Enumo is a domain-specific language for programmable theory exploration. It uses equality saturation to infer small, expressive rulesets for a domain.

• (OOPSLA 2023) A. Pal, B. Saiki, R. Tjoa, C. Richey, A. Zhu, O. Flatt, M. Willsey, Z. Tatlock, C. Nandi, Equality Saturation Theory Exploration à la Carte

• (OOPSLA 2021, Distinguished Paper Award) C. Nandi, M. Willsey, A. Zhu, Y. Wang, B. Saiki, A. Anderson, A. Schulz, D. Grossman, Z. Tatlock, Rewrite Rule Inference Using Equality Saturation. *

* This paper is based on an older version of this repository. If you are looking for the code associated with this paper, please use this branch.

Enumo is implemented in Rust. To install Enumo, the following dependencies must be installed:

• Rust
• libz3

If libz3 is not offered on your system, you can edit Cargo.toml in this directory by changing the dependency z3 = xxx to z3 = {version=xxx, features = ["static-link-z3"]}. This will statically link to a built copy of z3 instead of dynamically linking, but the build process will take considerably longer. It is recommended that you install libz3 if possible.

To build Enumo, type cargo build --release. This should take a few minutes.

Run cargo doc --open to build and open the documentation in a browser.

cargo test will run all the tests, including tests that find rules for a handful of example domains. See the tests directory for examples of how to set up a domain, construct workloads, and find rules.

• The source code resides in the src directory.
  • lib.rs is the main entrypoint and defines some auxiliary data types.
  • language.rs defines the SynthLanguage trait, which must be implemented in order to use the Ruler DSL to find rules for a domain. There are two main things that must be implemented: an interpreter and a rule validator. (In the case of rule lifting, the interpreter is not needed.)
  • workload.rs contains the Workload data type. Workloads evaluate to a list of terms (s-expressions). Workloads can be constructed directly from a list of s-expressions (Workload::Set), combined (Workload::Append), refined with a filter (Workload::Filter), or composed via plugs (Workload::Plug). Plug is a novel operation for generating workloads from smaller workloads. It takes two workloads, $W_1$ and $W_2$ and a string, $s$; for each term in $W_2$ that contains $s$, it “plugs” in the values in $W_1$ and generates a new workload which is a cross product of all the new plugged terms.
  • sexp.rs contains an implementation of s-expressions.
  • equality.rs defines a rewrite rule.
  • ruleset.rs contains the Ruleset data type. Rulesets are implemented as an IndexMap of Equality. There are several operations over Rulesets that can be used to combine, compose, and refine rulesets. For example, Ruleset::cvec_match extracts a set of equalities from an egraph via cvec-matching; Ruleset::minimize can be used to eliminate redundant rules from a ruleset; Ruleset::derive tests the proving power of one ruleset compared to another.
  • filter.rs defines the Filter data type which can be used to filter workloads. pattern.rs and metric.rs define data types that are used in Filter.
  • util.rs has some small helper functions.

Our goal is that Enumo is extensible and can support rule inference in any domain. There are some examples of Enumo programs in tests/recipes that can be used as a model. In addition, we provide some brief instructions for constructing a basic Enumo program below:

The Enumo DSL enables rewrite rule inference for any domain given a grammar, an interpreter, and a validation technique. To understand how to add support for a new domain, you can look at the domains in the tests directory. Note that some domains are experimental and not reported in the paper, but they all provide examples of how you can add support for new domains.

To use Enumo for a new domain, you must first implement the SynthLanguage trait for your domain. This requires implementing a rule validator and either an interpreter (for non-fast-forwarding domains) or a set of lifting rules (for fast-forwarding domains).

To show how users can write an Enumo program for rule inference, let's take a look at bv4_fancy.rs, located in the tests/recipes directory. This program showcases several of Enumo's provided features for "guided search"-style rule synthesis using one of the example domains, bv.rs, located in src/.

// create a new set of rules for bitvectors, initially empty
let mut rules: Ruleset<Bv> = Ruleset::default();

// define a new language we want to enumerate terms for
let lang = Lang::new(
    &["0", "1"],
    &["a", "b", "c"],
    &[&["~", "-"], &["&", "|", "*", "--", "+", "<<", ">>"]],
);

After initializing an empty ruleset, rules, we define a language we want to enumerate terms over. In this case, our language contains some constants (0 and 1), some variables (a, b, c), the unary operators (~ and -), and some binary operators, including (&, |, *), and others. Note that lang is actually a subset of the operators supported by the bv.rs implementation—the operator ^, for example, is not included. This is one way Enumo allows users to easily omit information that is not important for their purposes, enabling for faster, more scalable synthesis.

// find rules using terms over the provided language up to 5 atoms in size
// and add them to our ruleset
rules.extend(recursive_rules(
    enumo::Metric::Atoms,
    5,
    lang.clone(),
    Ruleset::default(),
));

The recursive_rules function, included in src/recipe_utils.rs, is one of several convenience features included in Enumo. It recursively builds up a ruleset by enumerating all terms over a passed-in Language up to a specified size. Enumo supports three measures of term size: Atoms (number of literals in the term), Depth (depth of s-expression), and Lists (number of operators in the term).

Once we've found all the rules up to 5 atoms in size, we append them to the starting ruleset.

let a6_canon = iter_metric(base_lang(2), "EXPR", enumo::Metric::Atoms, 6)
        .plug("VAR", &Workload::new(lang.vars))
        .plug("VAL", &Workload::empty())
        .plug("OP1", &Workload::new(lang.ops[0].clone()))
        .plug("OP2", &Workload::new(lang.ops[1].clone()))
        .filter(Filter::Canon(vec![
            "a".to_string(),
            "b".to_string(),
            "c".to_string(),
        ]));

Enumo allows its users to decouple workload generation from rule synthesis. In the above code snippet, we are not finding rules at all: we are just building up a workload. a6_canon is pretty complicated, so let's break it up a bit to make it easier:

iter_metric(base_lang(2), "EXPR", enumo::Metric::Atoms, 6)

Here, we specify that we want to enumerate all terms up to 6 atoms. base_lang(n) is a convenience function that constructs a base workload for any language consisting of variables, constants, and operators with up to n arguments.

.plug("VAR", &Workload::new(lang.vars))
.plug("VAL", &Workload::empty())

plug is the core Enumo operator for constructing and composing workloads. An EXPR contains VARS (variables) and VALS (values) as its leaves, and plug specifies what can be "plugged in" as variables and values—in this case, a workload containing lang's variables and an empty workload, respectively.

.filter(Filter::Canon(vec![
            "a".to_string(),
            "b".to_string(),
            "c".to_string(),
        ]));

Enumo also supports filtering terms out of generated workloads that do not interest the user. In this case, after the workload is generated, terms that are not canonicalized are removed. Canonicalization here means that a must be the first variable introduced. a can be followed by another a any number of times, but the next new variable introduced must be b, and so on. Canonicalization drastically expedites rule inference by eliminating duplicate terms, often representing the difference between a workload that is too large to perform rule inference over and one that finishes near-instantaneously.

let consts = Workload::new(["0", "1"]);
let wkld = Workload::Append(vec![a6_canon, consts]);

We can also compose workloads: here, we combine a workload consisting of the constants 0 and 1 with a6_canon.

let wkld = Workload::Append(vec![a6_canon, consts]);
    rules.extend(run_workload(
        wkld,
        rules.clone(),
        Limits::synthesis(),
        Limits::minimize(),
        true,
    ));
    rules

Finally, we are ready to run rule synthesis for the final time, which we do using the workload we just created, the rules we got from recursive_rules, and some resource limits. We return this final ruleset. This is a complete Enumo program!