clash-prelude-1.4.2: src/Clash/XException.hs
{-|
Copyright : (C) 2016, University of Twente,
2017, QBayLogic, Google Inc.
2017-2019, Myrtle Software Ltd
License : BSD2 (see the file LICENSE)
Maintainer : Christiaan Baaij <christiaan.baaij@gmail.com>
'XException': An exception for uninitialized values
>>> show (errorX "undefined" :: Integer, 4 :: Int)
"(*** Exception: X: undefined
CallStack (from HasCallStack):
...
>>> showX (errorX "undefined" :: Integer, 4 :: Int)
"(X,4)"
-}
{-# LANGUAGE CPP #-}
{-# LANGUAGE EmptyCase #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE NoImplicitPrelude #-}
{-# LANGUAGE StandaloneDeriving #-}
{-# LANGUAGE TemplateHaskell #-}
{-# LANGUAGE Trustworthy #-}
module Clash.XException
( -- * 'XException': An exception for uninitialized values
XException(..), errorX, isX, hasX, maybeIsX, maybeHasX, fromJustX, undefined,
xToErrorCtx, xToError
-- * Printing 'XException's as \"X\"
, ShowX (..), showsX, printX, showsPrecXWith
-- * Strict evaluation
, seqX, forceX, deepseqX, rwhnfX, defaultSeqX, hwSeqX
-- * Structured undefined / deep evaluation with undefined values
, NFDataX (rnfX, deepErrorX, hasUndefined, ensureSpine)
)
where
import Prelude hiding (undefined)
import Clash.Annotations.Primitive (hasBlackBox)
import Clash.CPP (maxTupleSize, fSuperStrict)
import Clash.XException.Internal
import Clash.XException.TH
import Control.Exception
(ErrorCall (..), catch, evaluate, throw)
import Control.DeepSeq (NFData, rnf)
import Data.Complex (Complex)
import Data.Either (isLeft)
import Data.Foldable (toList)
import Data.Int (Int8, Int16, Int32, Int64)
import Data.Ord (Down (Down))
import Data.Ratio (Ratio, numerator, denominator)
import qualified Data.Semigroup as SG
import qualified Data.Monoid as M
import Data.Sequence (Seq(Empty, (:<|)))
import Data.Word (Word8, Word16, Word32, Word64)
import Foreign.C.Types (CUShort)
import GHC.Generics
import GHC.Natural (Natural)
import GHC.Stack
(HasCallStack, callStack, prettyCallStack, withFrozenCallStack)
import Numeric.Half (Half)
import System.IO.Unsafe (unsafeDupablePerformIO)
-- $setup
-- >>> import Clash.Class.BitPack (pack)
-- >>> import Clash.Sized.Vector (Vec)
-- >>> import Clash.Sized.RTree (RTree)
-- >>> :set -fplugin GHC.TypeLits.Normalise
-- >>> :set -fplugin GHC.TypeLits.KnownNat.Solver
-- | Either 'seqX' or 'deepseqX' depending on the value of the cabal flag
-- '-fsuper-strict'. If enabled, 'defaultSeqX' will be 'deepseqX', otherwise
-- 'seqX'. Flag defaults to /false/ and thus 'seqX'.
defaultSeqX :: NFDataX a => a -> b -> b
defaultSeqX = if fSuperStrict then deepseqX else seqX
{-# INLINE defaultSeqX #-}
infixr 0 `defaultSeqX`
-- | Like 'error', but throwing an 'XException' instead of an 'ErrorCall'
--
-- The 'ShowX' methods print these error-values as \"X\"; instead of error'ing
-- out with an exception.
errorX :: HasCallStack => String -> a
errorX msg = throw (XException ("X: " ++ msg ++ "\n" ++ prettyCallStack callStack))
-- | Convert 'XException' to 'ErrorCall'
--
-- This is useful when tracking the source of 'XException' that gets eaten up by
-- 'Clash.Classes.BitPack.pack' inside of your circuit; since
-- 'Clash.Classes.BitPack.pack' translates 'XException' into undefined bits.
--
-- So for example if you have some large function f:
--
-- > f a b = ... pack a ... pack b ...
--
-- Where it is basically an error if either /a/ or /b/ ever throws an 'XException',
-- and so you want that to be reported the moment /a/ or /b/ is used, instead of
-- it being thrown when evaluating the result of /f/, then do:
--
-- > {-# LANGUAGE ViewPatterns #-}
-- > f (xToErrorCtx "a is X" -> a) (xToErrorCtx "b is X" -> b) = ...
--
-- Where we pass an extra string, for context, to know which argument evaluated
-- to an 'XException'. We can also use BangPatterns to report the potential
-- 'XException' being thrown by /a/ or /b/ even earlier, i.e. when /f/ is applied:
--
-- > {-# LANGUAGE ViewPatterns, BangPatterns #-}
-- > f (xToErrorCtx "a is X" -> !a) (xToErrorCtx "b is X" -> !b) = ...
--
-- __NB:__ Fully synthesizable, so doesn't have to be removed before synthesis
--
-- === __Example__
--
-- >>> :set -XViewPatterns -XDataKinds
-- >>> import Clash.Sized.BitVector
-- >>> import GHC.Stack
-- >>> :{
-- let h, h' :: Bit -> BitVector 8 -> BitVector 8
-- h (xToErrorCtx "a is X" -> a) (xToErrorCtx "b is X" -> b) = slice d7 d0 (pack a ++# b)
-- h' a b = slice d7 d0 (pack a ++# b)
-- :}
--
-- >>> h' (errorX "QQ") 3
-- 0000_0011
-- >>> h (errorX "QQ") 3
-- *** Exception: a is X
-- X: QQ
-- CallStack (from HasCallStack):
-- errorX, called at ...
-- <BLANKLINE>
xToErrorCtx :: String -> a -> a
xToErrorCtx ctx a = unsafeDupablePerformIO
(catch (evaluate a >> return a)
(\(XException msg) ->
throw (ErrorCall (unlines [ctx,msg]))))
{-# NOINLINE xToErrorCtx #-}
-- | Convert 'XException' to 'ErrorCall'
--
-- This is useful when tracking the source of 'XException' that gets eaten up by
-- 'Clash.Classes.BitPack.pack' inside of your circuit; since
-- 'Clash.Classes.BitPack.pack' translates 'XException' into undefined bits.
--
-- So for example if you have some large function f:
--
-- > f a b = ... pack a ... pack b ...
--
-- Where it is basically an error if either /a/ or /b/ ever throws an 'XException',
-- and so you want that to be reported the moment /a/ or /b/ is used, instead of
-- it being thrown when evaluating the result of /f/, then do:
--
-- > {-# LANGUAGE ViewPatterns #-}
-- > f (xToError -> a) (xToError -> b) = ...
--
-- Unlike 'xToErrorCtx', where we have an extra String argument to distinguish
-- one call to 'xToError' to the other, 'xToError' will use the 'GHC.CallStack'
-- mechanism to aid the user in distinguishing different call to 'xToError'.
-- We can also use BangPatterns to report the potential 'XException' being
-- thrown by /a/ or /b/ even earlier, i.e. when /f/ is applied:
--
-- > {-# LANGUAGE ViewPatterns, BangPatterns #-}
-- > f (xToError -> !a) (xToError -> !b) = ...
--
-- __NB:__ Fully synthesizable, so doesn't have to be removed before synthesis
--
-- === __Example__
--
-- >>> :set -XViewPatterns -XDataKinds
-- >>> import Clash.Sized.BitVector
-- >>> import GHC.Stack
-- >>> :{
-- let f, g, h, h' :: HasCallStack => Bit -> BitVector 8 -> BitVector 8
-- f = g
-- g = h
-- h (xToError -> a) (xToError -> b) = slice d7 d0 (pack a ++# b)
-- h' a b = slice d7 d0 (pack a ++# b)
-- :}
--
-- >>> h' (errorX "QQ") 3
-- 0000_0011
-- >>> f (errorX "QQ") 3
-- *** Exception: CallStack (from HasCallStack):
-- xToError, called at ...
-- h, called at ...
-- g, called at ...
-- f, called at ...
-- X: QQ
-- CallStack (from HasCallStack):
-- errorX, called at ...
-- <BLANKLINE>
xToError :: HasCallStack => a -> a
xToError = xToErrorCtx (prettyCallStack callStack)
{-# INLINE xToError #-}
-- | Like 'seq', however, whereas 'seq' will always do:
--
-- > seq _|_ b = _|_
--
-- 'seqX' will do:
--
-- > seqX (XException msg) b = b
-- > seqX _|_ b = _|_
seqX :: a -> b -> b
seqX a b = unsafeDupablePerformIO
(catch (evaluate a >> return b) (\(XException _) -> return b))
{-# NOINLINE seqX #-}
infixr 0 `seqX`
-- | Like 'seqX' in simulation, but will force its first argument to be rendered
-- in HDL. This is useful for components that need to be rendered in hardware,
-- but otherwise have no meaning in simulation. An example of such a component
-- would be an ILA: a component monitoring an internal signal of a design. The
-- output of such a component (typically a unit) can be passed as the first
-- argument to 'hwSeqX' to ensure the ILA ends up in the generated HDL.
--
-- __NB__: the result of 'hwSeqX' must (indirectly) be used at the very top of
-- a design. If it's not, Clash will remove it like it does for any other unused
-- circuit parts.
--
-- __NB__: Make sure the blackbox for the component with zero-width results
-- uses 'Clash.Netlist.BlackBox.Types.RenderVoid'
hwSeqX :: a -> b -> b
hwSeqX = seqX
{-# NOINLINE hwSeqX #-}
{-# ANN hwSeqX hasBlackBox #-}
infixr 0 `hwSeqX`
-- | Evaluate a value with given function, returning 'Nothing' if it throws
-- 'XException'.
--
-- > maybeX hasX 42 = Just 42
-- > maybeX hasX (XException msg) = Nothing
-- > maybeX hasX (3, XException msg) = Nothing
-- > maybeX hasX (3, _|_) = _|_
-- > maybeX hasX _|_ = _|_
-- >
-- > maybeX isX 42 = Just 42
-- > maybeX isX (XException msg) = Nothing
-- > maybeX isX (3, XException msg) = Just (3, XException msg)
-- > maybeX isX (3, _|_) = Just (3, _|_)
-- > maybeX isX _|_ = _|_
--
maybeX :: (a -> Either String a) -> a -> Maybe a
maybeX f a = either (const Nothing) Just (f a)
-- | Fully evaluate a value, returning 'Nothing' if it throws 'XException'.
--
-- > maybeX 42 = Just 42
-- > maybeX (XException msg) = Nothing
-- > maybeX (3, XException msg) = Nothing
-- > maybeX (3, _|_) = _|_
-- > maybeX _|_ = _|_
--
maybeHasX :: NFData a => a -> Maybe a
maybeHasX = maybeX hasX
-- | Evaluate a value to WHNF, returning 'Nothing' if it throws 'XException'.
--
-- > maybeIsX 42 = Just 42
-- > maybeIsX (XException msg) = Nothing
-- > maybeIsX (3, XException msg) = Just (3, XException msg)
-- > maybeIsX (3, _|_) = Just (3, _|_)
-- > maybeIsX _|_ = _|_
maybeIsX :: a -> Maybe a
maybeIsX = maybeX isX
-- | Fully evaluate a value, returning @'Left' msg@ if it throws 'XException'.
-- If you want to determine if a value contains undefined parts, use
-- 'hasUndefined' instead.
--
-- > hasX 42 = Right 42
-- > hasX (XException msg) = Left msg
-- > hasX (3, XException msg) = Left msg
-- > hasX (3, _|_) = _|_
-- > hasX _|_ = _|_
--
-- If a data structure contains multiple 'XException's, the "first" message is
-- picked according to the implementation of 'rnf'.
hasX :: NFData a => a -> Either String a
hasX a =
unsafeDupablePerformIO
(catch
(evaluate (rnf a) >> return (Right a))
(\(XException msg) -> return (Left msg)))
{-# NOINLINE hasX #-}
-- | Evaluate a value to WHNF, returning @'Left' msg@ if is a 'XException'.
--
-- > isX 42 = Right 42
-- > isX (XException msg) = Left msg
-- > isX (3, XException msg) = Right (3, XException msg)
-- > isX (3, _|_) = (3, _|_)
-- > isX _|_ = _|_
isX :: a -> Either String a
isX a =
unsafeDupablePerformIO
(catch
(evaluate a >> return (Right a))
(\(XException msg) -> return (Left msg)))
{-# NOINLINE isX #-}
-- | Like the 'Show' class, but values that normally throw an 'XException' are
-- converted to \"X\", instead of error'ing out with an exception.
--
-- >>> show (errorX "undefined" :: Integer, 4 :: Int)
-- "(*** Exception: X: undefined
-- CallStack (from HasCallStack):
-- ...
-- >>> showX (errorX "undefined" :: Integer, 4 :: Int)
-- "(X,4)"
--
-- Can be derived using 'GHC.Generics':
--
-- > {-# LANGUAGE DeriveGeneric, DeriveAnyClass #-}
-- >
-- > import Clash.Prelude
-- > import GHC.Generics
-- >
-- > data T = MkTA Int | MkTB Bool
-- > deriving (Show,Generic,ShowX)
class ShowX a where
-- | Like 'showsPrec', but values that normally throw an 'XException' are
-- converted to \"X\", instead of error'ing out with an exception.
showsPrecX :: Int -> a -> ShowS
-- | Like 'show', but values that normally throw an 'XException' are
-- converted to \"X\", instead of error'ing out with an exception.
showX :: a -> String
showX x = showsX x ""
-- | Like 'showList', but values that normally throw an 'XException' are
-- converted to \"X\", instead of error'ing out with an exception.
showListX :: [a] -> ShowS
showListX ls s = showListX__ showsX ls s
default showsPrecX :: (Generic a, GShowX (Rep a)) => Int -> a -> ShowS
showsPrecX = genericShowsPrecX
-- | Like 'print', but values that normally throw an 'XException' are
-- converted to \"X\", instead of error'ing out with an exception
printX :: ShowX a => a -> IO ()
printX x = putStrLn $ showX x
instance ShowX ()
instance {-# OVERLAPPABLE #-} ShowX a => ShowX [a] where
showsPrecX _ = showListX
instance ShowX Char where
showsPrecX = showsPrecXWith showsPrec
instance ShowX Bool
instance ShowX Double where
showsPrecX = showsPrecXWith showsPrec
instance ShowX a => ShowX (Down a) where
showsPrecX = showsPrecXWith showsPrecX
instance (ShowX a, ShowX b) => ShowX (Either a b)
instance ShowX Float where
showsPrecX = showsPrecXWith showsPrec
instance ShowX Int where
showsPrecX = showsPrecXWith showsPrec
instance ShowX Int8 where
showsPrecX = showsPrecXWith showsPrec
instance ShowX Int16 where
showsPrecX = showsPrecXWith showsPrec
instance ShowX Int32 where
showsPrecX = showsPrecXWith showsPrec
instance ShowX Int64 where
showsPrecX = showsPrecXWith showsPrec
instance ShowX Integer where
showsPrecX = showsPrecXWith showsPrec
instance ShowX Natural where
showsPrecX = showsPrecXWith showsPrec
instance ShowX a => ShowX (Seq a) where
showsPrecX _ = showListX . toList
instance ShowX Word where
showsPrecX = showsPrecXWith showsPrec
instance ShowX Word8 where
showsPrecX = showsPrecXWith showsPrec
instance ShowX Word16 where
showsPrecX = showsPrecXWith showsPrec
instance ShowX Word32 where
showsPrecX = showsPrecXWith showsPrec
instance ShowX Word64 where
showsPrecX = showsPrecXWith showsPrec
instance ShowX a => ShowX (Maybe a)
instance ShowX a => ShowX (Ratio a) where
showsPrecX = showsPrecXWith showsPrecX
instance ShowX a => ShowX (Complex a)
instance {-# OVERLAPPING #-} ShowX String where
showsPrecX = showsPrecXWith showsPrec
-- | a variant of 'deepseqX' that is useful in some circumstances:
--
-- > forceX x = x `deepseqX` x
forceX :: NFDataX a => a -> a
forceX x = x `deepseqX` x
{-# INLINE forceX #-}
-- | 'deepseqX': fully evaluates the first argument, before returning the
-- second. Does not propagate 'XException's.
deepseqX :: NFDataX a => a -> b -> b
deepseqX a b = rnfX a `seq` b
{-# NOINLINE deepseqX #-}
infixr 0 `deepseqX`
-- | Reduce to weak head normal form
--
-- Equivalent to @\\x -> 'seqX' x ()@.
--
-- Useful for defining 'NFDataX.rnfX' for types for which NF=WHNF holds.
rwhnfX :: a -> ()
rwhnfX = (`seqX` ())
{-# INLINE rwhnfX #-}
-- | Class that houses functions dealing with /undefined/ values in Clash. See
-- 'deepErrorX' and 'rnfX'.
class NFDataX a where
-- | Create a value where all the elements have an 'errorX',
-- but the spine is defined.
deepErrorX :: HasCallStack => String -> a
default deepErrorX :: (HasCallStack, Generic a, GDeepErrorX (Rep a)) => String -> a
deepErrorX = withFrozenCallStack $ to . gDeepErrorX
-- | Determines whether any of parts of a given construct contain undefined
-- parts. Note that a negative answer does not mean its bit representation
-- is fully defined. For example:
--
-- >>> m = Nothing :: Maybe Bool
-- >>> hasUndefined m
-- False
-- >>> pack m
-- 0.
-- >>> hasUndefined (pack m)
-- True
--
hasUndefined :: a -> Bool
default hasUndefined :: (Generic a, GHasUndefined (Rep a)) => a -> Bool
hasUndefined = gHasUndefined . from
-- | Create a value where at the very least the spine is defined. For example:
--
-- >>> spined = ensureSpine (errorX "?" :: (Int, Int))
-- >>> case spined of (_, _) -> 'a'
-- 'a'
-- >>> fmap (const 'b') (ensureSpine undefined :: Vec 3 Int)
-- <'b','b','b'>
-- >>> fmap (const 'c') (ensureSpine undefined :: RTree 2 Int)
-- <<'c','c'>,<'c','c'>>
--
-- For users familiar with 'Clash.Sized.Vector.lazyV': this is the generalized
-- version of it.
ensureSpine :: a -> a
default ensureSpine :: (Generic a, GEnsureSpine (Rep a)) => a -> a
ensureSpine = to . gEnsureSpine . from
-- | Evaluate a value to NF. As opposed to 'NFData's
-- 'rnf', it does not bubble up 'XException's.
rnfX :: a -> ()
default rnfX :: (Generic a, GNFDataX Zero (Rep a)) => a -> ()
rnfX = grnfX RnfArgs0 . from
instance NFDataX ()
instance NFDataX b => NFDataX (a -> b) where
deepErrorX = pure . deepErrorX
rnfX = rwhnfX
hasUndefined = error "hasUndefined on Undefined (a -> b): Not Yet Implemented"
ensureSpine = id
instance NFDataX a => NFDataX (Down a) where
deepErrorX = Down . deepErrorX
rnfX d@(~(Down x)) = if isLeft (isX d) then () else rnfX x
hasUndefined d@(~(Down x))= if isLeft (isX d) then True else hasUndefined x
ensureSpine ~(Down x) = Down (ensureSpine x)
instance NFDataX Bool
instance NFDataX a => NFDataX [a]
instance (NFDataX a, NFDataX b) => NFDataX (Either a b)
instance NFDataX a => NFDataX (Maybe a)
instance NFDataX Char where
deepErrorX = errorX
rnfX = rwhnfX
hasUndefined = isLeft . isX
ensureSpine = id
instance NFDataX Double where
deepErrorX = errorX
rnfX = rwhnfX
hasUndefined = isLeft . isX
ensureSpine = id
instance NFDataX Float where
deepErrorX = errorX
rnfX = rwhnfX
hasUndefined = isLeft . isX
ensureSpine = id
instance NFDataX Int where
deepErrorX = errorX
rnfX = rwhnfX
hasUndefined = isLeft . isX
ensureSpine = id
instance NFDataX Int8 where
deepErrorX = errorX
rnfX = rwhnfX
hasUndefined = isLeft . isX
ensureSpine = id
instance NFDataX Int16 where
deepErrorX = errorX
rnfX = rwhnfX
hasUndefined = isLeft . isX
ensureSpine = id
instance NFDataX Int32 where
deepErrorX = errorX
rnfX = rwhnfX
hasUndefined = isLeft . isX
ensureSpine = id
instance NFDataX Int64 where
deepErrorX = errorX
rnfX = rwhnfX
hasUndefined = isLeft . isX
ensureSpine = id
instance NFDataX Integer where
deepErrorX = errorX
rnfX = rwhnfX
hasUndefined = isLeft . isX
ensureSpine = id
instance NFDataX Natural where
deepErrorX = errorX
rnfX = rwhnfX
hasUndefined = isLeft . isX
ensureSpine = id
instance NFDataX Word where
deepErrorX = errorX
rnfX = rwhnfX
hasUndefined = isLeft . isX
ensureSpine = id
instance NFDataX Word8 where
deepErrorX = errorX
rnfX = rwhnfX
hasUndefined = isLeft . isX
ensureSpine = id
instance NFDataX Word16 where
deepErrorX = errorX
rnfX = rwhnfX
hasUndefined = isLeft . isX
ensureSpine = id
instance NFDataX Word32 where
deepErrorX = errorX
rnfX = rwhnfX
hasUndefined = isLeft . isX
ensureSpine = id
instance NFDataX Word64 where
deepErrorX = errorX
rnfX = rwhnfX
hasUndefined = isLeft . isX
ensureSpine = id
instance NFDataX CUShort where
deepErrorX = errorX
rnfX = rwhnfX
hasUndefined = isLeft . isX
ensureSpine = id
instance NFDataX Half where
deepErrorX = errorX
rnfX = rwhnfX
hasUndefined = isLeft . isX
ensureSpine = id
instance NFDataX a => NFDataX (Seq a) where
deepErrorX = errorX
rnfX s =
if isLeft (isX s) then () else go s
where
go Empty = ()
go (x :<| xs) = rnfX x `seq` go xs
ensureSpine = id
hasUndefined s =
if isLeft (isX s) then True else go s
where
go Empty = False
go (x :<| xs) = hasUndefined x || hasUndefined xs
instance NFDataX a => NFDataX (Ratio a) where
deepErrorX = errorX
rnfX r = rnfX (numerator r) `seq` rnfX (denominator r)
hasUndefined r = isLeft (isX (numerator r)) || isLeft (isX (denominator r))
ensureSpine = id
instance NFDataX a => NFDataX (Complex a) where
deepErrorX = errorX
instance (NFDataX a, NFDataX b) => NFDataX (SG.Arg a b)
instance NFDataX (SG.All)
instance NFDataX (SG.Any)
instance NFDataX a => NFDataX (SG.Dual a)
instance NFDataX a => NFDataX (SG.Endo a)
instance NFDataX a => NFDataX (SG.First a)
instance NFDataX a => NFDataX (SG.Last a)
instance NFDataX a => NFDataX (SG.Max a)
instance NFDataX a => NFDataX (SG.Min a)
instance NFDataX a => NFDataX (SG.Product a)
instance NFDataX a => NFDataX (SG.Sum a)
instance NFDataX a => NFDataX (M.First a)
instance NFDataX a => NFDataX (M.Last a)
-- Sg.Option will be removed in 9.2. We can't locally disable deprecation
-- warnings (i.e., for this instance only) so we're prematurely removing it
-- instead.
#if __GLASGOW_HASKELL__ < 900
instance NFDataX a => NFDataX (SG.Option a)
#endif
-- | __N.B.__: The documentation only shows instances up to /3/-tuples. By
-- default, instances up to and including /12/-tuples will exist. If the flag
-- @large-tuples@ is set instances up to the GHC imposed limit will exist. The
-- GHC imposed limit is either 62 or 64 depending on the GHC version.
mkShowXTupleInstances [2..maxTupleSize]
-- | __N.B.__: The documentation only shows instances up to /3/-tuples. By
-- default, instances up to and including /12/-tuples will exist. If the flag
-- @large-tuples@ is set instances up to the GHC imposed limit will exist. The
-- GHC imposed limit is either 62 or 64 depending on the GHC version.
mkNFDataXTupleInstances [2..maxTupleSize]
-- | Call to 'errorX' with default string
undefined :: HasCallStack => a
undefined = errorX "undefined"
-- | Same as 'Data.Maybe.fromJust', but returns a bottom/undefined value that
-- other Clash constructs are aware of.
fromJustX :: HasCallStack => Maybe a -> a
fromJustX Nothing = errorX "isJustX: Nothing"
fromJustX (Just a) = a