-----------------------------------------------------------------------------
-- |
-- Module      :  Data.SBV.Examples.Misc.Enumerate
-- Copyright   :  (c) Levent Erkok
-- License     :  BSD3
-- Maintainer  :  erkokl@gmail.com
-- Stability   :  experimental
--
-- Demonstrates how enumerations can be translated to their SMT-Lib
-- counterparts, without losing any information content. Also see
-- "Data.SBV.Examples.Puzzles.U2Bridge" for a more detailed
-- example involving enumerations.
-----------------------------------------------------------------------------

{-# LANGUAGE DeriveDataTypeable  #-}
{-# LANGUAGE DeriveAnyClass      #-}
{-# LANGUAGE ScopedTypeVariables #-}

module Data.SBV.Examples.Misc.Enumerate where

import Data.SBV
import Data.Generics

-- | A simple enumerated type, that we'd like to translate to SMT-Lib intact;
-- i.e., this type will not be uninterpreted but rather preserved and will
-- be just like any other symbolic type SBV provides. Note the automatically
-- derived classes we need: 'Eq', 'Ord', 'Data', 'Read', 'Show', 'SymWord',
-- 'HasKind', and 'SatModel'. (The last one is only needed if 'getModel' and friends are used.)
--
-- Also note that we need to @import Data.Generics@ and have the @LANGUAGE@
-- option @DeriveDataTypeable@ and @DeriveAnyClass@ set.
data E = A | B | C deriving (Eq, Ord, Show, Read, Data, SymWord, HasKind)

-- | Give a name to the symbolic variants of 'E', for convenience
type SE = SBV E

-- | Have the SMT solver enumerate the elements of the domain. We have:
--
-- >>> elts
-- Solution #1:
--   s0 = B :: E
-- Solution #2:
--   s0 = A :: E
-- Solution #3:
--   s0 = C :: E
-- Found 3 different solutions.
elts :: IO AllSatResult
elts = allSat $ \(x::SE) -> x .== x

-- | Shows that if we require 4 distinct elements of the type 'E', we shall fail; as
-- the domain only has three elements. We have:
--
-- >>> four
-- Unsatisfiable
four :: IO SatResult
four = sat $ \a b c (d::SE) -> allDifferent [a, b, c, d]

-- | Enumerations are automatically ordered, so we can ask for the maximum
-- element. Note the use of quantification. We have:
--
-- >>> maxE
-- Satisfiable. Model:
--   maxE = C :: E
maxE :: IO SatResult
maxE = sat $ do mx <- exists "maxE"
                e  <- forall "e"
                return $ mx .>= (e::SE)

-- | Similarly, we get the minumum element. We have:
--
-- >>> minE
-- Satisfiable. Model:
--   minE = A :: E
minE :: IO SatResult
minE = sat $ do mx <- exists "minE"
                e  <- forall "e"
                return $ mx .<= (e::SE)