Software is currently described by written text that is transformed by other process (compilers/interpreters) to a different state and then executed. Often the execution does not work as expected due to undefined conditions or states within the "mathematical language", or misunderstanding of the scope or memory allocation or release, etc.
There certainly could and should be visual representations of state, memory utilization, registers, variable values and execution sequence based on the textual conditions described. Contrasts of expected execution vs actual.
Perhaps using GPT-3 that is taught each programming language and then a designer can specify the behavior and GPT-X* can build a solution that can be formally verified as provable. Then generate test cases and show the flow and proof of correct execution based on test conditions.
> Often the execution does not work as expected due to undefined conditions or states within the "mathematical language", or misunderstanding of the scope or memory allocation or release, etc.
nah, 90%+ of bugs are already present in the "paper" specification in my experience, without any programming language involved (and I'm mostly writing in C++ which is prone to the issues you mention).
Other engineering professions make heavy use of visual modeling tools. Oddly, the industry that builds these tools is itself "the barefoot shoemaker."