I was surprised that Bit3 (and later) has no Num instance.
Easiest way is to go via Bits, as in
instance Num Bit3 where
fromInteger = fromBits . fromInteger
x + y = fromBits $ bits x + bits y
negate (Bit3 x2 x1 x0) = Bit3 (not x2) (not x1) (not x0) + 1
x * y = fromBits $ bits x * bits y
Implementation: this just throws away higher-order bits (that is, half of the work in multiplication), I hope that's still fine by lazy evaluation.
Semantics: this is inconsistent with type Decoded Bits3 = Word8 (the decoded type is mod 2^8 while the encoded type is mod 2^3) but this already happens for Bit1, Bit2.
I was surprised that
Bit3(and later) has no Num instance.Easiest way is to go via
Bits, as inImplementation: this just throws away higher-order bits (that is, half of the work in multiplication), I hope that's still fine by lazy evaluation.
Semantics: this is inconsistent with
type Decoded Bits3 = Word8(the decoded type is mod 2^8 while the encoded type is mod 2^3) but this already happens for Bit1, Bit2.