Action logic and pure induction [chapter]

Vaughan Pratt
1991 Lecture Notes in Computer Science  
In Floyd-Hoare logic, programs are dynamic while assertions are static (hold at states). In action logic the two notions become one, with programs viewed as on-the-fly assertions whose truth is evaluated along intervals instead of at states. Action logic is an equational theory ACT conservatively extending the equational theory REG of regular expressions with operations preimplication a→b (had a then b) and postimplication b←a (b if-ever a). Unlike REG, ACT is finitely based, makes a *
more » ... transitive closure, and has an equivalent Hilbert system. The crucial axiom is that of pure induction, (a→a) * = a→a.
doi:10.1007/bfb0018436 fatcat:75qausdsnvdopiudojseqmab5e