omega is a programming language created in 2005. The Ωmega interpreter is styled after the Hugs Haskell Interpreter. The Ωmega syntax is based upon the syntax of Haskell. If you’re unsure of what syntax to use, a best first approximation is to use Haskell syntax. It works most of the time. While clearly descended from Haskell, Ωmega has several important syntactic and semantic differences.

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  • the omega website
  • omega first appeared in 2005
  • omega was created by Tim Sheard
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Example code from the web:

-- This code written by James Hook
-- This file should work with Omega version 1.1
-- released May 23, 2005
-- See

{-- These are predefined by the compiler
kind Nat = Z | S Nat

data Nat' n
  = Z where n = Z
  | forall m . S (Nat' m) where n = S m

data LE a b
  = LeBase where a = b
  | ex c . LeStep (LE a c) where b = S c

reflLE :: LE a a
reflLE = LeBase

transLE :: (LE a b) -> (LE b c) -> (LE a c)
transLE p LeBase = p
transLE p (LeStep q) = LeStep (transLE p q)

compare :: Nat' a -> Nat' b -> ((LE a b)+(LE b a))
compare Z Z = L LeBase
compare Z (S x) =
  case compare Z x of L w -> L (LeStep w)
compare (S x) Z =
  case compare Z x of L w -> R (LeStep w)
compare (S x) (S y) = mapP g g (compare x y )
  where mapP f g (L x) = L(f x)
        mapP f g (R x) = R(g x)
        g :: LE x y -> LE (S x) (S y)
        g LeBase = LeBase
        g (LeStep x) = LeStep (g x)

data MonoList min max
  = MonoNil (LE min max)
  | forall n a . MonoCons (Nat' n) (LE a n) (LE n max) (MonoList min a)

appMonoList :: MonoList b c -> MonoList a b -> MonoList a c
appMonoList (MonoNil bc) (MonoNil ab) =
      MonoNil (transLE ab bc)
appMonoList (MonoNil bc) (MonoCons n an nb xs) =
      MonoCons n an (transLE nb bc) xs
appMonoList (MonoCons m dm mc ys) xs =
      MonoCons m dm mc (appMonoList ys xs)

singletonMonoList :: Nat' n -> MonoList n n
singletonMonoList n = MonoCons n reflLE reflLE (MonoNil reflLE)

data IntervalList min max
  = ILNil (LE min max)
  | forall x . ILCons (Nat' x) (LE min x) (LE x max) (IntervalList min max)

partition :: Nat' n -> LE a n -> LE n b -> IntervalList a b ->
                     (IntervalList a n, IntervalList n b)
partition x an nb xs = partitionAcc (ILNil an) (ILNil nb) xs
  where partitionAcc ls gs (ILNil ab) = (ls,gs)
        partitionAcc ls gs (ILCons y ay yb ys) =
            case compare y x of
              L yx -> partitionAcc (ILCons y ay yx ls) gs ys
              R xy -> partitionAcc ls (ILCons y xy yb gs) ys

qsort :: IntervalList a b -> MonoList a b
qsort (ILNil ab) = MonoNil ab
qsort (ILCons x ax xb (ILNil ab)) = MonoCons x ax xb (MonoNil reflLE)
qsort (ILCons x ax xb xs) =
     let (less,greater) = partition x ax xb xs
         sortedLess = qsort less
   sortedGreater = qsort greater
     in appMonoList sortedGreater (appMonoList (singletonMonoList x) sortedLess)


Last updated August 9th, 2020

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