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What counts as language#

The language defines some meanings of the specification of an optimisation model (a spec). It defines them for all software that reads a spec (every tool), and each tool decides the rest for itself. An engine, a renderer and a checker can all read one spec (the tools that read a spec).

One test separates what the language defines from what a tool decides. The test is whether two tools that answered a question about the file differently would give the file two meanings. Suppose the engine sums p over generator, and the renderer prints a sum over snapshot. The file now has two meanings, and that is wrong. So the language defines what sum(p, over=generator) means, and both tools read the definition instead of working it out.

Suppose instead that the engine writes the model in one solver's file format, and the renderer sets the page width to 80 characters. The two tools differ, and nothing is wrong, because each tool decides those things for itself.

What the language defines#

Five rules follow from that test:

  • A name means one thing, so p cannot be a variable in the engine and a parameter in the renderer.
  • The set of constructs built into the language (operators) is closed.
  • Each operator has one rule for the dimensions of its result. sum(p, over=generator, by=generator[bus]) groups by bus for every tool.
  • mathspec decides when to_spec reads the file (at load) whether an expression is linear or quadratic (its degree). Whether x * y is allowed does not depend on which engine builds the model.
  • An entry that expands into ordinary entries (a formulation) has one meaning for every tool. A piecewise: entry and a cap on non-zero members (an SOS) under sos: each state ordinary variables and constraints. spec.expand() writes them out the same way for every tool.

What each tool decides for itself#

A tool can refuse a spec for a reason of its own. One engine takes only a literal offset in shift. Another has no SOS, and a file format has no way to write a quadratic constraint. None of these is a disagreement about what the file means, so mathspec settles none of them at load.

Here a refusal by each tool is better than a refusal by mathspec of every construct that some tool cannot build. Otherwise every other tool loses the construct too. If mathspec refused sos: because one engine has no SOS, no engine could build an SOS from a spec.

So the test works in both directions. A rule about what the file means goes into the language, and a rule about what one tool can build stays with that tool.

You can now judge whether a rule belongs in the language or in a tool.

See also