A Refinement Based Framework for Computing Loop Behavior

TL;DR: The authors investigate the problem of proving (or disproving) if P computes F over D and show that if P satisfies certain natural constraints, then there is a loop assertion independent of the structure of the loop body, that is both necessary and sufficient for proving the hypothesis.

TL;DR: An abstract logical framework is presented for automating the discovery of invariants for loops without nesting, of which the algorithm based on algebraic geometry and Grobner bases is one particular instance and is proved to be correct and complete.

TL;DR: An algorithm is presented that generates automatically (algebraic) invariant properties of a loop with conditionals that are used for verifying partial correctness of imperative programs in the Theorema system.

TL;DR: 120 computer algebra systems – CAS, VIII computer language – semantics, 120 – syntax, 120 concept comprehension, 8 conditional statements – if-statement, 17 confluence, 18 constraints, 9.