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util.unification
- UnificationImplements unification algorithm.
The base API operates on abstract trees, while it is agnostic to the actual representation of the tree. The caller passes comparators and operators along the trees to unify.
We assume the abstract tree has the following structure:
Tree : Variable | Value | Tuple Tuple : { Tree ... }
Here, {...}
just represents a sequence of trees.
A variable can be bound to a tree. A value can only match itself.
To operate on this tree, we need the following comparators and procedures, which the API takes as arguments:
var-cmpr
A comparator to see if an item is a variable, and also check equality of two variables. It must be hashable. See Basic comparators, for the details of comparators.
val-cmpr
A comparator to see if an item is a value, and also check equality of two values. Note that if a tree satisfies neither var-cmpr nor val-compr, it is regarded as a tuple.
tuple-fold
A procedure (tuple-folde proc seed tuple1 [tuple2])
.
This procedure should work like fold
(see Walking over lists)
over the elements in the tuple(s). It is only called with
either one or two tuples.
make-tuple
A procedure (make-tuple proto elements)
, where
proto is a tuple and elements are a list of trees.
It must return a new tuple with the given elements,
while all other properties are the same as proto.
This procedure isn’t needed by unify
.
{util.unification} Unify two trees a and b and returns a substitution dictionary, which is a dictionary that maps variables to its bounded trees.
See the entry of util.unification
above for the description
of var-cmpr, val-cmpr and tuple-fold.
(dict->alist (unify '(a 3 (c b)) '(c b (2 e)) symbol-comparator number-comparator fold)) ⇒ ((e . 3) (a . c) (b . 3) (c . 2))
As you can see in the example above, a variable may be mapped to another variable, or even to a tree that contains variables. If you apply the substitution to the original tree, you must do it recursively until all the variables in the dictionary is eliminated.
If two trees cannot be unified, #f
is returned.
(unify '(a (a)) '(x x) symbol-comparator number-comparator fold) ⇒ #f
{util.unification} Unify two trees a and b, and apply the result substitutions to create a new tree eliminating variables.
See the entry of util.unification
above for the description
of var-cmpr, val-cmpr, tuple-fold and
make-tuple.
(unify-merge '(a 3 (c b)) '(c b (2 e)) symbol-comparator number-comparator fold (^[_ elts] elts)) ⇒ (2 3 (2 3))
If two trees can’t be unified, #f
is returned.
Next: www.cgi
- CGI utility, Previous: util.toposort
- Topological sort, Up: Library modules - Utilities [Contents][Index]