Mental MathRules and recipes

How to describe an abacus technique as an expression, and how to compose those expressions into an exercise generator that produces real practice material.

Start writing rules

Recipe cookbook

Language reference

Guide

A ground-up introduction to the rule expression language — variables, operators, decimal places, quantifiers — written for authors, not engineers. Start here if you have never written a rule.

Read the guide

Reference

Exact semantics for every context variable and built-in function, the grammar and precedence rules, and the full catalog of canonical rules with the expression behind each one.

Browse the reference

Recipes

How a recipe turns a set of rules into generated exercises — usage categories, count quotas, sum range, place restriction, and multi-place combo steps.

Build a recipe

What this site covers

A rule is one expression that decides whether a candidate value is allowed at a step:

current_value > 0 AND formula = 8 AND digitBefore IN (0, 1)

A recipe collects rules, assigns each one a job (target, review, filler, forbidden, constraint), and bounds the exercise — producing a concrete sequence like +8 +30 −7 +4 = 35.

If you are configuring training material, you will spend your time in the guide and the recipe cookbook. If you are verifying that an expression means exactly what you think it means, go to the reference.

Where to start

You want to…	Go to
Understand what a rule is at all	What is a rule?
Write your first expression	Your first rule
Understand `formula` and `digitBefore`	Decimal places
Look up exact semantics of a variable	Context variables
Find the expression behind a known technique	Canonical rules
Build a recipe that generates exercises	Recipe concepts
Train two-digit numbers like `+47`	Multi-place combo steps
Work out why a recipe generates nothing	Troubleshooting

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