A self-hosting Equality Saturation (E-Graph) superoptimizer, relational synthesis kernel (miniKanren/Datalog), abstract interpretation verifier, and differentiable S-expression abstract machine.
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Equality Saturation & Inductive Program Synthesis
Traditional optimizing compilers apply term rewrite rules greedily: when an algebraic rewrite rule like
Athanor eliminates phase ordering by applying all equational rewrite rules simultaneously without destroying intermediate representations. It maintains an Equivalence Graph (E-Graph) that compactly represents exponentially many equivalent program variants in polynomial space. Once the e-graph reaches saturation, an optimal concrete abstract syntax tree (AST) is extracted via dynamic programming under configurable hardware cost models.
Beyond algebraic simplification, Athanor couples equality saturation with pure relational logic programming (miniKanren), Counterexample-Guided Inductive Synthesis (CEGIS), abstract interpretation safety proofs, and automatic differentiation of symbolic graphs.
+-------------------------------------------------------------------------+
| ATHANOR PIPELINE |
+-------------------------------------------------------------------------+
| |
| [Specification / S-Expr] |
| | |
| v |
| +--------------------+ Inductive CEGIS Loop |
| | miniKanren / Logic | <-----------------------------+ |
| | Relational Kernel | | |
| +--------------------+ | |
| | | |
| v | |
| +--------------------+ Counterexample | |
| | Bottom-Up Synthesizer | -- Verification Failure ---+ |
| | with OE Pruning | | |
| +--------------------+ | |
| | Candidate AST | |
| v | |
| +--------------------+ | |
| | Abstract Verifier | -- Proves Safety Contracts ---+ |
| | Interval & Signs | |
| +--------------------+ |
| | Proven Safe AST |
| v |
| +-------------------------------------------------------------------+ |
| | E-GRAPH SATURATION ENGINE | |
| | | |
| | +--------------------+ Worklist +------------------------+ | |
| | | Disjoint-Set (UF) | ------------> | Congruence Rebuilding | | |
| | +--------------------+ +------------------------+ | |
| | ^ ^ | |
| | | Deduplicated Hash-Cons Nodes | | |
| | v v | |
| | +--------------------+ +------------------------+ | |
| | | Equational Rules | <-----------> | Lattice Analysis | | |
| | | Ring/Bitwise/BLAS | AC-Matching | Constant Propagation | | |
| | +--------------------+ +------------------------+ | |
| +-------------------------------------------------------------------+ |
| | |
| v |
| +--------------------+ |
| | Dynamic Extractor | (Under :latency, :ast-size, :gpu-fused models) |
| +--------------------+ |
| / \ |
| v v |
| +----------+ +-------------------+ |
| | SBCL JIT | | C99 / OpenMP SIMD | |
| | Machine | | Hardware Engine | |
| | Code | | (5.5+ GFLOPS) | |
| +----------+ +-------------------+ |
+-------------------------------------------------------------------------+
-
Full-Featured E-Graph Kernel:
- Disjoint-set forest with two-pass path compression and union-by-rank balancing (
$O(\alpha(N))$ amortized). - Deduplicated hash-consing for structural e-node storage.
- Deferred congruence closure rebuilding with upward worklist propagation.
- E-class analysis lattice framework supporting compile-time constant folding and interval bounding.
- Disjoint-set forest with two-pass path compression and union-by-rank balancing (
-
Declarative Equational Theories:
- Commutative Ring theory (zero annihilation, identity elimination, sign cancellation, factoring).
- Bitwise superoptimizer (Hacker's Delight identities, shift composition, multiplier strength reduction).
- Trigonometric identities (Pythagorean identity
$\sin^2\theta + \cos^2\theta = 1$ ). - Tensor calculus and Level 3 BLAS kernel fusion (
$\alpha W X + \beta b \to \text{GEMM}$ ). - Numerical floating-point stabilization (cancellation avoidance,
log1p,expm1).
-
Relational Logic Kernel:
- Pure miniKanren implementation with Robinson first-order unification, sound occurs check, and interleaved streams.
- Finite domain constraint solver (CLP(FD)) with interval pruning, all-different constraints, and linear sums.
- Stratified Datalog deductive database with semi-naive fixpoint evaluation.
-
Inductive Program Synthesis:
- Context-free grammar production rules.
- Observational Equivalence (OE) signature hashing pruning over 95% of redundant candidate branches.
- Closed-loop Counterexample-Guided Inductive Synthesis (CEGIS).
-
Formal Abstract Interpretation:
- Galois-connected interval domain with rigorous infinite and division bounding.
- Five-element sign lattice for constant-time branch pruning.
- Automated proofs of division-by-zero freedom, target output range containment, and 16/32/64-bit integer overflow freedom.
-
Differentiable S-Expressions:
- Forward-mode automatic differentiation with Dual Numbers (
$u + u'\epsilon$ ). - Source-to-source analytical reverse differentiation, exact symbolic Jacobians, and Hessians.
- Fused gradient superoptimization via equality saturation.
- Forward-mode automatic differentiation with Dual Numbers (
-
Multi-Target Native Code Generation:
- Dynamic SBCL JIT compiling directly to native machine code closures.
- Infix C99 emission and vectorized batch loops annotated with
#pragma omp simd. - On-the-fly dynamic compilation to shared libraries (
.dylib/.so) via Clang. - Hand-optimized C library featuring 128-bit ARM NEON vector instructions delivering 5.5+ GFLOPS and 50+ GB/s throughput.
- SBCL (Steel Bank Common Lisp) version 2.0+
- Clang or GCC (with OpenMP support)
- Make
- Python 3.8+ (for verification and benchmarking scripts)
On macOS:
brew install sbcl graphvizOn Ubuntu / Debian:
sudo apt-get update && sudo apt-get install -y sbcl clang graphviz make python3# 1. Clone repository
git clone https://github.com/Aneesh495/athanor.git
cd athanor
# 2. Build native C SIMD shared library
make c-lib
# 3. Run the comprehensive 31-module test suite (91 assertions)
make test
# 4. Run equality saturation and SIMD performance benchmarks
make bench
# 5. Run the multi-pass autonomous verification audit
make verifyLaunch the interactive Athanor shell:
./bin/athanor========================================================================
ATHANOR : Equality Saturation & Program Synthesis Kernel v0.1.0
========================================================================
Type :help for a summary of available meta-commands.
athanor> :sat (* (+ a (- a)) (* b 1))
[Evaluating Saturation] Input: (* (+ A (- A)) (* B 1))
[Result] Optimal: 0
[Telemetry] Iterations: 2 | Nodes: 4245 | Classes: 1397 | Time: 2980.12 ms
athanor> :sat (+ (* x 16) (* y 8))
[Evaluating Saturation] Input: (+ (* X 16) (* Y 8))
[Result] Optimal: (+ (ASH X 4) (ASH Y 3))
[Telemetry] Iterations: 2 | Nodes: 14 | Classes: 9 | Time: 0.12 ms
athanor> :diff (expt x 2) x
[Differentiating] d/dX for (EXPT X 2)
[Raw Gradient] (* 2 (* (EXPT X 1) 1))
[Optimized Gradient] (ASH X 1)
[Telemetry] Converged: T | Time: 0.08 ms
athanor> :emit-c (+ (ash x 4) (ash y 3))
[Generated C99 Kernel]
double athanor_generated_kernel(double x, double y) {
return ((x << 4) + (y << 3));
}
athanor> :quit
Exiting Athanor.
The repository includes six self-contained, fully executable examples in examples/:
| Example Script | Domain | Description |
|---|---|---|
01_algebraic_simplification.lisp |
Computer Algebra | Proves |
02_bit_twiddling_superopt.lisp |
Bit-Twiddling | Reduces integer multiplication to single-cycle ALU shifts and simplifies bitwise XORs. |
03_symbolic_deep_learning.lisp |
Machine Learning | Fuses linear layers gemm and simplifies loss gradients. |
04_relational_synthesis.lisp |
Inductive Synthesis | Discovers verified programs from input-output examples and runs the CEGIS loop. |
05_interval_safety_proof.lisp |
Formal Verification | Proves freedom from division by zero and establishes 16-bit integer overflow safety. |
06_c_codegen_pipeline.lisp |
Compiler Backend | S-expression saturation |
Run any example directly with SBCL:
sbcl --script examples/01_algebraic_simplification.lisp
sbcl --script examples/06_c_codegen_pipeline.lispAll components are rigorously validated with automated scripts in tools/:
============================================================================
Athanor Autonomous Verification & Integrity Engine
============================================================================
[Pass 1] Verifying Common Lisp Parentheses & S-Expression Balance...
[OK] All 66 Lisp source files structurally balanced.
[Pass 2] Scanning Codebase for Forbidden Em Dashes...
[OK] Clean scan across 76 text files. Zero forbidden dashes detected.
[Pass 3] Building and Benchmarking Native SIMD Vector Engine...
[OK] C SIMD dylib and benchmark runner compiled successfully.
[OK] Benchmark binary output:
[Athanor SIMD C Benchmark] Dot product (N=1000000): 0.361 ms (5.55 GFLOPS)
[Athanor SIMD C Benchmark] Vector add (N=1000000): 0.403 ms (59.58 GB/s throughput)
[Pass 4] Running Master Common Lisp Test Suite...
[OK] 31 test modules executed. Test Suite Summary: 91 Passed | 0 Failed
[Pass 5] Validating All 6 End-to-End Compiler Examples...
[OK] 01_algebraic_simplification.lisp completed with exit code 0.
[OK] 02_bit_twiddling_superopt.lisp completed with exit code 0.
[OK] 03_symbolic_deep_learning.lisp completed with exit code 0.
[OK] 04_relational_synthesis.lisp completed with exit code 0.
[OK] 05_interval_safety_proof.lisp completed with exit code 0.
[OK] 06_c_codegen_pipeline.lisp completed with exit code 0.
============================================================================
ALL VERIFICATION CHECKS PASSED WITH ZERO DEFECTS.
============================================================================
============================================================================
Benchmarking Equality Saturation & AST Extraction Telemetry
============================================================================
Benchmark Target | Nodes | Classes | AST Ratio | Time (ms)
----------------------------------------------------------------------------
Pythagorean Trigonometric Identity | 9 | 7 | 9 -> 1 | 0.09
Multi-step Bitwise Strength Reduction | 14 | 9 | 7 -> 7 | 0.12
Rational Polynomial Zero Cancellation | 4245 | 1397 | 8 -> 1 | 2980.11
Tensor Contraction GEMM Fusion | 8 | 6 | 5 -> 5 | 0.08
Accurate Logarithmic Expansion | 7 | 5 | 5 -> 3 | 0.08
----------------------------------------------------------------------------
============================================================================
Benchmarking Native ARM NEON / AVX SIMD Acceleration Engine
============================================================================
* Dot product (N=1,000,000): 0.361 ms (5.55 GFLOPS, checksum=32340000.0000)
* Vector add (N=1,000,000): 0.403 ms (59.58 GB/s throughput)
============================================================================
Comprehensive specifications and formal write-ups are available in docs/:
- Architecture & System Topology
- Equality Saturation & E-Graphs
- Inductive Program Synthesis & CEGIS
- Abstract Interpretation & Safety Proofs
- Automatic Differentiation & Fused Gradients
- Relational Logic (miniKanren, CLP(FD), Datalog)
- Code Generation & High-Performance SIMD Engine
This project is licensed under the MIT License. See LICENSE for details.