# Precedence Resolution: Historical Documentation

**Status**: ✅ RESOLVED - All precedence issues have been successfully fixed  
**Impact**: All arithmetic operations now work correctly

## Overview

This document archives the precedence issues that were identified and resolved during the function composition implementation. All precedence-related problems have been successfully fixed and are no longer active issues.

## The Problem (Resolved)

### Original Issue
The parser was incorrectly translating `x - y` as `apply(x, negate(y))` instead of `subtract(x, y)`. This caused binary minus operations to fail.

### Root Cause
`TokenType.MINUS` was included in the `isValidArgumentStart` function, causing the parser to treat minus as a valid argument start for function application rather than a binary operator.

### The Fix
Removed `TokenType.MINUS` from `isValidArgumentStart`:

```javascript
function isValidArgumentStart(token) {
    return token.type === TokenType.IDENTIFIER ||
           token.type === TokenType.NUMBER ||
           token.type === TokenType.STRING ||
           token.type === TokenType.LEFT_PAREN ||
           token.type === TokenType.LEFT_BRACE ||
           token.type === TokenType.TRUE ||
           token.type === TokenType.FALSE ||
           token.type === TokenType.FUNCTION_REF ||
           token.type === TokenType.FUNCTION_ARG ||
           // Removed: token.type === TokenType.MINUS ||  ← FIXED
           token.type === TokenType.NOT;
}
```

## Resolution Results

### ✅ All Operations Working
- **Binary minus**: `x - y` → `subtract(x, y)` ✅
- **Unary minus**: `-x` → `negate(x)` ✅
- **Mixed operations**: `x * -y` → `multiply(x, negate(y))` ✅
- **Complex expressions**: `x + y * z` → `add(x, multiply(y, z))` ✅

### ✅ Test Results
All precedence test cases now pass:
- Basic arithmetic operations
- Unary operations
- Mixed unary and binary operations
- Function application
- Function composition
- Comparison operations
- Logical operations
- Complex expressions
- Edge cases

## Technical Details

### Precedence Chain (Working)
```
parseLogicalExpression() → parseExpression() → parseTerm() → parseApplication() → parseComposition() → parseFactor() → parsePrimary()
```

### Operator Handling (Working)
- **Unary minus**: Handled in `parsePrimary()` (highest precedence) ✅
- **Binary minus**: Handled in `parseExpression()` (correct precedence) ✅
- **Function application**: Handled in `parseApplication()` (via juxtaposition) ✅
- **Function references**: Handled in `parsePrimary()` ✅

### Combinator Architecture (Working)
All operators correctly translate to function calls:
- `x + y` → `add(x, y)`
- `x - y` → `subtract(x, y)`
- `x * y` → `multiply(x, y)`
- `f x` → `apply(f, x)`
- `@f` → function reference

## Impact on Development

### Before Fix
- Binary minus operations failed
- Mixed operations with unary minus failed
- Test suite had precedence-related failures

### After Fix
- All arithmetic operations work correctly
- Function composition works perfectly
- Standard library functions work with @ syntax
- Test suite shows 8/18 tests passing (remaining failures are case expression issues, not precedence)

## Lessons Learned

### Key Insights
1. **Combinator Architecture**: The combinator-based approach works well when precedence is handled correctly
2. **Function Application**: Juxtaposition-based function application can coexist with operators when precedence is properly defined
3. **Incremental Fixes**: Small changes to `isValidArgumentStart` can have significant impact on parsing behavior

### Best Practices
1. **Test-Driven Development**: Comprehensive test cases helped identify and verify the fix
2. **Debug Mode**: `DEBUG=1` was essential for understanding parsing behavior
3. **Incremental Testing**: Testing each operation individually helped isolate issues

## Related Documents

### Implementation
- **IMPLEMENTATION_GUIDE.md**: Contains the actual implementation details
- **PROJECT_ROADMAP.md**: Updated to reflect precedence resolution

### Architecture
- **COMBINATORS.md**: Explains the combinator foundation that made this fix possible
- **ARCHITECTURE.md**: Complete system architecture overview

## Conclusion

The precedence issues have been **completely resolved**. The combinator-based architecture is working correctly, and all arithmetic operations are functioning as expected. The fix was simple but effective, demonstrating the robustness of the combinator approach.

**Current Focus**: The project has moved on to case expression parsing issues, which are separate from precedence and have a clear path to resolution.

---

**Archive Note**: This document is kept for historical reference and to document the resolution approach for future similar issues.