semiring::Boolean Class Reference

The Boolean semiring over bool. More...

#include "Boolean.h"

Inheritance diagram for semiring::Boolean:

Collaboration diagram for semiring::Boolean:

Public Member Functions
virtual value_type	zero () const override
	Return the additive identity \(\mathbb{0}\).
virtual value_type	one () const override
	Return the multiplicative identity \(\mathbb{1}\).
virtual value_type	plus (const std::vector< value_type > &v) const override
	Apply the additive operation to a list of values.
virtual value_type	times (const std::vector< value_type > &v) const override
	Apply the multiplicative operation to a list of values.
virtual value_type	monus (value_type x, value_type y) const override
	Apply the monus (m-semiring difference) operation.
virtual value_type	delta (value_type x) const override
	Apply the \(\delta\) operator.
virtual bool	absorptive () const override
	Return true if this semiring is absorptive ( \(\mathbb{1} \oplus a = \mathbb{1}\) for all \(a\)).
virtual bool	compatibleWithBooleanRewrite () const override
	The identity map BoolFunc(X) →+* Bool (evaluating a free Boolean function at a valuation) is an m-semiring homomorphism, so the safe-query Boolean rewrite preserves evaluation results in this semiring.
value_type	parse_leaf (const char *v) const
Public Member Functions inherited from semiring::Semiring< bool >
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

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

Detailed Description

The Boolean semiring over bool.

Provides the standard Boolean interpretation of provenance circuits.

Definition at line 40 of file Boolean.h.

Member Function Documentation

absorptive()

virtual bool semiring::Boolean::absorptive ( ) const

inlineoverridevirtual

Return true if this semiring is absorptive ( \(\mathbb{1} \oplus a = \mathbb{1}\) for all \(a\)).

When true, the circuit evaluator and HAVING-semantics machinery may exploit the resulting idempotency ( \(a \oplus a = a\), implied by absorptivity) to deduplicate children of plus gates and to short-circuit over the multiplicative identity.

Returns

false by default; override to return true.

Reimplemented from semiring::Semiring< bool >.

Definition at line 67 of file Boolean.h.

compatibleWithBooleanRewrite()

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

inlineoverridevirtual

The identity map BoolFunc(X) →+* Bool (evaluating a free Boolean function at a valuation) is an m-semiring homomorphism, so the safe-query Boolean rewrite preserves evaluation results in this semiring.

Lean: Provenance.Semirings.Bool.homomorphism_to_BoolFunc and Bool.homomorphism_from_BoolFunc (provenance-lean/Provenance/Semirings/Bool.lean).

Reimplemented from semiring::Semiring< bool >.

Definition at line 80 of file Boolean.h.

delta()

virtual value_type semiring::Boolean::delta ( value_type x ) const

inlineoverridevirtual

Apply the \(\delta\) operator.

Parameters

x	Input value.

Returns

\(\delta(x)\).

Implements semiring::Semiring< bool >.

Definition at line 63 of file Boolean.h.

monus()

virtual value_type semiring::Boolean::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< bool >.

Definition at line 59 of file Boolean.h.

one()

virtual value_type semiring::Boolean::one ( ) const

inlineoverridevirtual

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

Returns

The one element of the semiring.

Implements semiring::Semiring< bool >.

Definition at line 46 of file Boolean.h.

parse_leaf()

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

inline

Definition at line 83 of file Boolean.h.

plus()

virtual value_type semiring::Boolean::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< bool >.

Definition at line 49 of file Boolean.h.

times()

virtual value_type semiring::Boolean::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< bool >.

Definition at line 54 of file Boolean.h.

zero()

virtual value_type semiring::Boolean::zero ( ) const

inlineoverridevirtual

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

Returns

The zero element of the semiring.

Implements semiring::Semiring< bool >.

Definition at line 43 of file Boolean.h.

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

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