The Lean Language Reference

The Lean Language Reference

Table of Contents

1.	Introduction
2.	Elaboration and Compilation
3.	Interacting with Lean
4.	The Type System
5.	Source Files and Modules
6.	Namespaces and Sections
7.	Definitions
8.	Axioms
9.	Attributes
10.	Terms
11.	Type Classes
12.	Coercions
13.	Tactic Proofs
14.	Functors, Monads and `do`-Notation
15.	IO
16.	The Simplifier
17.	The `grind` tactic
18.	Basic Propositions
19.	Basic Types
20.	Dynamic Typing
21.	Standard Library
22.	Notations and Macros
23.	Run-Time Code
24.	Build Tools and Distribution
	Release Notes
	Index
	Progress

17. The grind tactic

17.1.	Quick Start
17.2.	What is `grind`?
17.3.	What `grind` is not.
17.4.	Congruence Closure
17.5.	Debugging tip
17.6.	Constraint Propagation
17.7.	Case Analysis
17.8.	E‑matching
17.9.	Linear Integer Arithmetic Solver
17.10.	Algebraic Solver (Commutative Rings, Fields)
17.11.	Normalizer / Pre‑processor
17.12.	Diagnostics
17.13.	Troubleshooting & FAQ
17.14.	Bigger Examples

17.10. Algebraic Solver (Commutative Rings, Fields)

Source Code
Report Issues

←17.9. Linear Integer Arithmetic Solver 17.11. Normalizer / Pre‑processor→

17.10. Algebraic Solver (Commutative Rings, Fields)

TBD Grobner‑style basis construction, class parameters (IsCharP, NoNatZeroDivisors), step budget algSteps.

←17.9. Linear Integer Arithmetic Solver 17.11. Normalizer / Pre‑processor→