Monads of sets

Handbook of Algebra

Volumn 3, Issue , 2003, Pages 67-153

  Manes, Ernie ^a  

^a UNIVERSITY OF MASSACHUSETTS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4544226339     PISSN: 15707954     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1570-7954(03)80059-1     Document Type: Article

References (112)

1. Appelgate H., and Tierney M. Categories with models. Lecture Notes in Math. Vol. 80 (1969), Springer-Verlag, Amsterdam 156-243
2. Barr M. Relational algebras. Lecture Notes in Math. Vol. 137 (1970), Springer-Verlag, Berlin 39-55
3. Barr M., and Wells C. Toposes, Triples and Theories (1984), Springer-Verlag, Berlin
4. Beck J. Triples, Algebras and Cohomology. Dissertation (1967), Columbia University, Berlin
5. Beck J. Distributive laws. Lecture Notes in Math. Vol. 80 (1969), Springer-Verlag 119-140
6. Bénabou J. Introduction to bicategories. Lecture Notes in Math. Vol. 47 (1967), Springer-Verlag, Berlin 1-77
7. NATO ASI Series F. Bird R. An introduction to the theory of lists. In: Broy M. (Ed). Logic of Programming and Calculi of Discrete Design Vol. 36 (1987), Springer-Verlag, Berlin 3-42
8. Bird R. Introduction to Functional Programming Using Haskell. 2nd edn (1998), Prentice Hall Europe, Berlin
9. Birkhoff G. On the structure of abstract algebras. Proc. Cambridge Philos. Soc. 31 (1935) 433-454
10. In: Bloom S.L. (Ed). Calvin C. Elgot, Selected Papers (1982), Springer-Verlag, London
11. Bloom S., and Ésik Z. Iteration Theories: The Equational Logic of Iterative Processes (1993), Springer-Verlag, Berlin
12. Cartan H., and Eilenberg S. Homological Algebra (1956), Princeton Univ. Press, Berlin
13. Cohn P.M. Universal Algebra (1965), Harper and Row, Princeton
14. Day A. Filter monads, continuous lattices and closure systems. Canadian J. Math. XXVII (1975) 50-59
15. Dijkstra E.W. A Discipline of Programming (1976), Prentice Hall, New York
16. Dijkstra E.W., and Scholten C.S. Predicate Calculus and Program Semantics (1990), Springer-Verlag, Englewood Cliffs, NJ
17. Duskin J. Variations on Beck's tripleability criterion. Lecture Notes in Math. Vol. 106 (1969), Springer-Verlag, Berlin 74-129
18. Edgar G.A. The class of topological spaces is equationally definable. Algebra Universalis 3 (1973) 139-146
19. Eilenberg S., and MacLane S. General theory of natural equivalences. Trans. Amer. Math. Soc. 58 (1945) 231-294
20. Eilenberg S., and Moore J.C. Adjoint functors and triples. Illinois J. Math. 9 (1965) 381-398
21. Eilenberg S., and Zilber J.A. Semi-simplicial complexes and singular homology. Ann. of Math. 51 (1950) 499-513
22. Elgot C.C. Algebraic theory of program schemes. Lecture Notes in Math. Vol. 188 (1971), Springer-Verlag, Berlin 71-88
23. Escardó M. Injective spaces via the filter monad. Topology Proc. 22 (1997) 97-110
24. Escardó M. The patch topology of a stably compact space. April 19. Northeastern Conference in Topological Methods in Computer Science (1999), University of Connecticut, Berlin unpublished
25. Filinski A. Representing monads. Proceedings of POPL'94 Symposium Principles of Programming Languages. ACM Press (1994) 446-457
26. Fischer M.J., and Ladner R.E. Propositional dynamic logic of regular programs. J. Comput. System Sci. 18 (1979) 286-294
27. Fokkinga M. Monadic maps and folds for arbitrary datatypes. Memoranda Informatica 94-28. University of Twente (1994)
28. Freyd P. Algebra-valued functors in general and tensor products in particular. Colloquium Math. 14 (1966) 89-106
29. Gabriel P., and Zisman M. Calculus of Fractions and Homotopy Theory (1967), Springer-Verlag, Stamford, Connecticut, USA
30. Gaifmann H. Infinite Boolean polynomials I. Fund. Math. 54 (1964) 229-250
31. Giertz G., et al. A Compendium of Continuous Lattices (1980), Springer-Verlag, Berlin
32. Godement R. Topologie Algébrique et Théorie des Faisceaux (1964), Hermann, Berlin
33. Gonshor H. An application of nonstandard analysis to category theory. Fund. Math. 104 (1979) 75-83
34. Goodman I.R., and Nguyen H.T. Uncertainty Models for Knowledge-Based Systems (1985), North-Holland, Paris
35. A.W. Hales, On the non-existence of free complete Boolean algebras, Fund. Math. 54, 45-66.
36. Harel D., Meyer A.R., and Pratt V.R. Computability and completeness in logics of programs. Proceedings of 9th ACM Symposium on the Theory of Computing (1977) 261-268
37. 583. Hoare C.A.R. An axiomatic basis for computer programming. Comm. ACM 12 (1969) 576-580
38. Huber P.J. Homotopy theory in general categories. Math. Ann. 144 (1961) 361-385
39. Hudak P. The Haskell School of Expression: Learning Functional Programming through Multimedia (2000), Cambridge University Press, Amsterdam
40. Warsaw. Isbell J.R. Subobjects, adequacy, completeness and categories of algebras. 32 pp. Rozprawy Matematyczne XXXVI (1964)
41. Isbell J.R. General functorial semantics I. Amer. J. Math. XCIV (1972) 535-596
42. Isbell J.R. Functorial implicit operations. Israel J. Math. 15 (1973) 185-188
43. Isbell J.R. Generating the algebraic theory of C(X). Algebra Universalis 15 (1982) 153-155
44. Jay C.B. A semantics for shape. Sci. Comput. Programming 25 (1995) 251-283
45. Johnstone P.T. Stone Spaces (1982), Cambridge University Press, New York
46. Berlin. Jones M.P. Functional programming with overloading and higher-order polymorphism. In: Jeuring J., and Meijer E. (Eds). Advanced Functional Programming (1995), Springer-Verlag, Bastad, Sweden 97-136
47. Kan D.M. Adjoint functors. Trans. Amer. Math. Soc. 87 (1958) 294-329
48. Kennison J.F., and Gildenhuys D. Equational completion, model-induced triples and pro-objects. J. Pure Appl. Algebra 1 (1971) 317-346
49. King D.J., and Wadler P. Combining monads. In: Scotland Ayr., Launchbury J., and Sansom P.M. (Eds). Proceedings of the Fifth Annual Glasgow Workshop on Functional Programming (1992), Springer-Verlag 134-143
50. Kleene S.C. Introduction to Metamathematics (1972), Van Nostrand, Berlin
51. Kleisli H. Every standard construction is induced by a pair of adjoint functors. Proc. Amer. Math. Soc. 16 (1965) 544-546
52. Lecture Notes. Kock A. On double-dualizntion monads Vol. 38 (1969), Mathematisk Institute, Aarhus Universitet, New York
53. Kock A. Monads for which structures are adjoint to units. J. Pure Appl. Algebra 104 (1995) 41-59
54. Kozen D. A representation theorem for models of *-free POL. Lecture Notes in Computer Science Vol. 85 (1980), Springer-Verlag 351-362
55. Lawvere F.W. Functorial Semantics of Algebraic Theories. Dissertation (1963), Columbia University, Berlin
56. Lawvere F.W. Functorial semantics of algebraic theories. Proc. Nat. Acad. Sci. USA 50 (1963) 869-872
57. Lawvere F.W. Algebraic theories, algebraic categories, and algebraic functors. In: Addison J.W., Henkin L., and Tarski A. (Eds). The Theory of Models. Proceedings of the 1963 International Symposium at Berkeley (1965), North-Holland 413-418
58. Lawvere F.W. Some algebraic problems in the context of functorial semantics of algebraic theories. Lecture Notes in Math. Vol. 61 (1968), Springer-Verlag, Amsterdam 41-61
59. Lellahi K., and Tannen V. A calculus for collections and aggregates. In: Moggi E., and Rosolini G. (Eds). Category Theory and Computer Science (1997), Springer-Verlag, Berlin 261-280
60. Liang S., Hudak P., and Jones M.P. Monad transformers and modular interpreters. Proceedings of POPL'95 Symposium Principles of Programming Languages. ACM Press (1995) 333-343
61. Linton F.E.J. Functorial measure theory. Dissertation (1963), Columbia University, Berlin
62. Linton F.E.J. Some aspects of equational categories. In: Eilenberg S., Harrison D.K., MacLane S., and Röhrl H. (Eds). Proceedings of the Conference on Categorical Algebra. La Jolla, 1965 (1966), Springer-Verlag 84-94
63. Linton F.E.J. Triples vs. theories. Notices Amer. Math. Soc. 13 (1966) 227
64. Linton F.E.J. Autonomous equational categories. J. Math. Mech. 15 (1966) 637-642
65. Linton F.E.J. An outline of functorial semantics. Lecture Notes in Math. Vol. 80 (1969), Springer-Verlag, Berlin 7-52
66. Linton F.E.J. Applied functorial semantics. Lecture Notes in Math. Vol. 80 (1969), Springer-Verlag, Berlin 53-74
67. Linton F.E.J. Coequalizers in categories of algebras. Lecture Notes in Math. Vol. 80 (1969), Springer-Verlag, Berlin 75-90
68. Linton F.E.J. Relative functorial semantics: adjointness results. Lecture Notes in Math. Vol. 99 (1969), Springer-Verlag, Berlin 384-418
69. Linton F.E.J. Applied functorial semantics I. Annali di Matematica Pura ed Applicata 86 (1970) 1-14
70. Unpublished Manuscript. Linton F.E.J. Relative functorial semantics III, triples vs. theories. 3 pages (1974)
71. MacLane S. Homologie des anneaux et des modules (1956), Colloque de topologie Algèbrique, Berlin 55-80
72. MacLane S. Homology (1963), Academic Press, Louvain
73. MacLane S. Categories for the Working Mathematician (1971), Springer-Verlag, New York
74. Manes E.G. A Triple Miscelleny: Some Aspects of the Theory of Algebras over a Triple. Dissertation (1967), Wesleyan University, Berlin
75. Manes E.G. A triple-theoretic construction of compact algebras. Lecture Notes in Math. Vol. 80 (1969), Springer-Verlag 91-118
76. Manes E.G. Algebraic Theories (1976), Springer-Verlag, Berlin
77. Manes E.G. A class of fuzzy theories. J. Math. Anal. Appl. 85 (1982) 409-451
78. Manes E.G. Predicate Transformer Semantics (1992), Cambridge University Press, Berlin
79. Manes E.G. Implementing collection classes with monads. Math. Structures Comput. Sci. 8 (1998) 231-276
80. Manes E.G. Boolean monads for functional programming. In: Callaos N., Long S., and Loutfi M. (Eds). Cybernetics and Informatics ISAS/SCI 2001. Proceedings of World Multiconference on Systemics XVII (2001), Orlando, New York 189-193
81. Manes E.G. Taut monads and TO spaces. Theoret. Comput. Sci. 275 (2002) 79-109
82. Maranda J.-M. On fundamental constructions and adjoint functors. Canadian Math. Bull. 9 (1966) 581-591
83. Meijer E., and Jeuring J. Merging monads and folds for functional programming. In: Scotland Ayr., Launchbury J., and Sansom P.M. (Eds). Proceedings of the Fifth Annual Glasgow Workshop on Functional Programming (1992), Springer-Verlag, Florida, USA 228-266
84. Moggi E. Computational lambda-calculus and monads. Proceedings of Symposium on Logic and Computer Science. IEEE (1989), Computer Society Press, Berlin 14-23
85. Moggi E. Notions of computation and monads. Inform, and Comput. 93 (1991) 55-92
86. Moggi E. A semantics for evaluation logic. Fund. Inform. 22 (1995) 117-152
87. Mulry P. Monads and algebras in the semantics of partial data types. Theor. Comput. Sci. 99 (1992) 141-155
88. 12 pp. Mulry P. Monads in semantics. Electronic Notes in Theoretical Computer Science 12 (1998). http://www.elsevier.nl/locate/entcs/volumel2.html
89. Negrepontis J.W. Duality in algebra from the point of view of analysis. J. Algebra 19 (1971) 228-253
90. Paré R. On absolute colimits. J. Algebra 19 (1971) 80-95
91. Peyton Jones S.L. The Implementation of Functional Programming Languages (1987), Prentice Hall International, Washington, DC
92. Peyton Jones S.L., and Wadler P. Imperative functional programming. Proceedings of POPL'93 Symposium Principles of Programming Languages. ACM Press (1993) 71-84
93. Pierce R.S. Introduction to the Theory of Abstract Algebras (1968), Holt, Rinehart and Winston, New York
94. Plotkin G.D. Call-by-name, call-by-value and the λ-calculus. Theoret. Comput. Sci. 1 (1975) 125-159
95. Pratt V.R. Semantical considerations on Floyd-Hoare Logic. Proceedings of 17th IEEE Symposium on the Foundations of Computer Science (1976) 109-121
96. Reynolds J. The essence of Algol. In: Bakker d., and Vleet V. (Eds). Algorithmic Languages (1981), North-Holland, New York 345-372
97. Scott D.S. Outline of a mathematical theory of computation. Technical Monograph PRG-2 (1970), Oxford University Computing Laboratory, Amsterdam
98. Scott D.S. Continuous lattices. Lecture Notes in Math. Vol. 234 (1972), Springer-Verlag 97-136
99. Scott D.S., and Strachey C. Towards a mathematical semantics for computer languages. In: Fox J. (Ed). Proceedings of the Symposium on Computers and Automata (1971), Polytechnic Institute of Brooklyn Press, Berlin 19-46
100. Semadeni Z. A simple topological proof that the underlying set functor from compact spaces is monadic. Lecture Notes in Math. Vol. 378 (1974), Springer-Verlag 429-435
101. Shafer G. A Mathematical Theory of Evidence (1976), Princeton University Press, Berlin
102. Slominski J. The theory of abstract algebras with infinitary operations. Dissertationes Math. 18 (1959)
103. Spivey M. A categorical approach to the theory of lists. Lecture Notes in Computer Science Vol. 375 (1989), Springer-Verlag, Princeton 399-408
104. Spivey M. A functional theory of exceptions. Sci. Comput. Programming 14 (1990) 25-42
105. Solovay R.M. New proof of a theorem of Gaifmann and Hales. Bull. Amer. Math. Soc. 72 (1966) 282-284
106. Steele G.L. Building interpreters by composing monads. Proceedings of POPL'94 Symposium Principles of Programming Languages. ACM Press (1994) 474-492
107. Trinder P. Comprehensions, a query language for DBPLs. In: Kanellakis P., and Schmidt J.W. (Eds). Database Programming Langues: Bulk Types and Persistent Data. Third International Workshop, August 27-30, 1991, Nafplion, Greece (1991), Morgan Kaufmann, Berlin 55-68
108. Wadler P. Comprehending monads. Math. Structures Comput. Sci. 2 (1992) 461-493
109. Wadler P. The essence of functional programming. Proceedings of POPL'92 Symposium Principles of Programming Languages. ACM Press (1992) 1-14
110. Bästad, Sweden. Wadler P. Monads for functional programming. In: Jeuring J., and Meijer E. (Eds). Advanced Functional Programming (1995), Springer-Verlag, San Mateo, CA, USA 24-52
111. Wyler O. Algebraic theories of continuous lattices. Lecture Notes in Math. Vol. 871 (1981), Springer-Verlag, Berlin 390-413
112. Yoneda N. On the homology of modules. J. Fac. Sci. Tokyo, Sec. I. 7 (1954) 193-227