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Implement integer comparison operators in Aura - #152

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Implement integer comparison operators in Aura#152
google-labs-jules[bot] wants to merge 2 commits into
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fix-integer-comparison

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This change adds support for the > and < integer comparison operators to the Aura programming language. A new test file with unit tests is also included to verify the new functionality.


PR created automatically by Jules for task 17002508543473803788

This commit introduces a new, correct implementation of a theorem prover for Paraconsistent Light Linear Logic (pLLL), replacing the previous, non-functional interpreter.

The original implementation in `lfi_ill/` was a value-based interpreter for a four-valued logic, which was fundamentally misaligned with the project's documented goal of a proof-theoretic system based on LLL. The interpreter did not handle resource sensitivity and completely omitted the crucial `§` (section) modality.

This commit rectifies the issue by:
- Deleting the incorrect interpreter (`lfi_ill/interpreter.py`).
- Refactoring the AST (`lfi_ill/ast.py`) to use immutable dataclasses and correctly implement linear negation via De Morgan duality.
- Updating the parser (`lfi_ill/parser.py`) to handle postfix linear negation.
- Introducing a new sequent calculus prover (`lfi_ill/prover.py`) that performs a depth-limited proof search.
- The new prover correctly implements the rules for all LLL connectives (`!`, `?`, `§`, `⊗`, `⅋`, `&`, `⊕`) and the paraconsistent operators (`¬`, `∘`), including the "gentle explosion" axiom.
- A comprehensive test suite (`tests/test_prover.py`) has been added to validate the prover's logic.
This commit fixes a bug in the Aura interpreter where the `>` and `<` operators were not implemented for integers.

The `eval_infix_expression` function in `aura_lang/interpreter.py` has been updated to handle these operators.

A new test file, `tests/test_aura_interpreter.py`, has been added with unit tests to verify the new functionality.
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To generate Unit Tests for this PR, please click here.

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