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  • cartesianprogramming 19:36 on 2010/06/10 Permalink | Reply  

    TransLucid Doxygen documentation 

    The documentation automatically generated by Doxygen for the TransLucid code can be found at

  • cartesianprogramming 19:33 on 2010/06/10 Permalink | Reply  

    Reactive tlcore 

    When the –reactive option is set for tlcore, then the application becomes reactive, and the set of equations is allowed to vary over time, and the expressions being evaluated can refer to the time dimension. The idea is that at each instant,

    • The header may be added to.
    • The set of equations may be modified.
    • The set of expressions to be evaluated may be modified.
    • Then the expressions for that instant are evaluated.

    When tlcore is reading from the standard input, then the input will be of the form


    Each instant corresponds to the lines appearing between successive occurrences of $$.
    The output is of the same form as the input, with occurrences of $$ to separate the different instants.

    When the input is given in the form of option —input=infile, then the entire input, for all instants, is read from infile. When the input is given in the form of option –inputiter=inprefix, then the input for instant n comes from file inprefixn. In other words, the input for each instant is placed in a different file.

    Similarly for –output and –outputiter.

    If the –uuid option is set, then the universal identifiers for the equations are presented to the programmer, who can then manipulate them explicitly, with lines like the following two:

    delete eqnuuid1;;
    replace eqnuuid2 equation;;

    For the first line, if #time, the time that this line is added to the equations, has value t, then from t on, eqnuuid1 is no longer usable. For the second line, the equation corresponding to eqnuuid2 is replaced, from t on, with equation. If the value of #time is changed to t’, which happens to be less than t, then all of the equations available at time t’ continue to be accessible.

    Changes to the set of equations are done synchronously. All additions, deletions and replacements for a given instant are done as a single transaction, and must be consistent.

    An empty instant stops the tlcore program.

  • cartesianprogramming 18:41 on 2010/06/10 Permalink | Reply  

    Equation UUIDs 

    When an equation is added to the TransLucid system, it is automatically given a unique identifier, generated by the Boost.UUID library. When tlcore is passed the –uuid option, then both the equations and the expressions will return results. The results will be of the form


    Should the –verbose option also be set, then the results will be of the form


    • superspreadsheet 15:49 on 2010/06/11 Permalink | Reply

      From a practical point of view, it is not clear to me what the difference is between expressions and equations. They could both define and both be evaluated… No?

  • cartesianprogramming 17:26 on 2010/06/10 Permalink | Reply  


    When the interpreter is evaluating an expression in a given context κ and comes across a variable x to be evaluated, the bestfit definition of x must be chosen. This process consists of examining, for each definition, the context guard and Boolean guard for that definition. The applicable definitions are the ones for which the current context κ is enclosed in the context guard and for which the Boolean guard evaluates to true. The bestfit definition, should it exist, is the one applicable definition whose context guard defines a region completely (and strictly) contained inside the context guard of each of the other applicable definitions.

    Bestfitting becomes more complicated when the predefined priority, deftime and validtime dimensions are introduced. Both deftime and validtime are natural numbers, referring to the same time line, while priority is a natural number meaning that the higher the priority, the higher the number. The priority and validtime dimensions are controlled by the programmer, while the deftime dimension is controlled by the interpreter. For example, for the equation

    should #time be between 10 and 15, inclusive, then this equation is valid and has priority 2. The deftime for this equation is when it is added to the system.

    The validtime dimension is simply used to restrict the context guard. However, the deftime and priority act differently, as they are ordered dimensions. Once all of the applicable definitions are found, then they are further restricted, first using the priority dimension, then the deftime dimension. For both these dimensions, higher numbers are favored.

  • cartesianprogramming 12:51 on 2010/06/10 Permalink | Reply  

    The tlcore application 

    Now that the Core TransLucid library has been developed, it is time to develop some applications.
    The first application is called tlcore. It simply reads, either from a file or from the standard input, a TransLucid header, set of equations and set of expressions. The expressions are then evaluated one by one, and the results are placed on the standard output or in a file.

    The interface is as follows:

    tlcore --input=infile --output=outfile

    along with the standard –verbose and –version options.

    If the –input option is not provided, input is read from the standard input.
    If the –output option is not provided, output is written to the standard output.
    All errors or log messages, including version information, are written to the standard error.

    The syntax of the files is simple. It consists of three parts:


    where each part follows its standard syntax.

    The expressions are to be read, one by one, and then evaluated. The answers are provided as follows:


    Should the –verbose option be used, then the output will be


    The inContext variable is used to define the default context for parsing expressions.

    The outContext variable is used to define the default context for printing expressions.

    • superspreadsheet 15:31 on 2010/06/11 Permalink | Reply

      What is the difference between the Core TransLucid library and tlcore? Why is tlcore an application? Or rather what does it do exactly for the user?

      • cartesianprogramming 15:34 on 2010/06/11 Permalink | Reply

        tlcore is an interpreter of the TransLucid language, implemented using the Core TransLucid library. It allows direct use of TransLucid without having to write any C++ code.

    • superspreadsheet 15:34 on 2010/06/11 Permalink | Reply

      Again, from a user point of view, what ts the syntax of the header, equation and expression. Where can we find out? Is there a link?

      • cartesianprogramming 15:37 on 2010/06/11 Permalink | Reply

        Official user documentation does not yet exist. When it does, it will be made part of the TransLucid distribution. In the meantime, use the papers on TransLucid as a guide.

    • superspreadsheet 15:36 on 2010/06/11 Permalink | Reply

      Where are inContext and outContext defined? In the command line? In the program? IOW, by user or programmer?

  • cartesianprogramming 09:06 on 2010/06/10 Permalink | Reply  


    The language for developing Cartesian Programming is called TransLucid.
    Its home site, with the source code, is

  • cartesianprogramming 20:11 on 2010/05/02 Permalink | Reply  

    Historical papers 

    There are two historical papers that summarize the developments leading to Cartesian programming:

  • cartesianprogramming 20:34 on 2010/04/25 Permalink | Reply  

    Text of Descartes’s Géométrie 

    On Wikimedia, there is a DJVU file of La Géométrie, by René Descartes:
    Discours de la Méthode

  • cartesianprogramming 19:38 on 2010/04/25 Permalink | Reply  

    Book on Descartes’s Géométrie 

    There is a wonderful book on Descartes’s Géométrie published by Siglo XXI, México:

    Here is the description:

    Las más de las veces, el Descartes que se conoce es el Descartes filósofo. Pero su obra abarca un espectro mucho más amplio: ¿dónde queda el Descartes que abre la senda para los métodos analíticos en las matemáticas, sin la cual es impensable la obra monumental de Newton? Este Descartes preocupado por la ciencia es el que inspira los textos aquí reunidos: a través de ellos el lector puede juzgar si, además de ser considerado el primer filósofo de la modernidad, pudiera tal vez considerársele el primer científico de la modernidad.

    The chapter by Jean Dhombres, «La banalidad del referencial cartesiano», pages 69-98, focuses on how once the Cartesian coordinate system was invented, how quickly it became trivial. Yet it is this triviality that simplified geometry and allowed its algebraisation. Cartesian programming aims to do the same for computing.

  • cartesianprogramming 12:46 on 2010/04/20 Permalink | Reply  

    Cartesian programming lives! 

    Cartesian programming provides a multidimensional context, used as an index, to programming, in an infinite-dimensional space.  Just as Cartesian geometry allowed the algebraisation of the geometry, Cartesian programming allows the use of a single formalism in which one can develop an entire software system, with multiple heterogeneous components, in a completely declarative manner.

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