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“…Consider the class of all programs from YP which disallow selfapplication and global simple variables in procedure bodies. Langmaack [34] proved that this class of programs satisfies condition l of Theorem 6 in the case of the ALGOL 60 copy rule. By Theorem 6 there exists a sound and complete Hoare's logic for this class of programs.…”

confidence: 96%

“…Consider the class of all programs from YP which disallow selfapplication and global simple variables in procedure bodies. Langmaack [34] proved that this class of programs satisfies condition l of Theorem 6 in the case of the ALGOL 60 copy rule. By Theorem 6 there exists a sound and complete Hoare's logic for this class of programs.…”

confidence: 96%

“…But (29) implies that q[x + I/x] ~ x + 1 = z is true; so, by (33), q~x+I=z is true. From (29) and (34) we get that…”

confidence: 99%

“…As a first step, Langmaack proved in [Lan82] that for all Algol-like programs in L 4 the divergence problem is decidable for finite interpretations. This is a necessary condition for the existence of a sound and relatively complete Hoare-like proof system according to Lemma A.…”

confidence: 99%

“…For several years the question of whether there existed a natural Hoare proof system for L4 that was sound and complete in the sense of Cook remained open. Langmaack (1979) proved that the halting problem for L4 was decidable and hence, by the characterization theorem given in §6, such a proof system should exist (although perhaps not a natural one!). Olderog (1982) and Damm & Josko (1982) devised proof systems for L4, which were based on the use of a higher order assertion language and the addition of relation variables to the programming language.…”

confidence: 99%