A great language should let you think useful thoughts you have never been able to think before. This new project I'm working on, whose code name is "Smalltalk of Modeling", is expanding my mind.
Here is one idea. Lets generalize the idea of grammars. A grammar is normally used to parse text to create a parse tree. But if you annotate the grammar with constructors then the parse tree can be instantiated create arbitrary information structures, which we can view as the semantics of the text. If you are careful, then you will find that there can be quite a bit of divergence between the syntax and the semantics; for example, while syntax is tree-based, the semantics may be a graph. We can also run the process backwards, where we take some semantic object and render it into the grammar to create a parse tree, which can then be written out to text. This amounts to putting some clothes onto the abstract semantic structure.
Text --parse(Grammar)---> ParseTree --instantiate(Factory)--> Semantic Structure
Semantic Structure --render(Grammar)--> ParseTree --------display----------> Text
Note that parse and render, which both use the Grammar, are not inverses of each other. Instead, they both output ParseTrees, but they do it from two different directions.
Now the interesting thing is that a Grammar is really just a ParseTree with added structure: to allow for alternation, repetition, and variable data. We don't need to add sequencing, because ParseTree already has that. That is, we can view a grammar as
ParseTreeGrammarStructure = Kleene(ParseTreeStructure)
This is probably not too surprising. The interesting thing is that once we make structural descriptions be values, then we can write the Kleene function, which "grammarizes" any structure. (Its called Kleene after the person who first formalized the idea of alternation, repetition, and sequencing.)
My new language lets me think about, and write down, the Kleene function. And use it in more general ways. For example, I can now contemplate constructing
DiagramGrammarStrucutre = Kleene(DiagramStructure)
This creates a semantic structure for the grammar of diagrams. I can then use it with my generic render routine to create diagrams of any semantic structure:
Semantic Structure ---render(DiagramGrammar)---> Diagram
This brings up the question of parsing diagrams. It turns out that we will edit them rather than parse them, but it will be the topic for a future post.
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