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https://github.com/blackboxprogramming/BlackRoad-Operating-System.git
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0108860bff
Create comprehensive research-lab pack structure with mathematical and quantum computing modules from blackroad-prism-console: Math Modules: - hilbert_core.py: Hilbert space symbolic reasoning - collatz/: Distributed Collatz conjecture verification - linmath/: Linear mathematics C library - lucidia_math_forge/: Symbolic proof engine - lucidia_math_lab/: Experimental mathematics Quantum Modules: - lucidia_quantum/: Quantum core - quantum_engine/: Circuit simulation Experiments: - br_math/: Gödel gap, quantum experiments Includes pack.yaml manifest and comprehensive README. 🤖 Generated with [Claude Code](https://claude.com/claude-code) Co-Authored-By: Claude <noreply@anthropic.com>
69 lines
2.1 KiB
Python
69 lines
2.1 KiB
Python
"""Custom symbolic operators for the Lucidia Math Forge.
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Three playful operators are provided:
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``paradox_merge`` (⊕)
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Combines two values in a way that remembers both sum and difference.
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``infinite_fold`` (⊗)
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Repeatedly applies a binary function, emulating an infinite folding.
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``collapse`` (↯)
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Reduces a nested structure to a single value.
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These operators are intentionally whimsical and serve as examples of how
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one might craft new algebraic toys in Python.
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"""
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from __future__ import annotations
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from functools import reduce
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from typing import Any, Callable, Iterable, Tuple
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def paradox_merge(a: Any, b: Any) -> Tuple[Any, Any]:
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"""Paradox merge operator ⊕.
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Returns a tuple of ``(a + b, a - b)``. The operator is non-
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commutative and non-associative, encouraging exploration of unusual
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algebraic structures.
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"""
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try:
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return a + b, a - b
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except TypeError as exc: # pragma: no cover - demonstration only
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raise TypeError("operands must support + and -") from exc
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def infinite_fold(func: Callable[[Any, Any], Any], values: Iterable[Any]) -> Any:
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"""Infinite fold operator ⊗.
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Conceptually applies ``func`` across ``values`` endlessly. In
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practice we simply use :func:`functools.reduce` but expose the idea of
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a never-ending fold.
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"""
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return reduce(func, values)
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def collapse(value: Any) -> Any:
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"""Collapse operator ↯.
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If ``value`` is iterable the items are combined using ``paradox_merge``
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until a single value remains; otherwise it is returned unchanged.
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"""
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if isinstance(value, Iterable) and not isinstance(value, (str, bytes)):
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items = list(value)
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if not items:
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return None
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result = items[0]
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for item in items[1:]:
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result = paradox_merge(result, item)[0]
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return result
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return value
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if __name__ == "__main__":
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# Example usage of the custom operators.
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print("Paradox merge of 3 and 1:", paradox_merge(3, 1))
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print("Infinite fold sum:", infinite_fold(lambda x, y: x + y, [1, 2, 3, 4]))
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print("Collapse list:", collapse([1, 2, 3]))
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