Type

Base Type

Arch comes equipped with some set \(\mathcal{A}\) of base types, with no primitive operations on them at all. This is accomplished simply by including the elements of \(\mathcal{A}\) (ranged over by the metavariable \(\mathcal{A}\)) in the set of types:

\[ \mathcal{A} \in \texttt{Type} \]

This means that any element of \(\mathcal{A}\) is considered a valid type in the system by default, serving as atomic units for constructing more complex types.

Here are all the base types in Arch:

• Char- The minimal representation of any symbol

• \(\mathbb{B}\) - \(\mathtt{true}\) or \(\mathtt{false}\)

• \(\mathbb{C}\) - Complex Numbers

• \(\mathbb{R}\) - Real Numbers

  • \(\mathbb{N}\) - Natural Number

  • \(\mathbb{N}^+\) - Positive Natural Number

  • \(\mathbb{Z}\) - Integer

  • \(\mathbb{Z}^+\) - Positive Integer
  • \(\mathbb{Z}^-\) - Negative Integer

• Vector - Vectors

• Matrix - Matrices