<s>
miniKanren	B-Application
is	O
a	O
family	O
of	O
programming	O
languages	O
for	O
relational	B-Language
programming	I-Language
.	O
</s>
<s>
As	O
relations	O
are	O
bidirectional	O
,	O
if	O
miniKanren	B-Application
is	O
given	O
an	O
expression	O
and	O
a	O
desired	O
output	O
,	O
miniKanren	B-Application
can	O
run	O
the	O
expression	O
"	O
backward	O
"	O
,	O
finding	O
all	O
possible	O
inputs	O
to	O
the	O
expression	O
that	O
produce	O
the	O
desired	O
output	O
.	O
</s>
<s>
miniKanren	B-Application
performs	O
an	O
interleaved	O
search	O
which	O
will	O
eventually	O
find	O
any	O
solution	O
that	O
exists	O
,	O
even	O
if	O
any	O
one	O
branch	O
of	O
the	O
search	O
tree	O
is	O
infinitely	O
long	O
and	O
contains	O
no	O
solutions	O
.	O
</s>
<s>
If	O
no	O
solution	O
exists	O
,	O
miniKanren	B-Application
may	O
search	O
forever	O
if	O
the	O
search	O
tree	O
is	O
infinite	O
.	O
</s>
<s>
An	O
example	O
of	O
miniKanren	B-Application
code	O
is	O
evalo	O
,	O
a	O
relational	O
goal	O
that	O
relates	O
expressions	O
to	O
the	O
values	O
that	O
they	O
evaluate	O
to	O
.	O
</s>
<s>
When	O
evalo	O
is	O
called	O
in	O
miniKanren	B-Application
like	O
so	O
:	O
(	O
evalo	O
q	O
q	O
)	O
,	O
it	O
will	O
generate	O
quines	O
,	O
that	O
is	O
,	O
expressions	O
q	O
that	O
when	O
run	O
will	O
evaluate	O
to	O
themselves	O
.	O
</s>
<s>
The	O
book	O
The	O
Reasoned	O
Schemer	O
uses	O
miniKanren	B-Application
to	O
demonstrate	O
relational	B-Language
programming	I-Language
,	O
and	O
provides	O
a	O
complete	O
implementation	O
in	O
Scheme	B-Language
.	O
</s>
<s>
The	O
Scheme	B-Language
implementation	O
of	O
miniKanren	B-Application
is	O
designed	O
to	O
be	O
easily	O
understood	O
,	O
modified	O
,	O
and	O
extended	O
.	O
</s>
<s>
αleanTAP	O
is	O
a	O
program	O
written	O
in	O
αKanren	O
,	O
an	O
extension	O
of	O
miniKanren	B-Application
for	O
nominal	O
logic	O
.	O
</s>
<s>
Given	O
a	O
theorem	O
,	O
it	O
can	O
find	O
a	O
proof	O
,	O
making	O
it	O
a	O
theorem-prover	B-Application
.	O
</s>
<s>
There	O
are	O
implementations	O
of	O
miniKanren	B-Application
in	O
Haskell	B-Language
,	O
Racket	B-Operating_System
,	O
Ruby	B-Language
,	O
Clojure	B-Language
,	O
JavaScript	B-Language
,	O
Scala	B-Application
,	O
Swift	B-Application
,	O
Dart	B-Language
and	O
Python	B-Language
.	O
</s>
<s>
The	O
canonical	O
implementation	O
is	O
an	O
embedded	O
language	O
in	O
Scheme	B-Language
.	O
</s>
<s>
The	O
Clojure	B-Language
core.logic	O
library	O
was	O
inspired	O
by	O
miniKanren	B-Application
.	O
</s>
