- Every AXIOM expression has a unique and precise type
- AXIOM has an inference mechanism to help the user
in the desk-calculator mode
- This mechanism uses coercions between types.
- A given mathematical object may have several implementations in AXIOM
which one with is different type (for instance multivariate
polynomials can be viewed recursively univariate or distributed).
- Types control internal representations and available methods.
- The AXIOM programming language offers types of types
which are extremely convenient for implementing algebraic structures.
- Types are organized in a hierarchical manner.
- Types of types are called categories.
Other types are called domains.
- An AXIOM function can return a type (or admit a type
among its arguments). Such a function is called a constructor.
Marc Moreno Maza
2008-01-07