E-graph representing terms of language l.

Intuitively, an e-graph is a set of equivalence classes (e-classes). Each e-class is a set of e-nodes representing equivalent terms from a given language, and an e-node is a function symbol paired with a list of children e-classes.

The empty e-graph. Nothing is represented in it yet.

Represent an expression (in it's fixed point form) in an e-graph. Returns the updated e-graph and the id from the e-class in which it was represented.

Add an e-node to the e-graph

If the e-node is already represented in this e-graph, the class-id of the class it's already represented in will be returned.

Merge 2 e-classes by id

The rebuild operation processes the e-graph's current worklist, restoring the invariants of deduplication and congruence. Rebuilding is similar to other approaches in how it restores congruence; but it uniquely allows the client to choose when to restore invariants in the context of a larger algorithm like equality saturation.

Find the canonical representation of an e-class id in the e-graph Invariant: The e-class id always exists.

Canonicalize an e-node

Two e-nodes are equal when their canonical form is equal. Canonicalization makes the list of e-class ids the e-node holds a list of canonical ids. Meaning two seemingly different e-nodes might be equal when we figure out that their e-class ids are represented by the same e-class canonical ids

canonicalize(𝑓(𝑎,𝑏,𝑐,...)) = 𝑓((find 𝑎), (find 𝑏), (find 𝑐),...)