Formula.h File Reference

Symbolic formula semiring producing readable provenance expressions. More...

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

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Classes
class	semiring::Formula
	Symbolic provenance formula semiring 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.

Detailed Description

Symbolic formula semiring producing readable provenance expressions.

The Formula semiring (std::string, \(\oplus\), \(\otimes\), "𝟘", "𝟙") represents provenance as a human-readable symbolic expression 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>

static 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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