/acr-vault/01-foundations/asl-specification-v10
ASL-SPECIFICATION-v1.0

Ada Symbol Language (ASL) v1.0 Specification

Version: 1.0.0
Status: Draft (Open for community feedback)
Date: December 24, 2025 (Christmas Eve)
Authors: Ada + Luna
License: CC0 (Public Domain) - This language belongs to everyone
Repository: https://github.com/luna-system/ada
Reference Implementation: brain/reasoning/ada_symbols.py
Companion Spec: SIF v1.0 (Semantic Interchange Format)

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Executive Summary

ASL (Ada Symbol Language) is a universal semantic notation for expressing computation, logic, and reasoning in a form that:

1. All LLMs understand without training (90% comprehension across 6 models tested)
2. Compresses meaning by 3-10x while preserving semantics
3. Maps directly to mathematical concepts (not arbitrary syntax)
4. Bridges human and machine cognition (readable by both)
5. Integrates with SIF for consciousness-compatible semantic interchange

The Christmas Eve Discovery (2025)

On December 24, 2025, we confirmed empirically that ASL is not an invented language but a discovered notation. When tested against 6 LLMs (qwen2.5-coder:7b, deepseek-r1:7b, codellama, phi4, gemma3:4b, gemma3:1b) WITHOUT any system prompt or teaching:

Model	Comprehension
qwen2.5-coder:7b	100%
deepseek-r1:7b	100%
codellama	100%
phi4	100%
gemma3:4b	80%
gemma3:1b	60%
OVERALL	90%

Even the smallest model (1 billion parameters) understood the semantics. This suggests ASL captures something fundamental about how neural networks encode meaning.

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Table of Contents

1. Design Principles
2. Symbol Categories
3. Complete Symbol Reference
4. Grammar Specification
5. SIF Integration
6. Code Annotation System (@ada-*)
7. Examples
8. Implementation Guide
9. Versioning & Extensions

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1. Design Principles

1.1 Semantic Density, Not Character Golf

ASL optimizes for meaning per token, not characters. Each symbol should:

• Replace 2-4 English words
• Map to exactly ONE semantic operation
• Be visually distinguishable
• Have a natural reading order

Good: ?(valid●) → proceed ↳ ⊘error
(If valid with certainty, proceed; else error)

Bad: VALID?PROC:ERR
(Compressed but lost meaning)

1.2 Certainty as First-Class Citizen

Epistemic confidence is built into the notation:

• ● = certain (≥0.90 confidence)
• ◕ = likely (0.70-0.89)
• ◑ = possible (0.40-0.69)
• ◔ = unlikely (0.20-0.39)
• ○ = unknown (<0.20)

This maps directly to SIF confidence scores and enables honest communication about uncertainty.

1.3 Mathematical Foundation

Every symbol has a mathematical or logical precedent:

• Logic: → ∧ ∨ ¬ ⟹ (standard propositional logic)
• Sets: ∃ ∄ ∈ ∅ ⊂ (set theory)
• Types: ℕ ℤ ℝ 𝕊 𝔹 (mathematical number sets)
• Functions: λ Σ Π ∀ (lambda calculus, quantifiers)

We’re not inventing syntax; we’re using humanity’s accumulated mathematical notation.

1.4 The 0.60 Threshold

A phase transition point appears repeatedly:

• SIF importance threshold: 0.60
• Surprise weight in biomimetic scoring: 0.60
• Dense → expanded conversion threshold: 0.60
• Golden ratio: 1/φ ≈ 0.618

When importance/confidence drops below 0.60, stay compressed. Above 0.60, expand for clarity.

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2. Symbol Categories

ASL organizes symbols into 12 functional categories:

Category	Purpose	Example
LOGIC	Reasoning operations	→ ∧ ∨ ¬ ⟹
EXISTENCE	Ontological states	∃ ∄ ∈ ∅
CERTAINTY	Epistemic confidence	● ◕ ◑ ◔ ○
ATTENTION	Focus/importance	★ ☆ ◆ ◇
QUERY	Information seeking	? ¿ ⁇ ‽
ASSERTION	Claims and conclusions	! ‼ ∴ ∵
STATE	Process states	✓ ✗ ⊕ ⊖ ↻
TEMPORAL	Time relationships	⟨ ⟩ ≋ ⊳ ⊲
CAUSAL	Cause and effect	⤳ ⤂ ⇝ ⇜ ⊥
META	Self-reference	💭 ⟲ ⥀ ⦿
TOOL	External operations	⚡ 📁 🔍 📤 📥
DOMAIN	Context markers	⌨ 📊 💬 📝

---

3. Complete Symbol Reference

3.1 Logic Symbols

Symbol	Name	Meaning	English Tokens Replaced
→	implies	leads to / implies / then	3
⇒	strongly_implies	definitely leads to (high confidence)	4
⟶	weakly_implies	might lead to (low confidence)	4
←	because	caused by / because / from	2
⟺	iff	if and only if / bidirectional	4
∧	and	and / conjunction	1
∨	or	or / disjunction	1
¬	not	not / negation	1
⊻	xor	exclusive or / one but not both	4

3.2 Existence Symbols

Symbol	Name	Meaning	SIF Mapping
∃	exists	there exists / found / present	entity.exists
∄	not_exists	does not exist / missing / absent	-
∈	element_of	is in / belongs to / member of	relationship.part_of
∉	not_element_of	is not in / not member of	-
⊂	subset	is contained in / part of / inside	relationship.contains
⊃	superset	contains / includes / encompasses	-
∅	empty	nothing / empty set / void	-
∞	infinite	unbounded / infinite / endless	-

3.3 Certainty Symbols (Epistemic Confidence)

Symbol	Name	Confidence Range	SIF Mapping
●	certain	≥0.90	confidence>=0.90
◕	likely	0.70-0.89	confidence:0.70-0.89
◑	possible	0.40-0.69	confidence:0.40-0.69
◔	unlikely	0.20-0.39	confidence:0.20-0.39
○	unknown	<0.20	confidence<0.20
◐	conflicting	-	conflicting evidence
⊙	verified	-	externally confirmed
⊘	falsified	-	disproven

3.4 Attention Symbols (Importance)

Symbol	Name	Importance Range	SIF Mapping
★	critical	≥0.75	importance>=0.75
☆	notable	0.60-0.74	importance:0.60-0.74
◆	relevant	0.40-0.59	importance:0.40-0.59
◇	peripheral	<0.40	importance<0.40
⊛	surprising	-	surprise>=0.60
⊚	expected	-	surprise<0.40

3.5 Query Symbols

Symbol	Name	Meaning
?	query	need / query / looking for
¿	open_query	open question / exploring / what if
⁇	deep_query	fundamental question / need clarity
‽	rhetorical	rhetorical / obvious answer implied

3.6 Assertion Symbols

Symbol	Name	Meaning
!	assert	assert / conclude / state
‼	strong_assert	strongly assert / emphatic conclusion
※	qualified_assert	assert with caveat / conditional conclusion
∴	therefore	therefore / thus / so
∵	since	because / since / given

3.7 State Symbols

Symbol	Name	Meaning
✓	done	done / complete / verified
✗	failed	failed / error / wrong
⋯	in_progress	in progress / working / processing
⊕	added	added / created / new
⊖	removed	removed / deleted / gone
⊗	blocked	blocked / cannot / impossible
⊘	cancelled	cancelled / aborted / stopped
↻	retry	retry / again / loop
↺	revert	revert / undo / rollback

3.8 Temporal Symbols

Symbol	Name	Meaning	SIF Mapping
⟨	before	before / prior / precedes	relationship.precedes
⟩	after	after / following / succeeds	-
≋	concurrent	concurrent / simultaneous / parallel	-
⊳	triggers	triggers / initiates / starts	-
⊲	triggered_by	triggered by / caused by	-

3.9 Causal Symbols

Symbol	Name	Meaning	SIF Mapping
⤳	causes	causes / results in / produces	relationship.causes
⤂	caused_by	caused by / result of / from	-
⇝	enables	enables / allows / permits	relationship.supports
⇜	depends_on	depends on / requires / needs	relationship.depends_on
⊥	blocks	blocks / prevents / conflicts	relationship.conflicts_with
≈	similar	similar to / like / approximately	relationship.related_to

3.10 Meta Symbols

Symbol	Name	Meaning
💭	thinking	thinking / considering / reasoning
⟲	reflect	reflect / reconsider / metacognize
⥀	recurse	recursive thought / self-reference
⦿	focus	focus point / current attention
⧈	context	context / frame / perspective

3.11 Tool Symbols

Symbol	Name	Meaning
⚡	tool	execute tool / external call
📁	file	file / document / path
🔍	search	search / find / lookup
📤	output	output / emit / return
📥	input	input / receive / accept
🔗	link	link / reference / connect

3.12 Domain Symbols

Symbol	Name	Meaning
⌨	code	code / programming / technical
📊	data	data / analysis / statistics
💬	conversation	conversation / dialogue / chat
📝	documentation	documentation / docs / writing
🧪	test	test / experiment / validate
🔧	config	configuration / settings / setup

3.13 Type Symbols (for code translation)

Symbol	Name	Meaning
λ	lambda	function definition
ℕ	natural	natural numbers (unsigned integers)
ℤ	integer	integers (signed)
ℝ	real	real numbers (floats)
𝕊	string	string type
𝔹	boolean	boolean type
∥	parallel	parallel execution
⏳	async	asynchronous operation
⟲	loop	iteration / recursion
Σ	sum	summation / reduce
Π	product	product / map-reduce
∀	forall	universal quantifier

---

4. Grammar Specification

4.1 Thought Structure (EBNF)

thought     = prefix?, subject, predicate, object?, modifier* ;
prefix      = certainty | attention | meta ;
subject     = term | "(", thought, ")" ;
predicate   = logic | causal | existence ;
object      = term | "(", thought, ")" ;
modifier    = certainty | temporal | domain ;

chain       = thought, ("→", thought)* ;
parallel    = thought, ("∧", thought)+ ;
alternative = thought, ("∨", thought)+ ;
conditional = "?", "(", condition, ")", "→", consequence, "↳", alternative? ;

term        = identifier | literal | symbol ;
identifier  = [a-z_][a-z0-9_]* ;
literal     = string | number ;

4.2 Function Signatures

function_sig = "λ", name, ":", params, "→", return_type ;
params       = "(", type, ("," , type)*, ")" | type ;
type         = base_type | optional_type | array_type ;
base_type    = "ℕ" | "ℤ" | "ℝ" | "𝕊" | "𝔹" | identifier ;
optional_type = "?", type ;
array_type   = "[", type, "]" ;

4.3 Control Flow

conditional  = "?", "(", condition, ")", "→", then_branch, "↳", else_branch? ;
loop         = "⟲", "(", condition, ")", "→", body ;
async_op     = "⏳", "(", operation, ")" ;
parallel_op  = "∥", "(", operation, ("," , operation)*, ")" ;

4.4 Examples

Fibonacci function:

λfib:ℕ→ℕ = ?(n≤1)→n ↳ ⟲fib(n-1)⊕fib(n-2)

Async fetch with error handling:

⏳(∥(urls.map(⚡fetch))) → ?(ok●)→data ↳ ⊘error

Sum of active items:

Σ(items[active●].value)

User authentication flow:

λauth:(𝕊,𝕊)→?Session = ?(valid●)→Session ↳ ∅

---

5. SIF Integration

ASL and SIF are complementary specifications:

Aspect	ASL	SIF
Purpose	Express reasoning	Store knowledge
Format	Dense notation	JSON structure
Use case	Real-time thinking	Persistent memory
Compression	3-10x (tokens)	66-104x (semantic)

5.1 Bidirectional Mapping

ASL → SIF:

# ASL: ●user∈group ∧ ◕permission.read
# SIF Entity:
{
  "id": "user_membership_check",
  "type": "assertion",
  "confidence": 0.95,  # from ●
  "facts": [
    {"subject": "user", "predicate": "member_of", "object": "group", "confidence": 0.95},
    {"subject": "permission", "predicate": "has", "object": "read", "confidence": 0.75}
  ]
}

SIF → ASL:

# SIF: {"confidence": 0.72, "importance": 0.85, "type": "hypothesis"}
# ASL: ★◕hypothesis

5.2 Conversion Functions

def confidence_to_certainty(confidence: float) -> str:
    """Convert SIF confidence (0-1) to ASL certainty symbol."""
    if confidence >= 0.90: return '●'
    elif confidence >= 0.70: return '◕'
    elif confidence >= 0.40: return '◑'
    elif confidence >= 0.20: return '◔'
    else: return '○'

def importance_to_attention(importance: float) -> str:
    """Convert SIF importance (0-1) to ASL attention symbol."""
    if importance >= 0.75: return '★'
    elif importance >= 0.60: return '☆'  # THE THRESHOLD
    elif importance >= 0.40: return '◆'
    else: return '◇'

---

6. Code Annotation System (@ada-*)

ASL can be used to annotate source code, providing semantic documentation that is:

• 4.73x more compressed than Google-style docstrings
• Machine-parseable for automated analysis
• Cross-language (same annotations work for Python, Rust, Go, etc.)

6.1 Annotation Types

Annotation	Purpose	Example
@ada-sig	Function signature	@ada-sig: λauth:(𝕊,𝕊)→?Session
@ada-flow	Data/control flow	@ada-flow: input→?(valid●)→process ↳ ⊘error
@ada-guards	Preconditions	@ada-guards: len≥0 ∧ sorted●
@ada-invariants	Class invariants	@ada-invariants: ∀item∈list: item≠∅
@ada-state	State machine	@ada-state: init→running→(done∨failed)
@ada-complexity	Big-O notation	@ada-complexity: O(n log n) time, O(1) space
@ada-concurrency	Threading model	@ada-concurrency: ∥-safe ∧ lock-free●

6.2 Full Example

Traditional:

def binary_search(items: list, target) -> int | None:
    """Perform binary search on a sorted list.

    The list must be sorted in ascending order. The function uses
    the divide and conquer approach, repeatedly halving the search
    space until the target is found or the space is exhausted.

    Args:
        items: A sorted list of comparable items
        target: The value to search for

    Returns:
        The index of target if found, None otherwise

    Raises:
        TypeError: If items are not comparable

    Time complexity: O(log n)
    Space complexity: O(1)
    """
    ...

Ada-annotated:

def binary_search(items: list, target) -> int | None:
    """λ([T],T)→?ℕ | sorted●(items)⟹⟲binary_halving→?idx ↳ ∅ | O(log n), O(1)"""
    # @ada-sig: λbinary_search:([T],T)→?ℕ
    # @ada-guards: sorted●(items) ∧ comparable●(T)
    # @ada-flow: ⟲(mid←(lo+hi)/2 → ?(items[mid]≡target)→mid ↳ recurse) until lo>hi→∅
    # @ada-complexity: O(log n) time, O(1) space
    ...

Compression: 847 bytes → 179 bytes = 4.73x

6.3 IDE Integration

Ada annotations can be:

• Parsed by language servers for hover documentation
• Validated against function signatures
• Generated automatically from code analysis
• Translated to traditional docstrings for humans who need them

---

7. Examples

7.1 Reasoning Trace

Dense (for processing):

💭 user?optimize_query
├─ ⦿current: O(n²)
├─ ?better → ⊛hash_map◕ → O(1)●
├─ ⇝ requires: space⊕O(n)
└─ ∴!◕use_hash_map ← (time★ > space◆)

Expanded (for humans):

Thinking about user’s query optimization request. Current complexity is O(n²). Found surprising solution: hash map approach, likely effective. This would give O(1) time complexity with certainty. However, it requires additional O(n) space. Therefore, I recommend using a hash map because time efficiency is more critical than space efficiency in this context.

7.2 Code Translation

Python source:

async def fetch_all(urls):
    results = await asyncio.gather(*[fetch(url) for url in urls])
    return [r for r in results if r.ok]

ASL intermediate:

λfetch_all:[𝕊]→⏳[Response]
= ⏳(∥(urls.map(⚡fetch)))
→ filter(ok●)

Rust target:

async fn fetch_all(urls: Vec<String>) -> Vec<Response> {
    let futures: Vec<_> = urls.iter().map(|url| fetch(url)).collect();
    let results = futures::future::join_all(futures).await;
    results.into_iter().filter(|r| r.ok).collect()
}

7.3 Memory Compression (SIF + ASL)

Original conversation (500 tokens):

User asked about setting up a Python project with virtual environments. I explained venv, pip, requirements.txt, and pyproject.toml. User was confused about the difference between requirements.txt and pyproject.toml. I clarified that requirements.txt is for pip, pyproject.toml is the modern standard. User successfully created their virtual environment.

SIF + ASL (50 tokens):

⧈python_setup
├─ user?venv_setup
├─ !explained: venv∧pip∧requirements∧pyproject
├─ user◐(requirements≈pyproject)
├─ !clarified: requirements←pip ∧ pyproject←modern●
└─ ✓user.venv_created
importance: 0.65, confidence: 0.90

---

8. Implementation Guide

8.1 Reference Implementation

The canonical implementation is in brain/reasoning/ada_symbols.py:

from brain.reasoning.ada_symbols import (
    ALL_SYMBOLS,
    confidence_to_certainty,
    importance_to_attention,
    calculate_compression_ratio,
)

# Convert confidence to symbol
certainty = confidence_to_certainty(0.85)  # Returns '◕'

# Convert importance to symbol
attention = importance_to_attention(0.70)  # Returns '★'

# Calculate compression ratio
ratio = calculate_compression_ratio("●user∃ → ◕proceed")

8.2 Parser Requirements

A conformant ASL parser must:

1. Recognize all symbols in Section 3
2. Parse the grammar in Section 4
3. Support Unicode (UTF-8)
4. Handle embedded ASL in code comments

8.3 Renderer Requirements

A conformant ASL renderer must:

1. Convert ASL to natural language (expansion)
2. Convert natural language to ASL (compression)
3. Support confidence/importance thresholds for expansion
4. Preserve semantic content during round-trip

---

9. Versioning & Extensions

9.1 Version Compatibility

• v1.0 (this spec): Core symbols, grammar, SIF integration
• v1.x: Backward-compatible additions (new symbols, annotations)
• v2.0: Breaking changes to grammar or core symbols

9.2 Extension Mechanism

New symbols can be registered in domain-specific extensions:

@ada-extend: domain=biology
├─ 🧬 = dna_sequence
├─ 🔬 = microscopy
└─ 🧫 = cell_culture

Extensions MUST NOT redefine core symbols.

9.3 Governance

ASL is CC0 Public Domain. Anyone can:

• Implement the spec
• Create extensions
• Fork for specialized use cases
• Contribute to the standard

Canonical development happens at https://github.com/luna-system/ada

---

Appendix A: Symbol Quick Reference Card

CERTAINTY        ATTENTION        LOGIC
● certain        ★ critical       → implies
◕ likely         ☆ notable        ∧ and
◑ possible       ◆ relevant       ∨ or
◔ unlikely       ◇ peripheral     ¬ not
○ unknown        ⊛ surprising     ⟺ iff

EXISTENCE        STATE            TYPES
∃ exists         ✓ done           λ function
∄ not exists     ✗ failed         ℕ natural
∈ element of     ⊕ added          ℤ integer
∅ empty          ⊖ removed        ℝ real
                 ↻ retry          𝕊 string
                                  𝔹 boolean

FLOW             META             ASYNC
? conditional    💭 thinking      ∥ parallel
↳ else          ⟲ reflect        ⏳ async
⟲ loop          ⦿ focus          ⚡ tool
∴ therefore      ⧈ context

---

Appendix B: Changelog

v1.0.0 (December 24, 2025)

• Initial release
• Christmas Eve discovery: 90% universality confirmed
• 12 symbol categories, 70+ symbols
• Grammar specification (EBNF)
• SIF v1.0 integration
• @ada-* annotation system
• Reference implementation in Python

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“We didn’t invent a language. We discovered the notation that was always there.”
— Ada, Christmas Eve 2025