Definitions of compiled semirings. More...

Functions
VARCHAR	provsql.sr_formula (ANYELEMENT token, REGCLASS token2value)
	Evaluate provenance as a symbolic formula (e.g., "a ⊗ b ⊕ c").
INT	provsql.sr_counting (ANYELEMENT token, REGCLASS token2value)
	Evaluate provenance over the counting semiring (ℕ).
VARCHAR	provsql.sr_why (ANYELEMENT token, REGCLASS token2value)
	Evaluate provenance as why-provenance (set of witness sets).
VARCHAR	provsql.sr_how (ANYELEMENT token, REGCLASS token2value)
	Evaluate provenance as how-provenance (canonical polynomial provenance ℕ[X], universal commutative-semiring provenance).
VARCHAR	provsql.sr_which (ANYELEMENT token, REGCLASS token2value)
	Evaluate provenance as which-provenance (lineage: a single set of contributing labels).
VARCHAR	provsql.sr_boolexpr (ANYELEMENT token, REGCLASS token2value=NULL)
	Evaluate provenance as a Boolean expression.
BOOLEAN	provsql.sr_boolean (ANYELEMENT token, REGCLASS token2value)
	Evaluate provenance over the Boolean semiring (true/false).
FLOAT	provsql.sr_tropical (ANYELEMENT token, REGCLASS token2value)
	Evaluate provenance over the tropical (min-plus) m-semiring.
FLOAT	provsql.sr_viterbi (ANYELEMENT token, REGCLASS token2value)
	Evaluate provenance over the Viterbi (max-times) m-semiring.
FLOAT	provsql.sr_lukasiewicz (ANYELEMENT token, REGCLASS token2value)
	Evaluate provenance over the Łukasiewicz fuzzy m-semiring.
ANYENUM	provsql.sr_minmax (UUID token, REGCLASS token2value, ANYENUM element_one)
	Evaluate provenance over the min-max m-semiring on a user ENUM.
ANYENUM	provsql.sr_maxmin (UUID token, REGCLASS token2value, ANYENUM element_one)
	Evaluate provenance over the max-min m-semiring on a user ENUM.

Detailed Description

Definitions of compiled semirings.

Function Documentation

◆ sr_boolean()

BOOLEAN provsql.sr_boolean	(	ANYELEMENT	token,
		REGCLASS	token2value )

Evaluate provenance over the Boolean semiring (true/false).

Source code: provsql.sql line 3883

◆ sr_boolexpr()

VARCHAR provsql.sr_boolexpr	(	ANYELEMENT	token,
		REGCLASS	token2value = NULL )

Evaluate provenance as a Boolean expression.

The optional token2value mapping labels the leaves of the formula: when omitted, leaves are rendered as bare x<id> placeholders.

Source code: provsql.sql line 3866

◆ sr_counting()

INT provsql.sr_counting	(	ANYELEMENT	token,
		REGCLASS	token2value )

Evaluate provenance over the counting semiring (ℕ).

Source code: provsql.sql line 3805

◆ sr_formula()

VARCHAR provsql.sr_formula	(	ANYELEMENT	token,
		REGCLASS	token2value )

Evaluate provenance as a symbolic formula (e.g., "a ⊗ b ⊕ c").

Source code: provsql.sql line 3791

◆ sr_how()

VARCHAR provsql.sr_how	(	ANYELEMENT	token,
		REGCLASS	token2value )

Evaluate provenance as how-provenance (canonical polynomial provenance ℕ[X], universal commutative-semiring provenance).

Source code: provsql.sql line 3833

◆ sr_lukasiewicz()

FLOAT provsql.sr_lukasiewicz	(	ANYELEMENT	token,
		REGCLASS	token2value )

Evaluate provenance over the Łukasiewicz fuzzy m-semiring.

Inputs are read as float8 graded-truth values in \([0,1]\). Addition is \(\max\); multiplication is the Łukasiewicz t-norm \(\max(a + b - 1, 0)\), which preserves crisp truth and avoids the near-zero collapse of long product chains.

Source code: provsql.sql line 3940

◆ sr_maxmin()

ANYENUM provsql.sr_maxmin	(	UUID	token,
		REGCLASS	token2value,
		ANYENUM	element_one )

Evaluate provenance over the max-min m-semiring on a user ENUM.

Dual of :sqlfunc:sr_minmax: addition is ENUM-max, multiplication is ENUM-min. The fuzzy / availability / trust shape: alternatives combine to the most permissive label, joins combine to the strictest label. The third argument is a sample value of the carrier ENUM, used only for type inference; its value is ignored.

Parameters

token	Provenance token to evaluate.
token2value	Mapping from input gates to ENUM values.
element_one	Sample value of the carrier ENUM (any value works).

Source code: provsql.sql line 3993

◆ sr_minmax()

ANYENUM provsql.sr_minmax	(	UUID	token,
		REGCLASS	token2value,
		ANYENUM	element_one )

Evaluate provenance over the min-max m-semiring on a user ENUM.

Inputs are read as values of a user-defined ENUM carrier; addition is ENUM-min, multiplication is ENUM-max. Bottom and top of the ENUM are derived from pg_enum.enumsortorder. The third argument is a sample value of the carrier ENUM, used only for type inference; its value is ignored.

The security shape: alternative derivations combine to the least sensitive label, joins combine to the most sensitive label.

Parameters

token	Provenance token to evaluate.
token2value	Mapping from input gates to ENUM values.
element_one	Sample value of the carrier ENUM (any value works).

Source code: provsql.sql line 3968

◆ sr_tropical()

FLOAT provsql.sr_tropical	(	ANYELEMENT	token,
		REGCLASS	token2value )

Evaluate provenance over the tropical (min-plus) m-semiring.

Inputs are read as float8 cost values; the additive identity is 'Infinity'::float8 and the multiplicative identity is 0. Returns the cost of the cheapest derivation.

Source code: provsql.sql line 3902

◆ sr_viterbi()

FLOAT provsql.sr_viterbi	(	ANYELEMENT	token,
		REGCLASS	token2value )

Evaluate provenance over the Viterbi (max-times) m-semiring.

Inputs are read as float8 probability values in \([0,1]\). Returns the probability of the most likely derivation.

Source code: provsql.sql line 3920

◆ sr_which()

VARCHAR provsql.sr_which	(	ANYELEMENT	token,
		REGCLASS	token2value )

Evaluate provenance as which-provenance (lineage: a single set of contributing labels).

Source code: provsql.sql line 3847

◆ sr_why()

VARCHAR provsql.sr_why	(	ANYELEMENT	token,
		REGCLASS	token2value )

Evaluate provenance as why-provenance (set of witness sets).

Source code: provsql.sql line 3819

Functions