semiring::Counting Class Reference

The counting semiring over unsigned. More...

#include "Counting.h"

Inheritance diagram for semiring::Counting:

Collaboration diagram for semiring::Counting:

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	compatibleWithBooleanRewrite () const override
	No semiring homomorphism BoolFunc(X) →+* ℕ exists: any such map would force 1 + a = 1 in ℕ (from var + 1 = 1 in BoolFunc), contradicting the non-absorptivity of ℕ.
value_type	parse_leaf (const char *v) const
Public Member Functions inherited from semiring::Semiring< unsigned >
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< unsigned >
typedef unsigned	value_type
	The carrier type of this semiring.

Detailed Description

The counting semiring over unsigned.

Each gate evaluates to the number of distinct derivations of the corresponding sub-formula.

Definition at line 41 of file Counting.h.

Member Function Documentation

compatibleWithBooleanRewrite()

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

inlineoverridevirtual

No semiring homomorphism BoolFunc(X) →+* ℕ exists: any such map would force 1 + a = 1 in ℕ (from var + 1 = 1 in BoolFunc), contradicting the non-absorptivity of ℕ.

The safe-query Boolean rewrite is therefore unsound under the counting semiring (read-once factoring loses derivation multiplicities). Inherits the false default from Semiring; this override exists for documentation.

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

Reimplemented from semiring::Semiring< unsigned >.

Definition at line 76 of file Counting.h.

delta()

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

inlineoverridevirtual

Apply the \(\delta\) operator.

Parameters

x	Input value.

Returns

\(\delta(x)\).

Implements semiring::Semiring< unsigned >.

Definition at line 60 of file Counting.h.

monus()

virtual value_type semiring::Counting::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< unsigned >.

Definition at line 56 of file Counting.h.

one()

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

inlineoverridevirtual

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

Returns

The one element of the semiring.

Implements semiring::Semiring< unsigned >.

Definition at line 47 of file Counting.h.

parse_leaf()

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

inline

Definition at line 79 of file Counting.h.

plus()

virtual value_type semiring::Counting::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< unsigned >.

Definition at line 50 of file Counting.h.

times()

virtual value_type semiring::Counting::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< unsigned >.

Definition at line 53 of file Counting.h.

zero()

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

inlineoverridevirtual

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

Returns

The zero element of the semiring.

Implements semiring::Semiring< unsigned >.

Definition at line 44 of file Counting.h.

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

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