Skip to content

Chacana

Chacana is a tensor calculus DSL with static type checking. It parses tensor expressions into a MathJSON-style AST and validates index consistency, rank, symmetry, and differential geometry operator constraints.

Features

  • PEG Grammar -- deterministic parsing of tensor expressions with Arpeggio
  • Static Type Checking -- contraction consistency, free index invariance, symmetry validation
  • MathJSON Output -- spec-compliant ValidationToken AST format
  • TOML Context -- declare manifolds, tensors, metrics, and strategies
  • Differential Geometry -- type-checked exterior derivatives, Lie derivatives, Hodge star, trace, determinant, inverse
  • Unicode Support -- Greek indices with NFC normalization and visual spoofing rejection
  • Tree-sitter Grammar -- incremental parsing, syntax highlighting, and real-time validation queries for IDE integration (try the playground)
  • .chcn file extension -- canonical extension for Chacana expression files

Quick Example

import chacana

# Load a TOML context declaring manifolds and tensors
ctx = chacana.load_context("examples/basic.toml")

# Parse and type-check a Riemann tensor expression
result = chacana.parse("R{^a _b _c _d}", context=ctx)
# {'type': 'TensorExpression', 'head': 'R', 'indices': [...]}

# Invalid expressions raise clear errors
chacana.parse("A{^a} + B{_a}", context=ctx)
# ChacanaTypeError: Free index mismatch in sum

Architecture

Expression String
    │
    ▼
normalize_input()     ← Unicode NFC + scope check
    │
    ▼
parse_and_validate()  ← Arpeggio PEG parser + nested sym rejection
    │
    ▼
parse_to_ast()        ← Visitor: parse tree → ValidationToken
    │
    ▼
check()               ← Static type checker (Rules 1-3 + operators)
    │
    ▼
ValidationToken.to_dict()  → MathJSON dict