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  • cartesianprogramming 04:01 on 2012/06/19 Permalink | Reply  

    Tournament computation in one dimension 

    In the post on factorial, the following code appears:

    var f = tournamentOp₁.d.n.times (default₁.d.1.n.1 (#!d)) ;;

    What is going on? Let us look at the definitions from the TransLucid Standard Header:

    fun default₁.d.m.n.val X = Y
      var Y [d : m..n] = X ;;
      var Y [d : nat] = val ;;
    end ;;
    fun tournamentOp₁.d.n.g X = Y @ [d <- 0]
      dim t <- ilog.n ;;
      var Y = fby.t X (g.(LofPair.d Y).(RofPair.d Y)) ;;
    end ;;

    The default₁ function creates a stream Y varying in dimension d such that in the interval [m,n], the result will be the value of X. Everywhere else, the value of Y is the default val.

    As for tournamentOp₁, when #!t ≡ 0, the value of Y is X. When #!t > 0, each element of Y is the result of applying the binary function g to a pair of elements from Y when #!t was one less. This process is completed until there is just one element left. Since the number n is not necessarily a power of 2, we use default₁ to fill in the slots of X with the neutral element of g.

    This form of computation is called tournament computation, and writing programs this way encourages parallel implementations.

  • cartesianprogramming 03:46 on 2012/06/19 Permalink | Reply  

    The intension as first-class value 

    The origins of Cartesian Programming came from what was called Intensional Programming, in which the behavior of a program was context-dependent: a context is a set of (dimension,ordinate) pairs,
    and the program can change behavior if some of the ordinates are changed. Formally, a variable in an intensional programming language is an intension, i.e., a mapping from contexts to values.

    In TransLucid, after several failed attempts at defining the semantics of functions over these intensions, it finally dawned on us that the intension itself needs to be a first-class value. What this means is that
    the context in which an intension is created is as important as the context in which it is evaluated. Consider:

    var tempAtLocation = ↑{location} temperature ;;
    var tempInInuvik = tempAtLocation @ [location ← "Inuvik"] ;;

    What this means is that whatever the value of the location-ordinate, variable tempInInuvik would always give the temperature in Inuvik, allowing any other dimensions to vary freely. Hence

    ↓tempInInuvik @ [location ← "Paris", date ← #!date - 1] ;;

    would give the temperature in Inuvik yesterday, not in Paris yesterday.

  • cartesianprogramming 05:56 on 2012/05/22 Permalink | Reply  

    Programming with infinite arrays: Factorial 

    Here we give an example of programming with infinite arrays. We take the well-known factorial function, and calculate using tournament computation. The TransLucid source code is found below.

    We build an array f which varies with respect to dimensions t and d, effectively creating a computation tree. For example, to compute the factorial of 3, the variable f becomes

      t 1 1 2 3 1 1 ...
        1 6 1 1 1 1 ...
        6 1 1 1 1 1 ...

    and the answer is 6, picked up when t=2 and d=0.

    Similarly, for the factorial of 6, f becomes

      t   1   1   2   3   4   5   6   1   1 ...
          1   6  20   6   1   1   1   1   1 ...
          6 120   1   1   1   1   1   1   1 ...
        720   1   1   1   1   1   1   1   1 ...

    and the answer is 720, picked up when t=3 and d=0.

    When t = 0, the value of f is a d-stream such that f is the current d-index if it is between 1 to n, and 1 otherwise. When t > 0, the value of f is a d-stream such that f is the product of pairs from the (t-1) d-stream.

    fun fact.n = f
      dim d <- 0 ;;
      var f = tournamentOp₁.d.n.times (default₁.d.1.n.1 (#!d)) ;;
    end ;;
  • cartesianprogramming 05:53 on 2012/05/22 Permalink | Reply  

    TransLucid preamble 

    There are now a number of TransLucid examples available at the TransLucid Web site.
    All of these examples use the declarations found in the preamble.


  • cartesianprogramming 05:30 on 2012/05/22 Permalink | Reply  

    Publication archive 

    To help gather the open problems related to implementing TransLucid,
    a publication archive has been prepared. It is available at
    Included in that archive are the collected works of John Plaice,
    Blanca Mancilla and Bill Wadge, along with all of the papers
    presented at the International Symposia on Lucid and
    Intensional Programming
    and the Conferences on
    Distributed Communities on the Web

  • cartesianprogramming 05:22 on 2012/05/22 Permalink | Reply  

    The first release of TransLucid is out! 

    It has taken a long time to come, but the first release of TransLucid,
    version 0.1.0, is out. It is available at the following link.

  • cartesianprogramming 03:22 on 2011/11/22 Permalink | Reply  

    The new C++ 

    The TransLucid interpreter is being written using the new standard C++, called C++11.
    For interesting discussions about C++11, I recommend the http://thenewcpp.wordpress.com blog.
    For a summary of the current C++11 implementation of the GNU gcc compiler suite, go to http://gcc.gnu.org/projects/cxx0x.html

  • cartesianprogramming 03:17 on 2011/11/22 Permalink | Reply  

    TransLucid is live and online 

    The TransLucid interpreter is coming alive. It now implements a full functional programming language. It can be used online at http://translucid.web.cse.unsw.edu.au

  • cartesianprogramming 09:59 on 2010/09/14 Permalink | Reply  

    Semantics of header entries 

    Since headers are needed for equations to be parsed, and (at least in theory) equations can come from multiple simultaneous sources, there will be a need for multiple simultaneous headers, which should simply be unioned together, no? This means that one should be able to load the same library multiple times and declare the same dimension multiple times, and so on. What is necessary is that everything be consistent, e.g., an operator cannot be defined to have multiple interpretations.

    • jarro2783 10:07 on 2010/09/14 Permalink | Reply

      I think this goes with the post 2 down. The header semantics need to be better defined, including the deletion of dimensions, and the parser should be sensitive to time and other context. Currently the header just gets added to and the parser parses by whatever the header says at the time that it was called.

  • cartesianprogramming 04:42 on 2010/09/13 Permalink | Reply  

    Formalization of the interpreter 

    The interpreter needs to be formalized once the operational semantics is finished. This is a necessary step towards writing TransLucid in TransLucid. The key missing parts for writing TL in TL are:

    1. Besfitting
    2. Parsing (a form of bestfitting)
    3. Printing (a form of bestfitting)
    4, Libraries

    We are close on all of these. But nothing is finalized.

    • jarro2783 10:05 on 2010/09/14 Permalink | Reply

      1. We need a good algorithm to determine the bestfit equation. The best I can think of would be n^2 because it has to determine for every equation whether it is more specific than every other.
      2. Not sure about how to tackle this still. Some sort of recursive descent thing which mimics spirit could be feasible. I can see that in the future we could even beat spirit, possibly blowing it out of the water. We quite possibly need functions in TL to do this.
      3. String operations are probably required, apart from that it seems trivial.
      4. It seems that we just need some proper semantics. At the moment a library adds equations when it’s loaded. Libraries are currently written in c++, we could allow these to be translucid files too.

      • cartesianprogramming 10:12 on 2010/09/14 Permalink | Reply

        If you store information separately for each variable, then testing applicability is linear in the number of entries for that variable. Among the applicable entries, finding bestfit ones is quadratic in the number of applicable entries.

        This can be improved by using just-in-time ideas. After each modification of the set of equations for a variable, the first time that a demand is made for that variable would force the creation of a finite-state automaton that would be run upon any request for that variable (until, of course, the next modification to the set of equations).

        • cartesianprogramming 10:14 on 2010/09/14 Permalink

          The initial implementation can be done using the linear-quadratic solution. Just-in-time ideas can be kept for future optimization.

        • jarro2783 00:18 on 2010/09/16 Permalink

          what about including priority in that?

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