J.A. Goguen, J. W. Thatcher, E.G. Wagner and J. B. Wright, A Junction between Computer Science and Category Theory: I Basic Concepts and Examples, Part 1, IBM Report RC-4526 (September 1973); Part 2, IBM Report RC-5908 (March 1976).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....orientation. The abstract domain also contains an auxiliary useful frame constructor that was used in an annotation to specify the frame of an input variable, as mentioned in Section 2.3. The frame constructor builds a frame from a translation and a rotation relative to j2000. The ADJ diagram [9] in Figure 2 depicts the sorts and the operations that form the abstract domain. The sorts are boxes and the operations are multisource arrows, each source standing for an argument. The operations having a circle index are partial. Because of space considerations we didn t draw the frame ....

Joseph Goguen, James Thatcher, Eric Wagner, and Jesse Wright. A junction between computer science and category theory, I: Basic concepts and examples (part 1). Technical report, IBM Watson Research Center, Yorktown Heights NY, 1973. Report RC 4526.

....other, unequal, sets, but I prefer not to speculate about what this means. 2 require large amounts of research, as well as enormous amounts of writing. This initial segment of the proposed first chapter appeared as a large IBM technical report [7] The second third appeared three years later [10], and later still Eric Wagner wrote something like a summary of some of ADJ s work on theories [9] The trouble was that it seemed desirable, or even necessary, to concentrate on research for a period, writing papers on the many new ideas that we were generating, and coming back to the book ....

Joseph Goguen, James Thatcher, Eric Wagner, and Jesse Wright. A junction between computer science and category theory, I: Basic concepts and examples (part 2). Technical report, IBM Watson Research Center, Yorktown Heights NY, 1976. Report RC 5908.

....footnote reads This set of authors is herein, and we hope subsequently will be, referred to by the symbols ADJ. Of course, this was an attempt to defeat the tyranny of the alphabet. A footnote on the third page of [11] attached not to the authors names, but rather to a citation of the report [7], reads The set of authors of this paper is referred to as ADJ ; the series referenced here is devoted to an exploration of the junction between category theory and computer science. By the way, this footnote is sic, because it has the subphrases category theory and computer science in ....

.... junction between category theory and computer science. By the way, this footnote is sic, because it has the subphrases category theory and computer science in the wrong order. Thus, perhaps confusingly, the 1977 footnote implies that ADJ was not the author of [11] but was the author of [7]. So ADJ was not an acronym, nor even a set, but instead a pun, and also a very curious kind of name, which in 1976 denoted a certain four element set, but in 1977 could only denote that set in certain contexts. I believe that ADJ was also been used later to denote other, unequal, sets, but I ....

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Joseph Goguen, James Thatcher, Eric Wagner, and Jesse Wright. A junction between computer science and category theory, I: Basic concepts and examples (part 1). Technical report, IBM Watson Research Center, Yorktown Heights NY, 1973. Report RC 4526.

....[45] The paper [22] gives a relatively concrete and self contained account of some basic category theory for computing scientists, using theories, equations, and unification as motivation, and many examples from that paper are used here. 1 As far as I know, the first such attempt is my own in [34], which gives four of the guidelines here. The only other attempt that I know is due to Lambek and Scott [45] who give a number of slogans in a similar style. 1 Categories The first dogma is as follows: To each species of mathematical structure, there corresponds a category whose objects ....

....two paths, p and p 0 , can be composed to form another path p; p 0 iff the source of p 0 equals the target of p. Clearly this composition is associative when defined, and each node can be given an identity path having no edges. This category is denoted Pa(G) Details may be found in [47] [34], 19] and many other places. 1.5 Automata. An automaton consists of an input set X, a state set S, an output set Y , a transition function f : X Theta S S, an initial state s 0 2 S, and an output function g : S Y . What does it mean to preserve all this structure Because the major ....

Joseph Goguen, James Thatcher, Eric Wagner, and Jesse Wright. A junction between computer science and category theory, I: Basic concepts and examples (part 1). Technical report, IBM Watson Research Center, Yorktown Heights NY, 1973. Report RC 4526.

....for engineering. My first attempt to use categories was in my thesis, which gave axioms for fuzzy set theory (see Section 3. 4) Because of this enthusiasm, I wrote several introductions to category theory for computer scientists, beginning in the early 1970s with the ADJ 3 report series [107, 108, 109], illustrating basic categorical concepts mainly with examples from automata and formal languages, which were the focus of theoretical computer science at that time. I ve been told that many East Europeans of that generation learned both basic category theory and theoretical computer science from ....

Joseph Goguen, James Thatcher, Eric Wagner, and Jesse Wright. A junction between computer science and category theory, I: Basic concepts and examples (part 2). Technical report, IBM Watson Research Center, Yorktown Heights NY, 1976. Report RC 5908.

....for engineering. My first attempt to use categories was in my thesis, which gave axioms for fuzzy set theory (see Section 3. 4) Because of this enthusiasm, I wrote several introductions to category theory for computer scientists, beginning in the early 1970s with the ADJ 3 report series [107, 108, 109], illustrating basic categorical concepts mainly with examples from automata and formal languages, which were the focus of theoretical computer science at that time. I ve been told that many East Europeans of that generation learned both basic category theory and theoretical computer science from ....

Joseph Goguen, James Thatcher, Eric Wagner, and Jesse Wright. A junction between computer science and category theory, I: Basic concepts and examples (part 1). Technical report, IBM Watson Research Center, Yorktown Heights NY, 1973. Report RC 4526.

No context found.

J.A. Goguen, J. W. Thatcher, E.G. Wagner and J. B. Wright, A Junction between Computer Science and Category Theory: I Basic Concepts and Examples, Part 1, IBM Report RC-4526 (September 1973); Part 2, IBM Report RC-5908 (March 1976).

No context found.

Goguen, J.A., J.W. Thatcher, E.G. Wagner and J.B. Wright, A Junction Between Computer Science and Category Theory (parts I and II), IBM T.J. Watson Research Center, Yorktown Heights, N.Y. Research Report, 1975.

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