Executable specifications for data-type constructors

John W. Gray

Diagrammes (1990)

  • Volume: 24, page 7-31
  • ISSN: 0224-3911

How to cite

top

Gray, John W.. "Executable specifications for data-type constructors." Diagrammes 24 (1990): 7-31. <http://eudml.org/doc/193037>.

@article{Gray1990,
author = {Gray, John W.},
journal = {Diagrammes},
keywords = {theory of sketches; algebraic theories; algebraic specification; abstract data types; natural numbers; symbolic program; Mathematica},
language = {eng},
pages = {7-31},
publisher = {Université Paris 7, Unité d'enseignement et de recherche de mathématiques},
title = {Executable specifications for data-type constructors},
url = {http://eudml.org/doc/193037},
volume = {24},
year = {1990},
}

TY - JOUR
AU - Gray, John W.
TI - Executable specifications for data-type constructors
JO - Diagrammes
PY - 1990
PB - Université Paris 7, Unité d'enseignement et de recherche de mathématiques
VL - 24
SP - 7
EP - 31
LA - eng
KW - theory of sketches; algebraic theories; algebraic specification; abstract data types; natural numbers; symbolic program; Mathematica
UR - http://eudml.org/doc/193037
ER -

References

top
  1. [1]: M. Barr and C. Wells, Toposes, Triples and Theories, Springer-Verlag, New York, 1985. Zbl0567.18001MR771116
  2. [2] : A. Bastiani and C. Ehresmann, Categories of sketched structures, Cahiers de Top. et Géom. Diff. 13 ( 1972), 103 - 214. Zbl0263.18009MR323856
  3. [3] : J. Benabou, Structures algébrique dans les catégories, Cahiers de Top. et Géom. Diff. 10 ( 1968), 1 - 126. Zbl0162.32602MR244335
  4. [4]: R. Burstall and D. Rydeheard, Computational Category Theory, preprint, 1985. MR999925
  5. [5]: L. Coppey and C. Lair, Leçons de Théorie des Esquisses (I), Diagrammes, Vol. 12, Paris, 1984. Zbl0562.18002MR800501
  6. [6]: H. Ehrig, H.-J. Kreowski, J. W. Thatcher, E. G. Wagner and J. B. Wright, Parameter passing in algebraic specification languages. Theoretical Computer Science 28 ( 1984),45 - 81. Zbl0522.68027MR741836
  7. [7]: H. Ehrig and B. Mahr, Fundamentals of Algebraic Specifications I. Equations and Initial Semantics, EATCS Monographs 6, Springer- Verlag, New York 1985. Zbl0557.68013MR788495
  8. [8]: A. C. Ehresmann, Synopsis and comments, in : Charles Ehresmann, Oeuvres Complètes et Commentées, Part IV - 1, Supp. 1, Vol. XXII ( 1981), and Part N - 2, Supp. 2, Vol. XXIII ( 1982) to Cahiers de Top. et Géom. Diff. 
  9. [9]: P. Freyd, Algebra valued functors in general and tensor products in particular. Colloq. Math. 14 ( 1966), 89 - 106. Zbl0144.01003MR195920
  10. [10]: J. Goguen, Parameterized programming, IEEE Transactions on Software Engineering, Vol. SE-10, No.5, 1984, 528 - 543. Zbl0545.68017
  11. [11]: J. Goguen and J. Meseguer, Initiality, induction, and computability, in Algebraic Methods in Semantics, M. Nivat and J. C. Reynolds (eds), Cambridge University Press, 1985. Zbl0571.68004MR835447
  12. [12]: J. W. Gray, Formal Category Theory: Adjointness for 2-Categories, Lecture Notes in Mathematics 391, Springer Verlag, New York, 1974. Zbl0285.18006MR371990
  13. [13]: J. W. Gray, Categorical aspects of data-type constructors, Theoretical Computer Science,50 ( 1987), 103-135 Zbl0629.68014MR907279
  14. [14]: J. W. Gray, The category of sketches as a model for algebraic semantics, in Categories in Computer Science and Logic, Contemporary Mathematics 92, Amer. Math. Soc. 1989, 109 - 135. Zbl0688.68077
  15. [15]: G. M. Kelly, Structures defined by finite limits in the enriched context, 1, Cahiers de Top. et Géom. Diff. 23 ( 1982), 3 - 42. Zbl0538.18006
  16. [16]: G. M. Kelly, On the essentially-algebraic theory generated by a sketch. Bull. Australian Math. Soc. 26 ( 1982), 45 - 56. Zbl0488.18001
  17. [17]: G. M. Kelly and R. Street, Lecture Notes in Mathematics 420, Springer-Verlag, New York, 1974. 
  18. [18]: C. Lair, Etude Générale de la Catégorie des Esquisses, Esquisses Mathématiques 23, Paris 1975, 1 - 62. Zbl0397.18007
  19. [19]: J. Lambek, and P. J. Scott, Introduction to Higher Order Categorical Logic, Cambridge Univ. Press, 1986. Zbl0596.03002MR856915
  20. [20]: F. W. Lawvere, Functorial semantics of algebraic theories, Proc. Nat. Acad. Sci. 50 ( 1963), 869 - 872. Zbl0119.25901MR158921
  21. [21]: S. Mac Lane, Categories for the Working Mathematician, Springer Verlag New York, 1972. Zbl0232.18001MR1712872
  22. [22]: J. C. Mitchell and P. J. Scott, Typed lambda models and cartesian closed categories, in Categories in Computer Science and Logic, Contemporary Mathematics 92, Amer Math. Soc. 1989, 301-316. Zbl0674.03004MR1003204
  23. [23]: J. W. Thatcher, E. G. Wagner and J. B. Wright, Data type specifications: Parameterizations and the power of specification techniques, ACM Trans. on Programming Languages and Systems, 4( 1982), 711 - 732. Zbl0495.68020

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.