JSKI Help

JSKI is a SK Machine as designed by David Turner in the 80's. This help is not a course about the theory of combinators invented by Haskell B. Curry and M. Schoenfinkel at the beginning of the 1900's. A course can be found at:

      http://www.infres.enst.fr/~bellot/CELSK/index.html

It will be refrered as "the course".

Execution

JSKI.jar is an executable jar. It can be executed by double clicking on it. Manually, the ideal command is:

     java -server -Xms1024M -Xmx1024M -Xss128M -da -dsa -XX:-UseGCOverheadLimit -jar JSKI.jar

Try to use these options!

Workspace

In JSKI, only S, K and I are primitive combinators. All other combinators are defined symbols. JSKI maintains a table of symbols and each symbol possibly has a functional definition. When a symbol is applied, it is replaced by its definition. The set of these definitions is called the workspace. The content of the workspace can be erased with the menu Workspace, menu item Empty workspace. The current state of the workspace can be saved in a text file by using the menu Workspace, menu item Save workspace. The current workspace memory occupation can be seen by using the menu Workspace, menu item Nodes count.

Classical definitions

The classical definitions of some well-known combinators, as defined in the course, can be loaded into the workspace by using the Load predefineds buttons. The name of the defined combinators are listed at the top of the JSKI window.

Programs

The text area in the program zone is where programs are edited. It is subject to the usual Open, Save and Save as... file menu. Don't forget to make a regular save in case something goes wrong. The current state is displayed just above the text area. The program text area must contain symbol definitions. A definition is an expression:

     #DEF <symbol> = <term> ;;

where <symbol> is any symbol beginning with a letter, made of letters and digits and different from S, K and I). When the program text area is compiled using the Compile buffer button, the definitions are registered in the current workspace. It is also possible to select a region in this buffer and use the Compile selection button.

To erase a definition in the current workspace, use:

     #UNDEF <symbol> ;;

Abstraction algorithms

In any term, especially in definitions, you can use one of the four abstraction algorithms of the course using the notations:

     (\+ <symbol> . <term>)
     (\++ <symbol> . <term>)
     (\+++ <symbol> . <term>)
     (\++++ <symbol> . <term>)

The parentheses around are mandatory. The values of these expression replace the expressions at the time the system reads them. Don't forget to load predefineds symbols if you use the three last abstraction algorithms.

Functional references

In a definition, you can use the functional value reference of a symbol f. It is noted @f. When the definition are reads, it is left as is. Then after the definition are reads, it is replaced by the functional value of the symbol f if there is one, or by f if there is not. For instance:

     #DEF factorial = (\+ N . (=0 N) 1 (* N (@factorial (1- N)))) ;;

This allows to create circular graphs for implementing recursion as mentionned in D. Turner fundation article.

Execution

You can enter term to evaluate in the Expression text area. Then you can do the Head reduction button or the Full reduction button. Hiting the enter key runs a head reduction. Computations may be interrupted using the Interrupt button. The results are displayed in the Result text area. A single head reduction can be obtain with the appropriate button. The Expression text area has an history mechanism accessible with the Up and Down arraows.

Under the Result text area, the three buttons Head reduction, Full reduction allow to finish the reduction of the term in the text area. The button Next head redex allows to do a single hed reduction of the term in the text area.

The button Interpret allows, sometimes, to make the result more humanly readable by searching the results for integers, for lists, for booleans, etc.

In the Expression text entry field, you can entrer # <symbol>, the result will be the functional value (the definition) of the symbol if any. In fact # is a combinator returning the functional value of its argument if there is one, returning its argument otherwise.

Data

In the terms, natural numbers can be written in base 10. At the reading, they are translated into Church's integers. Lists can be written using the bracket notation [a,b,c] or [a,b,c . d]

Enjoy ! Suggestions and bugs can be send to bellot@telecom-paristech.fr.