• constant : no label, just constraints
• variable : label, with or without constraints
• anonymous : no label, no constraints

mkGConst x :! [] creates a single constant. mkGConst x :! xs creates an atomic disjunction. It makes no difference which of the values you supply for x and xs as they will be sorted and nubed anyway.

Create a singleton constant (no disjunction here)

Create a variable

Create a variable with no constraints

Create an anonymous value

If v has exactly one value/constraint, returns it

An anonymous GeniVal (_ or ?_) has no labels/constraints

A variable substitution map. GenI unification works by rewriting variables

For debugging

unify performs unification on two lists of GeniVal. If unification succeeds, it returns Just (r,s) where r is the result of unification and verb!s! is a list of substitutions that this unification results in.

l1 allSubsume l2 returns the result of l1 unify l2 if doing a simultaneous traversal of both lists, each item in l1 subsumes the corresponding item in l2

unifyHelper unf gs1 gs2 zips two lists with some unification function.

It's meant to serve as a helper to unify and allSubsume

Note that the first Subst is assumed to come chronologically before the second one; so merging { X -> Y } and { Y -> 3 } should give us { X -> 3; Y -> 3 };

See prependToSubst for a warning!

Add to variable replacement to a Subst that logical comes before the other stuff in it. So for example, if we have Y -> foo and we want to insert X -> Y, we notice that, in fact, Y has already been replaced by foo, so we add X -> foo instead

Note that it is undefined if you try to append something like Y -> foo to Y -> bar, because that would mean that unification is broken

Unification can either…

See source code for details

Note that we assume that it's acceptable to generate new variable names by appending an x to them; this assumption is only safe if the variables have gone through the function finaliseVarsById or have been pre-processed and rewritten with some kind of common suffix to avoid an accidental match

intersectConstraints (Just cs1) (Just cs2) returns the intersection of cs1 and cs2 if non-empty (or Nothing if there's nothing in common)

If any of the arguments is unconstrained (Nothing), we simply return the other.

subsumeOne x y returns the same result as unifyOne x y if x subsumes y or Failure otherwise

Apply variable substitutions

Apply a single variable substitution

Here it is safe to say (X -> Y; Y -> Z) because this would be crushed down into a final value of (X -> Z; Y -> Z)

Core implementation for replace For use by the Uniplate-esq descendGeniVal

Core implementation for replaceOne For use by the Uniplate-esq descendGeniVal

A variable label and its constraints

A Collectable is something which can return its variables as a map from the variable to the number of times that variable occurs in it.

Important invariant: if the variable does not occur, then it does not appear in the map (ie. all counts must be >= 1 or the item does not occur at all)

By variables, what I most had in mind was the GVar values in a GeniVal. This notion is probably not very useful outside the context of alpha-conversion task, but it seems general enough that I'll keep it around for a good bit, until either some use for it creeps up, or I find a more general notion that I can transform this into.

An Idable is something that can be mapped to a unique id. You might consider using this to implement Ord, but I won't. Note that the only use I have for this so far (20 dec 2005) is in alpha-conversion.

Anonymise any variable that occurs only once in the object

finaliseVarsById appends a unique suffix to all variables in an object. This avoids us having to alpha convert all the time and relies on the assumption finding that a unique suffix is possible.

finaliseVars does the following:

• (if suffix is non-null) appends a suffix to all variable names to ensure global uniqueness
• intersects constraints for for all variables within the same object

A schema value is a disjunction of GenI values. It allows us to express “fancy” disjunctions in tree schemata, ie. disjunctions over variables and not just atoms (?X;?Y).

Our rule is that that when a tree schema is instantiated, any fancy disjunctions must be “crushed” into a single GeniVal lest it be rejected (see crushOne)

Note that this is still not recursive; we don't have disjunction over schema values, nor can schema values refer to schema values. It just allows us to express the idea that in tree schemata, you can have either variable ?X or ?Y.

Convert a fancy disjunction (allowing disjunction over variables) value into a plain old atomic disjunction. The idea is to support a limited notion of fancy disjunction by requiring that there be a single point where this disjunction can be converted into a plain old variable. Note that we currently convert these to constants only.

Convert a list of fancy disjunctions

A structure that can be traversed with a GeniVal-replacing function (typical use case: substitution after unification)

Approach suggested by Neil Mitchell after I found that Uniplate seemed to hurt GenI performance a bit.