Initial Algebra Semantics and Continuous Algebras

Journal of the ACM (JACM)

Volumn 24, Issue 1, 1977, Pages 68-95

  Goguen, J A ^a   Thatcher, J W ^b   Wagner, E G ^b   Wright, J B ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b IBM T J WATSON RESEARCH CENTER   (United States)

Author keywords

algebraic semantics; algebras; continuous algebras; flow diagrams; free algebras; posets; programming language semantics; solutions of equations; syntax directed translation

Indexed keywords

EID: 84976746763     PISSN: 00045411     EISSN: 1557735X     Source Type: Journal    
DOI: 10.1145/321992.321997     Document Type: Article

References (84)

1. Aho, A V, and Ullman, J D Properties of syntax directed translations J Computer and Syst. Sets. 3 (1969), 319-334.
2. Aho, A B, and Ullman, J D Translations of a context-free grammar Inform and Contr 19 (1971), 439-475.
3. Baker, B S Tree transductions and families of tree languages Tech Rep TR9-73, Center for Research in Computing Technology, Harvard U, Cambridge, Mass, 1973.
4. Bekic, H Definable operations in general algebra and the theory of automata and flowcharts Research Rep, IBM Laboratory, Vienna, Austria, 1969.
5. Bénabou J., Structures algébriques dans les catégories Thèse, fac sci, Université de Pans, March 1966.
6. Cahiers de Topologie et Géométrie Différentielle 10 (1968), 1-126.
7. Birkhoff, G Structure of abstract algebras Proc Cambridge Phil Soc 31 (1938), 433-454.
8. Birkhoff, G, and Lipson, J D Heterogeneous algebras J Combinatorial Theory 8 (1970), 115-133.
9. Blikle, A Equational languages Inform and Contr 21 (1972), 134-147.
10. Bloom, S L, and Elgot, C C The existence and construction of free iterative theories. Research Rep RC-4937, IBM Thomas J Watson Research Center, Yorktown Heights, N Y, 1974.
11. Burstall, R M, and Landin, F J Programs and their proofs An algebraic approach Machine Intelligence, Vol 4, B Meltzer and D Michie, Eds, Edinburgh U Press, Edinburgh, Scotland, 1969, pp 17-43.
12. Burstall, R M, and Thatcher, J W The algebraic theory of recursive program schemes. Lecture Notes in Computer Science, Vol. 25 Category Theory Applied to Computation and Control, Springer, Berlin, 1974, pp 126-131.
13. Chandra, A K Degrees of translatability and canonical forms of program schemes Part I Proc Sixth Ann ACM Symp on Theory of Computing, Seattle, 1974, pp 1-12.
14. Cohn, P M Universal Algebra Harper and Row, New York, 1965.
15. Courcelle, B, and Vuillemin, J. Semantics and axiomatics of a simple recursive language, Proc Sixth Ann ACM Symp on Theory of Computing, Seattle, 1974, pp 13-26.
16. Doner, J E Tree acceptors and some of their applications J Computer and Syst Scis 4 (1970), 406-451.
17. Eilenberg. S, and Wright, J B Automata in general algebras Inform and Control 11 (1967), 452-470.
18. Elgot, CC Monadic computation and iterative algebraic theories Research Rep. RC-4564, IBM Thomas J Watson Research Center, Yorktown Heights, N Y, 1973.
19. Proc Logic Colloquium 73, Bristol, England, North-Holland Pub Co, Amsterdam, 1975, pp 175-230.
20. Engelfriet, J, and Schmidt, E M IO and OI Datalogisk Afdeling Rep, DAIM1 PB-47, Aarhus U, Aarhus, Denmark, July 1975.
21. Ginsburg, S The Mathematical Theory of Context-Free Languages McGraw-Hill, New York, 1962.
22. Goguen, J A On homomorphisms, correctness, termination, unfoldments and equivalence of flow diagram programs Proc 13th Ann IEEE Symp on Switching and Automata Theory, 1972, pp 52-60.
23. J Computer and Syst Sets 8 (1974), 333-365.
24. Goguen, J A Semantics of computation Lecture Notes in Computer Science, Vol 25 Category Theory Applied to Computation and Control, Springer, Berlin, 1974, pp 151-163.
25. Goguen, J A, and Thatcher, J W Initial algebra semantics Extended Abstract, Research Rep RC-4865, IBM Thomas J Watson Research Center, Yorktown Heights, N Y, May 1974.
26. Proc 15th Ann IEEE Symp on Switching and Automata Theory, 1974, pp 63-77.
27. Goguen, J A, Thatcher, J W, Wagner, E G, and Wright, J B A junction between computer science and category theory, I Basic definitions and examples Part 1, Research Rep RC-4526, Pt 2, Research Rep RC-5908, IBM Thomas J Watson Research Center, Yorktown Heights, N Y, 1973, 1976.
28. Goguen, J A, Thatcher, J W, Wagner, E G, and Wright, J B Abstract data-types as initial algebras and correctness of data representations Proc. Conference on Computer Graphics, Pattern Recognition and Data Structure, May 1975, pp 89-93.
29. Goguen, J A, Thatcher, J W, Wagner, E G, and Wright, J B. Programs in categories (summary), in preparation.
30. Gordon, M Models of pure LISP Ph D Th, Edinburgh U, Edinburgh, Scotland, 1973.
31. Graetzer, G Universal Algebra Van Nostrand, Princeton, N J, 1968.
32. Higgins, P J Algebras with a schema of operators Math Nachr 27 (1963), 115-132.
33. Irons, E T A syntax directed compiler for ALGOL 60 Comm ACM 4 (1961), 51-55.
34. Knuth, D E Semantics of context-free languages Math Syst Theory 2 (1968), 127-145.
35. Landin, P J A program machine symmetric automata theory Machine Intelligence 5, B Meltzer and D Michie, Eds, Edinburgh U. Press, Edinburgh, Scotland, 1970, pp 99-120.
36. Lawvere, F W Functonal semantics of algebraic theories. Proc. Nat Acad Sci. 50 (1963), 869-872.
37. Lewis, C H, and Rosen, B K Recursively defined data types, Part 1 Proc ACM Symp on Principles of Programming Languages, 1973, pp 125-138.
38. Lewis, C H, and Rosen, B K Recursively defined data types, Part 2, Research Rep. RC-4713, IBM Thomas J Watson Research Center, Yorktown Heights, N Y, 1974.
39. Lewis, P.M. II, and Stearns, R E Syntax-directed transduction J ACM 15, 3 (July 1968), 465-488.
40. Lucas, P, Lauer, P, and Stigleitner, H Method and notation for the formal definition of programming languages Tech Rep TR 25 087, IBM Laboratory, Vienna, Austria, 1968.
41. McCarthy. J Towards a mathematical science of computation Proc IFIP Cong, North-Holland Pub Co, Amsterdam, 1962, pp 21-28.
42. McCarthy, J A formal description of a subset of ALGOL In “Formal Language Description Languages for Computer Programming,” Proc IFIP Working Conf 1964, T B Steel, Jr, Ed, North-Holland Pub Co, Amsterdam, 1966, pp 1-12.
43. McCarthy, J, and Painter, J Correctness of a compiler for arithmetic expressions In “Mathematical Aspects of Computer Science,” Proc of Symposia Applied Mathematics, Vol 19, J T Schwartz, Ed, Amer Math Soc, Providence, R I, 1967, pp 33-41.
44. MaClane, S Category Theory for the Working Mathematician Springer, New York, 1971.
45. Magidor, M, and Morgan, G Finite automata over finite trees Tech Rep 30, Hebrew U, Jerusalem, Israel, 1969.
46. Maibaum, T S E The characterization of the derivation trees of context-free sets of terms as regular sets Proc 13th Ann IEEE Symp on Switching and Automata Theory, 1972, pp. 224-230.
47. Maibaum, T S E Generalized grammars and homomorphic images of regular sets Research Rep CS-73-30, U of Waterloo, Waterloo, Ontario, Canada, 1973.
48. Manna, Z Properties of programs and the first-order predicate calculus J ACM 16, 2 (April 1969), 244-255.
49. Markowsky, G Cham-complete posets and directed sets with applications Research Rep RC-5024, IBM Thomas J Watson Research Center, Yorktown Heights, N Y, Aug 1974.
50. Mezei, J, and Wright, J B Algebraic automata and context-free sets Inform and Contr 11 (1967), 329.
51. Morris, F L Correctness of translations of programming languages Ph D Th, Computer Science Memo CS72-303, Stanford U, Stanford, Calif, 1972.
52. Morris, F.L. Advice on structuring compilers and proving them correct Proc Symp on Principles of Programming Lanugages, Boston, 1973, pp 144-152.
53. Nivat, M Languages algebraic sur le magna libre et sémantique des schémas de programme In Automata, Languages and Programming, M Nivat (Ed), North-Holland Pub Co, Amsterdam, 1972, pp 293-308.
54. Park, D Fixpoint induction and proofs of program properties Machine Intelligence. Vol 5, B Meltzer and D Michie, Eds, Edinburgh U Press, Edinburgh, Scotland, 1970. pp 59-78.
55. Petrone, L Syntactic mappings of context-free languages Proc IFIP Cong 1965, Vol 2, North-Holland Pub Co, Amsterdam, pp 590-591.
56. Pottenger, R ARBOL, a system for defining functions on trees Al Memo 3, UCLA, 1976.
57. Rabin, M P, and Scorr, D Finite automata and their decision problems IBM J Res Develop 3 (1959), 114-125.
58. Reynolds, J C Definitional interpreters for higher-order programming languages Proc 25th National ACM Conference, Boston, Mass, Aug 1972, pp 717-740.
59. Reynolds, J C On the relation between direct and continuation semantics Lecture Notes in Computer Science, Vol 14 Automata, Languages and Programming, Springer, Berlin, 1974, pp 141-156.
60. Reynolds, J C. Semantics of the lattice of flow diagrams. Manuscript, Syracuse U, Syracuse, N Y, submitted for publication, July 1975.
61. Rosen, B K Program equivalence and context-free grammars Proc 13th Ann IEEE Symp on Switching and Automata Theory, 1972, pp 7-18, revised as Research Rep RC-4822, IBM Thomas J Watson Research Center, Yorktown Heights, N Y, 1974.
62. Rounds, W C Mappings and grammars on trees Math Syst Theory 4 (1970), 256-287.
63. Schutzenberger, M P Context-free languages and push down automata Inform and Contr 6 (1963), 246-264.
64. Schwartz, J T Semantic definition methods In Formal Semantics of Programming Languages, R Rustin, Ed, Prentice-Hall, Englewood Cliffs, N J, 1972, pp 1-23.
65. Scott, D Outline of a mathematical theory of computation Proc 4th Ann Princeton Conf on Information Sciences and Systems, 1970, pp 169-176.
66. Scott. D The lattice of flow diagrams Tech Monograph PRG 3, Oxford U Computing Lab, Oxford U, Oxford, England, also, Lecture Notes in Mathematics, Vol 182 Semantics of Algorithmic Languages, E Engeler, Ed, Springer, Berlin, 1971, pp 311-366.
67. Scott, D Continuous lattices Tech. Monograph PRG 7, Oxford U Computing Lab, Oxford U, Oxford, England, 1971.
68. Lecture Notes in Mathematics, Vol 274, Sponger, Berlin, 1971, pp 97-136.
69. Scott, D Data types as lattices Unpublished notes, Amsterdam, 1972.
70. Scott, D Data types as lattices Unpublished notes, Oxford, 1974.
71. Scott, D, and Strachey, C Towards a mathematical semantics for computer languages Tech Monograph PRG 6, Oxford U. Computing Lab., Oxford U., Oxford, England, 1971.
72. Computers and Automata, J Fox, Ed, Wiley, New York, 1971, pp 19-46.
73. Strachey, C, and Wadsworth, C P Continuations — A mathematical semantics for handling full jumps Tech Monograph PRG-11, Programming Research Group, Oxford U Computing Lab, Oxford, England, 1974.
74. Thatcher, J.W. Characterizing derivation trees of context free grammars through a generalization of finite automata theory J Computer and Syst Sets 1 (1967), 317-322.
75. Thatcher, J W Generalizede sequential machines J Computer and Syst. Scis 4 (1970), 339-367.
76. Thatcher, J W Tree automata An informal survey In Currents in Computing, A V. Aho, Ed. Prentice-Hall, Englewood Cliffs, N J 1973, 143-172.
77. Thatcher, J W., and Wright, J B. Generalized finite automata theory with an application to a decision problem of second-order logic Math Systems Theory 2 (1968), 57-81.
78. Turner, R Doctoral Diss, U of London, London, England, 1973.
79. Vuillemin, J Syntaxe, Sémantique et Axiomatique d'un Langage de Programmation Simple These d'Etat, Université Pans 6, France, 1974.
80. Wagner, E.G. An algebraic theory of recursive definitions and recursive languages. Proc. Third Annual ACM Symposium on Theory of Computing, 1971, pp 12-23.
81. Wagner, E G Languages for defining sets in arbitrary algebras. Proc 11th Ann IEEE Symp on Switching and Automata Theory, 1971, pp 191-201.
82. Wand, M A concrete approach to abstract recursive definitions In Automata, Languages and Programming, M Nivat, Ed, North-Holland Pub Co., Amsterdam, 1972, pp 331-341.
83. Wand, M An algebraic formulation of the Chomsky hierarchy Lecture Notes in Computer Science, Vol 25 Category Theory Applied to Computation and Control, Springer, Berlin, 1974, pp 209-213.
84. Van Wijngaarden, A., Ed Report on the algorithmic language ALGOL 68 Numer Math 14 (1969), 79-218.