Partial interpretations of higher order algebraic types

Manfred Broy

doi:10.1007/BFb0016232

Partial interpretations of higher order algebraic types

Manfred Broy

Universität Passau

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

5 Scopus citations

Abstract

The theory of algebraic abstract types specified by conditional equations is extended to types with “nonstrict” operations, partial and even infinite objects based on the concept of partial interpretations. Models of such types are studied where all explicit equations have solutions. Higher order types, i.e. types comprising higher order functions are treated, too. This allows an algebraic (“equational”) specification of algebras including sorts with “infinite” objects and higher order functions (“functionals”).

Original language	English
Title of host publication	Mathematical Foundations of Computer Science 1986 - Proceedings of the 12th Symposium
Editors	Jozef Gruska, Branislav Rovan, Juraj Wiedermann
Publisher	Springer Verlag
Pages	29-43
Number of pages	15
ISBN (Print)	9783540167839
DOIs	https://doi.org/10.1007/BFb0016232
State	Published - 1986
Externally published	Yes
Event	12th Symposium on Mathematical Foundations of Computer Science, MFCS 1986 - Bratislava, Serbia Duration: 25 Aug 1986 → 29 Aug 1986

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	233 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	12th Symposium on Mathematical Foundations of Computer Science, MFCS 1986
Country/Territory	Serbia
City	Bratislava
Period	25/08/86 → 29/08/86

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10.1007/BFb0016232

Cite this

Broy, M. (1986). Partial interpretations of higher order algebraic types. In J. Gruska, B. Rovan, & J. Wiedermann (Eds.), Mathematical Foundations of Computer Science 1986 - Proceedings of the 12th Symposium (pp. 29-43). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 233 LNCS). Springer Verlag. https://doi.org/10.1007/BFb0016232

Broy, Manfred. / Partial interpretations of higher order algebraic types. Mathematical Foundations of Computer Science 1986 - Proceedings of the 12th Symposium. editor / Jozef Gruska ; Branislav Rovan ; Juraj Wiedermann. Springer Verlag, 1986. pp. 29-43 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Partial interpretations of higher order algebraic types",

abstract = "The theory of algebraic abstract types specified by conditional equations is extended to types with “nonstrict” operations, partial and even infinite objects based on the concept of partial interpretations. Models of such types are studied where all explicit equations have solutions. Higher order types, i.e. types comprising higher order functions are treated, too. This allows an algebraic (“equational”) specification of algebras including sorts with “infinite” objects and higher order functions (“functionals”).",

author = "Manfred Broy",

note = "Publisher Copyright: {\textcopyright} 1986, Springer-Verlag.; 12th Symposium on Mathematical Foundations of Computer Science, MFCS 1986 ; Conference date: 25-08-1986 Through 29-08-1986",

year = "1986",

doi = "10.1007/BFb0016232",

language = "English",

isbn = "9783540167839",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "29--43",

editor = "Jozef Gruska and Branislav Rovan and Juraj Wiedermann",

booktitle = "Mathematical Foundations of Computer Science 1986 - Proceedings of the 12th Symposium",

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Broy, M 1986, Partial interpretations of higher order algebraic types. in J Gruska, B Rovan & J Wiedermann (eds), Mathematical Foundations of Computer Science 1986 - Proceedings of the 12th Symposium. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 233 LNCS, Springer Verlag, pp. 29-43, 12th Symposium on Mathematical Foundations of Computer Science, MFCS 1986, Bratislava, Serbia, 25/08/86. https://doi.org/10.1007/BFb0016232

Partial interpretations of higher order algebraic types. / Broy, Manfred.
Mathematical Foundations of Computer Science 1986 - Proceedings of the 12th Symposium. ed. / Jozef Gruska; Branislav Rovan; Juraj Wiedermann. Springer Verlag, 1986. p. 29-43 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 233 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - The theory of algebraic abstract types specified by conditional equations is extended to types with “nonstrict” operations, partial and even infinite objects based on the concept of partial interpretations. Models of such types are studied where all explicit equations have solutions. Higher order types, i.e. types comprising higher order functions are treated, too. This allows an algebraic (“equational”) specification of algebras including sorts with “infinite” objects and higher order functions (“functionals”).

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SN - 9783540167839

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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BT - Mathematical Foundations of Computer Science 1986 - Proceedings of the 12th Symposium

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PB - Springer Verlag

T2 - 12th Symposium on Mathematical Foundations of Computer Science, MFCS 1986

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Broy M. Partial interpretations of higher order algebraic types. In Gruska J, Rovan B, Wiedermann J, editors, Mathematical Foundations of Computer Science 1986 - Proceedings of the 12th Symposium. Springer Verlag. 1986. p. 29-43. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/BFb0016232

Partial interpretations of higher order algebraic types

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