Undefined Symbols

[tbennun]

Following the discussion on May 16, we would like to have a special kind of symbol, which is undefined.

Motivation: Symbolic analysis is crucial to DaCe and transformations. However, not every data container needs to have a concrete symbolic value for a program to function (nor does it have one). For example, if a pointer is given from an external source without a size, the resulting data container's size is undefined. The fact that some containers do not have a symbolic size should not disrupt the analysis of other symbols (iterates, transient containers, other data containers with size information).

Why is it a problem? Right now, if such a data container has no concrete size, or any other symbol remains in an SDFG, the generated code will include another argument with that symbol. This defers the error to a compilation error, or a segmentation fault if the SDFG is called with one fewer parameter. Such errors are unclear to a user, are reported too late, and are not attached to the right source information as to which part of the code caused it. For example, is it a result of an erroneous transformation? If it's not part of SDFG validation, one can never debug such an issue.

Implementation: symbolic.UndefinedSymbol will be a subclass of symbolic.symbol. Therefore, it will behave the same way as a normal symbol, with a few exceptions:

• Undefined symbols have a name of "?" and any comparison with another symbolic expression will yield an indeterminate solution.
• Like NaN values, any operation on an undefined symbol results in an undefined symbol after simplification. For example: N + ? = ?
• During validation and code generation, if such a symbol is ever used in a way that would generate code, an informative exception will be raised.