Name
Abstract | ||
|---|---|---|
We generalise the designs of the Unifying Theories of Programming (UTP) by defining them as matrices over semirings with ideals. This clarifies the algebraic structure of designs and considerably simplifies reasoning about them, for example, since they form a Kleene and omega algebra and a test semiring. We apply our framework to investigate symmetric linear recursion and its relation to tail-recursion. This substantially involves Kleene and omega algebra as well as additional algebraic formulations of determinacy, invariants, domain, pre-image, convergence and Noetherity. Due to the uncovered algebraic structure of UTP designs, all our general results also directly apply to UTP. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1016/j.jlap.2009.07.002 | The Journal of Logic and Algebraic Programming |
Keywords | Field | DocType |
Unifying Theories of Programming,Semantics,Semiring,Kleene algebra,Omega algebra,Fixpoint,Linear recursion | Kleene algebra,Discrete mathematics,Algebraic number,Algebra,Algebraic structure,Kleene's recursion theorem,Filtered algebra,Invariant (mathematics),Mathematics,Recursion,Semiring | Journal |
Volume | Issue | ISSN |
79 | 2 | 1567-8326 |
Citations | PageRank | References |
9 | 0.51 | 27 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Walter Guttmann | 1 | 196 | 16.53 |
| Bernhard Möller | 2 | 788 | 55.89 |