On procedures as open subroutines. II

SummaryIn part I [11] of the paper elimination of global procedure parameters and modularity of programming languages have been investigated. The methods developed there are used in the present part II to prove that the so called macro program problem for ALGOL 60 and other ALGOL-like languages is algorithmically unsolvable (Theorem 4.3 and 4.4). Macro grammars theory is applied in order to determine sublanguages for which the macro program problem is solvable (Theorem 4.1, 5.2–5.5).

[1]  B. J. Mailloux,et al.  Report on the Algorithmic Language ALGOL 68 , 1969 .

[2]  S. Kleene $\lambda$-definability and recursiveness , 1936 .

[3]  Alfred V. Aho,et al.  Indexed Grammars—An Extension of Context-Free Grammars , 1967, SWAT.

[4]  J. R. Büchi Regular Canonical Systems , 1964 .

[5]  Wolfram-Manfred Lippe Entscheidbarkeitsprobleme bei der Übersetzung von Programmen mit einparametrigen Prozeduren , 1974, Fachtagung über Programmiersprachen.

[6]  Friedrich L. Bauer,et al.  Revised report on the algorithm language ALGOL 60 , 1963, CACM.

[7]  Seymour Ginsburg,et al.  Stack automata and compiling , 1967, JACM.

[8]  Michael J. Fischer,et al.  Grammars with Macro-Like Productions , 1968, SWAT.

[9]  S. Kleene,et al.  λ-Definability and Recursiveness. , 1937 .

[10]  F. L. Bauer,et al.  Revised report on the algorithmic languageAlgol 60 , 1962 .

[11]  Hans Langmaack On procedures as open subroutines. I , 2004, Acta Informatica.

[12]  A. Church The calculi of lambda-conversion , 1941 .

[13]  Jeffrey D. Ullman,et al.  Formal languages and their relation to automata , 1969, Addison-Wesley series in computer science and information processing.

[14]  E. Lohse,et al.  A Correspondence Between ALGOL 60 and Church's Lambda- Notation: Part I* , 1965 .

[15]  William C. Rounds,et al.  Mappings and grammars on trees , 1970, Mathematical systems theory.

[16]  J. Bormann A. van Wijngaarden (Ed.), B. J. Mailloux, J. E. L. Peck and C. H. A. Koster, Report on the Algorithmic Language ALGOL 68. Amsterdam 1969. Printing by the Mathematisch Centrum. Preis brosch. $ 4.50 . , 1970 .

[17]  Michael J. Fischer,et al.  Lambda-calculus schemata , 1993, LISP Symb. Comput..

[18]  Hans Langmaack,et al.  On correct procedure parameter transmission in higher programming languages , 1973, Acta Informatica.

[19]  B. J. Mailloux,et al.  Report of Algorithmic Language ALGOL 68 , 1969 .

[20]  Friedrich Ludwig Bauer Advanced Course on Software Engineering , 1973 .