Projection Semantics for Rigid Loops

A rigid loop is a for-loop with a counter not accessible to the loop body or any other part of a program. Special instructions for rigid loops are introduced on top of the syntax of the program algebra PGA. Two different semantic projections are provided and proven equivalent. One of these is taken to have definitional status on the basis of two criteria: 'Normative semantic adequacy' and 'Indicative algorithmic adequacy'. In this paper the authors extend the program algebra PGA with several new instructions to deal with so-called rigid loops. Rigid loops are just program fragments that impose the repetition of a body a fixed number of times.