{- Data/Singletons/TH/Single/Decide.hs

(c) Richard Eisenberg 2014
rae@cs.brynmawr.edu

Defines functions to generate SDecide instances, as well as TestEquality and
TestCoercion instances that leverage SDecide.
-}

module Data.Singletons.TH.Single.Decide where

import Language.Haskell.TH.Syntax
import Language.Haskell.TH.Desugar
import Data.Singletons.TH.Deriving.Infer
import Data.Singletons.TH.Names
import Data.Singletons.TH.Options
import Data.Singletons.TH.Util
import Control.Monad

-- Make an instance of SDecide.
mkDecideInstance :: DsMonad q => Maybe DCxt -> DKind
                 -> [DCon] -- ^ The /original/ constructors (for inferring the instance context)
                 -> [DCon] -- ^ The /singletons/ constructors
                 -> q DDec
mkDecideInstance :: forall (q :: * -> *).
DsMonad q =>
Maybe DCxt -> DKind -> [DCon] -> [DCon] -> q DDec
mkDecideInstance Maybe DCxt
mb_ctxt DKind
k [DCon]
ctors [DCon]
sctors = do
  let sctorPairs :: [(DCon, DCon)]
sctorPairs = [ (DCon
sc1, DCon
sc2) | DCon
sc1 <- [DCon]
sctors, DCon
sc2 <- [DCon]
sctors ]
  [DClause]
methClauses <- if [DCon] -> Bool
forall a. [a] -> Bool
forall (t :: * -> *) a. Foldable t => t a -> Bool
null [DCon]
sctors
                 then (DClause -> [DClause] -> [DClause]
forall a. a -> [a] -> [a]
:[]) (DClause -> [DClause]) -> q DClause -> q [DClause]
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> q DClause
forall (q :: * -> *). Quasi q => q DClause
mkEmptyDecideMethClause
                 else ((DCon, DCon) -> q DClause) -> [(DCon, DCon)] -> q [DClause]
forall (t :: * -> *) (m :: * -> *) a b.
(Traversable t, Monad m) =>
(a -> m b) -> t a -> m (t b)
forall (m :: * -> *) a b. Monad m => (a -> m b) -> [a] -> m [b]
mapM (DCon, DCon) -> q DClause
forall (q :: * -> *). Quasi q => (DCon, DCon) -> q DClause
mkDecideMethClause [(DCon, DCon)]
sctorPairs
  DCxt
constraints <- Maybe DCxt -> DKind -> DKind -> [DCon] -> q DCxt
forall (q :: * -> *).
DsMonad q =>
Maybe DCxt -> DKind -> DKind -> [DCon] -> q DCxt
inferConstraintsDef Maybe DCxt
mb_ctxt (Name -> DKind
DConT Name
sDecideClassName) DKind
k [DCon]
ctors
  DDec -> q DDec
forall a. a -> q a
forall (m :: * -> *) a. Monad m => a -> m a
return (DDec -> q DDec) -> DDec -> q DDec
forall a b. (a -> b) -> a -> b
$ Maybe Overlap
-> Maybe [DTyVarBndrUnit] -> DCxt -> DKind -> [DDec] -> DDec
DInstanceD Maybe Overlap
forall a. Maybe a
Nothing Maybe [DTyVarBndrUnit]
forall a. Maybe a
Nothing
                     DCxt
constraints
                     (DKind -> DKind -> DKind
DAppT (Name -> DKind
DConT Name
sDecideClassName) DKind
k)
                     [DLetDec -> DDec
DLetDec (DLetDec -> DDec) -> DLetDec -> DDec
forall a b. (a -> b) -> a -> b
$ Name -> [DClause] -> DLetDec
DFunD Name
sDecideMethName [DClause]
methClauses]

data TestInstance = TestEquality
                  | TestCoercion

-- Make an instance of TestEquality or TestCoercion by leveraging SDecide.
mkTestInstance :: OptionsMonad q => Maybe DCxt -> DKind
               -> Name   -- ^ The name of the data type
               -> [DCon] -- ^ The /original/ constructors (for inferring the instance context)
               -> TestInstance -> q DDec
mkTestInstance :: forall (q :: * -> *).
OptionsMonad q =>
Maybe DCxt -> DKind -> Name -> [DCon] -> TestInstance -> q DDec
mkTestInstance Maybe DCxt
mb_ctxt DKind
k Name
data_name [DCon]
ctors TestInstance
ti = do
  Options
opts <- q Options
forall (m :: * -> *). OptionsMonad m => m Options
getOptions
  DCxt
constraints <- Maybe DCxt -> DKind -> DKind -> [DCon] -> q DCxt
forall (q :: * -> *).
DsMonad q =>
Maybe DCxt -> DKind -> DKind -> [DCon] -> q DCxt
inferConstraintsDef Maybe DCxt
mb_ctxt (Name -> DKind
DConT Name
sDecideClassName) DKind
k [DCon]
ctors
  DDec -> q DDec
forall a. a -> q a
forall (f :: * -> *) a. Applicative f => a -> f a
pure (DDec -> q DDec) -> DDec -> q DDec
forall a b. (a -> b) -> a -> b
$ Maybe Overlap
-> Maybe [DTyVarBndrUnit] -> DCxt -> DKind -> [DDec] -> DDec
DInstanceD Maybe Overlap
forall a. Maybe a
Nothing Maybe [DTyVarBndrUnit]
forall a. Maybe a
Nothing
                    DCxt
constraints
                    (DKind -> DKind -> DKind
DAppT (Name -> DKind
DConT Name
tiClassName)
                           (Name -> DKind
DConT (Options -> Name -> Name
singledDataTypeName Options
opts Name
data_name)
                             DKind -> DKind -> DKind
`DSigT` (DKind
DArrowT DKind -> DKind -> DKind
`DAppT` DKind
k DKind -> DKind -> DKind
`DAppT` Name -> DKind
DConT Name
typeKindName)))
                    [DLetDec -> DDec
DLetDec (DLetDec -> DDec) -> DLetDec -> DDec
forall a b. (a -> b) -> a -> b
$ Name -> [DClause] -> DLetDec
DFunD Name
tiMethName
                                     [[DPat] -> DExp -> DClause
DClause [] (Name -> DExp
DVarE Name
tiDefaultName)]]
  where
    (Name
tiClassName, Name
tiMethName, Name
tiDefaultName) =
      case TestInstance
ti of
        TestInstance
TestEquality -> (Name
testEqualityClassName, Name
testEqualityMethName, Name
decideEqualityName)
        TestInstance
TestCoercion -> (Name
testCoercionClassName, Name
testCoercionMethName, Name
decideCoercionName)

mkDecideMethClause :: Quasi q => (DCon, DCon) -> q DClause
mkDecideMethClause :: forall (q :: * -> *). Quasi q => (DCon, DCon) -> q DClause
mkDecideMethClause (DCon
c1, DCon
c2)
  | Name
lname Name -> Name -> Bool
forall a. Eq a => a -> a -> Bool
== Name
rname =
    if Int
lNumArgs Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
== Int
0
    then DClause -> q DClause
forall a. a -> q a
forall (m :: * -> *) a. Monad m => a -> m a
return (DClause -> q DClause) -> DClause -> q DClause
forall a b. (a -> b) -> a -> b
$ [DPat] -> DExp -> DClause
DClause [Name -> DCxt -> [DPat] -> DPat
DConP Name
lname [] [], Name -> DCxt -> [DPat] -> DPat
DConP Name
rname [] []]
                          (DExp -> DExp -> DExp
DAppE (Name -> DExp
DConE Name
provedName) (Name -> DExp
DConE Name
reflName))
    else do
      [Name]
lnames <- Int -> q Name -> q [Name]
forall (m :: * -> *) a. Applicative m => Int -> m a -> m [a]
replicateM Int
lNumArgs (String -> q Name
forall (m :: * -> *). Quasi m => String -> m Name
qNewName String
"a")
      [Name]
rnames <- Int -> q Name -> q [Name]
forall (m :: * -> *) a. Applicative m => Int -> m a -> m [a]
replicateM Int
lNumArgs (String -> q Name
forall (m :: * -> *). Quasi m => String -> m Name
qNewName String
"b")
      Name
contra <- String -> q Name
forall (m :: * -> *). Quasi m => String -> m Name
qNewName String
"contra"
      let lpats :: [DPat]
lpats = (Name -> DPat) -> [Name] -> [DPat]
forall a b. (a -> b) -> [a] -> [b]
map Name -> DPat
DVarP [Name]
lnames
          rpats :: [DPat]
rpats = (Name -> DPat) -> [Name] -> [DPat]
forall a b. (a -> b) -> [a] -> [b]
map Name -> DPat
DVarP [Name]
rnames
          lvars :: [DExp]
lvars = (Name -> DExp) -> [Name] -> [DExp]
forall a b. (a -> b) -> [a] -> [b]
map Name -> DExp
DVarE [Name]
lnames
          rvars :: [DExp]
rvars = (Name -> DExp) -> [Name] -> [DExp]
forall a b. (a -> b) -> [a] -> [b]
map Name -> DExp
DVarE [Name]
rnames
      Name
refl <- String -> q Name
forall (m :: * -> *). Quasi m => String -> m Name
qNewName String
"refl"
      DClause -> q DClause
forall a. a -> q a
forall (m :: * -> *) a. Monad m => a -> m a
return (DClause -> q DClause) -> DClause -> q DClause
forall a b. (a -> b) -> a -> b
$ [DPat] -> DExp -> DClause
DClause
        [Name -> DCxt -> [DPat] -> DPat
DConP Name
lname [] [DPat]
lpats, Name -> DCxt -> [DPat] -> DPat
DConP Name
rname [] [DPat]
rpats]
        (DExp -> [DMatch] -> DExp
DCaseE ([DExp] -> DExp
mkTupleDExp ([DExp] -> DExp) -> [DExp] -> DExp
forall a b. (a -> b) -> a -> b
$
                 (DExp -> DExp -> DExp) -> [DExp] -> [DExp] -> [DExp]
forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
zipWith (\DExp
l DExp
r -> DExp -> [DExp] -> DExp
foldExp (Name -> DExp
DVarE Name
sDecideMethName) [DExp
l, DExp
r])
                         [DExp]
lvars [DExp]
rvars)
                ((DPat -> DExp -> DMatch
DMatch ([DPat] -> DPat
mkTupleDPat (Int -> DPat -> [DPat]
forall a. Int -> a -> [a]
replicate Int
lNumArgs
                                        (Name -> DCxt -> [DPat] -> DPat
DConP Name
provedName [] [Name -> DCxt -> [DPat] -> DPat
DConP Name
reflName [] []])))
                        (DExp -> DExp -> DExp
DAppE (Name -> DExp
DConE Name
provedName) (Name -> DExp
DConE Name
reflName))) DMatch -> [DMatch] -> [DMatch]
forall a. a -> [a] -> [a]
:
                 [DPat -> DExp -> DMatch
DMatch ([DPat] -> DPat
mkTupleDPat (Int -> DPat -> [DPat]
forall a. Int -> a -> [a]
replicate Int
i DPat
DWildP [DPat] -> [DPat] -> [DPat]
forall a. [a] -> [a] -> [a]
++
                                       Name -> DCxt -> [DPat] -> DPat
DConP Name
disprovedName [] [Name -> DPat
DVarP Name
contra] DPat -> [DPat] -> [DPat]
forall a. a -> [a] -> [a]
:
                                       Int -> DPat -> [DPat]
forall a. Int -> a -> [a]
replicate (Int
lNumArgs Int -> Int -> Int
forall a. Num a => a -> a -> a
- Int
i Int -> Int -> Int
forall a. Num a => a -> a -> a
- Int
1) DPat
DWildP))
                         (DExp -> DExp -> DExp
DAppE (Name -> DExp
DConE Name
disprovedName)
                                ([Name] -> DExp -> DExp
DLamE [Name
refl] (DExp -> DExp) -> DExp -> DExp
forall a b. (a -> b) -> a -> b
$
                                 DExp -> [DMatch] -> DExp
DCaseE (Name -> DExp
DVarE Name
refl)
                                        [DPat -> DExp -> DMatch
DMatch (Name -> DCxt -> [DPat] -> DPat
DConP Name
reflName [] []) (DExp -> DMatch) -> DExp -> DMatch
forall a b. (a -> b) -> a -> b
$
                                         (DExp -> DExp -> DExp
DAppE (Name -> DExp
DVarE Name
contra)
                                                (Name -> DExp
DConE Name
reflName))]))
                 | Int
i <- [Int
0..Int
lNumArgsInt -> Int -> Int
forall a. Num a => a -> a -> a
-Int
1] ]))

  | Bool
otherwise = do
    Name
x <- String -> q Name
forall (m :: * -> *). Quasi m => String -> m Name
qNewName String
"x"
    DClause -> q DClause
forall a. a -> q a
forall (m :: * -> *) a. Monad m => a -> m a
return (DClause -> q DClause) -> DClause -> q DClause
forall a b. (a -> b) -> a -> b
$ [DPat] -> DExp -> DClause
DClause
      [Name -> DCxt -> [DPat] -> DPat
DConP Name
lname [] (Int -> DPat -> [DPat]
forall a. Int -> a -> [a]
replicate Int
lNumArgs DPat
DWildP),
       Name -> DCxt -> [DPat] -> DPat
DConP Name
rname [] (Int -> DPat -> [DPat]
forall a. Int -> a -> [a]
replicate Int
rNumArgs DPat
DWildP)]
      (DExp -> DExp -> DExp
DAppE (Name -> DExp
DConE Name
disprovedName) ([Name] -> DExp -> DExp
DLamE [Name
x] (DExp -> [DMatch] -> DExp
DCaseE (Name -> DExp
DVarE Name
x) [])))

  where
    (Name
lname, Int
lNumArgs) = DCon -> (Name, Int)
extractNameArgs DCon
c1
    (Name
rname, Int
rNumArgs) = DCon -> (Name, Int)
extractNameArgs DCon
c2

mkEmptyDecideMethClause :: Quasi q => q DClause
mkEmptyDecideMethClause :: forall (q :: * -> *). Quasi q => q DClause
mkEmptyDecideMethClause = do
  Name
x <- String -> q Name
forall (m :: * -> *). Quasi m => String -> m Name
qNewName String
"x"
  DClause -> q DClause
forall a. a -> q a
forall (f :: * -> *) a. Applicative f => a -> f a
pure (DClause -> q DClause) -> DClause -> q DClause
forall a b. (a -> b) -> a -> b
$ [DPat] -> DExp -> DClause
DClause [Name -> DPat
DVarP Name
x, DPat
DWildP]
       (DExp -> DClause) -> DExp -> DClause
forall a b. (a -> b) -> a -> b
$ Name -> DExp
DConE Name
provedName DExp -> DExp -> DExp
`DAppE` DExp -> [DMatch] -> DExp
DCaseE (Name -> DExp
DVarE Name
x) []