-----------------------------------------------------------------------------
-- |
-- Module    : Documentation.SBV.Examples.Puzzles.DogCatMouse
-- Copyright : (c) Levent Erkok
-- License   : BSD3
-- Maintainer: erkokl@gmail.com
-- Stability : experimental
--
-- Puzzle:
--   Spend exactly 100 dollars and buy exactly 100 animals.
--   Dogs cost 15 dollars, cats cost 1 dollar, and mice cost 25 cents each.
--   You have to buy at least one of each.
--   How many of each should you buy?
-----------------------------------------------------------------------------

{-# OPTIONS_GHC -Wall -Werror #-}

module Documentation.SBV.Examples.Puzzles.DogCatMouse where

import Data.SBV

-- | Prints the only solution:
--
-- >>> puzzle
-- Solution #1:
--   dog   =  3 :: Integer
--   cat   = 41 :: Integer
--   mouse = 56 :: Integer
-- This is the only solution.
puzzle :: IO AllSatResult
puzzle :: IO AllSatResult
puzzle = forall a. Provable a => a -> IO AllSatResult
allSat forall a b. (a -> b) -> a -> b
$ do
           [SInteger
dog, SInteger
cat, SInteger
mouse] <- [String] -> Symbolic [SInteger]
sIntegers [String
"dog", String
"cat", String
"mouse"]
           [SBool] -> SymbolicT IO SBool
solve [ SInteger
dog   forall a. OrdSymbolic a => a -> a -> SBool
.>= SInteger
1                                           -- at least one dog
                 , SInteger
cat   forall a. OrdSymbolic a => a -> a -> SBool
.>= SInteger
1                                           -- at least one cat
                 , SInteger
mouse forall a. OrdSymbolic a => a -> a -> SBool
.>= SInteger
1                                           -- at least one mouse
                 , SInteger
dog forall a. Num a => a -> a -> a
+ SInteger
cat forall a. Num a => a -> a -> a
+ SInteger
mouse forall a. EqSymbolic a => a -> a -> SBool
.== SInteger
100                             -- buy precisely 100 animals
                 , SReal
15 forall {a}. (Integral a, SymVal a) => SReal -> SBV a -> SReal
`per` SInteger
dog forall a. Num a => a -> a -> a
+ SReal
1 forall {a}. (Integral a, SymVal a) => SReal -> SBV a -> SReal
`per` SInteger
cat forall a. Num a => a -> a -> a
+ SReal
0.25 forall {a}. (Integral a, SymVal a) => SReal -> SBV a -> SReal
`per` SInteger
mouse forall a. EqSymbolic a => a -> a -> SBool
.== SReal
100 -- spend exactly 100 dollars
                 ]
  where SReal
p per :: SReal -> SBV a -> SReal
`per` SBV a
q = SReal
p forall a. Num a => a -> a -> a
* (forall a b.
(Integral a, HasKind a, Num a, SymVal a, HasKind b, Num b,
 SymVal b) =>
SBV a -> SBV b
sFromIntegral SBV a
q :: SReal)