<s>
Flix	B-Language
is	O
a	O
functional	B-Language
,	O
imperative	B-Application
,	O
and	O
logic	B-Language
programming	I-Language
language	I-Language
developed	O
at	O
Aarhus	O
University	O
,	O
with	O
funding	O
from	O
the	O
Independent	O
Research	O
Fund	O
Denmark	O
,	O
and	O
by	O
a	O
community	O
of	O
open	B-License
source	I-License
contributors	O
.	O
</s>
<s>
The	O
Flix	B-Language
language	O
supports	O
algebraic	O
data	O
types	O
,	O
pattern	B-Language
matching	I-Language
,	O
parametric	O
polymorphism	O
,	O
currying	B-Application
,	O
higher-order	B-Language
functions	I-Language
,	O
extensible	O
records	O
,	O
channel	O
and	O
process-based	O
concurrency	O
,	O
and	O
tail	B-Language
call	I-Language
elimination	I-Language
.	O
</s>
<s>
Two	O
notable	O
features	O
of	O
Flix	B-Language
are	O
its	O
type	O
and	O
effect	O
system	O
and	O
its	O
support	O
for	O
first-class	O
Datalog	B-Language
constraints	O
.	O
</s>
<s>
The	O
Flix	B-Language
type	O
and	O
effect	O
system	O
supports	O
Hindley-Milner-style	O
type	O
inference	O
.	O
</s>
<s>
Higher-order	B-Language
functions	I-Language
can	O
enforce	O
that	O
they	O
are	O
given	O
pure	O
(	O
or	O
impure	O
)	O
function	O
arguments	O
.	O
</s>
<s>
The	O
type	O
and	O
effect	O
system	O
supports	O
effect	O
polymorphism	O
which	O
means	O
that	O
the	O
effect	O
of	O
a	O
higher-order	B-Language
function	I-Language
may	O
depend	O
on	O
the	O
effect(s )	O
of	O
its	O
argument(s )	O
.	O
</s>
<s>
Flix	B-Language
supports	O
Datalog	B-Language
programs	O
as	O
first-class	O
values	O
.	O
</s>
<s>
A	O
Datalog	B-Language
program	O
value	O
,	O
i.e.	O
</s>
<s>
a	O
collection	O
of	O
Datalog	B-Language
facts	O
and	O
rules	B-Application
,	O
can	O
be	O
passed	O
to	O
and	O
returned	O
from	O
functions	O
,	O
stored	O
in	O
data	O
structures	O
,	O
and	O
composed	O
with	O
other	O
Datalog	B-Language
program	O
values	O
.	O
</s>
<s>
The	O
minimal	O
model	O
of	O
a	O
Datalog	B-Language
program	O
value	O
can	O
be	O
computed	O
and	O
is	O
itself	O
a	O
Datalog	B-Language
program	O
value	O
.	O
</s>
<s>
In	O
this	O
way	O
,	O
Flix	B-Language
can	O
be	O
viewed	O
as	O
a	O
meta	B-Application
programming	I-Application
language	O
for	O
Datalog	B-Language
.	O
</s>
<s>
Flix	B-Language
supports	O
stratified	O
negation	O
and	O
the	O
Flix	B-Language
compiler	B-Language
ensures	O
stratification	O
at	O
compile-time	O
.	O
</s>
<s>
Flix	B-Language
also	O
supports	O
an	O
enriched	O
form	O
of	O
Datalog	B-Language
constraints	O
where	O
predicates	O
are	O
given	O
lattice	O
semantics	O
.	O
</s>
<s>
Flix	B-Language
is	O
a	O
programming	O
language	O
in	O
the	O
ML-family	O
of	O
languages	O
.	O
</s>
<s>
Its	O
type	O
and	O
effect	O
system	O
is	O
based	O
on	O
Hindley-Milner	B-Algorithm
with	O
several	O
extensions	O
,	O
including	O
row	O
polymorphism	O
and	O
Boolean	O
unification	O
.	O
</s>
<s>
The	O
syntax	O
of	O
Flix	B-Language
is	O
inspired	O
by	O
Scala	B-Application
and	O
uses	O
short	O
keywords	O
and	O
curly	O
braces	O
.	O
</s>
<s>
Flix	B-Language
supports	O
uniform	O
function	O
call	O
syntax	O
which	O
allows	O
a	O
function	O
call	O
f(x, y, z )	O
to	O
be	O
written	O
as	O
x.f(y, z )	O
.	O
</s>
<s>
The	O
concurrency	O
model	O
of	O
Flix	B-Language
is	O
inspired	O
by	O
Go	B-Application
and	O
based	O
on	O
channels	O
and	O
processes	O
.	O
</s>
<s>
While	O
many	O
programming	O
languages	O
support	O
a	O
mixture	O
of	O
functional	B-Language
and	O
imperative	B-Application
programming	I-Application
,	O
the	O
Flix	B-Language
type	O
and	O
effect	O
system	O
tracks	O
the	O
purity	O
of	O
every	O
expression	O
making	O
it	O
possible	O
to	O
write	O
parts	O
of	O
a	O
Flix	B-Language
program	O
in	O
a	O
purely	B-Application
functional	I-Application
style	I-Application
with	O
purity	O
enforced	O
by	O
the	O
effect	O
system	O
.	O
</s>
<s>
Flix	B-Language
programs	O
compile	B-Language
to	O
JVM	B-Language
bytecode	I-Language
and	O
are	O
executable	O
on	O
the	O
Java	B-Language
Virtual	I-Language
Machine	I-Language
(	O
JVM	B-Language
)	O
.	O
</s>
<s>
The	O
Flix	B-Language
compiler	B-Language
performs	O
whole	O
program	B-Language
compilation	I-Language
,	O
eliminates	O
polymorphism	O
via	O
monomorphization	O
,	O
and	O
uses	O
tree	O
shaking	O
to	O
remove	O
unreachable	O
code	O
.	O
</s>
<s>
Monomorphization	O
avoids	O
boxing	O
of	O
primitive	O
values	O
at	O
the	O
cost	O
of	O
longer	O
compilation	B-Language
times	O
and	O
larger	O
executable	O
binaries	O
.	O
</s>
<s>
Flix	B-Language
has	O
some	O
support	O
for	O
interoperability	O
with	O
programs	O
written	O
in	O
Java	B-Language
.	O
</s>
<s>
Flix	B-Language
supports	O
tail	B-Language
call	I-Language
elimination	I-Language
which	O
ensures	O
that	O
function	O
calls	O
in	O
tail	O
position	O
never	O
consume	O
stack	O
space	O
and	O
hence	O
cannot	O
cause	O
the	O
call	O
stack	O
to	O
overflow	O
.	O
</s>
<s>
Since	O
the	O
JVM	B-Language
instruction	I-Language
set	I-Language
lacks	O
explicit	O
support	O
for	O
tail	B-Language
calls	I-Language
,	O
such	O
calls	O
are	O
emulated	O
using	O
a	O
form	O
of	O
reusable	O
stack	O
frames	O
.	O
</s>
<s>
Support	O
for	O
tail	B-Language
call	I-Language
elimination	I-Language
is	O
important	O
since	O
all	O
iteration	O
in	O
Flix	B-Language
is	O
expressed	O
through	O
recursion	O
.	O
</s>
<s>
The	O
Flix	B-Language
compiler	B-Language
disallows	O
most	O
forms	O
of	O
unused	O
or	O
redundant	O
code	O
,	O
including	O
:	O
unused	O
local	O
variables	O
,	O
unused	O
functions	O
,	O
unused	O
formal	O
parameters	O
,	O
unused	O
type	O
parameters	O
,	O
and	O
unused	O
type	O
declarations	O
,	O
such	O
unused	O
constructs	O
are	O
reported	O
as	O
compiler	B-Language
errors	O
.	O
</s>
<s>
Variable	B-Language
shadowing	I-Language
is	O
also	O
disallowed	O
.	O
</s>
<s>
A	O
Visual	B-Language
Studio	I-Language
Code	I-Language
extension	O
for	O
Flix	B-Language
is	O
available	O
.	O
</s>
<s>
The	O
extension	O
is	O
based	O
on	O
the	O
Language	O
Server	O
Protocol	O
,	O
a	O
common	O
interface	O
between	O
IDEs	B-Application
and	O
compilers	B-Language
being	O
developed	O
by	O
Microsoft	O
.	O
</s>
<s>
Flix	B-Language
is	O
open	B-Application
source	I-Application
software	I-Application
available	O
under	O
the	O
Apache	B-Application
2.0	I-Application
License	I-Application
.	O
</s>
<s>
when	O
compiled	B-Language
and	O
executed	O
:	O
</s>
<s>
The	O
following	O
program	O
fragment	O
uses	O
pattern	B-Language
matching	I-Language
to	O
destruct	O
a	O
Shape	O
value	O
:	O
</s>
<s>
The	O
following	O
program	O
fragment	O
defines	O
a	O
higher-order	B-Language
function	I-Language
named	O
twice	O
that	O
when	O
given	O
a	O
function	O
f	O
from	O
Int	O
to	O
Int	O
returns	O
a	O
function	O
that	O
applies	O
f	O
to	O
its	O
input	O
two	O
times	O
:	O
</s>
<s>
Flix	B-Language
supports	O
type	O
parameter	O
elision	O
hence	O
it	O
is	O
not	O
required	O
that	O
the	O
type	O
parameters	O
a	O
and	O
b	O
are	O
explicitly	O
introduced	O
.	O
</s>
<s>
Flix	B-Language
uses	O
row	O
polymorphism	O
to	O
type	O
records	O
.	O
</s>
<s>
The	O
Flix	B-Language
type	O
and	O
effect	O
system	O
separates	O
pure	O
and	O
impure	O
expressions	O
.	O
</s>
<s>
A	O
higher-order	B-Language
function	I-Language
can	O
specify	O
that	O
a	O
function	O
argument	O
must	O
be	O
pure	O
,	O
impure	O
,	O
or	O
that	O
it	O
is	O
effect	O
polymorphic	O
.	O
</s>
<s>
A	O
higher-order	B-Language
function	I-Language
can	O
also	O
require	O
that	O
a	O
function	O
is	O
impure	O
.	O
</s>
<s>
A	O
higher-order	B-Language
function	I-Language
can	O
also	O
be	O
effect	O
polymorphic	O
:	O
its	O
effect(s )	O
can	O
depend	O
on	O
its	O
argument(s )	O
.	O
</s>
<s>
A	O
higher-order	B-Language
function	I-Language
that	O
takes	O
multiple	O
function	O
arguments	O
may	O
combine	O
their	O
effects	O
.	O
</s>
<s>
For	O
example	O
,	O
the	O
standard	O
library	O
definition	O
of	O
forward	O
function	B-Application
composition	I-Application
>>	O
is	O
pure	O
if	O
both	O
its	O
function	O
arguments	O
are	O
pure	O
:	O
</s>
<s>
For	O
example	O
,	O
it	O
is	O
possible	O
to	O
express	O
a	O
higher-order	B-Language
function	I-Language
h	O
that	O
accepts	O
two	O
function	O
arguments	O
f	O
and	O
g	O
of	O
which	O
at	O
most	O
one	O
is	O
impure	O
:	O
</s>
<s>
It	O
is	O
a	O
compile-time	O
error	O
to	O
call	O
h	O
with	O
two	O
impure	O
functions	O
.	O
</s>
<s>
For	O
example	O
,	O
compiling	B-Language
the	O
program	O
fragment	O
below	O
:	O
</s>
<s>
causes	O
a	O
compiler	B-Language
error	O
:	O
</s>
<s>
Consequently	O
,	O
Flix	B-Language
rejects	O
such	O
programs	O
.	O
</s>
<s>
Flix	B-Language
supports	O
Datalog	B-Language
programs	O
as	O
first-class	O
values	O
.	O
</s>
<s>
A	O
Datalog	B-Language
program	O
is	O
a	O
logic	B-Language
program	I-Language
that	O
consists	O
of	O
a	O
collection	O
of	O
unordered	O
facts	O
and	O
rules	B-Application
.	O
</s>
<s>
Together	O
,	O
the	O
facts	O
and	O
rules	B-Application
imply	O
a	O
minimal	O
model	O
,	O
a	O
unique	O
solution	O
to	O
any	O
Datalog	B-Language
program	O
.	O
</s>
<s>
In	O
Flix	B-Language
,	O
Datalog	B-Language
program	O
values	O
can	O
be	O
passed	O
to	O
and	O
returned	O
from	O
functions	O
,	O
stored	O
in	O
data	O
structures	O
,	O
composed	O
with	O
other	O
Datalog	B-Language
program	O
values	O
,	O
and	O
solved	O
.	O
</s>
<s>
The	O
solution	O
to	O
a	O
Datalog	B-Language
program	O
(	O
the	O
minimal	O
model	O
)	O
is	O
itself	O
a	O
Datalog	B-Language
program	O
.	O
</s>
<s>
Thus	O
,	O
it	O
is	O
possible	O
to	O
construct	O
pipelines	O
of	O
Datalog	B-Language
programs	O
where	O
the	O
solution	O
,	O
i.e.	O
</s>
<s>
"	O
output	O
"	O
,	O
of	O
one	O
Datalog	B-Language
program	O
becomes	O
the	O
"	O
input	O
"	O
to	O
another	O
Datalog	B-Language
program	O
.	O
</s>
<s>
The	O
following	O
Datalog	B-Language
rules	B-Application
compute	O
the	O
transitive	O
closure	O
of	O
the	O
edge	O
relation	O
:	O
</s>
<s>
The	O
minimal	O
model	O
of	O
the	O
facts	O
and	O
rules	B-Application
is	O
:	O
</s>
<s>
In	O
Flix	B-Language
,	O
Datalog	B-Language
programs	O
are	O
values	O
.	O
</s>
<s>
The	O
above	O
program	O
can	O
be	O
embedded	B-Language
in	O
Flix	B-Language
as	O
follows	O
:	O
</s>
<s>
The	O
local	O
variable	O
f	O
holds	O
a	O
Datalog	B-Language
program	O
value	O
that	O
consists	O
of	O
the	O
edge	O
facts	O
.	O
</s>
<s>
Similarly	O
,	O
the	O
local	O
variable	O
p	O
is	O
a	O
Datalog	B-Language
program	O
value	O
that	O
consists	O
of	O
the	O
two	O
rules	B-Application
.	O
</s>
<s>
union	O
)	O
of	O
the	O
two	O
Datalog	B-Language
programs	O
f	O
and	O
p	O
.	O
The	O
solve	O
expression	O
computes	O
the	O
minimal	O
model	O
of	O
the	O
combined	O
Datalog	B-Language
program	O
,	O
returning	O
the	O
edge	O
and	O
path	O
facts	O
shown	O
above	O
.	O
</s>
<s>
Since	O
Datalog	B-Language
programs	O
are	O
first-class	O
values	O
,	O
we	O
can	O
refactor	O
the	O
above	O
program	O
into	O
several	O
functions	O
.	O
</s>
<s>
The	O
Flix	B-Language
type	O
system	O
ensures	O
that	O
Datalog	B-Language
program	O
values	O
are	O
well-typed	O
.	O
</s>
<s>
The	O
Flix	B-Language
compiler	B-Language
rejects	O
such	O
programs	O
as	O
ill-typed	O
.	O
</s>
<s>
The	O
Flix	B-Language
compiler	B-Language
ensures	O
that	O
every	O
Datalog	B-Language
program	O
value	O
constructed	O
at	O
run-time	O
is	O
stratified	O
.	O
</s>
<s>
Intuitively	O
,	O
a	O
Datalog	B-Language
program	O
is	O
stratified	O
if	O
there	O
is	O
no	O
recursion	O
through	O
negation	O
,	O
i.e.	O
</s>
<s>
Given	O
a	O
Datalog	B-Language
program	O
,	O
a	O
cycle	B-Algorithm
detection	I-Algorithm
algorithm	O
can	O
be	O
used	O
to	O
determine	O
if	O
it	O
is	O
stratified	O
.	O
</s>
<s>
For	O
example	O
,	O
the	O
following	O
Flix	B-Language
program	O
contains	O
an	O
expression	O
that	O
cannot	O
be	O
stratified	O
:	O
</s>
<s>
because	O
the	O
last	O
expression	O
constructs	O
a	O
Datalog	B-Language
program	O
value	O
whose	O
precedence	O
graph	O
contains	O
a	O
negative	O
cycle	O
:	O
the	O
Bachelor	O
predicate	O
negatively	O
depends	O
on	O
the	O
Husband	O
predicate	O
which	O
in	O
turn	O
(	O
positively	O
)	O
depends	O
on	O
the	O
Bachelor	O
predicate	O
.	O
</s>
<s>
The	O
Flix	B-Language
compiler	B-Language
computes	O
the	O
precedence	O
graph	O
for	O
every	O
Datalog	B-Language
program	O
valued	O
expression	O
and	O
determines	O
its	O
stratification	O
at	O
compile-time	O
.	O
</s>
<s>
If	O
an	O
expression	O
is	O
not	O
stratified	O
,	O
the	O
program	O
is	O
rejected	O
by	O
the	O
compiler	B-Language
.	O
</s>
<s>
This	O
is	O
despite	O
the	O
fact	O
that	O
at	O
run-time	O
the	O
main	O
function	O
always	O
returns	O
a	O
stratified	O
Datalog	B-Language
program	O
value	O
.	O
</s>
<s>
Flix	B-Language
is	O
designed	O
around	O
a	O
collection	O
of	O
stated	O
principles	O
:	O
</s>
<s>
Most	O
Flix	B-Language
constructs	O
,	O
except	O
for	O
top-level	O
declarations	O
,	O
are	O
expressions	O
that	O
evaluate	O
to	O
values	O
.	O
</s>
<s>
Closed-world	B-Application
assumption	I-Application
.	O
</s>
<s>
The	O
Flix	B-Language
compiler	B-Language
assumes	O
that	O
the	O
source	O
code	O
of	O
the	O
entire	O
program	O
is	O
available	O
at	O
compile-time	O
.	O
</s>
<s>
The	O
language	O
has	O
no	O
compile-time	O
warnings	O
,	O
only	O
errors	O
.	O
</s>
<s>
In	O
particular	O
,	O
Flix	B-Language
lacks	O
support	O
for	O
:	O
</s>
<s>
Reflection	B-Language
.	O
</s>
