parallel	O
to	O
work	O
in	O
ILP	O
,	O
Koza	O
proposed	O
genetic	B-Algorithm
programming	I-Algorithm
in	O
the	O
early	O
1990s	O
as	O
a	O
generate-and-test	O
based	O
approach	O
to	O
learning	O
programs	O
.	O
</s>
<s>
The	O
idea	O
of	O
genetic	B-Algorithm
programming	I-Algorithm
was	O
further	O
developed	O
into	O
the	O
inductive	B-Application
programming	I-Application
system	O
ADATE	O
and	O
the	O
systematic-search-based	O
system	O
MagicHaskeller	O
.	O
</s>
<s>
Here	O
again	O
,	O
functional	B-Language
programs	I-Language
are	O
learned	O
from	O
sets	O
of	O
positive	O
examples	O
together	O
with	O
an	O
output	O
evaluation	O
(	O
fitness	O
)	O
function	O
which	O
specifies	O
the	O
desired	O
input/output	O
behavior	O
of	O
the	O
program	O
to	O
be	O
learned	O
.	O
</s>
<s>
The	O
early	O
work	O
in	O
grammar	B-Algorithm
induction	I-Algorithm
(	O
also	O
known	O
as	O
grammatical	B-Algorithm
inference	I-Algorithm
)	O
is	O
related	O
to	O
inductive	B-Application
programming	I-Application
,	O
as	O
rewriting	O
systems	O
or	O
logic	B-Language
programs	I-Language
can	O
be	O
used	O
to	O
represent	O
production	O
rules	O
.	O
</s>
<s>
In	O
fact	O
,	O
early	O
works	O
in	O
inductive	O
inference	O
considered	O
grammar	B-Algorithm
induction	I-Algorithm
and	O
Lisp	B-Language
program	O
inference	O
as	O
basically	O
the	O
same	O
problem	O
.	O
</s>
<s>
More	O
recently	O
,	O
the	O
language	O
learning	O
problem	O
was	O
addressed	O
by	O
the	O
inductive	B-Application
programming	I-Application
community	O
.	O
</s>
<s>
Therefore	O
,	O
the	O
synthesis	O
problem	O
has	O
been	O
reformulated	O
on	O
the	O
background	O
of	O
constructor-based	O
term	O
rewriting	O
systems	O
taking	O
into	O
account	O
modern	O
techniques	O
of	O
functional	B-Language
programming	I-Language
,	O
as	O
well	O
as	O
moderate	O
use	O
of	O
search-based	O
strategies	O
and	O
usage	O
of	O
background	O
knowledge	O
as	O
well	O
as	O
automatic	O
invention	O
of	O
subprograms	O
.	O
</s>
<s>
Many	O
new	O
and	O
successful	O
applications	O
have	O
recently	O
appeared	O
beyond	O
program	B-Application
synthesis	I-Application
,	O
most	O
especially	O
in	O
the	O
area	O
of	O
data	O
manipulation	O
,	O
programming	B-Application
by	I-Application
example	I-Application
and	O
cognitive	O
modelling	O
(	O
see	O
below	O
)	O
.	O
</s>
<s>
Other	O
ideas	O
have	O
also	O
been	O
explored	O
with	O
the	O
common	O
characteristic	O
of	O
using	O
declarative	B-Language
languages	I-Language
for	O
the	O
representation	O
of	O
hypotheses	O
.	O
</s>
<s>
One	O
powerful	O
paradigm	O
that	O
has	O
been	O
recently	O
used	O
for	O
the	O
representation	O
of	O
hypotheses	O
in	O
inductive	B-Application
programming	I-Application
(	O
generally	O
in	O
the	O
form	O
of	O
generative	O
models	O
)	O
is	O
probabilistic	O
programming	B-General_Concept
(	O
and	O
related	O
paradigms	O
,	O
such	O
as	O
stochastic	O
logic	B-Language
programs	I-Language
and	O
Bayesian	O
logic	B-Language
programming	I-Language
)	O
.	O
</s>
<s>
The	O
held	O
in	O
conjunction	O
with	O
ICML	B-General_Concept
2005	O
identified	O
all	O
applications	O
where	O
"	O
learning	O
of	O
programs	O
or	O
recursive	O
rules	O
are	O
called	O
for	O
,	O
 [ ... ] 	O
first	O
in	O
the	O
domain	O
of	O
software	O
engineering	O
where	O
structural	O
learning	O
,	O
software	O
assistants	O
and	O
software	O
agents	O
can	O
help	O
to	O
relieve	O
programmers	O
from	O
routine	O
tasks	O
,	O
give	O
programming	B-General_Concept
support	O
for	O
end	O
users	O
,	O
or	O
support	O
of	O
novice	O
programmers	O
and	O
programming	B-General_Concept
tutor	O
systems	O
.	O
</s>
<s>
Further	O
areas	O
of	O
application	O
are	O
language	O
learning	O
,	O
learning	O
recursive	O
control	O
rules	O
for	O
AI-planning	O
,	O
learning	O
recursive	O
concepts	O
in	O
web-mining	O
or	O
for	O
data-format	O
transformations	O
"	O
.	O
</s>
<s>
Since	O
then	O
,	O
these	O
and	O
many	O
other	O
areas	O
have	O
shown	O
to	O
be	O
successful	O
application	O
niches	O
for	O
inductive	B-Application
programming	I-Application
,	O
such	O
as	O
end-user	O
programming	B-General_Concept
,	O
the	O
related	O
areas	O
of	O
programming	B-Application
by	I-Application
example	I-Application
and	O
programming	B-Application
by	I-Application
demonstration	I-Application
,	O
and	O
intelligent	O
tutoring	O
systems	O
.	O
</s>
