# Documentation

Mathlib.Util.AtomM

# A monad for tracking and deduplicating atoms #

This monad is used by tactics like ring and abel to keep uninterpreted atoms in a consistent order, and also to allow unifying atoms up to a specified transparency mode.

• The reducibility setting for definitional equality of atoms

• A simplification to apply to atomic expressions when they are encountered, before interning them in the atom list.

evalAtom :

The context (read-only state) of the AtomM monad.

Instances For
Equations
• The list of atoms-up-to-defeq encountered thus far, used for atom sorting.

atoms :

The mutable state of the AtomM monad.

Instances For
@[inline]

The monad that ring works in. This is only used for collecting atoms.

Equations
def Mathlib.Tactic.AtomM.run {α : Type} (red : Lean.Meta.TransparencyMode) (m : ) (evalAtom : optParam () fun e => pure { expr := e, proof? := none, dischargeDepth := 0 }) :

Run a computation in the AtomM monad.

Equations

Get the index corresponding to an atomic expression, if it has already been encountered, or put it in the list of atoms and return the new index, otherwise.

Equations
• One or more equations did not get rendered due to their size.