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An attempt at general-purpose fixity resolution code for Standard ML
Standard ML
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An attempt at general-purpose fixity resolution code for Standard ML. Fixity resolution is a general problem with a simple, yet fiddly solutions, and I wasn't able to find code that was simultaneously:

  1. Sufficiently general that it could be reused in a variety of applications.

  2. Useful in a situation where good error messages are (or might eventually be) required.

  3. Sufficiently well-written and well-documented that I was able to tell what was going on.

The first and second problem are addressed by functorizing the fixity code; this allows us to throw different exceptions for different errors that arise during fixity resolution -- client code can then handle these errors in a way that is informative to the user. If the input "tok" type includes position information, then the information carried by exceptions will allow for good error reporting.

In order to make the code comprehensible, the implementation is simplified: in particular, it is limited to prefix and infix operators (no postfix operators). There are lots of comments in the code, and the runtime invariants can be dynamically checked or not by changing which of the two functions in assert.sml is commented out. A couple of simple examples of using the fixity resolver are given in examples.sml.

Initializing simple-fixity

Assuming that you want precedence to be an integer, then you want to instantiate the fixity resolving structure like this:

structure Fix = 
IntFixityFn (type tok = (* my type of input tokens *)
             type result = (* my type of output tree-structured data *))

See here for two examples of instantiating this functor. If you have some different notion of precedence, then you will want to instantiate the functor like this, using an instance of the ORDERED signature from CMLib:

structure Fix = 
SimplestFixityFn (structure Precedence = (* Some instance of ORDERED *)
                  type tok = (* my type of input tokens *)
                  type result = (* my type of output tree-structured data *))

You need to build an element of the Fix.resolver type to resolve fixity. Fix.AdjResolver builds a resolver that allows adjacent non-fixity tokens, and Fix.NoAdjResolver builds a resolver that doesn't allow that adjacent non-fixity tokens.

Using simple-fixity

Any partial fixity-resolution problem is in one of four states: it is (potentially) Complete, Incomplete, Wrong, or (potentially) Ambiguous. These four states correspond to exceptions that may be thrown by the functions Fix.resolve, Fix.resumeTotal, Fix.resumePartial.

  1. raise Fix.Complete

    The parse successfully returned. If you're parsing progressively, then you don't want to reduce "5 + 9" to 14 if the next tokens you're going to get are "*" and "2".

    If you don't care about resumption, use Fix.resolveStream or Fix.resolveList, which handle this exception internally and just return the answer.

  2. raise Fix.Incomplete

    Either there was no input or there was a trailing infix operator. This would be recoverable if there was more input using Fix.resumePartial.

  3. raise Fix.Wrong

    A leading infix operator or an infix operator following an infix or prefix operator. This is just wrong, there is no recovery.

  4. raise Fix.Ambiguous

    The parsing problem seems to have more than one valid solution: an exception is conservatively thrown in lieu of doing something arbitrary.

    This exception can be completely avoided if all prefix operators have the same precedence that is higher than all other precedences, if all infix operators are either LEFT or RIGHT associative (not NON associative), and if LEFT and RIGHT associative operators never have the same precedence.

More documentation is given in the FIXITY signature

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