* Functional programming and William Lawvere's notion of "variable sets"(vs topos of "static sets") in a Topos ...
@ 2014-08-04 7:03 Vasili I. Galchin
2014-09-04 12:07 ` Harley Eades III
0 siblings, 1 reply; 2+ messages in thread
From: Vasili I. Galchin @ 2014-08-04 7:03 UTC (permalink / raw)
To: Categories mailing list
Dear Cat People ...
I have been re-reading William Lawvere's description of "variable
sets" (a functor category) in "a elementary topoi" on a discrete
poset/preset vs a "abstract sets" in the topos of abstract sets . In
Haskell( and other FPLs .. ) aren't "pure" computations just over the
topos of abstract sets and "mutable" /"time-varying/stateful"
computations aren't just "variable sets" (i.e. a functor over a
discrete preset-poset)?? Please forgive my germ of an idea
Kind regards,
Vasya
P.S. Yes I am familiar with Eugenio Moggi's papers on using monads for
stateful computations ..
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
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* Re: Functional programming and William Lawvere's notion of "variable sets"(vs topos of "static sets") in a Topos ...
2014-08-04 7:03 Functional programming and William Lawvere's notion of "variable sets"(vs topos of "static sets") in a Topos Vasili I. Galchin
@ 2014-09-04 12:07 ` Harley Eades III
0 siblings, 0 replies; 2+ messages in thread
From: Harley Eades III @ 2014-09-04 12:07 UTC (permalink / raw)
To: Vasili I. Galchin; +Cc: Categories mailing list
Hi, Vasya.
Something you might find interesting is that stateful computations can be
modeled — very nicely in fact — using co-algebras. They have been used
to give a formal semantics to object oriented (OO) programming languages,
as well, as embedding OO in purely functions programming languages.
I am not aware of a connection between co-algebras and variable sets, but
I am not familiar with the latter.
I just thought you might find these interesting.
Thanks,
.\ Harley
Here are a list of references from my DB:
@article{Setzer:2006,
Author = {Anton Setzer},
Journal = {Trends in Functional Programming},
Title = {Object-Oriented Programming in Dependent Type Theory},
Year = {2006}}
@article{Jacobs:2003,
Author = {Bart Jacobs and Erik Poll},
Journal = {Theoretical Computer Science},
Number = {3},
Pages = {329 - 349},
Title = {Coalgebras and monads in the semantics of Java},
Volume = {291},
Year = {2003}}
@article{Jacobs:2002b,
Author = {Jacobs, Bart},
Journal = {Mathematical. Structures in Comp. Sci.},
Month = dec,
Number = {6},
Pages = {875--903},
Title = {The Temporal Logic of Coalgebras via Galois Algebras},
Volume = {12},
Year = {2002}}
@incollection{Jacobs:2002,
Author = {Jacobs, Bart},
Booktitle = {Algebraic and Coalgebraic Methods in the Mathematics of Program Construction},
Editor = {Backhouse, Roland and Crole, Roy and Gibbons, Jeremy},
Pages = {237-281},
Publisher = {Springer Berlin Heidelberg},
Series = {Lecture Notes in Computer Science},
Title = {Exercises in Coalgebraic Specification},
Volume = {2297},
Year = {2002}}
@article{Jacobs:2002a,
Author = {Bart Jacobs},
Journal = {Electronic Notes in Theoretical Computer Science},
Number = {1},
Pages = {112 - 134},
Title = {Comprehension for Coalgebras},
Volume = {65},
Year = {2002}}
@article{Rothe:2001,
Author = {Jan Rothe and Hendrik Tews and Bart Jacobs},
Journal = j-jucs,
Month = {feb},
Number = {2},
Pages = {175--193},
Title = {The Coalgebraic Class Specification Language CCSL},
Volume = {7},
Year = {2001}}
@article{Kurz:20011,
Author = {Alexander Kurz},
Journal = {Theoretical Computer Science},
Number = {1--2},
Pages = {119 - 138},
Title = {Specifying coalgebras with modal logic},
Volume = {260},
Year = {2001}}
@article{Jacobs:2000,
Author = {Bart Jacobs},
Journal = {Electronic Notes in Theoretical Computer Science},
Number = {0},
Pages = {160 - 195},
Title = {Towards a Duality Result in Coalgebraic Modal Logic},
Volume = {33},
Year = {2000}}
@article{Hensel:1999,
Author = {Hensel, U and Jacobs, B},
Journal = {Journal of Logic and Computation},
Number = {4},
Pages = {463-500},
Title = {Coalgebraic theories of sequences in PVS},
Volume = {9},
Year = {1999}}
@article{Jacobs:1999,
Author = {Bart Jacobs},
Journal = {Newsletter 3 of the Dutch Association for Theoretical Computer Science (NVTI)},
Pages = {15-27},
Title = {Coalgebras in Specification and Verification for Object-Oriented Languages},
Year = {1999}}
@article{Jacobs:1998a,
Author = {Jacobs, Bart and van den Berg, Joachim and Huisman, Marieke and van Berkum, Martijn and Hensel, U. and Tews, H.},
Journal = {SIGPLAN Not.},
Month = oct,
Number = {10},
Pages = {329--340},
Title = {Reasoning About Java Classes: Preliminary Report},
Volume = {33},
Year = {1998}}
@incollection{Hensel:1998,
Author = {Hensel, Ulrich and Huisman, Marieke and Jacobs, Bart and Tews, Hendrik},
Booktitle = {Programming Languages and Systems},
Editor = {Hankin, Chris},
Pages = {105-121},
Publisher = {Springer Berlin Heidelberg},
Series = {Lecture Notes in Computer Science},
Title = {Reasoning about classes in object-oriented languages: Logical models and tools},
Volume = {1381},
Year = {1998}}
@article{Jacobs:1998,
Author = {Bart Jacobs},
Journal = {Electronic Notes in Theoretical Computer Science},
Number = {0},
Pages = {231 - 242},
Title = {Coalgebraic Reasoning about Classes in Object-Oriented Languages},
Volume = {11},
Year = {1998}}
@incollection{Jacobs:1996,
Author = {Jacobs, Bart},
Booktitle = {Object Orientation with Parallelism and Persistence},
Editor = {Freitag, Burkhard and Jones, CliffB. and Lengauer, Christian and Schek, Hans-J{\"o}rg},
Pages = {83-103},
Publisher = {Springer US},
Series = {The Kluwer International Series in Engineering and Computer Science},
Title = {Objects And Classes, Co-Algebraically},
Volume = {370},
Year = {1996}}
On Aug 4, 2014, at 3:03 AM, Vasili I. Galchin <vigalchin@gmail.com> wrote:
> Dear Cat People ...
>
> I have been re-reading William Lawvere's description of "variable
> sets" (a functor category) in "a elementary topoi" on a discrete
> poset/preset vs a "abstract sets" in the topos of abstract sets . In
> Haskell( and other FPLs .. ) aren't "pure" computations just over the
> topos of abstract sets and "mutable" /"time-varying/stateful"
> computations aren't just "variable sets" (i.e. a functor over a
> discrete preset-poset)?? Please forgive my germ of an idea
>
> Kind regards,
>
> Vasya
>
> P.S. Yes I am familiar with Eugenio Moggi's papers on using monads for
> stateful computations ..
>
>
> [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
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