[WIP] On IValue to IAction dispatch

[greymistcube]

Definitions

Let $\mathbb{N}$ be the set of all block indices, $\mathbb{S}$ be the set of all IValues, and $\mathbb{T}$ be the set of all types, including null for the undefined type. Furthermore, we define $X_{\mathbb{T}}$ to be the set of all instances of types in $\mathbb{T}$.

Maps

We define TypeLoad function to be a map

$$ \Sigma: \mathbb{N} \times \mathbb{S} \to \mathbb{T}. $$

We can define Instantiate function to be a map

$$ \Phi: \mathbb{N} \times \mathbb{S} \to X_\mathbb{T}. $$

We also define Bencoding function to be a map

$$ \Gamma: X_{\mathbb{T}} \to \mathbb{S}. $$

Then we want the following properties:

• $\Sigma(i, s) = t \implies \Phi(i, s) = x_{t}$
  • If $(i, s)$ type-loads to some type $t$, its instantiated object must be
    of type $t$.
• $\Phi(i, s) = x_{t} \implies \Gamma(x_{t}) = s$
  • If one can instantiate an IValue with index $i$ to some instance $x_{t}$
    of type $t$, then its bencoded IValue must be $s$.
• $\Gamma(x_{t}) = s \implies \Phi(i, s) = x_{t}$ for some $i \in \mathbb{N}$
  • If the bencoded IValue for some instance $x_{t}$ is $s$, then there
    is some index $i$ where $(i, s)$ can be instantiated to $x_{t}$.

Preliminary Analysis

Although the maps $\Sigma, \Phi$, and $\Gamma$ may be arbitrary, what we really want is $\Sigma$ to schematically map to $\mathbb{T}$.

For example, we can have

• If $s$ is an Integer, map to type $t_{1}$, and if $s$ is a Text, map to type $t_{2}$.

However, it is lot more practical to have type $t$ itself have the information required so that TypeLoad function is intuitively defined.

Hence, we further require $\mathbb{T}$ to have the following property:

• $\mathbb{T}$ has a well-defined id map $e: \mathbb{T} \to \mathbb{S}$ that is injective. That is, $t_{i} \neq t_{j} \implies e(t_{i}) \neq e(t_{j})$.

To make use of this, we also need to require every IValue $s \in \mathbb{S}$ to have include $e(t)$ schematically. This is currently semi-enforced by the usage of type_id field in the codebase¹.

So we also require $\mathbb{S}$ to have the following property:

• $\mathbb{S}$ has a well-defined id map $\tilde{e}: \mathbb{S} \to \mathbb{S}$ where $\Gamma(x_{t}) = s \implies e(t) = \tilde{e}(s)$.
  • If the bencoded representation of $x_{t}$ is $s$, then id of type $t$ and id of IValue $s$ should be equal.

Footnotes

1. This forces $s$ to be a Dictionary with a type_id field. Sadly, for backward compatibility, this must be supported going onwards. ↩