Incremental Parametric Development of Greedy Algorithms

The event B method provides a general framework for modelling both data structures and algorithms. B models are validated by discharging proof obligations ensuring safety properties. We address the problem of development of greedy algorithms using the seminal work of S. Curtis; she has formalised greedy algorithms in a relational calculus and has provided a list of results ensuring optimality results. Our first contribution is a re-modelling of Curtis's results in the event B framework and a mechanical checking of theorems on greedy algorithms The second contribution is the reuse of the mathematical framework for developing greedy algorithms from event B models; since the resulting event B models are generic, we show how to instantiate generic event B models to derive specific greedy algorithms; generic event B developments help in managing proofs complexity. Consequently, we contribute to the design of a library of proof-based developed algorithms.