All ASPL symbolic operators are typable on any standard keyboard. The basic ASCII 95 printable characters are the only ones used in representing any symbolic operator. None of ASPL operators depends on any particular keyboard, or on entering escape sequence to ASCII control-character to emit its symbols.

Most symbols start with a first letter referring to the subject (with an 'f' for elements, 'd' for subgroup, and 'g' for group), then followed by a second letter referring to the type of operation; this makes a mnemonic easy for the user to remember. Some other symbols have to operate on the checksum, or the fuzzyness of the elements, hence the symbols start with 'c' and 'y'. The main motivation for deriving the ASPL symbolic operators, and make them typable in basic ASCII, is to facilitate entering these symbols at the shell prompt, and to make ASPL a lightweight interpreter that run on any system without the usage of any GUI library. After all, group operations are limited to the following four: union, intersection, difference, and symmetric difference, that are to be performed on three subjects: elements, subgroups, or groups. Considering the three subjects and the four actions, we can express the operations with simple mnemomics. Other operators are simple plain words or verbs, and do not require any symbolic representation: such as merge, split, similarity, density, etc.

There is another class of operators that act on differential group variables. Since these require specific verbs to assess the temporal changes in a variable, then they are not covered in this guide. Differential group variables are covered in ASPL User Guide.

ASPL symbolic processing does not depend on a particular computer system, it is machine independent, so the program can run on various UNIX systems.

Another feature of the ASPL interpreter is in its many operational characteristics. Abundant set operations such as set operations, sequence operations, similarity calculation, statistical operations, among many others that can execute complex algebraic set calculations with simple commands. In addition, the ASPL interpreter has a new and unique implementation for the env's shebang (or hashbang) that breaks from the traditional non-portable one liner entry in UNIX scripts, making ASPL scripts runnable on various UNIX implementations. The shebang is discussed in ASPL User Guide.

In this guide we refer to the UNIX shell prompt with the hash symbol # as shown here

#  aspl

The commands issued at the aspl prompt start with aspl> as shown here

aspl> sim a1 a2 a3
    (show the similarity between a1, a2, and a3)

A series of commands can be numbered, for example:

①  aspl> sim a1 a2 a3
    (show the similarity between a1, a2, and a3)

②  aspl> sim`c a1 a2 a3
    (show the similarity between a1, a2, and a3 considering the checksum attribute)

③  aspl> sima123 = sim a1 a2 a3
    (assign to the COS variable sima123 the similarity result)

ASPL set operators are setadic: the operator symbol is firstly to appear on the left of the line, then followed by one more operands, or by a curly set expression. When an aperator is issued by itself, then it is called niladic, in which case, if the operator requires to be followed by any operand, then the operation is carried out on the objects on the top of the stack.
Each operator is introduced on one page showing the symbolic operator in a syntax box. The top line on the box shows the symbolic operator, it is followed by a brief description of the operator. Properties of the operator are shown at the bottom of the box. The syntax box is explained in Appendix C The Syntax Box.



Bassem W. Jamaleddine
November 23 2025
New York, NY

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