Formula.h File Reference

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

#include <numeric>
#include <vector>
#include <string>
#include <sstream>
#include <iomanip>
#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.
static std::string	format_number (double v)
	Render a probability for display in a symbolic formula.

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
• unmapped_input() → the leaf's abbreviated UUID ("1361b50e…")

It also renders the measure-carrier gates that carry no algebraic meaning, and that every proper semiring therefore refuses – being a serialisation of the circuit rather than an evaluation of it, Formula has a faithful rendering for each and refuses nothing:

• rv() → "normal(2.5, 0.5)" (wired parameters substituted)
• arith() → ordinary arithmetic notation ("(a + b)", "ln(a)"…), kept visually distinct from the semiring's \(\oplus\) / \(\otimes\)
• mixture() → "(p ? x : y)"
• categorical() → "categorical(κ; 0.3: a, 0.7: b)"
• guarded_case()→ "case(g → v; else d)"
• observe() → "observe(x = 2.5)"
• conditioned() → "(x | c)"

Definition in file Formula.h.

Function Documentation

format_number()

std::string format_number ( double v )

static

Render a probability for display in a symbolic formula.

Enough significant digits that the usual decimal probabilities print back as themselves (0.3, not 0.299999), without the full round-trip verbosity of setprecision(17).

Definition at line 125 of file Formula.h.

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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 62 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 88 of file Formula.h.

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