iso is an interpreted programming language that explores the computational power of pattern matching. In this language we don't define functions, we define isomorphisms. They can execute in either direction.
This has some interesting consequences. Imagine you are writing Python like this:
[a, b] = [1, 2]This assigns 1 to a and 2 to b. Nothing that special, many languages have this feature.
Now imagine you could write this in Python:
def fn(x):
return x+1
[fn(a), fn(b)] = [1, 2]If this did work, it would have to answer the question: what value of a gives 1 when passed to fn()?
Now try this in iso, which does work.
You can define fn with a bit of boilerplate as we haven't added integer math as a builtin yet:
type Int4 = Bool * Bool * Bool * Bool
iso fn :: Int4 <-> Int4
| a,b,c,0 <-> a,b,c,1
| a,b,0,1 <-> a,b,1,0
| a,0,1,1 <-> a,1,0,0
| 0,1,1,1 <-> 1,0,0,0
| 1,1,1,1 <-> 0,0,0,0
Then you can run it forwards:
> :evall fn (0,0,0,1)
(0,0,1,0)
And backwards:
> :evalr fn (0,0,1,0)
(0,0,0,1)
- Parametric polymorphism has some interesting consequences (though it is not implemented)
For example, consider the isomorphism
if :: Bool <-> Either a b. Both sides actually hold the same amount of "information", even though they may not have the same "size". This could be an interesting area for further research.
stack build && stack exec iso