Portability  FlexibleInstances, TypeSynonymInstances, MultiParamTypeClasses 

Stability  experimental 
Maintainer  Douglas Burke 
This module contains graphmatching logic.
The algorithm used is derived from a paper on RDF graph matching by Jeremy Carroll [1].
 graphMatch :: Label lb => (lb > lb > Bool) > [Arc lb] > [Arc lb] > (Bool, LabelMap (ScopedLabel lb))
 type LabelMap lb = GenLabelMap lb LabelIndex
 data (Label lb, Eq lv, Show lv) => GenLabelMap lb lv = LabelMap Int (LookupMap (GenLabelEntry lb lv))
 type LabelEntry lb = GenLabelEntry lb LabelIndex
 data Label lb => GenLabelEntry lb lv = LabelEntry lb lv
 data Label lb => ScopedLabel lb = ScopedLabel Int lb
 makeScopedLabel :: Label lb => Int > lb > ScopedLabel lb
 makeScopedArc :: Label lb => Int > Arc lb > Arc (ScopedLabel lb)
 type LabelIndex = (Int, Int)
 type EquivalenceClass lb = (LabelIndex, [lb])
 nullLabelVal :: LabelIndex
 emptyMap :: Label lb => LabelMap lb
 labelIsVar :: Label lb => lb > Bool
 labelHash :: Label lb => Int > lb > Int
 mapLabelIndex :: Label lb => LabelMap lb > lb > LabelIndex
 setLabelHash :: Label lb => LabelMap lb > (lb, Int) > LabelMap lb
 newLabelMap :: Label lb => LabelMap lb > [(lb, Int)] > LabelMap lb
 graphLabels :: Label lb => [Arc lb] > [lb]
 assignLabelMap :: Label lb => [lb] > LabelMap lb > LabelMap lb
 newGenerationMap :: Label lb => LabelMap lb > LabelMap lb
 graphMatch1 :: Label lb => Bool > (lb > lb > Bool) > [Arc lb] > [Arc lb] > LabelMap lb > [(EquivalenceClass lb, EquivalenceClass lb)] > (Bool, LabelMap lb)
 graphMatch2 :: Label lb => (lb > lb > Bool) > [Arc lb] > [Arc lb] > LabelMap lb > [(EquivalenceClass lb, EquivalenceClass lb)] > (Bool, LabelMap lb)
 equivalenceClasses :: Label lb => LabelMap lb > [lb] > [EquivalenceClass lb]
 reclassify :: Label lb => [Arc lb] > [Arc lb] > LabelMap lb > [(EquivalenceClass lb, EquivalenceClass lb)] > (LabelMap lb, [(EquivalenceClass lb, EquivalenceClass lb)], Bool, Bool)
Documentation
:: Label lb  
=> (lb > lb > Bool)  a function that tests for additional constraints
that may prevent the matching of a supplied pair
of nodes. Returns 
> [Arc lb]  the first graph to be compared, as a list of arcs 
> [Arc lb]  the second graph to be compared, as a list of arcs 
> (Bool, LabelMap (ScopedLabel lb))  If the first element is 
Graph matching function accepting two lists of arcs and returning a node map if successful
type LabelMap lb = GenLabelMap lb LabelIndexSource
data (Label lb, Eq lv, Show lv) => GenLabelMap lb lv Source
Type for label>index lookup table
LabelMap Int (LookupMap (GenLabelEntry lb lv)) 
type LabelEntry lb = GenLabelEntry lb LabelIndexSource
data Label lb => GenLabelEntry lb lv Source
LabelEntry lb lv 
data Label lb => ScopedLabel lb Source
This instance of class label adds a graph identifier to each variable label, so that variable labels from different graphs are always seen as distinct values.
The essential logic added by this class instance is embodied in the eq and hash functions. Note that variable label hashes depend only on the graph in which they appear, and nonvariable label hashes depend only on the variable. Label hash values are used when initializing a label equivalenceclass map (and, for nonvariable labels, also for resolving hash collisions).
ScopedLabel Int lb 
Label lb => Eq (ScopedLabel lb)  
Label lb => Ord (ScopedLabel lb)  
Label lb => Show (ScopedLabel lb)  
Label lb => Label (ScopedLabel lb) 
makeScopedLabel :: Label lb => Int > lb > ScopedLabel lbSource
makeScopedArc :: Label lb => Int > Arc lb > Arc (ScopedLabel lb)Source
type LabelIndex = (Int, Int)Source
LabelIndex is a unique value assigned to each label, such that labels with different values are definitely different values in the graph; e.g. do not map to each other in the graph bijection. The first member is a generation counter that ensures new values are distinct from earlier passes.
type EquivalenceClass lb = (LabelIndex, [lb])Source
Type for equivalence class description (An equivalence class is a collection of labels with the same LabelIndex value.)
labelIsVar :: Label lb => lb > BoolSource
Does this node have a variable binding?
labelHash :: Label lb => Int > lb > IntSource
Calculate the hash of the label using the supplied seed.
mapLabelIndex :: Label lb => LabelMap lb > lb > LabelIndexSource
Map a label to its corresponding label index value in the supplied LabelMap
setLabelHash :: Label lb => LabelMap lb > (lb, Int) > LabelMap lbSource
Replace a label and its associated value in a label map
with a new value using the supplied hash value and the current
LabelMap
generation number. If the key is not found, then no change
is made to the label map.
newLabelMap :: Label lb => LabelMap lb > [(lb, Int)] > LabelMap lbSource
Replace selected values in a label map with new values from the supplied list of labels and new label index values. The generation number is supplied from the current label map. The generation number in the resulting label map is incremented.
graphLabels :: Label lb => [Arc lb] > [lb]Source
Return list of distinct labels used in a graph
assignLabelMap :: Label lb => [lb] > LabelMap lb > LabelMap lbSource
Scan label list, assigning initial label map values, adding new values to the label map supplied.
Label map values are assigned on the basis of the
label alone, without regard for it's connectivity in
the graph. (cf. reclassify
).
All variable node labels are assigned the same initial value, as they may be matched with each other.
newGenerationMap :: Label lb => LabelMap lb > LabelMap lbSource
Increment the generation of the label map.
Returns a new label map identical to the supplied value but with an incremented generation number.
:: Label lb  
=> Bool 

> (lb > lb > Bool)  Test for additional constraints that may prevent the matching
of a supplied pair of nodes. Returns 
> [Arc lb]  ( 
> [Arc lb]  ( 
> LabelMap lb  the map so far used to map label values to equivalence class values 
> [(EquivalenceClass lb, EquivalenceClass lb)]  (the 
> (Bool, LabelMap lb)  the pair 
Recursive graph matching function
This function assumes that no variable label appears in both graphs.
(Function graphMatch
, which calls this, ensures that all variable
labels are distinct.)
TODO:
 replace Equivalence class pair by
(index,[lb],[lb])
?  possible optimization: the
graphMapEq
test should be needed only ifgraphMatch2
has been used to guess a mapping; either: a) supply flag saying guess has been used, or b) move test tographMatch2
and use different test to prevent rechecking for each guess used.
graphMatch2 :: Label lb => (lb > lb > Bool) > [Arc lb] > [Arc lb] > LabelMap lb > [(EquivalenceClass lb, EquivalenceClass lb)] > (Bool, LabelMap lb)Source
Auxiliary graph matching function
This function is called when deterministic decomposition of node mapping equivalence classes has run its course.
It picks a pair of equivalence classes in ecpairs, and arbitrarily matches pairs of nodes in those equivalence classes, recursively calling the graph matching function until a suitable node mapping is discovered (success), or until all such pairs have been tried (failure).
This function represents a point to which arbitrary choices are backtracked.
The list comprehension glp
represents the alternative choices at the
point of backtracking
The selected pair of nodes are placed in a new equivalence class based on their original equivalence class value, but with a new NodeVal generation number.
:: Label lb  
=> LabelMap lb  label map 
> [lb]  list of nodes to be reclassified 
> [EquivalenceClass lb]  the equivalence classes of the supplied labels under the supplied label map 
:: Label lb  
=> [Arc lb]  (the 
> [Arc lb]  (the 
> LabelMap lb  the label map used for classification of the labels in the supplied equivalence classes 
> [(EquivalenceClass lb, EquivalenceClass lb)]  (the 
> (LabelMap lb, [(EquivalenceClass lb, EquivalenceClass lb)], Bool, Bool)  The output tuple consists of: 1) a revised label map reflecting the reclassification 2) a new list of equivalence class pairs based on the new node map 3) if the reclassification partitions any of the
supplied equivalence classes then 4) if reclassification results in each equivalence class
being split samesized equivalence classes in the two graphs,
then 
Reclassify labels
Examines the supplied label equivalence classes (based on the supplied label map), and evaluates new equivalence subclasses based on node values and adjacency (for variable nodes) and rehashing (for nonvariable nodes).
Note, assumes that all all equivalence classes supplied are nonsingletons; i.e. contain more than one label.