Maxim Sokhatsky
Live
Erlang
System Fω
LOL WUT
Types
fun(A,B,...) -> A -> B -> ...
product(A,...) -> {A,...}
sum(A,B,...) -> A | B | ... cat(A,B,...) ->
Domains(A,B,...),
Morphisms(A,B,...), ... end.
Type Constructors
type/Arity = product/Arity | sum/Arity |
fun/Arity | cat/Arity | list/1 | any
Sample
string() = list(char) = string/0.
integer().
atom().
tree(A) = sum(product(A),product(tree(A),tree(A)))
= {A} | {tree(A),tree(A)}.
array(T) = list(list(T)).
cube(T) = list(array(T)).
typeCons(A,B,C) = product(A,B,list(C)).
Non-proper
typeCons = product(any(),any(),list/1).
main = fun/2.
product/3 = product(any(),any(),any()).
mylist = product(list(product/3),sum/2,any).
lst = list/1.
functorArg = type/1.
Functions
listmap = fun((Fun::fun(A::X,B::Y),In::list(X))-> list(Y)) ->
io:format("In: ~p",[In]),
Out = [ Fun(E) || E <- In],
io:format("Out: ~p",[Out]),
Out end.
fmap = fun(fun(any(),any()),type/1).
listmap = fun(fun(A,B),list(A),list(B)).
unimap(A,B,T::type/1) = fun(fun(A,B),T(A),T(B)).
Simple Functors
tree(A) = sum(product(A),product(tree(A),tree(A)))
= {A} | {tree(A),tree(A)}.
Functor = cat(Type::type/1) ->
fmap = fun(fun(A,B),Type(A),Type(B)). end.
Listfunctor = Functor(list/1) ->
fmap(F,X) -> listmap(F,X). end.
Square = fun(X) -> X * X end.
Listfunctor:fmap(Square,[1,2,3,4]).
Kinds
Typed Erlang System Fω
type(A) * -> *
type(A,B) * -> * -> *
type(A::type/1) (* -> *) -> *
Free Monads
functor = cat(Type::type/1) ->
fmap = fun(fun(A,B),Type(A),Type(B)). end.
other = fun((F::type(A))->lift(F,A)).
pure = fun((A)->lift(type(A))).
lift(F::type(A)) = sum(pure(A),other(F(A))).
free(F::functor(A)) = sum(pure(A), free(F(free(F(A))))).
Discussion
https://github.com/5HT/et
Typed Erlang
By Maxim Sokhatsky
Typed Erlang
- 5,047
