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|
-----------------------------------------------------------------------------
-- |
-- Module : Data.SBV.Maybe
-- Copyright : (c) Joel Burget
-- Levent Erkok
-- License : BSD3
-- Maintainer: erkokl@gmail.com
-- Stability : experimental
--
-- Symbolic option type, symbolic version of Haskell's 'Maybe' type.
-----------------------------------------------------------------------------
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE Rank2Types #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeApplications #-}
{-# OPTIONS_GHC -Wall -Werror -fno-warn-orphans #-}
module Data.SBV.Maybe (
-- * Constructing optional values
sJust, sNothing, liftMaybe
-- * Destructing optionals
, maybe
-- * Mapping functions
, map, map2
-- * Scrutinizing the branches of an option
, isNothing, isJust, fromMaybe, fromJust
) where
import Prelude hiding (maybe, map)
import qualified Prelude
import Data.Proxy (Proxy(Proxy))
import Data.SBV.Core.Data
import Data.SBV.Core.Model (ite)
-- $setup
-- >>> -- For doctest purposes only:
-- >>> import Prelude hiding (maybe, map)
-- >>> import Data.SBV
-- | The symbolic 'Nothing'.
--
-- >>> sNothing :: SMaybe Integer
-- Nothing :: SMaybe Integer
sNothing :: forall a. SymVal a => SMaybe a
sNothing = SBV $ SVal k $ Left $ CV k $ CMaybe Nothing
where k = kindOf (Proxy @(Maybe a))
-- | Check if the symbolic value is nothing.
--
-- >>> isNothing (sNothing :: SMaybe Integer)
-- True
-- >>> isNothing (sJust (literal "nope"))
-- False
isNothing :: SymVal a => SMaybe a -> SBool
isNothing = maybe sTrue (const sFalse)
-- | Construct an @SMaybe a@ from an @SBV a@.
--
-- >>> sJust (3 :: SInteger)
-- Just 3 :: SMaybe Integer
sJust :: forall a. SymVal a => SBV a -> SMaybe a
sJust sa
| Just a <- unliteral sa
= literal (Just a)
| True
= SBV $ SVal kMaybe $ Right $ cache res
where ka = kindOf (Proxy @a)
kMaybe = KMaybe ka
res st = do asv <- sbvToSV st sa
newExpr st kMaybe $ SBVApp (MaybeConstructor ka True) [asv]
-- | Check if the symbolic value is not nothing.
--
-- >>> isJust (sNothing :: SMaybe Integer)
-- False
-- >>> isJust (sJust (literal "yep"))
-- True
-- >>> prove $ \x -> isJust (sJust (x :: SInteger))
-- Q.E.D.
isJust :: SymVal a => SMaybe a -> SBool
isJust = maybe sFalse (const sTrue)
-- | Return the value of an optional value. The default is returned if Nothing. Compare to 'fromJust'.
--
-- >>> fromMaybe 2 (sNothing :: SMaybe Integer)
-- 2 :: SInteger
-- >>> fromMaybe 2 (sJust 5 :: SMaybe Integer)
-- 5 :: SInteger
-- >>> prove $ \x -> fromMaybe x (sNothing :: SMaybe Integer) .== x
-- Q.E.D.
-- >>> prove $ \x -> fromMaybe (x+1) (sJust x :: SMaybe Integer) .== x
-- Q.E.D.
fromMaybe :: SymVal a => SBV a -> SMaybe a -> SBV a
fromMaybe def = maybe def id
-- | Return the value of an optional value. The behavior is undefined if
-- passed Nothing, i.e., it can return any value. Compare to 'fromMaybe'.
--
-- >>> fromJust (sJust (literal 'a'))
-- 'a' :: SChar
-- >>> prove $ \x -> fromJust (sJust x) .== (x :: SChar)
-- Q.E.D.
-- >>> sat $ \x -> x .== (fromJust sNothing :: SChar)
-- Satisfiable. Model:
-- s0 = 'A' :: Char
--
-- Note how we get a satisfying assignment in the last case: The behavior
-- is unspecified, thus the SMT solver picks whatever satisfies the
-- constraints, if there is one.
fromJust :: forall a. SymVal a => SMaybe a -> SBV a
fromJust ma
| Just (Just x) <- unliteral ma
= literal x
| True
= SBV $ SVal ka $ Right $ cache res
where ka = kindOf (Proxy @a)
res st = do ms <- sbvToSV st ma
newExpr st ka (SBVApp MaybeAccess [ms])
-- | Construct an @SMaybe a@ from a @Maybe (SBV a)@.
--
-- >>> liftMaybe (Just (3 :: SInteger))
-- Just 3 :: SMaybe Integer
-- >>> liftMaybe (Nothing :: Maybe SInteger)
-- Nothing :: SMaybe Integer
liftMaybe :: SymVal a => Maybe (SBV a) -> SMaybe a
liftMaybe = Prelude.maybe (literal Nothing) sJust
-- | Map over the 'Just' side of a 'Maybe'.
--
-- >>> prove $ \x -> fromJust (map (+1) (sJust x)) .== x+(1::SInteger)
-- Q.E.D.
-- >>> let f = uninterpret "f" :: SInteger -> SBool
-- >>> prove $ \x -> map f (sJust x) .== sJust (f x)
-- Q.E.D.
-- >>> map f sNothing .== sNothing
-- True
map :: forall a b. (SymVal a, SymVal b)
=> (SBV a -> SBV b)
-> SMaybe a
-> SMaybe b
map f = maybe sNothing (sJust . f)
-- | Map over two maybe values.
map2 :: forall a b c. (SymVal a, SymVal b, SymVal c) => (SBV a -> SBV b -> SBV c) -> SMaybe a -> SMaybe b -> SMaybe c
map2 op mx my = ite (isJust mx .&& isJust my)
(sJust (fromJust mx `op` fromJust my))
sNothing
-- | Case analysis for symbolic 'Maybe's. If the value 'isNothing', return the
-- default value; if it 'isJust', apply the function.
--
-- >>> maybe 0 (`sMod` 2) (sJust (3 :: SInteger))
-- 1 :: SInteger
-- >>> maybe 0 (`sMod` 2) (sNothing :: SMaybe Integer)
-- 0 :: SInteger
-- >>> let f = uninterpret "f" :: SInteger -> SBool
-- >>> prove $ \x d -> maybe d f (sJust x) .== f x
-- Q.E.D.
-- >>> prove $ \d -> maybe d f sNothing .== d
-- Q.E.D.
maybe :: forall a b. (SymVal a, SymVal b)
=> SBV b
-> (SBV a -> SBV b)
-> SMaybe a
-> SBV b
maybe brNothing brJust ma
| Just (Just a) <- unliteral ma
= brJust (literal a)
| Just Nothing <- unliteral ma
= brNothing
| True
= SBV $ SVal kb $ Right $ cache res
where ka = kindOf (Proxy @a)
kb = kindOf (Proxy @b)
res st = do mav <- sbvToSV st ma
let justVal = SBV $ SVal ka $ Right $ cache $ \_ -> newExpr st ka $ SBVApp MaybeAccess [mav]
justRes = brJust justVal
br1 <- sbvToSV st brNothing
br2 <- sbvToSV st justRes
-- Do we have a value?
noVal <- newExpr st KBool $ SBVApp (MaybeIs ka False) [mav]
newExpr st kb $ SBVApp Ite [noVal, br1, br2]
-- | Custom 'Num' instance over 'SMaybe'
instance {-# OVERLAPPING #-} (Ord a, SymVal a, Num a) => Num (SBV (Maybe a)) where
(+) = map2 (+)
(-) = map2 (-)
(*) = map2 (*)
abs = map abs
signum = map signum
fromInteger = sJust . fromInteger
|
