Codec

Not every value of A can be encoded to a bit vector and similarly, not every bit vector can be decoded to a value
of type A. Hence, both encode and decode return either an error or the result. Furthermore, decode returns the
remaining bits in the bit vector that it did not use in decoding.

There are various ways to create instances of Codec. The trait can be implemented directly or one of the
constructor methods in the companion can be used (e.g., apply). Most of the methods on Codec
create return a new codec that has been transformed in some way. For example, the xmap method
converts a Codec[A] to a Codec[B] given two functions, A => B and B => A.

One of the simplest transformation methods is def withContext(context: String): Codec[A], which
pushes the specified context string in to any errors (i.e., Errs) returned from encode or decode.

See the methods on this trait for additional transformation types.

See the codecs package object for pre-defined codecs for many common data types and combinators for building larger
codecs out of smaller ones.

== Tuple Codecs ==

The :: operator supports combining a Codec[A] and a Codec[B] in to a Codec[(A, B)].

For example:
{{{
val codec: Codec[(Int, Int, Int)] = uint8 :: uint8 :: uint8
}}}
}}}

There are various methods on Codec that only work on Codec[A] for some A <: Tuple. Besides the aforementioned
:: method, they include methods like ++, flatPrepend, flatConcat, etc. One particularly useful method is
dropUnits, which removes any Unit values from the tuple.

Given a Codec[(X0, X1, ..., Xn)] and a case class with types X0 to Xn in the same order,
the codec can be turned in to a case class codec via the as method. For example:
{{{
case class Point(x: Int, y: Int, z: Int)
val threeInts: Codec[(Int, Int, Int)] = uint8 :: uint8 :: uint8
val point: Codec[Point] = threeInts.as[Point]
}}}

=== flatZip ===

Sometimes when combining codecs, a latter codec depends on a formerly decoded value.
The flatZip method is important in these types of situations -- it represents a dependency between
the left hand side and right hand side. Its signature is def flatZip[B](f: A => Codec[B]): Codec[(A, B)].
This is similar to flatMap except the return type is Codec[(A, B)] instead of Decoder[B].

Consider a binary format of an 8-bit unsigned integer indicating the number of bytes following it.
To implement this with flatZip, we could write:
{{{
val x: Codec[(Int, ByteVector)] = uint8.flatZip { numBytes => bytes(numBytes) }
val y: Codec[ByteVector] = x.xmap[ByteVector] ({ case (_, bv) => bv }, bv => (bv.size, bv))
}}}
In this example, x is a Codec[(Int, ByteVector)] but we do not need the size directly in the model
because it is redundant with the size stored in the ByteVector. Hence, we remove the Int by
xmap-ping over x. The notion of removing redundant data from models comes up frequently.
Note: there is a combinator that expresses this pattern more succinctly -- variableSizeBytes(uint8, bytes).

=== flatPrepend ===

When the function passed to flatZip returns a Codec[B] where B <: Tuple, you end up creating
right nested tuples instead of a extending the arity of a single tuple. To do the latter, there's
flatPrepend. It has the signature:
{{{
def flatPrepend[B <: Tuple] (f: A => Codec[B] ): Codec[A *: B]
}}}
It forms a codec of A consed on to B when called on a Codec[A] and passed a function A => Codec[B].
Note that the specified function must return a tuple codec. Implementing our example from earlier
using flatPrepend:
{{{
val x: Codec[(Int, ByteVector)] = uint8.flatPrepend { numBytes => bytes(numBytes).tuple }
}}}
In this example, bytes(numBytes) returns a Codec[ByteVector] so we called .tuple on it to lift it
in to a Codec[ByteVector *: Unit].

There are similar methods for flat appending and flat concating.

== Derived Codecs ==

Codecs for case classes and sealed class hierarchies can often be automatically derived.

Consider this example:
{{{
case class Point(x: Int, y: Int, z: Int) derives Codec
Codec[Point] .encode(Point(1, 2, 3))
}}}
In this example, no explicit codec was defined for Point and instead, an implicit one was derived as a result
of the derives Codec clause. Derivation of a codec for a case class requires each element of the case class to
have an implicitly available codec of the corresponding type. In this case, each element was an Int and there is
an implicit Codec[Int] in the companion of Codec.

Derived codecs include the name of each element in any errors produced when encoding/decoding the element.

This works similarly for ADTs / sealed class hierarchies. The binary form is represented as a single
unsigned 8-bit integer representing the ordinal of the sum, followed by the derived form of the product.

Full examples are available in the test directory of this project.