Formula.h File Reference

Symbolic representation of provenance as a human-readable formula. More...

#include <numeric>
#include <vector>
#include <string>
#include <sstream>
#include <iterator>
#include "Semiring.h"

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Classes
class	semiring::Formula
	Symbolic provenance representation over std::string. More...

Namespaces
namespace	semiring

Functions
template<typename Range, typename Value = typename Range::value_type>
static std::string	join (Range const &elements, const char *const delimiter)
	Concatenate elements of a range with a delimiter.
static std::string	strip_wrap_if_op (const std::string &s, const std::string &op)
	If s is wrapped in a single matched outer paren pair AND its top-level operator (depth 1, inside that pair) is op, return the inner content; otherwise return s unchanged.

Detailed Description

Symbolic representation of provenance as a human-readable formula.

The Formula pseudo-semiring (std::string, \(\oplus\), \(\otimes\), "𝟘", "𝟙") produces a symbolic representation of provenance using Unicode semiring symbols. It is primarily used for debugging and testing.

Each gate evaluates to a string:

• zero() → "𝟘"
• one() → "𝟙"
• plus() → "(a ⊕ b ⊕ …)" or just "a" for singletons
• times() → "(a ⊗ b ⊗ …)" or just "a" for singletons
• monus() → "(a ⊖ b)"
• delta() → "δ(a)" or "δa" if a starts with (
• cmp() → "[s1 op s2]"
• semimod()→ "x*s"
• agg() → operator-specific notation (e.g., "min(a,b)")
• value() → the literal string itself

Definition in file Formula.h.

Function Documentation

join()

template<typename Range, typename Value = typename Range::value_type>

std::string join ( Range const & elements, const char *const delimiter )

static

Concatenate elements of a range with a delimiter.

Used internally by Formula::plus(), Formula::times(), and Formula::agg() to build operator-separated strings.

Template Parameters

Range	Any range type with a value_type typedef.
Value	Element type (defaults to Range::value_type).

Parameters

elements	The range to join.
delimiter	String to insert between adjacent elements.

Returns

All elements concatenated with delimiter between them.

Definition at line 46 of file Formula.h.

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strip_wrap_if_op()

std::string strip_wrap_if_op ( const std::string & s, const std::string & op )

static

If s is wrapped in a single matched outer paren pair AND its top-level operator (depth 1, inside that pair) is op, return the inner content; otherwise return s unchanged.

Used by Formula::plus() and Formula::times() to flatten same-op nested gates by associativity: a child "(a ⊕ b)" feeding into a parent plus is unwrapped to "a ⊕ b" so the join produces "a ⊕ b ⊕ c" instead of "(a ⊕ b) ⊕ c". A different top-level op (e.g., a times child) keeps its parens.

Definition at line 72 of file Formula.h.

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