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1987

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“…The origin of Apt's obserbjation is the argument of Theorem 2 in [lo] which shows that HLo(A) is incompiete in case A is Presburger Arithmetic; and we again find it in use in [9], there applied to finite structures A which interpret much richer programming languages than WV with undecidable halting problems for IAl 2 2. Actually, the termination of programs over finite interpretations was considered, independently of Hoare's logic, in Langmaack [14,15]; for example the observation applies there to sharpen one of Clarke's incompleteness results to include structures A with IA I= 1, and it a;speai ;. often in Langmaack and Olderog's extensive studies of Hoare-like logics for the higher progralm languages, see [16f and the references there cited.…”

confidence: 99%

“…The origin of Apt's obserbjation is the argument of Theorem 2 in [lo] which shows that HLo(A) is incompiete in case A is Presburger Arithmetic; and we again find it in use in [9], there applied to finite structures A which interpret much richer programming languages than WV with undecidable halting problems for IAl 2 2. Actually, the termination of programs over finite interpretations was considered, independently of Hoare's logic, in Langmaack [14,15]; for example the observation applies there to sharpen one of Clarke's incompleteness results to include structures A with IA I= 1, and it a;speai ;. often in Langmaack and Olderog's extensive studies of Hoare-like logics for the higher progralm languages, see [16f and the references there cited.…”

confidence: 99%

“…Es entsteht ein formal ~iquivalentes Programm [2]. Eine Prozedur mit globalen Parametern wird gemiil3 Lemma 4.1 auf Schachtelungstiefe 1 gebracht; es bleibt eine ,,unwesentliche" Prozedur auf Schachtelungstiefe n stehen.…”

“…Earlier, Kruseman Aretz [5] has used Algol 60's name parameter mechanism instead of formal procedures. Actually, arbitrary Turing machines and similar devices can be simulated by procedures and recursion only (and without other data types like integer and boolean), as shown by Langmaack [6,7,8] and Fokkinga [3]. (Of course, for anyone familiar with the Lambda calculus this comes as no surprise, but what is important here is that procedures as result are not needed in these programs.…”

confidence: 99%