Module FMInt

emptyFM :: FMI   

The empty finite map.

Example call:

(emptyFM le)

Parameters:

• le : an irreflexive order predicate on the keys.

Further infos:

• solution complete, i.e., able to compute all solutions

unitFM :: Int -> Int -> FMI   

Construct a finite map with only a single element.

Example call:

(unitFM le key elt)

Parameters:

• le : an irreflexive order predicate on the keys.
• key : key of
• elt : the single element to form

Further infos:

• solution complete, i.e., able to compute all solutions

listToFM :: [(Int,Int)] -> FMI   

Builts a finite map from given list of tuples (key,element). For multiple occurences of key, the last corresponding element of the list is taken.

Example call:

(listToFM le)

Parameters:

• le : an irreflexive order predicate on the keys.

addToFM :: FMI -> Int -> Int -> FMI   

Throws away any previous binding and stores the new one given.

addListToFM :: FMI -> [(Int,Int)] -> FMI   

Throws away any previous bindings and stores the new ones given. The items are added starting with the first one in the list

addToFM_C :: (Int -> Int -> Int) -> FMI -> Int -> Int -> FMI   

Instead of throwing away the old binding, addToFM_C combines the new element with the old one.

Example call:

(addToFM_C combiner fm key elt)

Parameters:

• combiner : a function combining to elements
• fm : a finite map
• key : the key of the elements to be combined
• elt : the new element

addListToFM_C :: (Int -> Int -> Int) -> FMI -> [(Int,Int)] -> FMI   

Combine with a list of tuples (key,element), cf. addToFM_C

delFromFM :: FMI -> Int -> FMI   

Deletes key from finite map. Deletion doesn't complain if you try to delete something which isn't there

delListFromFM :: FMI -> [Int] -> FMI   

Deletes a list of keys from finite map. Deletion doesn't complain if you try to delete something which isn't there

updFM :: FMI -> Int -> (Int -> Int) -> FMI   

Applies a function to element bound to given key.

splitFM :: FMI -> Int -> Maybe (FMI,(Int,Int))   

Combines delFrom and lookup.

plusFM :: FMI -> FMI -> FMI   

Efficiently add key/element mappings of two maps into a single one. Bindings in right argument shadow those in the left

plusFM_C :: (Int -> Int -> Int) -> FMI -> FMI -> FMI   

Efficiently combine key/element mappings of two maps into a single one, cf. addToFM_C

minusFM :: FMI -> FMI -> FMI   

(minusFM a1 a2) deletes from a1 any bindings which are bound in a2

intersectFM :: FMI -> FMI -> FMI   

Filters only those keys that are bound in both of the given maps. The elements will be taken from the second map.

intersectFM_C :: (Int -> Int -> Int) -> FMI -> FMI -> FMI   

Filters only those keys that are bound in both of the given maps and combines the elements as in addToFM_C.

foldFM :: (Int -> Int -> a -> a) -> a -> FMI -> a   

sizeFM :: FMI -> Int   

How many elements does given map contain?

Further infos:

• solution complete, i.e., able to compute all solutions

eqFM :: FMI -> FMI -> Bool   

Do two given maps contain the same key/element pairs?

isEmptyFM :: FMI -> Bool   

Is the given finite map empty?

elemFM :: Int -> FMI -> Bool   

Does given map contain given key?

lookupFM :: FMI -> Int -> Maybe Int   

Retrieves element bound to given key

lookupWithDefaultFM :: FMI -> Int -> Int -> Int   

Retrieves element bound to given key. If the element is not contained in map, return default value.

keyOrder :: FMI -> Int -> Int -> Bool   

Retrieves the ordering on which the given finite map is built.

minFM :: FMI -> Maybe (Int,Int)   

Retrieves the smallest key/element pair in the finite map according to the basic key ordering.

maxFM :: FMI -> Maybe (Int,Int)   

Retrieves the greatest key/element pair in the finite map according to the basic key ordering.

fmToList :: FMI -> [(Int,Int)]   

Builds a list of key/element pairs. The list is ordered by the initially given irreflexive order predicate on keys.

keysFM :: FMI -> [Int]   

Retrieves a list of keys contained in finite map. The list is ordered by the initially given irreflexive order predicate on keys.

eltsFM :: FMI -> [Int]   

Retrieves a list of elements contained in finite map. The list is ordered by the initially given irreflexive order predicate on keys.

fmToListPreOrder :: FMI -> [(Int,Int)]   

Retrieves list of key/element pairs in preorder of the internal tree. Useful for lists that will be retransformed into a tree or to match any elements regardless of basic order.

Further infos:

• solution complete, i.e., able to compute all solutions

showFM :: FMI -> String   

Sorts a given list by inserting and retrieving from finite map. Duplicates are deleted. Transforms a finite map into a string. For efficiency reasons, the tree structure is shown which is valid for reading only if one uses the same ordering predicate.

readFM :: String -> FMI   

Transforms a string representation of a finite map into a finite map. One has two provide the same ordering predicate as used in the original finite map.