Subject: Re: [bitcoin-dev] A Method for Computing Merkle Roots of Annotated Binary Trees

From: "Russell O'Connor" <[email-masked]>
Date: Sat, 27 May 2017 18:07:07 -0400

On May 28, 2017 06:09, "Russell O'Connor" <[email-masked]> wrote:

On May 28, 2017 03:16, "Peter Todd" <[email-masked]> wrote:

On Mon, May 22, 2017 at 06:32:38PM -0400, Russell O'Connor wrote:
> On May 22, 2017 23:05, "Peter Todd" <[email-masked]> wrote:
>
> On Mon, May 22, 2017 at 03:05:49AM -0400, Russell O'Connor via bitcoin-dev
> wrote:
> >     MerkleRoot := SHA256(SHA256(LeftRoot ⋅ RightRoot))
> >     sha256Compress : Word256 × Word512 -> Word256
>
> To be clear, what math operations do you mean by "⋅" and "×"?
>
>
> By "⋅", I usually mean concatenation (though I also use it for function
> composition in one instance).   By "×", I mean the Cartesian product.

Cartesian product can mean a lot of things.

What specifically do you mean by "cartesian product" here?

Oops, I forgot to reply all.  Below is my reply.

Given two types A and B, then A × B is the type of pairs of A and B in the
sense of type theory as used in Standard ML or Haskell or other typed
languages.

To follow up, by "sha256Compress : Word256 × Word512 -> Word256" I mean
that sha256Compress is a function that takes two arguments, the first being
a 256 bit word and the second being a 512 bit word, and returns a 256 bit
word (or equivalently sha256Compress is a function that takes a pair as
input, the first component being a 256 bit word and the second component
being a 512 bit word, and returns a 256 bit word).

sha256Compress is meant to be the compression function defined by the
SHA256 standard, though nothing here depends on anything more that its type
signature.