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 value_type	unmapped_input (const std::string &uuid) const
	Value of a variable leaf (`gate_input` / `gate_mulinput`) that the provenance mapping does not name.
virtual value_type	rv (const std::string &spec, const std::vector< value_type > &params) const
	Evaluate a continuous random-variable leaf (`gate_rv`).
virtual value_type	arith (ArithmeticOperator op, const std::vector< value_type > &children, const std::string &extra) const
	Evaluate an arithmetic gate over scalar children (`gate_arith`).
virtual value_type	mixture (value_type p, value_type x, value_type y) const
	Evaluate a Bernoulli mixture (`gate_mixture`, three wires).
virtual value_type	categorical (value_type key, const std::vector< double > &probs, const std::vector< std::string > &outcomes) const
	Evaluate a categorical mixture (`gate_mixture` over `gate_mulinput` outcomes).
virtual value_type	guarded_case (const std::vector< value_type > &children) const
	Evaluate a guarded selection (`gate_case`).
virtual value_type	observe (value_type child, const std::string &datum) const
	Evaluate a latent-variable observation (`gate_observe`).
virtual value_type	conditioned (const std::vector< value_type > &children) const
	Evaluate a conditioning marker (`gate_conditioned`).
virtual	~Semiring ()=default
virtual bool	absorptive () const
	Return `true` if this semiring is absorptive ( \(\mathbb{1} \oplus a = \mathbb{1}\) for all \(a\)).
virtual bool	idempotent () const
	Return `true` if this semiring is idempotent ( \(a \oplus a = a\) for all \(a\)).
virtual bool	mul_sub_left_distributive () const
	Return `true` if \(\otimes\) distributes over the monus on the left: \(a \otimes (b \ominus c) = (a \otimes b) \ominus (a \otimes c)\) for all \(a, b, c\).
virtual bool	certifying () const
	Whether this semiring builds certified exclusive enumerations (see the three hooks below).
virtual bool	independent_literal (const value_type &) const
	Whether `v` is an independent literal for certification purposes: a base Bernoulli variable (or a constant), so that distinct literals have disjoint supports and an AND over them is decomposable.
virtual value_type	certified_world_term (const std::vector< value_type > &, const std::vector< value_type > &) const
	Build one complete world term: the conjunction of the `present` literals and the negations of the `missing` literals, certified decomposable.
virtual value_type	certified_exclusive_plus (const std::vector< value_type > &) const
	Build the disjunction of pairwise-exclusive `disjuncts`, certified deterministic.

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

Public Member Functions

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ compatibleWithBooleanRewrite()

◆ delta()

◆ monus()

◆ one()

◆ parse_leaf()

◆ plus()

◆ times()

◆ to_text()

◆ zero()