Hi Oleg, On 01/11/2018 09:17 AM, Oleg Grenrus wrote:
Hi Benjamin
Let's see what you ask for, you have *new* syntax for types:
a[N] and a[D]
what are a[N][N] or a[N][D] or a[N][D] or a[D][D]?
Aren't they a[N], a[N], a[N] and a[D] respectively? That's what monads are about! Just to be clear, I'm not using [N] as an operator on types, but as part of the type. So a type could be something like the pair (Int,D) or (Int,N). In that context a[N][N] is not part of the system.
So
a[N] ~ Distr a a[D] ~ Identity a ~ a
No need to complicate type-system! You just to not be afraid of monads!
Monads aren't sequencing, they are computational context.
I guess, you just want more natural term-level syntax.
You can use ApplicativeDo [1] (in GHC-8.0+), so e.g.
do x <- normal 0 1 y <- normal 0 1 return (f x y)
will be transformed into
liftA2 f (normal 0 1) (normal 0 1)
That's almost like
f (normal 0 1) (normal 0 1)
if you have proper syntax highlighting ;)
Note: various term syntax extensions been proposed. E.g. idiom brackets in the "Applicative programming with effects" [2]:
(| f (normal 0 1) (normal 0 1) |)
to mean
pure f <*> normal 0 1 <*> normal 0 1
which is equivalent to above liftA2 expression. If you like that, you can check "the Strathclyde Haskell Enhancement", it supports idiom brackets. In my other message I posted an example that doesn't fit this very well:
do { x <- f x } does not work, where as let x = f x does work. Basically I'm trying to avoid monads because I want to use the full features of the Haskell language, instead of programming in an embedded language. In that context "more natural" term-level syntax is not sufficient. Also, it seems possible that everything in Haskell COULD be written in a monad. We could eliminate recursive let bindings, and tell people to create a giant state machine which they use by reading and writing IORefs. But then you also eliminate some of the point of using Haskell and may as well go write in C or something. So it seems to me that just because you CAN use a monad doesn't mean you SHOULD use a monad, and the question is "when is a monad better than something else?" Does that make sense? Am I missing something? -BenRI