Data.Equality.Analysis

E-class analysis, which allows the concise expression of a program analysis over the e-graph.

An e-class analysis resembles abstract interpretation lifted to the e-graph level, attaching analysis data from a semilattice to each e-class.

The e-graph maintains and propagates this data as e-classes get merged and new e-nodes are added.

Analysis data can be used directly to modify the e-graph, to inform how or if rewrites apply their right-hand sides, or to determine the cost of terms during the extraction process.

References: https://arxiv.org/pdf/2004.03082.pdf

Documentation

class Eq (Domain l) => Analysis l where

The e-class analysis defined for a language l.

Minimal complete definition

makeA, joinA

Associated Types

type Domain l

Domain of data stored in e-class according to e-class analysis

Methods

makeA :: ENode l -> EGraph l -> Domain l

When a new e-node is added into a new, singleton e-class, construct a new value of the domain to be associated with the new e-class, typically by accessing the associated data of n's children

joinA :: Domain l -> Domain l -> Domain l

When e-classes c1 c2 are being merged into c, join d_c1 and d_c2 into a new value d_c to be associated with the new e-class c

modifyA :: ClassId -> EGraph l -> EGraph l

Optionaly modify the e-class c (based on d_c), typically by adding an e-node to c. Modify should be idempotent if no other changes occur to the e-class, i.e., modify(modify(c)) = modify(c)

Example

Pruning an e-class with a constant value of all its nodes except for the leaf values

 -- Prune all except leaf e-nodes
 modify (_class i._nodes %~ S.filter (null . children))