Mathics3 Core Interpreter Overview

At its heart, the Mathics3 interpreter works over a generalization of an S-expression, called an M-expresssion. An M-expression is a nested and/or sequenced lists, pretty much the same as simple Lisp interpreters work, except the head element can be an expression rather than just a simple function name. See also Everything is an Expression.

When you enter a string to Mathics3 there is a 3-step process:

  • the input string is parsed to FullForm

  • The FullForm M-expression is evaluated giving another M-expression

  • The result is formatted to the kind of output desired. Formatting can cause additional evaluations to occurs

This is mentioned from the user perspective in the Figure “Steps in the operation of Wolfram Language”

Each of the above steps can be involved, so we break these down below.