What the source specifies
A candidate repair minimizes residual bug loss and edit cost under compile, type, test and safety predicates, with a program recurrence and two self-extension expressions.
Equations and variants
Every visible complete mathematical relation has a linked record, including parameter definitions, constraints, decorative corner equations and repeated formula variants. The original images and full reading copies are available through the source links.
Source findings and limits
The large objective, all four acceptance equalities, recurrence, eight variable definitions and both self-extension expressions were inspected.
Tiny code-like glyphs inside the broken-program and candidate-file illustrations are decorative, incomplete and not a recoverable source listing. No additional complete analytic equation is legible there.
The title and caption claim safe minimal fixes. The source records a constrained optimization design; tests and predicates require independent implementation and validation.
Equations in this build
16 linked mathematical records. Each opens its notation, interpretation and source.
Rhiannon constrained repair objective
Select a candidate program that minimizes residual bug loss plus a weighted cost of changing the original program. The displayed compile, type, test and safety predicates restrict…
Rhiannon Compile acceptance condition
The poster uses a binary acceptance predicate requiring that the candidate compiles. It is one of four conditions restricting the repair search.
Rhiannon TypeSafe acceptance condition
The poster uses a binary acceptance predicate requiring that the candidate passes the chosen type check. It is one of four conditions restricting the repair search.
Rhiannon Tests acceptance condition
The poster uses a binary acceptance predicate requiring that the candidate passes the specified diagnostics and tests. It is one of four conditions restricting the repair search.
Rhiannon Safety acceptance condition
The poster uses a binary acceptance predicate requiring that the candidate passes the specified safety check. It is one of four conditions restricting the repair search.
Rhiannon repeated program repair
Apply the repair operator R to the current program and current diagnostics to obtain the next program. Repeating this interface describes an iterative repair process; it does not…
P: the current program and reference for a repair
P names the existing program or codebase at the repair step under consideration. It stays fixed while different candidate programs P′ are compared, so the change-cost term C(P′−P)…
P′: a candidate program in the Rhiannon repair search
P′ names one proposed modified program considered by the repair objective. The prime distinguishes a candidate from the current program P; it does not denote a derivative. In the…
Rhiannon selected-program definition
The star labels an optimizer of the stated constrained objective, if such a candidate exists and is found.
Rhiannon restraint-weight definition
A larger nonnegative λ makes disruptive changes more costly relative to residual bug loss.
Rhiannon diagnostics definition
D collects the evidence against which a candidate is assessed.
Rhiannon bug-loss definition
B scores residual failure in candidate P′ relative to diagnostic evidence D.
Rhiannon change-cost definition
C measures how disruptive the difference from the original program is. Program subtraction is a change representation rather than ordinary numeric subtraction unless encoded.
Rhiannon repair-operator definition
R names the process that transforms program and diagnostics into the next candidate state.
Rhiannon seven-stage self-extension sum
Apply each of seven stage operators twice to x and sum the resulting outputs. This expression is a sum of self-composed stage transforms, not the sequential composition S_7∘…∘S_1.…
Rhiannon seventh-stage self-composition
The seventh stage operator is applied twice to the input. This names a repeated transformation; it does not by itself provide the stage function or establish an implemented…