Counting.h File Reference

Counting semiring (ℕ, +, ×, 0, 1). More...

#include <numeric>
#include <vector>
#include <stdexcept>
#include "Semiring.h"

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Classes
class	semiring::Counting
	The counting semiring over unsigned. More...

Namespaces
namespace	semiring

Detailed Description

Counting semiring (ℕ, +, ×, 0, 1).

The counting semiring ( \(\mathbb{N}\), \(+\), \(\times\), 0, 1) counts the number of distinct derivations (proof witnesses) of each query result tuple.

Operations:

• zero() → 0
• one() → 1
• plus() → sum of all operands
• times() → product of all operands
• monus() → truncated subtraction: max(0, x − y)
• delta() → 1 if x ≠ 0, else 0

This semiring is not absorptive.

Definition in file Counting.h.