semiring::How Class Reference

How-provenance m-semiring over \(\mathbb{N}[X]\). More...

#include "How.h"

Inheritance diagram for semiring::How:

Collaboration diagram for semiring::How:

Public Member Functions
value_type	zero () const override
	Return the additive identity \(\mathbb{0}\).
value_type	one () const override
	Return the multiplicative identity \(\mathbb{1}\).
value_type	plus (const std::vector< value_type > &vec) const override
	Apply the additive operation to a list of values.
value_type	times (const std::vector< value_type > &vec) const override
	Apply the multiplicative operation to a list of values.
value_type	monus (value_type x, value_type y) const override
	Apply the monus (m-semiring difference) operation.
value_type	delta (value_type x) const override
	Apply the \(\delta\) operator.
virtual bool	compatibleWithBooleanRewrite () const override
	No semiring homomorphism BoolFunc(Y) →+* ℕ[X] exists, so the safe-query Boolean rewrite is unsound under how-provenance (which is sensitive to derivation multiplicities and monomial structure that the read-once rewrite collapses).
value_type	parse_leaf (const char *v) const
	Parse a leaf value into a how-provenance polynomial.
std::string	to_text (const value_type &prov) const
Public Member Functions inherited from semiring::Semiring< how_provenance_t >
virtual value_type	cmp (value_type s1, ComparisonOperator op, value_type s2) const
	Evaluate a comparison gate.
virtual value_type	semimod (value_type x, value_type s) const
	Apply a semimodule scalar multiplication.
virtual value_type	agg (AggregationOperator op, const std::vector< value_type > &s)
	Evaluate an aggregation gate.
virtual value_type	value (const std::string &s) const
	Interpret a literal string as a semiring value.
virtual	~Semiring ()=default
virtual bool	absorptive () const
	Return true if this semiring is absorptive ( \(\mathbb{1} \oplus a = \mathbb{1}\) for all \(a\)).

Additional Inherited Members
Public Types inherited from semiring::Semiring< how_provenance_t >
typedef how_provenance_t	value_type
	The carrier type of this semiring.

Detailed Description

How-provenance m-semiring over \(\mathbb{N}[X]\).

Each gate evaluates to a how_provenance_t, a polynomial in canonical sum-of-products form. Two semantically-equal polynomials compare equal under std::map's lexicographic equality, so this semiring supports provenance-aware query equivalence.

Definition at line 72 of file How.h.

Member Function Documentation

compatibleWithBooleanRewrite()

virtual bool semiring::How::compatibleWithBooleanRewrite ( ) const

inlineoverridevirtual

No semiring homomorphism BoolFunc(Y) →+* ℕ[X] exists, so the safe-query Boolean rewrite is unsound under how-provenance (which is sensitive to derivation multiplicities and monomial structure that the read-once rewrite collapses).

Inherits the false default from Semiring; this override exists for documentation.

Lean: Provenance.Semirings.How.no_hom_from_BoolFunc (provenance-lean/Provenance/Semirings/How.lean).

Reimplemented from semiring::Semiring< how_provenance_t >.

Definition at line 139 of file How.h.

delta()

value_type semiring::How::delta ( value_type x ) const

inlineoverridevirtual

Apply the \(\delta\) operator.

Parameters

x	Input value.

Returns

\(\delta(x)\).

Implements semiring::Semiring< how_provenance_t >.

Definition at line 124 of file How.h.

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monus()

value_type semiring::How::monus ( value_type x, value_type y ) const

inlineoverridevirtual

Apply the monus (m-semiring difference) operation.

Parameters

x	Minuend.
y	Subtrahend.

Returns

\(x \ominus y\).

Implements semiring::Semiring< how_provenance_t >.

Definition at line 112 of file How.h.

one()

value_type semiring::How::one ( ) const

inlineoverridevirtual

Return the multiplicative identity \(\mathbb{1}\).

Returns

The one element of the semiring.

Implements semiring::Semiring< how_provenance_t >.

Definition at line 78 of file How.h.

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parse_leaf()

value_type semiring::How::parse_leaf ( const char * v ) const

inline

Parse a leaf value into a how-provenance polynomial.

Accepted input formats (round-trip with to_text):

• "0" → zero polynomial
• Bare label: "Alice" → {Alice}
• Constant: "5" → 5 (polynomial 5⋅1)
• Monomial: "2⋅Alice⋅Bob^2"
• Sum of monomials: "2⋅Alice⋅Bob^2 + 3⋅Charlie"

Variables may contain any character except '⋅', '+', '^'. The " + " separator must use ASCII spaces around the '+'.

Definition at line 156 of file How.h.

plus()

value_type semiring::How::plus ( const std::vector< value_type > & v ) const

inlineoverridevirtual

Apply the additive operation to a list of values.

Parameters

v	Ordered list of operands (empty list should return zero()).

Returns

\(v_0 \oplus v_1 \oplus \cdots\).

Implements semiring::Semiring< how_provenance_t >.

Definition at line 82 of file How.h.

times()

value_type semiring::How::times ( const std::vector< value_type > & v ) const

inlineoverridevirtual

Apply the multiplicative operation to a list of values.

Parameters

v	Ordered list of operands (empty list should return one()).

Returns

\(v_0 \otimes v_1 \otimes \cdots\).

Implements semiring::Semiring< how_provenance_t >.

Definition at line 92 of file How.h.

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to_text()

std::string semiring::How::to_text ( const value_type & prov ) const

inline

Definition at line 237 of file How.h.

zero()

value_type semiring::How::zero ( ) const

inlineoverridevirtual

Return the additive identity \(\mathbb{0}\).

Returns

The zero element of the semiring.

Implements semiring::Semiring< how_provenance_t >.

Definition at line 74 of file How.h.

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The documentation for this class was generated from the following file:

• /home/pierre/git/software/provsql/src/semiring/How.h