Polytope.hs

{-# LANGUAGE QualifiedDo, RebindableSyntax #-}
-- | Polytope credal sets from composed intervals.
module Imp.Examples.Polytope
  ( Three(..)
  , polytope
  , polytope2
  ) where

import Imp

-- | Three-valued outcome.
data Three = Red | Green | Blue
  deriving stock (Eq, Ord, Show)

-- | Two independent intervals composed to give an imprecise distribution.
polytope :: Imp '["p", "q"] Three
polytope = Imp.do
  p <- interval @"p" 0.2 0.8
  q <- interval @"q" 0.3 0.7
  Imp.return $ if p then Red else (if q then Green else Blue)

-- | Three intervals composed to give a finer polytope.
polytope2 :: Imp '["b", "g", "r"] Three
polytope2 = Imp.do
  r <- interval @"r" 0.2 0.5
  g <- interval @"g" 0.2 0.5
  b <- interval @"b" 0.2 0.5
  Imp.return $ if r then Red else (if g then Green else (if b then Blue else Red))