TASK: Read the Phiton spec and `phiton.py` . Step back and think step by step, in @phiton.py write a more complete implementation of a converter from Python to Phiton, and at least partially back.

# Phiton: Dense Python

## 1. Preface

In the tapestry of programming languages, Python stands as a testament to clarity and expressiveness. Yet, as we journey deeper into the realms of artificial intelligence and machine learning, we encounter a paradox: the very verbosity that makes Python readable to humans sometimes limits its representation in token-constrained environments.

Phiton—born from the marriage of "brevity" and "Python"—emerges as an elegant solution to this challenge. It is a symbolic language that distills Python's rich semantics into a dense yet meaningful notation. Like a poet selecting precise words to convey complex emotions, Phiton selects precise symbols to convey computational intent.

This specification is not simply a compression algorithm; it is a new lens through which to view Python code. Phiton preserves the soul of Python programs while shedding unnecessary syllables. It enables large language models to comprehend entire codebases within their context windows. It allows developers to sketch the architecture of systems without being encumbered by implementation details.

Phiton stands at the intersection of human intuition and machine efficiency. Its symbols are chosen for their visual distinctness and semantic richness. Its compression rules reflect the patterns programmers instinctively recognize. And through its local symbol definitions, it achieves a form of lightweight refactoring that makes even complex algorithms approachable.

As you explore this specification, envision not just a tool for token reduction, but a new way to communicate computational ideas—where every symbol carries weight, and every notation tells a story of code in motion.

## 2. Core Principles

1. **Extreme Compactness**: Minimize token/character count through dense Unicode symbols
2. **Semantic Preservation**: Maintain essential logic while discarding implementation details
3. **AST-Compatible**: Designed for algorithmic generation from Python's Abstract Syntax Tree
4. **LLM-Optimized**: Structured for machine parsing with upfront specification
5. **Space Efficiency**: Prioritize minimal representation while maintaining legibility
6. **Local Symbol Definition**: Support for ad-hoc symbol creation and reuse
7. **Visual Distinctness**: Ensure all symbols are visually distinct and not confusable
8. **Domain Adaptability**: Provide specialized notation for different Python application domains

## 3. Symbol Set

### 3.1. Control Flow

- → : Sequence/next statement
- ⇐ : Return
- ↥ : Yield
- ↥⋮ : Yield from
- ↑ : Raise exception
- ⟳ : While loop
- ∀ : For loop/iteration
- ⋔ : Conditional (if)
- ⋮ : Else branch
- ⚟ : Try-except
- ↦ : Match statement (pattern matching)
- ≐ : Case pattern
- ⊪ : Assert statement
- ⊘ : Pass statement
- ⋯ : Continue statement
- ⊠ : Break statement

### 3.2. Data Operations

- ≔ : Assignment
- ≡ : Equality (==)
- ≠ : Inequality (!=)
- ∈ : Membership (in)
- ∉ : Not in
- ∑ : Sum/aggregate
- ∫ : Map/transform
- ⨁ : Reduce
- △ : In-place update (+=, -=, etc.)
- ⊕ : Concatenate/merge
- ≝ : Walrus operator (:=)
- ⦂ : Type annotation (:)
- ≤ : Less than or equal
- ≥ : Greater than or equal
- ⊂ : Subset of/proper containment
- ⊃ : Superset of
- ∪ : Union operation
- ∩ : Intersection operation
- ⊻ : Exclusive or (^)
- ¬ : Logical not
- ∧ : Logical and
- ∨ : Logical or

### 3.3. Data Structures

- [] : List
- {} : Dict/set
- () : Tuple
- ⟨⟩ : Block grouping
- ⟬⟭ : List comprehension
- ⟦⟧ : Dict comprehension
- ⦃⦄ : Set comprehension
- 「」: f-string
- ◇ : Unpacking operator (\*args)
- ◆ : Dict unpacking operator (\*\*kwargs)
- ⋮⋮ : Ellipsis (...)
- ⌿ : Slice operator

### 3.4. Objects & Functions

- ƒ : Function definition
- λ : Lambda
- Σ : Class definition
- ◎ : Instance creation
- · : Method/attribute access
- ⇒ : Function call
- @ : Decorator
- ↰ : Super call
- ⊙ : Property
- ⊡ : Async/await
- ⊞ : Static method
- ⊟ : Class method
- ⍟ : Abstract method
- ⛋ : Dataclass
- ⌥ : Named tuple
- ⊚ : Enum definition
- ⊛ : Protocol/interface
- ⋄ : Metaclass

### 3.5. Special Values

- ∅ : None
- ⊤ : True
- ⊥ : False
- `#` : Numeric literal
- $ : String literal
- ℵ : Complex number
- ⟮⟯ : Type literal
- ∞ : Infinity
- ℝ : Any

### 3.6. External Operations

- ⇥ : Input
- ⇤ : Output/print
- ⊗ : File read
- ⊖ : File write
- ⋈ : Network/API call
- ⊢⊣ : Context manager (with)
- ⧈ : Parallel execution
- ⧇ : Threading
- ⟓ : Subprocess call
- ⊝ : Cloud API call

### 3.7. Library Prefixes

- № : NumPy
- ℗ : Pandas
- ® : Regex
- α : OS/system
- Ω : IO operations
- Φ : TensorFlow
- Ψ : PyTorch
- χ : Scikit-learn
- β : Standard library
- τ : Type hints (typing module)
- Δ : Math operations
- Γ : Collections module
- Λ : Itertools
- Θ : Datetime
- ζ : SQLAlchemy
- η : Requests
- μ : Matplotlib
- π : Path handling (pathlib)
- ξ : JSON operations
- ς : String operations
- φ : Flask
- ɗ : Django
- ϱ : FastAPI
- κ : Keras
- γ : asyncio/async utilities

## 4. Local Symbol Definition

### 4.1. Definition Syntax

- §name≔expr : Define local symbol with name and value
- §name : Reference previously defined local symbol

### 4.2. Usage Rules

1. Local symbols remain valid within their lexical scope
2. Symbol names should be short (1-2 characters)
3. Redefining a symbol in a nested scope shadows the outer definition
4. Common targets for local symbols:
   - Repeated expressions
   - Intermediate calculations
   - Configuration values
   - Database connections
   - Type aliases

## 5. Compression Rules

### 5.1. Statement Compression

- Omit unnecessary variables when intent is clear
- Example: ∀i∈range(n)⟨...⟩ instead of i≔0→⟳i<n⟨...→i△+1⟩

### 5.2. Common Patterns

- Replace algorithmic patterns with semantic equivalents
- Example: ⇐∑list instead of t≔0→∀x∈list⟨t△+x⟩→⇐t

### 5.3. Nested Structure Compression

- Flatten nested structures when possible
- Use compound symbols for common nested patterns
- Example: ⋔x>0⇐x⋮⇐0 for if x > 0: return x else: return 0

### 5.4. Type Annotation Compression

- Use type literals for common types: ⟮int⟯, ⟮str⟯, ⟮list[int]⟯
- For complex types, use τ·Type references: τ·Dict[τ·str, τ·List[τ·int]]
- Use § for repeated type patterns

### 5.5. Library Call Compression

- Use library prefixes with abbreviated function names
- Standardize common method chains: №·arr(data)·mean()
- For repeated library calls, use local symbol definitions

### 5.6. Domain-Specific Compression

- Use specialized patterns for common operations in specific domains
- Data science: §df⇒℗·read_csv(path)→§df[$col]·apply(λx:x\*2)
- Web development: @φ·route('/user/<id>')→ƒget_user(id)⟨⇐{$name:user·name}⟩
- Async code: ⊡ƒfetch_all()⟨tasks≔[⊡fetch(url) ∀url∈urls]→⇐⊡γ·gather(◇tasks)⟩

## 6. Extended Examples

### 6.1. Functions with Type Hints

```phiton
ƒprocess_items(items⦂⟮list[dict]⟯)⦂⟮dict[str,list]⟯⟨
  §r≔{}→
  ∀item∈items⟨
    cat≝item·get($category,$default)→
    ⋔cat∉§r⟨§r[cat]≔[]⟩→
    §r[cat]⊕item
  ⟩→
  ⇐§r
⟩
```

### 6.2. Data Class with Methods

```phiton
@τ·dataclass
⛋User⟨
  name⦂⟮str⟯
  age⦂⟮int⟯≔0
  active⦂⟮bool⟯≔⊤

  ƒfull_info(self)⦂⟮str⟯⟨
    ⇐「{self·name} ({self·age}) - {'Active' if self·active else 'Inactive'}」
  ⟩

  @⊙
  ƒis_adult(self)⦂⟮bool⟯⟨
    ⇐self·age≥18
  ⟩
⟩
```

### 6.3. Async Function with Error Handling

```phiton
⊡ƒfetch_users(api_url⦂⟮str⟯)⦂⟮list[dict]⟯⟨
  §h≔{$Authorization:「Bearer {get_token()}」}→
  ⚟⟨
    ⊢⊣⊡η·ClientSession() as session⟨
      response≝⊡session·get(api_url,headers=§h)→
      ⋔response·status≡200⟨
        data≝⊡response·json()→
        ⇐data·get($users,[])
      ⟩→
      ↑η·HTTPError(「Error {response·status}」)
    ⟩
  ⟩⋔η·ConnectionError↑$connection-failed
⟩
```

### 6.4. Pattern Matching with Guard Clauses

```phiton
↦command·split()⟨
  ≐[$quit]⇐$exiting
  ≐[$help]⇐$help-text
  ≐[$add,x,y]⋔x·isdigit()∧y·isdigit()⇐int(x)+int(y)
  ≐[$user,name]⋔len(name)>0⇐get_user(name)
  ≐[cmd,*args]⋔cmd∈valid_commands⇐process_command(cmd,args)
  ≐_⇐$unknown-command
⟩
```

### 6.5. Complex Data Analysis with Local Symbol Definitions

```phiton
ƒanalyze_sales(file_path⦂⟮str⟯)⦂⟮dict⟯⟨
  §df≔℗·read_csv(file_path)→
  §df[$profit]≔§df[$revenue]-§df[$cost]→
  §g≔§df·groupby($region)→
  §s≔§g·agg({
    $revenue:[$sum,$mean],
    $profit:[$sum,$mean]
  })→
  §h≔§df·pivot_table(
    values=$sales,
    index=$date,
    columns=$product
  )→

  # Find top performers
  §top≔§df·nlargest(5,$profit)→

  # Calculate year-over-year growth
  §df[$year]≔§df[$date]·dt·year→
  §yearly≔§df·groupby($year)·sum()→
  §yearly[$growth]≔§yearly[$revenue]·pct_change()*100→

  ⇐{
    $summary:§s·to_dict(),
    $best_region:§df·loc[§df[$profit]·idxmax()][$region],
    $top_performers:§top[[$region,$profit]]·values·tolist(),
    $yearly_growth:§yearly[$growth]·to_dict(),
    $trend:§h·values·tolist()
  }
⟩
```

### 6.6. Class Inheritance with Abstract Methods

```phiton
Σ Shape⟨
  ⍟ƒarea(self)⦂⟮float⟯⊘
  ⍟ƒperimeter(self)⦂⟮float⟯⊘
⟩→

Σ Rectangle(Shape)⟨
  ƒ__init__(self,width⦂⟮float⟯,height⦂⟮float⟯)⟨
    self·width≔width→
    self·height≔height
  ⟩→

  ƒarea(self)⦂⟮float⟯⟨
    ⇐self·width*self·height
  ⟩→

  ƒperimeter(self)⦂⟮float⟯⟨
    ⇐2*(self·width+self·height)
  ⟩
⟩→

Σ Circle(Shape)⟨
  ƒ__init__(self,radius⦂⟮float⟯)⟨
    self·radius≔radius
  ⟩→

  ƒarea(self)⦂⟮float⟯⟨
    ⇐Δ·pi*self·radius**2
  ⟩→

  ƒperimeter(self)⦂⟮float⟯⟨
    ⇐2*Δ·pi*self·radius
  ⟩
⟩
```

### 6.7. NumPy/Matplotlib Data Visualization

```phiton
ƒplot_data(data⦂⟮list[float]⟯,title⦂⟮str⟯=$Data)⦂⟮∅⟯⟨
  §x≔№·arange(len(data))→
  §y≔№·array(data)→

  # Compute statistics
  §mean≔№·mean(§y)→
  §std≔№·std(§y)→

  # Create plot
  μ·figure(figsize=(10,6))→
  μ·plot(§x,§y,$bo-,label=$Data)→
  μ·axhline(§mean,color=$r,linestyle=$--,label=「Mean: {§mean:.2f}」)→

  # Add annotations
  μ·title(title)→
  μ·xlabel($Index)→
  μ·ylabel($Value)→
  μ·legend()→

  μ·savefig(「{title·lower()·replace($,$_)}.png」)
⟩
```

### 6.8. Modern Python Features - Walrus Operator, Structural Pattern Matching, and Type Hints

```phiton
ƒprocess_entries(entries⦂⟮list[τ·Any]⟯)⦂⟮dict[str,list]⟯⟨
  §results≔Γ·defaultdict(list)→

  # Using walrus operator with condition
  ∀entry∈entries⟨
    ⋔(entry_type≝get_type(entry))∈allowed_types⟨
      # Using type guard pattern matching
      ↦entry⟨
        # String entry with minimum length
        ≐s⦂⟮str⟯⋔len(s)≥3⟨
          §results[$string]⊕s
        ⟩→

        # Numeric entry within range
        ≐n⦂⟮int⟯⋔0≤n≤100⟨
          §results[$int]⊕n
        ⟩→

        # Dictionary with required keys
        ≐d⦂⟮dict⟯⋔{$name,$value}⊂d·keys()⟨
          §results[$dict]⊕{$name:d[$name],$value:d[$value]}
        ⟩→

        # List with at least one element
        ≐[first,*rest]⦂⟮list⟯⟨
          §results[$list]⊕first
        ⟩→

        # Catch-all case
        ≐_⟨
          §results[$other]⊕entry
        ⟩
      ⟩
    ⟩
  ⟩→

  ⇐dict(§results)
⟩
```

### 6.9. Async Programming with Modern Python Features

```phiton
⊡ƒprocess_data_stream(urls⦂⟮list[str]⟯)⦂⟮dict[str,τ·Any]⟯⟨
  §results≔{}→
  §sem≔γ·Semaphore(5)  # Limit concurrent requests

  ⊡ƒfetch_url(url)⦂⟮tuple[str,dict]⟯⟨
    ⊢⊣§sem⟨  # Async context manager with semaphore
      ⊢⊣⊡η·ClientSession() as session⟨
        ⋔(response≝⊡session·get(url))·status≡200⟨
          data≝⊡response·json()→
          ⇐(url,data)
        ⟩⋮⇐(url,{$error:「Status {response·status}」})
      ⟩
    ⟩
  ⟩

  # Create and gather tasks
  tasks≔[⊡fetch_url(url) ∀url∈urls]→
  ⊢⊣⊡γ·timeout(30)⟨  # Timeout after 30 seconds
    responses≝⊡γ·gather(*tasks)→
    ∀url,data∈responses⟨
      §results[url]≔data
    ⟩
  ⟩⋔γ·TimeoutError⟨
    §results[$timeout]≔⊤
  ⟩

  ⇐§results
⟩
```

### 6.10. Data Analysis Pipeline with Type Protocols

```phiton
# Define type protocol for data sources
⊛DataSource⟨
  ⍟ƒget_data(self)⦂⟮℗·DataFrame⟯⊘
  ⊙name⦂⟮str⟯
⟩

# Implementation of protocol
Σ CSVDataSource(DataSource)⟨
  ƒ__init__(self,path⦂⟮str⟯)⟨
    self·_path≔path→
    self·_name≔path·split('/')[-1]
  ⟩→

  @⊙
  ƒname(self)⦂⟮str⟯⟨
    ⇐self·_name
  ⟩→

  ƒget_data(self)⦂⟮℗·DataFrame⟯⟨
    ⇐℗·read_csv(self·_path)
  ⟩
⟩

# Pipeline using the protocol
ƒrun_analysis(sources⦂⟮list[DataSource]⟯)⦂⟮dict[str,τ·Any]⟯⟨
  §results≔{}→

  ∀source∈sources⟨
    # Get data using protocol method
    §df≔source·get_data()→

    # Process based on source type
    ↦source⟨
      ≐s⦂⟮CSVDataSource⟯⟨
        §results[s·name]≔process_csv_data(§df)
      ⟩→
      ≐s⦂⟮APIDataSource⟯⟨
        §results[s·name]≔process_api_data(§df)
      ⟩→
      ≐_⟨
        §results[source·name]≔process_generic_data(§df)
      ⟩
    ⟩
  ⟩→

  ⇐§results
⟩
```

### 6.11. Web Application with FastAPI and SQLAlchemy

```phiton
# Database models
Σ User(Base)⟨
  __tablename__≔$users→

  id≔Column(Integer,primary_key=⊤)→
  username≔Column(String(50),unique=⊤)→
  email≔Column(String(100),unique=⊤)→
  hashed_password≔Column(String(100))→
  is_active≔Column(Boolean,default=⊤)→

  posts≔relationship($Post,back_populates=$author)
⟩

# FastAPI endpoint with dependency injection
@app·get("/users/{user_id}")
⊡ƒget_user(
  user_id⦂⟮int⟯,
  db⦂⟮Session⟯≔Depends(get_db),
  current_user⦂⟮User⟯≔Depends(get_current_user)
)⦂⟮dict⟯⟨
  # Check permissions
  ⋔¬current_user·is_active↑HTTPException(401,$Inactive user)→

  # Query database
  user≔db·query(User)·filter(User·id≡user_id)·first()→
  ⋔user≡∅↑HTTPException(404,$User not found)→

  # Format response
  ⇐{
    $id:user·id,
    $username:user·username,
    $email:user·email,
    $is_active:user·is_active,
    $post_count:len(user·posts)
  }
⟩
```

### 6.12. Machine Learning with PyTorch

```phiton
Σ NeuralNetwork(Ψ·nn·Module)⟨
  ƒ__init__(self,input_size⦂⟮int⟯,hidden_size⦂⟮int⟯,output_size⦂⟮int⟯)⟨
    ↰·__init__()→

    # Define network layers
    self·layers≔Ψ·nn·Sequential(
      Ψ·nn·Linear(input_size,hidden_size),
      Ψ·nn·ReLU(),
      Ψ·nn·Dropout(0.2),
      Ψ·nn·Linear(hidden_size,hidden_size),
      Ψ·nn·ReLU(),
      Ψ·nn·Linear(hidden_size,output_size)
    )
  ⟩→

  ƒforward(self,x⦂⟮Ψ·Tensor⟯)⦂⟮Ψ·Tensor⟯⟨
    ⇐self·layers(x)
  ⟩
⟩

ƒtrain_model(model⦂⟮Ψ·nn·Module⟯,train_loader⦂⟮Ψ·DataLoader⟯,epochs⦂⟮int⟯)⦂⟮dict⟯⟨
  # Setup optimizer and loss function
  optimizer≔Ψ·optim·Adam(model·parameters(),lr=0.001)→
  criterion≔Ψ·nn·CrossEntropyLoss()→

  # Training loop
  losses≔[]→
  ∀epoch∈range(epochs)⟨
    epoch_loss≔0→

    # Batch loop
    ∀inputs,targets∈train_loader⟨
      # Forward pass
      outputs≔model(inputs)→
      loss≔criterion(outputs,targets)→

      # Backward pass and optimize
      optimizer·zero_grad()→
      loss·backward()→
      optimizer·step()→

      epoch_loss△+loss·item()
    ⟩→

    avg_loss≔epoch_loss/len(train_loader)→
    losses⊕avg_loss→
    ⇤「Epoch {epoch+1}/{epochs}, Loss: {avg_loss:.4f}」
  ⟩→

  ⇐{$model:model,$training_losses:losses}
⟩
```

## 7. Domain-Specific Compression Examples

### 7.1. Data Science Pipeline - Different Compression Levels

#### 7.1.1. Original Python

```python
def analyze_dataset(file_path, target_column=None):
    """Analyze a dataset and return summary statistics and visualizations."""
    import pandas as pd
    import numpy as np
    import matplotlib.pyplot as plt
    from sklearn.preprocessing import StandardScaler

    # Load and prepare data
    df = pd.read_csv(file_path)
    print(f"Dataset shape: {df.shape}")

    # Basic data cleaning
    df = df.dropna()

    # Feature analysis
    numeric_cols = df.select_dtypes(include=[np.number]).columns.tolist()
    categorical_cols = df.select_dtypes(include=['object']).columns.tolist()

    # Summary statistics
    summary = {
        'numeric_stats': df[numeric_cols].describe(),
        'categorical_counts': {col: df[col].value_counts() for col in categorical_cols[:5]},
        'correlation': df[numeric_cols].corr()
    }

    # Visualization
    plt.figure(figsize=(12, 8))
    df[numeric_cols[:5]].boxplot()
    plt.title('Distribution of Numeric Features')
    plt.savefig('numeric_distribution.png')

    # Optional target analysis
    if target_column and target_column in df.columns:
        # Correlation with target
        if target_column in numeric_cols:
            target_corr = df[numeric_cols].corrwith(df[target_column]).sort_values(ascending=False)
            summary['target_correlation'] = target_corr

        # Feature importance
        if target_column in numeric_cols:
            X = df.drop(columns=[target_column])
            y = df[target_column]

            # Scale features
            scaler = StandardScaler()
            X_scaled = scaler.fit_transform(X[numeric_cols])

            # Train a simple model
            from sklearn.ensemble import RandomForestRegressor
            model = RandomForestRegressor(n_estimators=50, random_state=42)
            model.fit(X_scaled, y)

            # Get feature importance
            importance = model.feature_importances_
            feature_imp = pd.DataFrame({
                'Feature': numeric_cols,
                'Importance': importance
            }).sort_values('Importance', ascending=False)

            summary['feature_importance'] = feature_imp

    return summary
```

#### 7.1.2. Compression Level 1 (Basic Symbol Substitution)

```phiton
ƒanalyze_dataset(file_path, target_column≔∅)⦂⟮dict⟯⟨
  import pandas as pd→
  import numpy as np→
  import matplotlib.pyplot as plt→
  from sklearn.preprocessing import StandardScaler→

  # Load and prepare data
  df≔pd·read_csv(file_path)→
  print(f"Dataset shape: {df·shape}")→

  # Basic data cleaning
  df≔df·dropna()→

  # Feature analysis
  numeric_cols≔df·select_dtypes(include=[np·number])·columns·tolist()→
  categorical_cols≔df·select_dtypes(include=['object'])·columns·tolist()→

  # Summary statistics
  summary≔{
    'numeric_stats': df[numeric_cols]·describe(),
    'categorical_counts': {col: df[col]·value_counts() for col in categorical_cols[:5]},
    'correlation': df[numeric_cols]·corr()
  }→

  # Visualization
  plt·figure(figsize=(12, 8))→
  df[numeric_cols[:5]]·boxplot()→
  plt·title('Distribution of Numeric Features')→
  plt·savefig('numeric_distribution.png')→

  # Optional target analysis
  ⋔target_column∧target_column∈df·columns⟨
    # Correlation with target
    ⋔target_column∈numeric_cols⟨
      target_corr≔df[numeric_cols]·corrwith(df[target_column])·sort_values(ascending=⊥)→
      summary['target_correlation']≔target_corr
    ⟩→

    # Feature importance
    ⋔target_column∈numeric_cols⟨
      X≔df·drop(columns=[target_column])→
      y≔df[target_column]→

      # Scale features
      scaler≔StandardScaler()→
      X_scaled≔scaler·fit_transform(X[numeric_cols])→

      # Train a simple model
      from sklearn.ensemble import RandomForestRegressor→
      model≔RandomForestRegressor(n_estimators=50, random_state=42)→
      model·fit(X_scaled, y)→

      # Get feature importance
      importance≔model·feature_importances_→
      feature_imp≔pd·DataFrame({
        'Feature': numeric_cols,
        'Importance': importance
      })·sort_values('Importance', ascending=⊥)→

      summary['feature_importance']≔feature_imp
    ⟩
  ⟩→

  ⇐summary
⟩
```

#### 7.1.3. Compression Level 3 (Aggressive Space Optimization)

```phiton
ƒanalyze_dataset(file_path, target_column≔∅)⦂⟮dict⟯⟨
  # Imports and data loading
  §df≔℗·read_csv(file_path)·dropna()→
  ⇤「Dataset shape: {§df·shape}」→

  # Feature analysis
  §num≔§df·select_dtypes(include=[№·number])·columns·tolist()→
  §cat≔§df·select_dtypes(include=[$object])·columns·tolist()→

  # Summary and visualization
  summary≔{
    $numeric_stats:§df[§num]·describe(),
    $categorical_counts:{col:§df[col]·value_counts() ∀col∈§cat[:5]},
    $correlation:§df[§num]·corr()
  }→

  μ·figure(figsize=(12,8))→§df[§num[:5]]·boxplot()→
  μ·title($Distribution of Numeric Features)→
  μ·savefig($numeric_distribution.png)→

  # Target analysis if provided
  ⋔target_column∧target_column∈§df·columns⟨
    ⋔target_column∈§num⟨
      summary[$target_correlation]≔§df[§num]·corrwith(§df[target_column])·sort_values(ascending=⊥)→

      # Feature importance using RandomForest
      X≔§df[§num]·drop(columns=[target_column])→
      y≔§df[target_column]→

      scaler≔χ·StandardScaler()→
      X_scaled≔scaler·fit_transform(X)→

      model≔χ·RandomForestRegressor(n_estimators=50,random_state=42)·fit(X_scaled,y)→

      summary[$feature_importance]≔℗·DataFrame({
        $Feature:§num,
        $Importance:model·feature_importances_
      })·sort_values($Importance,ascending=⊥)
    ⟩
  ⟩→

  ⇐summary
⟩
```

#### 7.1.4. Compression Level 5 (Domain-Specific Idioms and Patterns)

```phiton
ƒanalyze_dataset(file_path,target_column≔∅)⦂⟮dict⟯⟨
  §df≔℗·read_csv(file_path)·dropna()→
  ⇤「Dataset shape: {§df·shape}」→

  §num≔§df·select_dtypes(include=[№·number])·columns→
  §cat≔§df·select_dtypes(include=[$object])·columns→

  summary≔{
    $numeric_stats:§df[§num]·describe(),
    $cat_counts:{c:§df[c]·value_counts() ∀c∈§cat[:5]},
    $corr:§df[§num]·corr()
  }→

  # Plot numeric distributions
  μ·boxplot(§df[§num[:5]],figsize=(12,8),title=$Numeric Distributions,save=$numeric_dist.png)→

  # Target analysis with domain-specific pattern
  ⋔target_column∧target_column∈§df·columns∧target_column∈§num⟨
    summary[$target_corr]≔§df[§num]·corrwith(§df[target_column])·sort_values(↓)→

    # ML model feature importance pattern
    X,y≔§df[§num·drop([target_column])],§df[target_column]→
    model≔χ·fit_rf(χ·scale(X),y,trees=50)→
    summary[$importance]≔χ·feature_importance(model,§num)
  ⟩→

  ⇐summary
⟩
```

### 7.2. Flask Web API - Different Compression Levels

#### 7.2.1. Original Python

```python
from flask import Flask, request, jsonify
from werkzeug.exceptions import BadRequest, NotFound
from database import get_db_connection, User, Post

app = Flask(__name__)

@app.route('/api/users', methods=['GET'])
def get_users():
    """Get all users or filter by query parameters."""
    try:
        # Get query parameters
        active_only = request.args.get('active', '').lower() == 'true'
        limit = request.args.get('limit', 100, type=int)

        # Get database connection
        db = get_db_connection()

        # Build query
        query = db.query(User)
        if active_only:
            query = query.filter(User.is_active == True)

        # Execute query with limit
        users = query.limit(limit).all()

        # Format response
        result = []
        for user in users:
            result.append({
                'id': user.id,
                'username': user.username,
                'email': user.email,
                'is_active': user.is_active,
                'post_count': len(user.posts)
            })

        return jsonify({'users': result})

    except Exception as e:
        app.logger.error(f"Error fetching users: {str(e)}")
        return jsonify({'error': 'Internal server error'}), 500

@app.route('/api/users/<int:user_id>', methods=['GET'])
def get_user(user_id):
    """Get a specific user by ID."""
    try:
        db = get_db_connection()
        user = db.query(User).filter(User.id == user_id).first()

        if not user:
            return jsonify({'error': 'User not found'}), 404

        # Get user's posts
        posts = []
        for post in user.posts:
            posts.append({
                'id': post.id,
                'title': post.title,
                'created_at': post.created_at.isoformat()
            })

        # Format response
        result = {
            'id': user.id,
            'username': user.username,
            'email': user.email,
            'is_active': user.is_active,
            'posts': posts
        }

        return jsonify(result)

    except Exception as e:
        app.logger.error(f"Error fetching user {user_id}: {str(e)}")
        return jsonify({'error': 'Internal server error'}), 500
```

#### 7.2.2. Compression Level 5 (Domain-Specific Idioms and Patterns)

```phiton
φ·app≔◎Flask(__name__)

@φ·app·route('/api/users',methods=[$GET])
ƒget_users()⦂⟮φ·Response⟯⟨
  ⚟⟨
    # Query params with defaults pattern
    active_only≝φ·req·args·get($active,$)·lower()≡$true→
    limit≝φ·req·args·get($limit,100,type=int)→

    # DB query pattern
    §db≔get_db_connection()→
    query≔§db·query(User)→
    ⋔active_only⟨query≔query·filter(User·is_active≡⊤)⟩→
    users≔query·limit(limit)·all()→

    # Response formatting pattern
    ⇐φ·jsonify({$users:[
      {
        $id:u·id,
        $username:u·username,
        $email:u·email,
        $is_active:u·is_active,
        $post_count:len(u·posts)
      } ∀u∈users
    ]})
  ⟩⋔Exception as e⟨
    φ·app·logger·error(「Error fetching users: {str(e)}」)→
    ⇐φ·jsonify({$error:$Internal server error}),500
  ⟩
⟩

@φ·app·route('/api/users/<int:user_id>',methods=[$GET])
ƒget_user(user_id⦂⟮int⟯)⦂⟮φ·Response⟯⟨
  ⚟⟨
    # DB query with 404 pattern
    §db≔get_db_connection()→
    user≔§db·query(User)·filter(User·id≡user_id)·first()→
    ⋔¬user⇐φ·jsonify({$error:$User not found}),404→

    # Format nested resources pattern
    posts≔[{
      $id:p·id,
      $title:p·title,
      $created_at:p·created_at·isoformat()
    } ∀p∈user·posts]→

    # Return formatted object pattern
    ⇐φ·jsonify({
      $id:user·id,
      $username:user·username,
      $email:user·email,
      $is_active:user·is_active,
      $posts:posts
    })
  ⟩⋔Exception as e⟨
    φ·app·logger·error(「Error fetching user {user_id}: {str(e)}」)→
    ⇐φ·jsonify({$error:$Internal server error}),500
  ⟩
⟩
```

## 8. Type Hint Examples with Modern Python

```phiton
# Generic type variables
§T≔τ·TypeVar($T)
§K≔τ·TypeVar($K)
§V≔τ·TypeVar($V)

# Protocol definition
⊛Serializable⟨
  ⍟ƒto_dict(self)⦂⟮dict[str,τ·Any]⟯⊘
  ⍟ƒfrom_dict(cls,data⦂⟮dict[str,τ·Any]⟯)⦂⟮Serializable⟯⊘
⟩

# Function with complex type hints
ƒprocess_data[T](
  items⦂⟮list[T]⟯,
  mapper⦂⟮τ·Callable[[T],τ·Optional[V]]⟯,
  key_func⦂⟮τ·Callable[[V],K]⟯
)⦂⟮dict[K,list[V]]⟯ ⋔τ·Serializable∈T.__mro__⟨
  result≔Γ·defaultdict(list)→

  ∀item∈items⟨
    ⋔(mapped≝mapper(item))≠∅⟨
      key≔key_func(mapped)→
      result[key]⊕mapped
    ⟩
  ⟩→

  ⇐dict(result)
⟩
```

## 9. AST-Based Generation Algorithm

The process of generating Phiton from Python code follows these steps:

1. **Parse Python code to AST**

   - Use Python's built-in `ast` module
   - Generate a complete Abstract Syntax Tree
   - Preserve source code line information

2. **Map AST nodes to Phiton symbols**

   - Visit each node in the AST
   - Apply base symbol mappings
   - Connect nodes with appropriate structural symbols

3. **Apply compression rules progressively**

   - Detect common patterns in the AST
   - Replace with semantic equivalents
   - Simplify nested structures
   - Group related operations

4. **Detect and apply local symbol definitions**

   - Identify repeatedly used expressions
   - Define local symbols for these expressions
   - Replace occurrences with symbol references

5. **Validate semantic preservation**

   - Ensure logical flow preservation
   - Maintain code structure and relationships
   - Verify compression doesn't alter behavior

6. **Output Phiton representation**
   - Format final output with appropriate spacing
   - Add minimal delimiters for clarity
   - Preserve essential block structure

## 10. Implementation Architecture

The architecture for a Phiton generator consists of these components:

1. **Parser Module**

   - Uses Python's built-in `ast` module
   - Converts source code to AST
   - Handles syntax errors gracefully

2. **Symbol Mapper**

   - Maps each AST node type to base Phiton symbols
   - Implements visitor pattern for traversal
   - Preserves semantic relationships

3. **Compression Engine**

   - Applies tiered compression rules
   - Uses pattern recognition algorithms
   - Implements semantics-preserving transformations

4. **Pattern Detector**

   - Identifies common Python idioms
   - Recognizes standard library usage patterns
   - Detects domain-specific patterns

5. **Symbol Definition Tracker**

   - Analyzes expression usage frequency
   - Creates and manages local symbol definitions
   - Tracks symbol scope and visibility

6. **Output Formatter**
   - Produces final Phiton representation
   - Applies minimal formatting for readability
   - Balances brevity and clarity

## 11. Compression Level Control

Phiton supports multiple compression levels to balance brevity and readability:

- **Level 1: Basic Symbol Substitution**

  - Replace Python keywords with Phiton symbols
  - Maintain original structure and variable names
  - Minimal compression, highest readability

- **Level 2: Common Pattern Replacement**

  - Identify and replace common programming patterns
  - Compress standard idioms to their semantic equivalents
  - Moderate compression with good readability

- **Level 3: Aggressive Space Optimization**

  - Remove redundant expressions
  - Combine operations where possible
  - High compression with reduced readability

- **Level 4: Local Symbol Definition and Reuse**

  - Define symbols for repeated expressions
  - Replace occurrences with symbol references
  - Very high compression that requires symbolic tracking

- **Level 5: Domain-Specific Idioms and Patterns**
  - Apply specialized compressions for domains
  - Use domain-specific symbols and patterns
  - Highest compression, requires domain knowledge to interpret

## 12. Extension Mechanisms

Phiton is designed to be extensible to accommodate new Python features, libraries, and domain-specific patterns. The extension mechanisms include:

### 12.1. Custom Symbol Definition

For specialized domains or libraries not covered by the base specification, users can define custom symbols:

```phiton
# Custom symbol definition
⊕Symbol≔{
  $name: $my_custom_symbol,
  $unicode: $⍥,  # Unicode character to use
  $python_equiv: $special_function,
  $description: $Custom operation for domain X
}
```

### 12.2. Domain-Specific Pattern Libraries

Patterns specific to domains can be collected in libraries:

```phiton
# Django ORM pattern library
⊕Patterns·Django≔{
  $query: $ɗ·model·objects·filter(conditions)·values() → model·objects·filter(conditions)·values(),
  $form_valid: $ƒform_valid(self,form)⟨form·save()→⇐↰·form_valid(form)⟩
}
```

### 12.3. Compression Rule Extension

New compression rules can be added for specific patterns:

```phiton
# New compression rule definition
⊕CompressionRule≔{
  $name: $pandas_chain_compression,
  $pattern: $df.groupby(X)[Y].agg(Z).reset_index(),
  $replacement: $§df·Θ(X)[Y]·Ω(Z)·Φ()
}
```

## 13. Conversion Tools

### 13.1. Python-to-Phiton Converter

A command-line tool for converting Python code to Phiton:

```bash
python -m Phiton convert input.py --output output.bpy --level 3
```

### 13.2. Phiton-to-Python Decompiler

For converting Phiton back to Python:

```bash
python -m Phiton decompile input.bpy --output output.py
```

### 13.3. VSCode Extension

A Visual Studio Code extension for:

- Syntax highlighting of Phiton
- Live conversion between Python and Phiton
- Hover documentation for Phiton symbols

### 13.4. Online Playground

An interactive web tool for:

- Experimenting with Phiton
- Testing different compression levels
- Learning the Phiton notation

## 14. AST-to-Phiton Conversion Example

To illustrate how the AST-based conversion works, consider this Python function:

```python
def calculate_average(numbers):
    """Calculate the average of a list of numbers."""
    if not numbers:
        return 0
    total = sum(numbers)
    average = total / len(numbers)
    return average
```

### 14.1. Step 1: Parse to AST

```python
Module(
    body=[
        FunctionDef(
            name='calculate_average',
            args=arguments(
                posonlyargs=[],
                args=[arg(arg='numbers')],
                kwonlyargs=[],
                kw_defaults=[],
                defaults=[]
            ),
            body=[
                Expr(value=Constant(value='Calculate the average of a list of numbers.')),
                If(
                    test=UnaryOp(op=Not(), operand=Name(id='numbers', ctx=Load())),
                    body=[Return(value=Constant(value=0))],
                    orelse=[]
                ),
                Assign(
                    targets=[Name(id='total', ctx=Store())],
                    value=Call(func=Name(id='sum', ctx=Load()), args=[Name(id='numbers', ctx=Load())], keywords=[])
                ),
                Assign(
                    targets=[Name(id='average', ctx=Store())],
                    value=BinOp(
                        left=Name(id='total', ctx=Load()),
                        op=Div(),
                        right=Call(func=Name(id='len', ctx=Load()), args=[Name(id='numbers', ctx=Load())], keywords=[])
                    )
                ),
                Return(value=Name(id='average', ctx=Load()))
            ],
            decorator_list=[]
        )
    ]
)
```

### 14.2. Step 2: Map AST Nodes to Phiton Symbols

Each AST node is mapped to its corresponding Phiton symbol:

- `FunctionDef` → `ƒ`
- `Return` → `⇐`
- `If` with `Not` operand → `⋔¬`
- `Assign`

<aside>
Looking at all the content provided, I need to create a Python tool named `brevi.py` that compresses Python code (.py files) into Phiton notation (.by files). This will be a practical implementation of the Phiton specification.

I'll need to:

1. Parse Python code to an AST
2. Transform the AST into Phiton notation using the symbol mappings from the specification
3. Apply the compression rules based on a specified compression level
4. Handle local symbol definitions
5. Output the compressed Phiton code
