, From Weakest Pre-Conditions to Victory Invariants We now state the main correctness result for our verification language, as a transfer property from language W G to games. Essentially, we claim that weakest pre-conditions for W G induce the existence of victory invariants
,
,
We define the base specification context ? G associated to game G = (G, ?) as the single-element specification context mapping CONT ,
We derive from Theorem 4 an immediate corollary, which concludes the existence of a victory invariant for a pair of sets definable in the meta-logic as long as we can ,
? {0}|? ? : {0} of W G , all formula pairs ? 0 , ? 1 well-typed in context ?, now : G, and all ?-assignations ?, if the contract satisfaction property C, Corollary 1. For all games G = (G, ?), all well-typed programs CONT : P(G), vol.27, pp.583-625, 1990. ,
Proving pointer programs in Hoare logic, Mathematics of Program Construction, pp.102-126, 2000. ,
Méthodes et outils pour la spécification et la preuve de propriétés difficiles de programmes séquentiels, 2018. ,
Deductive verification via ghost debugging, Research Report, vol.9219, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01907894
Guarded commands, nondeterminacy and formal derivation of programs, Commun. ACM, vol.18, pp.453-457, 1975. ,
DOI : 10.1145/360933.360975
The spirit of ghost code, Formal Methods in System Design, vol.48, issue.3, pp.152-174, 2016. ,
The essence of higher-order concurrent separation logic, 26th European Symposium on Programming Languages and Systems, vol.10201, pp.696-723, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01633133
Dafny: An automatic program verifier for functional correctness, LPAR-16, vol.6355, pp.348-370, 2010. ,
DOI : 10.1007/978-3-642-17511-4_20
Synthesis of strategies using the Hoare logic of angelic and demonic nondeterminism, Logical Methods in Computer Science, vol.12, issue.3, 2016. ,
Properties of programs and partial function logic, Machine Intelligence, vol.5, 1970. ,
Tools and Algorithms for the Construction and Analysis of Systems, pp.568-582, 2007. ,
An efficient machine-independent procedure for garbage collection in various list structures, Communications of the ACM, vol.10, pp.501-506, 1967. ,
DOI : 10.1145/363534.363554
Relational separation logic, Theoretical Computer Science, vol.375, issue.1, pp.308-334, 2007. ,
DOI : 10.1016/j.tcs.2006.12.036
URL : https://doi.org/10.1016/j.tcs.2006.12.036