There's a Prolog in your Scala!

There is a Prolog
in your Scala!
@folone Scala eXchange ‘13

programmation en
logique, 1972, 5GL
Lingua franca

A language that doesn't
affect the way you think
about programming,
is not worth knowing.
— Alan J. Perlis

What > How
Relations > Functions
Facts
Rules (to generate more facts)
Main principles
It's all about formulating the question.
Expressed with

Predicates > Functions
Map inputs to outputs
Run
Return some output
Define constraints
Match
Only return yes or no*
*If "yes", they may add bindings to variables.
log(2, 16, 4). log(2, 16) = 4

— How many Prolog
programmers does it take
to change a lightbulb?

— How many Prolog
programmers does it take
to change a lightbulb?
NO.

Scala eXchange
tracks planning
https://github.com/folone/scalaeXchange/

Facts
talk_about(dpp, webdev).
talk_about(milessabin, typelevel).
talk_about(larsr_h, typelevel).
talk_about(xeno_by, macros).
talk_about(milessabin, macros).
talk_about(sirthias, webdev).

Questions
?- talk_about(milessabin, webdev).
no
?- talk_about(larsr_h, typelevel).
yes
?- talk_about(dpp, X).
X = webdev.
?- talk_about(milessabin, X).
X = typelevel ;
X = macros.

Questions
?- talk_about(Who, What).
Who = dpp, What = webdev ;
Who = milessabin, What = typelevel ;
Who = milessabin, What = macros ;
Who = larsr_h, What = typelevel ;
Who = xeno_by, What = macros ;
Who = sirthias, What = webdev.

Rules
same_topic(Person1, Person2) :-
talk_about(Person1, Topic),
Person1 == Person2.
?- same_topic(milessabin, Who).
Who = larsr_h ;
Who = xeno_by.

Facts
works_in(dpp, industry).
works_in(milessabin, industry).
works_in(milessabin, academia).
works_in(larsr_h, academia).
works_in(xeno_by, academia).
works_in(sirthias, industry).

Person1 == Person2.
works_in(Person1, Area),
Person1 == Person2.

Questions
?- same_topic(dpp, Who).
Who = sirthias ;
Who = milessabin ;
Who = sirthias.

Rules
exactly_same_topic(Person1, Person2) :-
Person1 == Person2.

Questions
?- exactly_same_topic(dpp, Who).
Who = sirthias.
?- exactly_same_topic(milessabin, Who).
Who = larsr_h ;
Who = xeno_by.

topic(Topic, Res) :-
findall(Person, talk_about(Person, Topic), L1),
Res = (Topic, L1).
environment(Area, Res) :-
findall(Person, works_in(Person, Area), L1),
Res = (Area, L1).
?- topic(webdev, List).
List = (webdev, [dpp, sirthias]).
?- environment(academia, List).
List = (academia, [milessabin, larsr_h, xeno_by]).

topics(L) :-
findall(Topic, talk_about(_, Topic), L1),
list_to_set(L1, L).
tracks(L) :-
topics(L1),
member(Topic, L1),
topic(Topic, L).
?- topics(L).
L = [webdev, typelevel, macros].
?- tracks(L).
L = (webdev, [dpp, sirthias]) ;
L = (typelevel, [milessabin, larsr_h]) ;
L = (macros, [xeno_by, milessabin]).

Functional is imperative without state.
Logic is functional without manual search*.
* DFS

Scala is a logic
programming language...

in type system!
Scala is a logic

TYPELEVEL
programming in Scala is...
in type system!

logic programming
TYPELEVEL
programming in Scala is...
in type system!
in Scala!

Prolog
gcd(X, X, X).
gcd(X, Y, Out) :-
X < Y
Z is Y - X
gcd(X, Z, Out).
gcd(X, Y, Out) :-
Y < X,
gcd(Y, X, Out).

trait GCD[X <: Nat, Y <: Nat] { type Out <: Nat }
object GCD
def gcd[N<:Nat](x:Nat,y:Nat)(implicit gcd:Aux[x.N,y.N,N],wn:Witness.Aux[N]):N =
wn.value
type Aux[X <: Nat, Y <: Nat, Z <: Nat] = GCD[X, Y] { type Out = Z }
Scala
{
implicit def gcd0[X <: Nat]:
Aux[X, X, X] =
new GCD[X, X] { type Out = X }
implicit def gcd1[X <: Nat, Y <: Nat, Z <: Nat,
Out0 <: Nat]
(implicit ev0 : LT[X, Y],
ev1 : Diff.Aux[Y, X, Z],
ev2 : Aux[X, Z, Out0]):
Aux[X, Y, Out0] =
new GCD[X, Y] { type Out = Out0 }
implicit def gcd2[X <: Nat, Y <: Nat, Out0 <: Nat]
(implicit ev0 : LT[Y, X],
ev1 : Aux[Y, X, Out0]):
Aux[X, Y, Out0] =
new GCD[X, Y] { type Out = Out0}
}

Facts — implicit vals.
Rules — implicit defs taking implicit
vals as parameters.
Implication is the other way around.

Gotchas:
• Scala does not perform the DFS. In case of
multiple implicits, it does not compile. Prioritizing
implicits via inheritance.
• Diverging implicit expansion -Xlog-implicits.
• Extremely hard to debug (pen and paper style).
• Peculiar exceptions (SO in compiler, Method too
large, etc.)

— So now I need to redefine all the
goodness from prolog stdlib?! Lists,
naturals, etc.
Shapeless: stdlib for logic programming
in scala.

DEMO
https://github.com/folone/scalaeXchange/

Functional in the small,
OO in the large,
logic in the type system!

http://mitpress.mit.edu/books/art-prolog
shapeless (and all the typelevel.scala libraries)
metascala https://www.assembla.com/spaces/metascala/wiki
Links

@milessabin
@xeno_by
@travisbrown
@larsr_h
@killnicole
Thanks

?-
(λx.folonexlambda-calcul.us)@

There's a Prolog in your Scala!

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