semiring::Which Class Reference

Which-provenance (lineage) semiring. More...

#include "Which.h"

Inheritance diagram for semiring::Which:

Collaboration diagram for semiring::Which:

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) →+* Which exists, so the safe-query Boolean rewrite is unsound under which-provenance.
value_type	parse_leaf (const char *v) const
	Parse a leaf value into a which-provenance set.
std::string	to_text (const value_type &prov) const
Public Member Functions inherited from semiring::Semiring< which_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< which_provenance_t >
typedef which_provenance_t	value_type
	The carrier type of this semiring.

Detailed Description

Which-provenance (lineage) semiring.

Each gate evaluates to a which_provenance_t (set of contributing labels, or \(\bot\)).

Definition at line 58 of file Which.h.

Member Function Documentation

compatibleWithBooleanRewrite()

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

inlineoverridevirtual

No semiring homomorphism BoolFunc(Y) →+* Which exists, so the safe-query Boolean rewrite is unsound under which-provenance.

(Lineage tracks the union of contributing labels per derivation; the read-once rewrite collapses alternative derivations to a single shared label set, which is not in general the union produced by the original circuit.) Inherits the false default from Semiring; this override exists for documentation.

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

Reimplemented from semiring::Semiring< which_provenance_t >.

Definition at line 126 of file Which.h.

delta()

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

inlineoverridevirtual

Apply the \(\delta\) operator.

Parameters

x	Input value.

Returns

\(\delta(x)\).

Implements semiring::Semiring< which_provenance_t >.

Definition at line 109 of file Which.h.

monus()

value_type semiring::Which::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< which_provenance_t >.

Definition at line 93 of file Which.h.

one()

value_type semiring::Which::one ( ) const

inlineoverridevirtual

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

Returns

The one element of the semiring.

Implements semiring::Semiring< which_provenance_t >.

Definition at line 64 of file Which.h.

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parse_leaf()

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

inline

Parse a leaf value into a which-provenance set.

Accepted input formats (round-trip with to_text):

• "⊥" → zero (no derivation)
• Bare label (no leading '{'): "Alice" → {Alice}
• Empty set: "{}" → one (a derivation requiring no witnesses)
• Full set: "{a,b,c}" → {a,b,c}

Labels may contain any character except ',', '{', '}'.

Definition at line 141 of file Which.h.

plus()

value_type semiring::Which::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< which_provenance_t >.

Definition at line 68 of file Which.h.

times()

value_type semiring::Which::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< which_provenance_t >.

Definition at line 80 of file Which.h.

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to_text()

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

inline

Definition at line 177 of file Which.h.

zero()

value_type semiring::Which::zero ( ) const

inlineoverridevirtual

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

Returns

The zero element of the semiring.

Implements semiring::Semiring< which_provenance_t >.

Definition at line 60 of file Which.h.

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

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