The type of terms generated by structures t over variables v. The structure type should implement Unifiable and the variable type should implement Variable.

The Show instance doesn't show the constructors, in order to improve legibility for large terms.

All the category theoretic instances (Functor, Foldable, Traversable,...) are provided because they are often useful; however, beware that since the implementations must be pure, they cannot read variables bound in the current context and therefore can create incoherent results. Therefore, you should apply the current bindings before using any of the functions provided by those classes.

O(n). Extract a pure term from a mutable term, or return Nothing if the mutable term actually contains variables. N.B., this function is pure, so you should manually apply bindings before calling it.

O(n). Embed a pure term as a mutable term.

The possible failure modes that could be encountered in unification and related functions. While many of the functions could be given more accurate types if we used ad-hoc combinations of these constructors (i.e., because they can only throw one of the errors), the extra complexity is not considered worth it.

This is a finally-tagless encoding of the UFailure data type so that we can abstract over clients adding additional domain-specific failure modes, introducing monoid instances, etc.

Since: 0.10.0

A concrete representation for the Fallible type class. Whenever possible, you should prefer to keep the concrete representation abstract by using the Fallible class instead.

Updated: 0.10.0 Used to be called UnificationFailure. Removed the UnknownError constructor, and the Control.Monad.Error.Error instance associated with it. Renamed OccursIn constructor to OccursFailure; and renamed TermMismatch constructor to MismatchFailure.

Updated: 0.8.1 added Functor, Foldable, and Traversable instances.

An implementation of syntactically unifiable structure. The Traversable constraint is there because we also require terms to be functors and require the distributivity of sequence or mapM.

Updated: 0.11 This class can now be derived so long as you have a Generic1 instance.

An implementation of unification variables. The Eq requirement is to determine whether two variables are equal as variables, without considering what they are bound to. We use Eq rather than having our own eqVar method so that clients can make use of library functions which commonly assume Eq.

The basic class for generating, reading, and writing to bindings stored in a monad. These three functionalities could be split apart, but are combined in order to simplify contexts. Also, because most functions reading bindings will also perform path compression, there's no way to distinguish "true" mutation from mere path compression.

The superclass constraints are there to simplify contexts, since we make the same assumptions everywhere we use BindingMonad.

The target of variables for RankedBindingMonads. In order to support weighted path compression, each variable is bound to both another term (possibly) and also a "rank" which is related to the length of the variable chain to the term it's ultimately bound to.

The rank can be at most log V, where V is the total number of variables in the unification problem. Thus, A Word8 is sufficient for 2^(2^8) variables, which is far more than can be indexed by getVarID even on 64-bit architectures.

An advanced class for BindingMonads which also support weighted path compression. The weightedness adds non-trivial implementation complications; so even though weighted path compression is asymptotically optimal, the constant factors may make it worthwhile to stick with the unweighted path compression supported by BindingMonad.