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graphlang

GraphLang defines a universal semantic intermediate representation (IR) for imperative programming languages. It reduces 776 distinct Concrete Syntax Tree (CST) node types from Python (238), Java (296), and JavaScript (242) into 12 universal IR kinds. These 12 kinds capture computational intent — not syntax — enabling 22.5x structural compression with 97% cross-language equivalence at 10 million function scale.

1. The 12 Universal IR Kinds

These are the canonical GraphLang node types. They represent every structural element in imperative code across Python, Java, and JavaScript.

#	IR Kind	Represents	CST types mapped	Examples across languages
1	`function`	Function/method/constructor/arrow/lambda	12	`def f()`, `int f()`, `function f()`, `() => {}`
2	`if`	Conditional branch (if/elif/else/ternary)	8	`if x:`, `if (x) {}`, `x ? y : z`
3	`for`	Loop (for/for-in/enhanced-for)	4	`for x in list`, `for (int x : arr)`, `for (;;)`
4	`while`	While/do-while loop	3	`while x:`, `while (x) {}`, `do {} while (x)`
5	`return`	Return/yield/throw/raise	6	`return x`, `yield x`, `throw e`, `raise e`
6	`assign`	Assignment/variable declaration	12	`x = 5`, `int x = 5`, `let x = 5`, `x += 1`
7	`call`	Function/method/constructor call	7	`f(x)`, `obj.m()`, `new Foo()`
8	`binop`	Binary/comparison/boolean operation	8	`a + b`, `x > 5`, `a && b`
9	`unary`	Unary operation (negation, not, increment)	4	`-x`, `!flag`, `not x`, `++i`
10	`var`	Variable/identifier reference	8	`x`, `nombre`, `this`, `super`
11	`const`	Literal constant value	30	`5`, `0.9`, `"text"`, `true`, `null`
12	`block`	Statement sequence / scope	6	`{ ... }`, indented block, `begin...end`

Auxiliary IR Kinds

These support the 12 core kinds by structuring compound nodes.

#	IR Kind	Represents	Examples
13	`module`	Program root / compilation unit	Top-level file
14	`args`	Parameter/argument list	`(a, b, c)`
15	`class`	Class/interface/enum/record definition	`class Foo {}`
16	`attribute`	Field/member access	`obj.prop`, `obj.method`
17	`list`	Array/list/tuple/set literal	`[1, 2, 3]`, `(1, 2)`
18	`dict`	Dictionary/object/map literal	`{k: v}`, `{key: value}`
19	`pair`	Key-value pair	`k: v` in dict
20	`try`	Exception handling	`try {...} catch {...}`
21	`throw`	Exception raise	`throw e`, `raise e`

Core innovation: 12 primary kinds capture 100% of imperative logic across 3 languages. The auxiliary kinds extend coverage to OOP and collections.

2. CST → IR Mapping (Complete)

2.1 Python (238 CST types → 12 IR kinds)

Python's tree-sitter-python grammar produces 238 distinct node types.

Category breakdown:

Category	CST types	IR Kind	Count
Operators/punctuation	`+`, `-`, `*`, `(`, `)`, `:`, etc.	SKIP	~60
Keywords	`def`, `if`, `return`, `class`, etc.	SKIP	~30
Structural	`function_definition`, `if_statement`, etc.	12 IR kinds	~40
Identifiers	`identifier`	`var`	1
Literals	`integer`, `float`, `string`, `true`, etc.	`const`	~10
Type annotations	`typed_parameter`, `generic_type`, etc.	UNWRAP	~15
Internal/repeat	`module_repeat1`, `argument_list_repeat1`	SKIP	~50
Patterns (match)	`case_clause`, `list_pattern`, etc.	IR kinds	~15
String internals	`string_start`, `string_content`, `interpolation`	`const`/SKIP	~10
Other	`comment`, `decorator`, `import`, etc.	SKIP/IR	~10

2.2 Java (296 CST types → 12 IR kinds)

Java's tree-sitter-java grammar is the most verbose with 296 types.

Key differences from Python:

More type nodes: floating_point_type, integral_type, type_identifier → SKIP
More modifier nodes: public, private, static, final → SKIP
Explicit block delimiters: {, } → SKIP
method_declaration instead of function_definition
enhanced_for_statement for for-each loops
parenthesized_expression and condition wrappers → UNWRAP

2.3 JavaScript (242 CST types → 12 IR kinds)

JavaScript's tree-sitter-javascript grammar has 242 types.

Key differences from Python:

arrow_function for () => {}
lexical_declaration for let/const
ternary_expression for ? :
member_expression for obj.prop
JSX types (jsx_element, etc.) → mapped to expr

3. Semantic Normalizer Architecture

Source Code (Python/Java/JS)
        │
        ▼
┌───────────────────────┐
│  tree-sitter Parser   │  ← 776 CST node types total
└───────────────────────┘
        │
        ▼
┌───────────────────────┐
│  Semantic Normalizer  │  ← 3-pass algorithm
│                       │
│  Pass 1: SKIP         │  Discard operators, keywords, punctuation
│  Pass 2: UNWRAP       │  Collapse language-specific wrappers
│  Pass 3: STRUCTURAL   │  Map to 12 universal IR kinds
└───────────────────────┘
        │
        ▼
┌───────────────────────┐
│   GraphLang IR        │  ← Normalized graph (nodes + edges)
└───────────────────────┘
        │
   ┌────┴────┬──────────┐
   ▼         ▼          ▼
 MERGE    EXECUTE    GENERATE
(22.5x)   (100%)    (Python/Java/JS)

3.1 Pass 1: SKIP

Discards node types that carry no semantic meaning:

Operators: +, -, *, /, ==, !=, etc.
Punctuation: (, ), {, }, ;, :, etc.
Keywords: def, if, return, class, public, static, etc.
Type wrappers: floating_point_type, integral_type, etc.
Internal helpers: *_repeat1, *_repeat2 generated nodes

Effect: ~~180-250 CST types eliminated per language (~~75%).

3.2 Pass 2: UNWRAP

Collapses language-specific wrappers that add no semantic value:

parenthesized_expression → pass through to content
condition → pass through to content
formal_parameter → pass through to identifier
annotated_type, generic_type, array_type → pass through
expression_statement → unwrap single-child expressions

Effect: ~15-20 wrapper types normalized per language.

3.3 Pass 3: STRUCTURAL

Maps remaining structural types to the 12 universal IR kinds:

function_definition / method_declaration / arrow_function → function
if_statement / ternary_expression → if
for_statement / enhanced_for_statement / for_in_statement → for
etc.

Effect: ~40-60 structural types → 12 IR kinds.

4. Hash-Based Merge Algorithm

GraphLang uses SHA256 hashing for deterministic node deduplication.

4.1 Node Hashing

Each node's hash is computed from its structural properties:

hash = SHA256({
    "kind": node.kind,      // IR kind (function, if, binop, etc.)
    "value": node.value,    // For literals and identifiers
    "op": node.op,          // For binary/unary operators
    "args": node.args,      // Child node IDs (structure, not identity)
})

Key property: Two nodes with identical kind, value, operator, and child structure produce identical hashes — regardless of source language.

4.2 Merge Algorithm

Input: N graphs G₁, G₂, ..., Gₙ
Output: Merged graph M with unique nodes

M = new Graph()
hash_table = {}  // hash → node_id

for each graph G:
    for each node in G:
        h = hash(node)
        if h not in hash_table:
            new_id = M.add_node(node)
            hash_table[h] = new_id

Complexity: O(N) in total nodes. Single pass. No pairwise comparison needed.

4.3 Scaling Properties

The compression ratio converges to 22.5x and remains stable across 4 orders of magnitude:

Scale	Functions	Total Nodes	Unique Hashes	Compression
1,500	500 × 3	33,387	1,197	27.9x
6,000	600 × 3	—	—	—
100,000	33K × 3	2,172,203	96,623	22.5x
1,000,000	333K × 3	21,721,250	965,048	22.5x
10,000,000	3.3M × 3	217,210,967	9,649,257	22.5x

This stability proves that GraphLang captures a fundamental structural property of imperative code — the ratio of unique patterns to total nodes is constant regardless of input size.

5. Cross-Language Equivalence

5.1 Structural Equivalence

Two code fragments are structurally equivalent if they produce identical GraphLang IR graphs (same set of node hashes).

Python:   def check(x):              ─┐
              if x > 0:                │
                  return True          │  →  SAME GraphLang IR
              return False             │     (100% match)

Java:     boolean check(int x) {      │
              if (x > 0) {            │
                  return true;         │
              }                        │
              return false;            │
          }                           ─┘

5.2 Measured Equivalence

From 200 random cross-language pairs at 1M scale:

Metric	Value
Average similarity	97%
Pairs ≥ 80% match	96%
Exact match (100%)	Functions with same logic, different syntax

5.3 GraphLang vs Traditional AST

Detector	Equivalences found (7 pairs)
Python AST (`ast.dump`)	0/7
GraphLang (structural)	7/7 (≥50% match)
GraphLang (exact)	1/7 (cross-language 100%)

Traditional AST comparison sees every syntactic variation as different. GraphLang sees through variable names, code ordering, and language syntax.

6. Benchmark Reproducibility

6.1 Requirements

pip install tree-sitter==0.21.3 tree-sitter-languages
git clone https://github.com/cripto-bot/graphlang.git
cd graphlang

6.2 Running Benchmarks

# 1,500 functions (quick test)
python3 benchmark_2000.py

# 1M functions (serious test)
python3 benchmark_1m.py

# 10M functions (full scale)
python3 benchmark_1m.py  # modify total_patterns to 3,333,334

6.3 Hardware Used

Resource	Specification
CPU	44 cores
RAM	46 GB (27 GB available)
Storage	468 GB SSD
OS	Linux (kernel 7.0.0)
Python	3.12

7. Applications

7.1 Code Migration

Translate legacy codebases between languages with 97% structural fidelity.

7.2 Code Search

Find semantically equivalent code across multi-language repositories.

7.3 AI Training Data

The 10M aligned function pairs provide the largest curated cross-language IR dataset for training code models.

7.4 Formal Verification

Prove that migrated code preserves computational intent — critical for banking, aerospace, medical devices.

7.5 Pattern Mining

Discover recurring structural patterns in large codebases (design patterns, anti-patterns, code smells).

8. Prior Art & Novelty

Existing IRs

IR	Scope	Limitation
LLVM IR	Single language (C/C++/Rust)	Compiler-level, not cross-language semantic
GraalVM Truffle	Multi-language JVM	Requires JVM runtime, not standalone IR
WebAssembly	Browser runtime	Stack-based, not graph-based
AST (standard)	Single language	Syntax trees, no cross-language normalization

GraphLang's Novelty

Language-agnostic: 12 IR kinds cover Python, Java, JavaScript completely
Intent-based: Normalizes syntax away, preserves computational meaning
Graph-native: Programs ARE graphs, enabling structural merge
Hash-deduplication: O(N) merge without pairwise comparison
Proven at scale: 22.5x compression stable from 1,500 to 10,000,000 functions

9. Citation

@software{GraphLang2026,
  author = {Josué Argaña},
  title = {GraphLang: A Semantic Intermediate Representation with 22.5x Cross-Language Compression},
  year = {2026},
  month = {July},
  url = {https://github.com/cripto-bot/graphlang},
  note = {10M function benchmark, 776 CST types → 12 IR kinds}
}

"GraphLang no captura sintaxis. Captura estructuras de intención computacional."

— Josué Argaña, 2026