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.

• Session
  • Definitions
  • session.evaluate() at a High Level
  • Expression.format()
• Scanning
• Parsing
  • Parsing Overview
    • Precedence-Climbing Parser
  • Precedence-Climbing Parser
    • Introduction
    • Precedence Climbing
    • Mathics3 implementation
    • Recursive descent parsers in Python
    • References
  • Python Code for Scanning and Parsing a String
• AST, M-Expression, General List: same thing
• Evaluation of an Expression
  • Evaluation Overview
  • Evaluation can leave an Expression Seemingly Unchanged
  • Broad Description of the Rewrite/Apply/Eval Process
  • Detailed Rewrite/Apply/Eval Process
    • Gather information from Head and gather its elements
    • Build a new Expression
    • Compute evaluation timestamp
    • Setup Thread rewrite Listable Functions
    • Search for a Rule in Head to apply
    • Apply Rule or restore Expression
  • Mathics3 Function Application
  • Built-in Function Name Descriptions
  • Python Code for Evaluating an Expression
• Pattern Matching in Evaluation
  • Pattern Classes
• Forms, Boxes, and Formats
  • Forms
  • The Box Model
  • Output Formats
• Python Modules in Mathics-Core
  • mathics.builtin
  • mathics.core
    • mathics.core.builtin
    • mathics.core.convert
  • mathics.core.compile
  • mathics.core.eval
    • mathics.core.parser
  • mathics.doc
  • mathics.format
• Object Classes
  • Class Diagram for Some of the Classes
  • Mathics3 Core Classes
    • Atom Class
    • BaseElement Class
    • Definition Class
    • Definitions Class
    • Expression Class
    • Symbol Class
  • Classes for Defining Builtin Functions
    • Builtin class
    • Predefined Class
    • Test Class
    • Operator
    • PrefixOperator and PostFixOperator
    • BinaryOperator and UnaryOperator
    • SympyConstant, MPMathConstant, and NumpyConstant
    • SympyFunction and MPMathFunction
    • Which class should be used for a Mathics3 Object?
• Glossary