Mathics Core Interpreter Overview

At its heart, the Mathics interpreter works over S-expressions: combinations of nested and/or sequenced lists, pretty much the same as simple Lisp interpreters work. See also Everything is an Expression.

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

• the string is parsed to FullForm

• The full form S-expression is interpreted

• The result, also an S-expression, is formatted to the kind of output desired.

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

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

• Scanning and Parsing
  • Tokeniser
  • Parser
  • Python Code for Parsing an String
• AST, S-Expression, General List: same thing
• Evaluation of an Expression
  • Function Name to Python method lookup
  • Function Name Descriptions
  • Python Code for Evaluating an Expression
• Object Classes
  • Atom Class Attributes
  • Builtin and Predefined
  • Operator
  • PrefixOperator and PostFixOperator
  • BinaryOperator and UnaryOperator
  • SympyFunction and _MPMathFunction