    -- |
    -- Module      :  $Header$
    -- Copyright   :  (c) 2013-2016 Galois, Inc.
    -- License     :  BSD3
    -- Maintainer  :  cryptol@galois.com
    -- Stability   :  provisional
    -- Portability :  portable

    {-# LANGUAGE Trustworthy #-}
    {-# LANGUAGE TupleSections #-}
    {-# LANGUAGE RecordWildCards #-}
    {-# LANGUAGE Rank2Types #-}
    {-# LANGUAGE PatternGuards #-}
    {-# LANGUAGE ViewPatterns #-}
    {-# LANGUAGE BangPatterns #-}
    module Cryptol.Prims.Eval where

    import Cryptol.TypeCheck.AST
    import Cryptol.TypeCheck.Solver.InfNat (Nat'(..),fromNat,genLog, nMul)
    import qualified Cryptol.Eval.Arch as Arch
    import Cryptol.Eval.Error
    import Cryptol.Eval.Type(evalTF)
    import Cryptol.Eval.Value
    import Cryptol.Testing.Random (randomValue)
    import Cryptol.Utils.Panic (panic)
    import Cryptol.ModuleSystem.Name (asPrim)
    import Cryptol.Utils.Ident (Ident,mkIdent)

    import Data.List (sortBy, transpose, genericTake, genericDrop,
                      genericReplicate, genericSplitAt, genericIndex)
    import Data.Ord (comparing)
    import Data.Bits (Bits(..))

    import qualified Data.Map.Strict as Map
    import qualified Data.Text as T

    import System.Random.TF.Gen (seedTFGen)

    -- Primitives ------------------------------------------------------------------

    evalPrim :: Decl -> Value
    evalPrim Decl { dName = n, .. }
      | Just prim <- asPrim n, Just val <- Map.lookup prim primTable = val

    evalPrim Decl { .. } =
        panic "Eval" [ "Unimplemented primitive", show dName ]

    primTable :: Map.Map Ident Value
    primTable = Map.fromList $ map (\(n, v) -> (mkIdent (T.pack n), v))
      [ ("+"          , binary (arithBinary (liftBinArith (+))))
      , ("-"          , binary (arithBinary (liftBinArith (-))))
      , ("*"          , binary (arithBinary (liftBinArith (*))))
      , ("/"          , binary (arithBinary (liftBinArith divWrap)))
      , ("%"          , binary (arithBinary (liftBinArith modWrap)))
      , ("^^"         , binary (arithBinary modExp))
      , ("lg2"        , unary  (arithUnary lg2))
      , ("negate"     , unary  (arithUnary negate))
      , ("<"          , binary (cmpOrder (\o -> o == LT           )))
      , (">"          , binary (cmpOrder (\o -> o == GT           )))
      , ("<="         , binary (cmpOrder (\o -> o == LT || o == EQ)))
      , (">="         , binary (cmpOrder (\o -> o == GT || o == EQ)))
      , ("=="         , binary (cmpOrder (\o ->            o == EQ)))
      , ("!="         , binary (cmpOrder (\o ->            o /= EQ)))
      , ("&&"         , binary (logicBinary (.&.)))
      , ("||"         , binary (logicBinary (.|.)))
      , ("^"          , binary (logicBinary xor))
      , ("complement" , unary  (logicUnary complement))
      , ("<<"         , logicShift shiftLW shiftLS)
      , (">>"         , logicShift shiftRW shiftRS)
      , ("<<<"        , logicShift rotateLW rotateLS)
      , (">>>"        , logicShift rotateRW rotateRS)
      , ("True"       , VBit True)
      , ("False"      , VBit False)

      , ("demote"     , ecDemoteV)

      , ("#"          , nlam $ \ front ->
                        nlam $ \ back  ->
                        tlam $ \ elty  ->
                        lam  $ \ l     ->
                        lam  $ \ r     -> ccatV front back elty l r)

      , ("@"          , indexPrimOne  indexFront)
      , ("@@"         , indexPrimMany indexFrontRange)
      , ("!"          , indexPrimOne  indexBack)
      , ("!!"         , indexPrimMany indexBackRange)

      , ("zero"       , tlam zeroV)

      , ("join"       , nlam $ \ parts ->
                        nlam $ \ each  ->
                        tlam $ \ a     -> lam (joinV parts each a))

      , ("split"      , ecSplitV)

      , ("splitAt"    , nlam $ \ front ->
                        nlam $ \ back  ->
                        tlam $ \ a     -> lam (splitAtV front back a))

      , ("fromThen"   , fromThenV)
      , ("fromTo"     , fromToV)
      , ("fromThenTo" , fromThenToV)

      , ("infFrom"    , nlam $ \(finNat'  -> bits)  ->
                         lam $ \(fromWord -> first) ->
                        toStream (map (word bits) [ first .. ]))

      , ("infFromThen", nlam $ \(finNat'  -> bits)  ->
                         lam $ \(fromWord -> first) ->
                         lam $ \(fromWord -> next)  ->
                        toStream [ word bits n | n <- [ first, next .. ] ])

      , ("error"      , tlam $ \_              ->
                        tlam $ \_              ->
                         lam $ \(fromStr -> s) -> cryUserError s)

      , ("reverse"    , nlam $ \a ->
                        tlam $ \b ->
                         lam $ \(fromSeq -> xs) -> toSeq a b (reverse xs))

      , ("transpose"  , nlam $ \a ->
                        nlam $ \b ->
                        tlam $ \c ->
                         lam $ \((map fromSeq . fromSeq) -> xs) ->
                            case a of
                               Nat 0 ->
                                 let val = toSeq a c []
                                 in case b of
                                      Nat n -> toSeq b (tvSeq a c) $ genericReplicate n val
                                      Inf   -> VStream $ repeat val
                               _ -> toSeq b (tvSeq a c) $ map (toSeq a c) $ transpose xs)

      , ("pmult"       ,
        let mul !res !_ !_ 0 = res
            mul  res bs as n = mul (if even as then res else xor res bs)
                                   (bs `shiftL` 1) (as `shiftR` 1) (n-1)
         in nlam $ \(finNat'  -> a) ->
            nlam $ \(finNat'  -> b) ->
             lam $ \(fromWord -> x) ->
             lam $ \(fromWord -> y) -> word (max 1 (a + b) - 1) (mul 0 x y b))

      , ("pdiv"        , nlam $ \(fromInteger . finNat' -> a) ->
                         nlam $ \(fromInteger . finNat' -> b) ->
                          lam $ \(fromWord  -> x) ->
                          lam $ \(fromWord  -> y) -> word (toInteger a)
                                                          (fst (divModPoly x a y b)))

      , ("pmod"        , nlam $ \(fromInteger . finNat' -> a) ->
                         nlam $ \(fromInteger . finNat' -> b) ->
                          lam $ \(fromWord  -> x) ->
                          lam $ \(fromWord  -> y) -> word (toInteger b)
                                                          (snd (divModPoly x a y (b+1))))
      , ("random"      , tlam $ \a ->
                          lam $ \(fromWord -> x) -> randomV a x)
      ]

    -- | Make a numeric constant.
    ecDemoteV :: Value
    ecDemoteV = nlam $ \valT ->
                nlam $ \bitT ->
                case (valT, bitT) of
                  (Nat v, Nat bs) -> VWord (mkBv bs v)
                  _ -> evalPanic "Cryptol.Eval.Prim.evalConst"
                           ["Unexpected Inf in constant."
                           , show valT
                           , show bitT
                           ]

    --------------------------------------------------------------------------------
    divModPoly :: Integer -> Int -> Integer -> Int -> (Integer, Integer)
    divModPoly xs xsLen ys ysLen
      | ys == 0   = divideByZero
      | otherwise = go 0 initR (xsLen - degree) todoBits

      where
      downIxes n  = [ n - 1, n - 2 .. 0 ]

      degree      = head [ n | n <- downIxes ysLen, testBit ys n ]

      initR       = xs `shiftR` (xsLen - degree)
      nextR r b   = (r `shiftL` 1) .|. (if b then 1 else 0)

      go !res !r !bitN todo =
         let x = xor r ys
             (res',r') | testBit x degree = (res,             r)
                       | otherwise        = (setBit res bitN, x)
         in case todo of
              b : bs -> go res' (nextR r' b) (bitN-1) bs
              []     -> (res',r')

      todoBits  = map (testBit xs) (downIxes (xsLen - degree))

    -- | Create a packed word
    modExp :: Integer -- ^ bit size of the resulting word
           -> Integer -- ^ base
           -> Integer -- ^ exponent
           -> Integer
    modExp bits base e
      | bits == 0            = 0
      | base < 0 || bits < 0 = evalPanic "modExp"
                                 [ "bad args: "
                                 , "  base = " ++ show base
                                 , "  e    = " ++ show e
                                 , "  bits = " ++ show modulus
                                 ]
      | otherwise            = doubleAndAdd base e modulus
      where
      modulus = 0 `setBit` fromInteger bits

    doubleAndAdd :: Integer -- ^ base
                 -> Integer -- ^ exponent mask
                 -> Integer -- ^ modulus
                 -> Integer
    doubleAndAdd base0 expMask modulus = go 1 base0 expMask
      where
      go acc base k
        | k > 0     = acc' `seq` base' `seq` go acc' base' (k `shiftR` 1)
        | otherwise = acc
        where
        acc' | k `testBit` 0 = acc `modMul` base
             | otherwise     = acc

        base' = base `modMul` base

        modMul x y = (x * y) `mod` modulus

    -- Operation Lifting -----------------------------------------------------------

    type GenBinary b w = TValue -> GenValue b w -> GenValue b w -> GenValue b w
    type Binary = GenBinary Bool BV

    binary :: GenBinary b w -> GenValue b w
    binary f = tlam $ \ ty ->
                lam $ \ a  ->
                lam $ \ b  -> f ty a b

    type GenUnary b w = TValue -> GenValue b w -> GenValue b w
    type Unary = GenUnary Bool BV

    unary :: GenUnary b w -> GenValue b w
    unary f = tlam $ \ ty ->
               lam $ \ a  -> f ty a

    -- Arith -----------------------------------------------------------------------

    -- | Turn a normal binop on Integers into one that can also deal with a bitsize.
    liftBinArith :: (Integer -> Integer -> Integer) -> BinArith
    liftBinArith op _ = op

    type BinArith = Integer -> Integer -> Integer -> Integer

    arithBinary :: BinArith -> Binary
    arithBinary op = loop
      where
      loop ty l r = case ty of

        -- words and finite sequences
        TVSeq w a
          | isTBit a  -> VWord (mkBv w (op w (fromWord l) (fromWord r)))
          | otherwise -> VSeq False (zipWith (loop a) (fromSeq l) (fromSeq r))

        -- streams
        TVStream a -> toStream (zipWith (loop a) (fromSeq l) (fromSeq r))

        -- functions
        TVFun _ ety ->
          lam $ \ x -> loop ety (fromVFun l x) (fromVFun r x)

        -- tuples
        TVTuple tys ->
          let ls = fromVTuple l
              rs = fromVTuple r
           in VTuple (zipWith3 loop tys ls rs)

        -- records
        TVRec fs ->
          VRecord [ (f, loop fty (lookupRecord f l) (lookupRecord f r))
                  | (f,fty) <- fs ]

        _ -> evalPanic "arithBinop" ["Invalid arguments"]

    arithUnary :: (Integer -> Integer) -> Unary
    arithUnary op = loop
      where
      loop ty x = case ty of

        -- words and finite sequences
        TVSeq w a
          | isTBit a  -> VWord (mkBv w (op (fromWord x)))
          | otherwise -> VSeq False (map (loop a) (fromSeq x))

        -- infinite sequences
        TVStream a -> toStream (map (loop a) (fromSeq x))

        -- functions
        TVFun _ ety ->
          lam $ \ y -> loop ety (fromVFun x y)

        -- tuples
        TVTuple tys ->
          let as = fromVTuple x
           in VTuple (zipWith loop tys as)

        -- records
        TVRec fs ->
          VRecord [ (f, loop fty (lookupRecord f x)) | (f,fty) <- fs ]

        _ -> evalPanic "arithUnary" ["Invalid arguments"]

    lg2 :: Integer -> Integer
    lg2 i = case genLog i 2 of
      Just (i',isExact) | isExact   -> i'
                        | otherwise -> i' + 1
      Nothing                       -> 0

    divWrap :: Integral a => a -> a -> a
    divWrap _ 0 = divideByZero
    divWrap x y = x `div` y

    modWrap :: Integral a => a -> a -> a
    modWrap _ 0 = divideByZero
    modWrap x y = x `mod` y

    -- Cmp -------------------------------------------------------------------------

    -- | Lexicographic ordering on two values.
    lexCompare :: TValue -> Value -> Value -> Ordering
    lexCompare ty l r =
      case ty of
        TVBit         -> compare (fromVBit l) (fromVBit r)
        TVSeq _ TVBit -> compare (fromWord l) (fromWord r)
        TVSeq _ e     -> zipLexCompare (repeat e) (fromSeq l) (fromSeq r)
        TVTuple etys  -> zipLexCompare etys (fromVTuple l) (fromVTuple r)
        TVRec fields  ->
          let tys    = map snd (sortBy (comparing fst) fields)
              ls     = map snd (sortBy (comparing fst) (fromVRecord l))
              rs     = map snd (sortBy (comparing fst) (fromVRecord r))
           in zipLexCompare tys ls rs
        _ -> evalPanic "lexCompare" ["invalid type"]

    -- XXX the lists are expected to be of the same length, as this should only be
    -- used with values that come from type-correct expressions.
    zipLexCompare :: [TValue] -> [Value] -> [Value] -> Ordering
    zipLexCompare tys ls rs = foldr choose EQ (zipWith3 lexCompare tys ls rs)
      where
      choose c acc = case c of
        EQ -> acc
        _  -> c

    -- | Process two elements based on their lexicographic ordering.
    cmpOrder :: (Ordering -> Bool) -> Binary
    cmpOrder op ty l r = VBit (op (lexCompare ty l r))

    withOrder :: (Ordering -> TValue -> Value -> Value -> Value) -> Binary
    withOrder choose ty l r = choose (lexCompare ty l r) ty l r

    maxV :: Ordering -> TValue -> Value -> Value -> Value
    maxV o _ l r = case o of
      LT -> r
      _  -> l

    minV :: Ordering -> TValue -> Value -> Value -> Value
    minV o _ l r = case o of
      GT -> r
      _  -> l

    funCmp :: (Ordering -> Bool) -> Value
    funCmp op =
      tlam $ \ _a ->
      tlam $ \  b ->
       lam $ \  l ->
       lam $ \  r ->
       lam $ \  x -> cmpOrder op b (fromVFun l x) (fromVFun r x)

    -- Logic -----------------------------------------------------------------------

    zeroV :: TValue -> Value
    zeroV ty = case ty of

      -- bits
      TVBit ->
        VBit False

      -- finite sequences
      TVSeq w ety
        | isTBit ety -> word w 0
        | otherwise  -> toFinSeq ety (replicate (fromInteger w) (zeroV ety))

      -- infinite sequences
      TVStream ety -> toStream (repeat (zeroV ety))

      -- functions
      TVFun _ bty ->
        lam (\ _ -> zeroV bty)

      -- tuples
      TVTuple tys ->
        VTuple (map zeroV tys)

      -- records
      TVRec fields ->
        VRecord [ (f,zeroV fty) | (f,fty) <- fields ]

    -- | Join a sequence of sequences into a single sequence.
    joinV :: Nat' -> Nat' -> TValue -> Value -> Value
    joinV parts each a val =
      let len = parts `nMul` each
      in toSeq len a (concatMap fromSeq (fromSeq val))

    splitAtV :: Nat' -> Nat' -> TValue -> Value -> Value
    splitAtV front back a val =
      case back of

        -- Remember that words are big-endian in cryptol, so the first component
        -- needs to be shifted, and the second component just needs to be masked.
        Nat rightWidth | aBit, VWord (BV _ i) <- val ->
              VTuple [ VWord (BV leftWidth (i `shiftR` fromInteger rightWidth))
                     , VWord (mkBv rightWidth i) ]

        _ ->
          let (ls,rs) = genericSplitAt leftWidth (fromSeq val)
           in VTuple [VSeq aBit ls, toSeq back a rs]

      where

      aBit = isTBit a

      leftWidth = case front of
        Nat n -> n
        _     -> evalPanic "splitAtV" ["invalid `front` len"]

    -- | Split implementation.
    ecSplitV :: Value
    ecSplitV =
      nlam $ \ parts ->
      nlam $ \ each  ->
      tlam $ \ a     ->
      lam  $ \ val ->
      let mkChunks f = map (toFinSeq a) $ f $ fromSeq val
      in case (parts, each) of
           (Nat p, Nat e) -> VSeq False $ mkChunks (finChunksOf p e)
           (Inf  , Nat e) -> toStream   $ mkChunks (infChunksOf e)
           _              -> evalPanic "splitV" ["invalid type arguments to split"]

    -- | Split into infinitely many chunks
    infChunksOf :: Integer -> [a] -> [[a]]
    infChunksOf each xs = let (as,bs) = genericSplitAt each xs
                          in as : infChunksOf each bs

    -- | Split into finitely many chunks
    finChunksOf :: Integer -> Integer -> [a] -> [[a]]
    finChunksOf 0 _ _ = []
    finChunksOf parts each xs = let (as,bs) = genericSplitAt each xs
                                in as : finChunksOf (parts - 1) each bs

    ccatV :: Nat' -> Nat' -> TValue -> Value -> Value -> Value
    ccatV _front _back (isTBit -> True) (VWord (BV i x)) (VWord (BV j y)) =
      VWord (BV (i + j) (shiftL x (fromInteger j) + y))
    ccatV front back elty l r =
      toSeq (evalTF TCAdd [front,back]) elty (fromSeq l ++ fromSeq r)

    -- | Merge two values given a binop.  This is used for and, or and xor.
    logicBinary :: (forall a. Bits a => a -> a -> a) -> Binary
    logicBinary op = loop
      where
      loop ty l r = case ty of
        TVBit -> VBit (op (fromVBit l) (fromVBit r))
        -- words or finite sequences
        TVSeq w aty
          | isTBit aty -> VWord (BV w (op (fromWord l) (fromWord r)))
                          -- We assume that bitwise ops do not need re-masking
          | otherwise -> VSeq False (zipWith (loop aty) (fromSeq l)
                                                        (fromSeq r))

        -- streams
        TVStream aty -> toStream (zipWith (loop aty) (fromSeq l) (fromSeq r))

        TVTuple etys ->
          let ls = fromVTuple l
              rs = fromVTuple r
           in VTuple (zipWith3 loop etys ls rs)

        TVFun _ bty ->
          lam $ \ a -> loop bty (fromVFun l a) (fromVFun r a)

        TVRec fields ->
          VRecord [ (f,loop fty a b) | (f,fty) <- fields
                                     , let a = lookupRecord f l
                                           b = lookupRecord f r
                                     ]

    logicUnary :: (forall a. Bits a => a -> a) -> Unary
    logicUnary op = loop
      where
      loop ty val = case ty of
        TVBit -> VBit (op (fromVBit val))

        -- words or finite sequences
        TVSeq w ety
          | isTBit ety -> VWord (mkBv w (op (fromWord val)))
          | otherwise -> VSeq False (map (loop ety) (fromSeq val))

        -- streams
        TVStream ety -> toStream (map (loop ety) (fromSeq val))

        TVTuple etys ->
          let as = fromVTuple val
           in VTuple (zipWith loop etys as)

        TVFun _ bty ->
          lam $ \ a -> loop bty (fromVFun val a)

        TVRec fields ->
          VRecord [ (f,loop fty a) | (f,fty) <- fields, let a = lookupRecord f val ]

    logicShift :: (Integer -> Integer -> Integer -> Integer)
                  -- ^ The function may assume its arguments are masked.
                  -- It is responsible for masking its result if needed.
               -> (Nat' -> TValue -> [Value] -> Integer -> [Value])
               -> Value
    logicShift opW opS
      = nlam $ \ a ->
        tlam $ \ _ ->
        tlam $ \ c ->
         lam  $ \ l ->
         lam  $ \ r ->
            if isTBit c
              then -- words
                let BV w i  = fromVWord l
                in VWord (BV w (opW w i (fromWord r)))

              else toSeq a c (opS a c (fromSeq l) (fromWord r))

    -- Left shift for words.
    shiftLW :: Integer -> Integer -> Integer -> Integer
    shiftLW w ival by
      | by >= w   = 0
      | otherwise = mask w (shiftL ival (fromInteger by))

    shiftLS :: Nat' -> TValue -> [Value] -> Integer -> [Value]
    shiftLS w ety vs by =
      case w of
        Nat len
          | by < len  -> genericTake len (genericDrop by vs ++ repeat (zeroV ety))
          | otherwise -> genericReplicate len (zeroV ety)
        Inf           -> genericDrop by vs

    shiftRW :: Integer -> Integer -> Integer -> Integer
    shiftRW w i by
      | by >= w   = 0
      | otherwise = shiftR i (fromInteger by)

    shiftRS :: Nat' -> TValue -> [Value] -> Integer -> [Value]
    shiftRS w ety vs by =
      case w of
        Nat len
          | by < len  -> genericTake len (genericReplicate by (zeroV ety) ++ vs)
          | otherwise -> genericReplicate len (zeroV ety)
        Inf           -> genericReplicate by (zeroV ety) ++ vs

    -- XXX integer doesn't implement rotateL, as there's no bit bound
    rotateLW :: Integer -> Integer -> Integer -> Integer
    rotateLW 0 i _  = i
    rotateLW w i by = mask w $ (i `shiftL` b) .|. (i `shiftR` (fromInteger w - b))
      where b = fromInteger (by `mod` w)

    rotateLS :: Nat' -> TValue -> [Value] -> Integer -> [Value]
    rotateLS w _ vs at =
      case w of
        Nat len -> let at'     = at `mod` len
                       (ls,rs) = genericSplitAt at' vs
                    in rs ++ ls
        _ -> panic "Cryptol.Eval.Prim.rotateLS" [ "unexpected infinite sequence" ]

    -- XXX integer doesn't implement rotateR, as there's no bit bound
    rotateRW :: Integer -> Integer -> Integer -> Integer
    rotateRW 0 i _  = i
    rotateRW w i by = mask w $ (i `shiftR` b) .|. (i `shiftL` (fromInteger w - b))
      where b = fromInteger (by `mod` w)

    rotateRS :: Nat' -> TValue -> [Value] -> Integer -> [Value]
    rotateRS w _ vs at =
      case w of
        Nat len -> let at'     = at `mod` len
                       (ls,rs) = genericSplitAt (len - at') vs
                    in rs ++ ls
        _ -> panic "Cryptol.Eval.Prim.rotateRS" [ "unexpected infinite sequence" ]

    -- Sequence Primitives ---------------------------------------------------------

    -- | Indexing operations that return one element.
    indexPrimOne :: (Maybe Integer -> [Value] -> Integer -> Value) -> Value
    indexPrimOne op =
      nlam $ \ n  ->
      tlam $ \ _a ->
      nlam $ \ _i ->
       lam $ \ l  ->
       lam $ \ r  ->
         let vs  = fromSeq l
             ix  = fromWord r
          in op (fromNat n) vs ix

    indexFront :: Maybe Integer -> [Value] -> Integer -> Value
    indexFront mblen vs ix =
      case mblen of
        Just len | len <= ix -> invalidIndex ix
        _                    -> genericIndex vs ix

    indexBack :: Maybe Integer -> [Value] -> Integer -> Value
    indexBack mblen vs ix =
      case mblen of
        Just len | len > ix  -> genericIndex vs (len - ix - 1)
                 | otherwise -> invalidIndex ix
        Nothing              -> evalPanic "indexBack"
                                ["unexpected infinite sequence"]

    -- | Indexing operations that return many elements.
    indexPrimMany :: (Maybe Integer -> [Value] -> [Integer] -> [Value]) -> Value
    indexPrimMany op =
      nlam $ \ n  ->
      tlam $ \ a  ->
      nlam $ \ m  ->
      tlam $ \ _i ->
       lam $ \ l  ->
       lam $ \ r  ->
         let vs    = fromSeq l
             ixs   = map fromWord (fromSeq r)
         in toSeq m a (op (fromNat (n)) vs ixs)

    indexFrontRange :: Maybe Integer -> [Value] -> [Integer] -> [Value]
    indexFrontRange mblen vs = map (indexFront mblen vs)

    indexBackRange :: Maybe Integer -> [Value] -> [Integer] -> [Value]
    indexBackRange mblen vs = map (indexBack mblen vs)

    -- @[ 0, 1 .. ]@
    fromThenV :: Value
    fromThenV  =
      nlam $ \ first ->
      nlam $ \ next  ->
      nlam $ \ bits  ->
      nlam $ \ len   ->
        case (first, next, len, bits) of
          (_         , _        , _       , Nat bits')
            | bits' >= Arch.maxBigIntWidth -> wordTooWide bits'
          (Nat first', Nat next', Nat len', Nat bits') ->
            let nums = enumFromThen first' next'
             in VSeq False (genericTake len' (map (VWord . BV bits') nums))
          _ -> evalPanic "fromThenV" ["invalid arguments"]

    -- @[ 0 .. 10 ]@
    fromToV :: Value
    fromToV  =
      nlam $ \ first ->
      nlam $ \ lst   ->
      nlam $ \ bits  ->
        case (first, lst, bits) of
          (_         , _       , Nat bits')
            | bits' >= Arch.maxBigIntWidth -> wordTooWide bits'
          (Nat first', Nat lst', Nat bits') ->
            let nums = enumFromThenTo first' (first' + 1) lst'
                len  = 1 + (lst' - first')
             in VSeq False (genericTake len (map (VWord . BV bits') nums))

          _ -> evalPanic "fromThenV" ["invalid arguments"]

    -- @[ 0, 1 .. 10 ]@
    fromThenToV :: Value
    fromThenToV  =
      nlam $ \ first ->
      nlam $ \ next  ->
      nlam $ \ lst   ->
      nlam $ \ bits  ->
      nlam $ \ len   ->
        case (first, next, lst, len, bits) of
          (_         , _        , _       , _       , Nat bits')
            | bits' >= Arch.maxBigIntWidth -> wordTooWide bits'
          (Nat first', Nat next', Nat lst', Nat len', Nat bits') ->
            let nums = enumFromThenTo first' next' lst'
             in VSeq False (genericTake len' (map (VWord . BV bits') nums))

          _ -> evalPanic "fromThenV" ["invalid arguments"]

    -- Random Values ---------------------------------------------------------------

    -- | Produce a random value with the given seed. If we do not support
    -- making values of the given type, return zero of that type.
    -- TODO: do better than returning zero
    randomV :: TValue -> Integer -> Value
    randomV ty seed =
      case randomValue (tValTy ty) of
        Nothing -> zeroV ty
        Just gen ->
          -- unpack the seed into four Word64s
          let mask64 = 0xFFFFFFFFFFFFFFFF
              unpack s = fromIntegral (s .&. mask64) : unpack (s `shiftR` 64)
              [a, b, c, d] = take 4 (unpack seed)
          in fst $ gen 100 $ seedTFGen (a, b, c, d)