Universal Semantic Graph
A language-agnostic graph representation that captures the pure semantics of programs beyond syntactic diversity
Formal Definition
Mathematically rigorous structure and components of USG
Graph Structure
USG is a directed graph defined as a 5-tuple. Each component represents the core semantic structure of programs.
Node Set (N)
Finite set of representative atomic motifs (versioned catalog, not fixed)
Control Flow (E_c)
Directed edges representing program execution order
Data Dependencies (E_d)
Edges representing definition-use relationships of values
Type Function (η)
Maps each node to a semantic atom type
Semantic Atoms
Rep. atomic motifs (versioned) to express fundamental computation units
Major Atom Categories
- Control Flow: Sequence, Conditional, Loop, Call
- Data Manipulation: Binding, Assignment, Access, Literal
- Operations: Arithmetic, Logical, Comparison, Type
- Structure: Module, Function, Class, Interface
1// Conceptual sketch of representative atom motifs
2let representativeAtoms = [
3 { kind: "Sequence", category: "control" },
4 { kind: "Conditional", category: "control" },
5 { kind: "Binding", category: "data" },
6 { kind: "Literal", category: "data" },
7 { kind: "BinaryOp", category: "operation" }
8]
9
10// Usage example
11let node = {
12 kind: "Conditional",
13 condition: comparisonNode,
14 thenBranch: executionNode1,
15 elseBranch: Some(executionNode2)
16}Graph Properties
Mathematical properties and semantic guarantees of USG
Completeness
Designed to capture broad patterns with representative atoms (not a formal completeness claim)
Canonicality
Strives for consistent canonicalization for same-semantics programs (excluding boundary cases)
Minimality
Eliminates unnecessary redundancy to include only essential program semantics
Type Safety
Aims to preserve and use type hints/annotations.
Effect Label Lattice
Example relation: pure ⊑ read ⊑ write ⊑ io ⊑ global
Construction Process
Systematic transformation process from source code to USG
Transformation Steps
- Phase 1: Language-specific parsing and AST generation
- Phase 2: Semantic analysis and type inference
- Phase 3: Translation to semantic atoms
- Phase 4: Control/data flow graph construction
1// USG construction process example
2function constructUSG(sourceCode: string, language: string) -> Result<USG, Error> {
3 // 1. Language-specific parsing
4 let ast = parseLanguageSpecific(sourceCode, language)?
5
6 // 2. Semantic analysis
7 let semanticInfo = analyzeSemantics(ast)?
8
9 // 3. Atom transformation
10 let atoms = transformToAtoms(semanticInfo)?
11
12 // 4. Graph construction
13 let controlFlow = buildControlFlow(atoms)
14 let dataFlow = buildDataFlow(atoms)
15
16 return Ok(buildUSG(atoms, controlFlow, dataFlow))
17}
18
19// Call example: any language normalizes to the same USG
20let source = """
21 def factorial(n):
22 return 1 if n <= 1 else n * factorial(n - 1)
23 """
24
25match constructUSG(source, "python") {
26 case Ok(usg) => print("USG node count: {usg.nodeCount()}")
27 case Err(error) => print("Normalization error: {error}")
28}Applications
Various application domains leveraging USG's language-agnostic nature
Cross-language Translation
Use the USG graph projection for semantic-preserving cross-language analysis and reconstruction
Code Analysis
Development of language-agnostic static analysis, optimization, and bug detection tools
Program Verification
Mathematical foundation for behavior-gated verification and correctness review
Core Components
Relationship between USG and other core components of Core Semantic Kernel