Module "FiniteMap.curry"

A finite map is an efficient purely functional data structure to store a mapping from keys to values. In order to store the mapping efficiently, an irreflexive(!) order predicate has to be given, i.e., the order predicate le should not satisfy (le x x) for some key x.
Example: To store a mapping from Int -> String, the finite map needs a Boolean predicate like (<). This version was ported from a corresponding Haskell library

Author: Frank Huch, Bernd Brassel

Version: May 2005

Datatypes:
FM

Functions:
addListToFM | addListToFM_C | addToFM | addToFM_C | delFromFM | delListFromFM | elemFM | eltsFM | emptyFM | eqFM | filterFM | fmSortBy | fmToList | fmToListPreOrder | foldFM | intersectFM | intersectFM_C | isEmptyFM | keyOrder | keysFM | listToFM | lookupFM | lookupWithDefaultFM | mapFM | maxFM | minFM | minusFM | plusFM | plusFM_C | sizeFM | splitFM | unitFM | updFM

emptyFM  :: (a -> a -> Bool) -> FM a b              The empty finite map.

unitFM  :: (a -> a -> Bool) -> a -> b -> FM a b              Construct a finite map with only a single element.

listToFM  :: (a -> a -> Bool) -> [(a,b)] -> FM a b              Builts a finite map from given list of tuples (key,element).

addToFM  :: FM a b -> a -> b -> FM a b              Throws away any previous binding and stores the new one given.

addListToFM  :: FM a b -> [(a,b)] -> FM a b              Throws away any previous bindings and stores the new ones given.

addToFM_C  :: (a -> a -> a) -> FM b a -> b -> a -> FM b a              Instead of throwing away the old binding, addToFM_C combines the new element with the old one.

addListToFM_C  :: (a -> a -> a) -> FM b a -> [(b,a)] -> FM b a              Combine with a list of tuples (key,element), cf.

delFromFM  :: FM a b -> a -> FM a b              Deletes key from finite map.

delListFromFM  :: FM a b -> [a] -> FM a b              Deletes a list of keys from finite map.

updFM  :: FM a b -> a -> (b -> b) -> FM a b              Applies a function to element bound to given key.

splitFM  :: FM a b -> a -> Maybe (FM a b,(a,b))              Combines delFrom and lookup.

plusFM  :: FM a b -> FM a b -> FM a b              Efficiently add key/element mappings of two maps into a single one.

plusFM_C  :: (a -> a -> a) -> FM b a -> FM b a -> FM b a              Efficiently combine key/element mappings of two maps into a single one, cf.

minusFM  :: FM a b -> FM a b -> FM a b              (minusFM a1 a2) deletes from a1 any bindings which are bound in a2

intersectFM  :: FM a b -> FM a b -> FM a b              Filters only those keys that are bound in both of the given maps.

intersectFM_C  :: (a -> a -> b) -> FM c a -> FM c a -> FM c b              Filters only those keys that are bound in both of the given maps and combines the elements as in addToFM_C.

foldFM  :: (a -> b -> c -> c) -> c -> FM a b -> c              Folds finite map by given function.

mapFM  :: (a -> b -> c) -> FM a b -> FM a c              Applies a given function on every element in the map.

filterFM  :: (a -> b -> Bool) -> FM a b -> FM a b              Yields a new finite map with only those key/element pairs matching the given predicate.

sizeFM  :: FM a b -> Int              How many elements does given map contain?

eqFM  :: FM a b -> FM a b -> Bool              Do two given maps contain the same key/element pairs?

isEmptyFM  :: FM a b -> Bool              Is the given finite map empty?

elemFM  :: a -> FM a b -> Bool              Does given map contain given key?

lookupFM  :: FM a b -> a -> Maybe b              Retrieves element bound to given key

lookupWithDefaultFM  :: FM a b -> b -> a -> b              Retrieves element bound to given key.

keyOrder  :: FM a b -> a -> a -> Bool              Retrieves the ordering on which the given finite map is built.

minFM  :: FM a b -> Maybe (a,b)              Retrieves the smallest key/element pair in the finite map according to the basic key ordering.

maxFM  :: FM a b -> Maybe (a,b)              Retrieves the greatest key/element pair in the finite map according to the basic key ordering.

fmToList  :: FM a b -> [(a,b)]              Builds a list of key/element pairs.

keysFM  :: FM a b -> [a]              Retrieves a list of keys contained in finite map.

eltsFM  :: FM a b -> [b]              Retrieves a list of elements contained in finite map.

fmToListPreOrder  :: FM a b -> [(a,b)]              Retrieves list of key/element pairs in preorder of the internal tree.

fmSortBy  :: (a -> a -> Bool) -> [a] -> [a]              Sorts a given list by inserting and retrieving from finite map.

FM

Constructors:

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Exported functions:

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emptyFM :: (a -> a -> Bool) -> FM a b   

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 :: (a -> a -> Bool) -> a -> b -> FM a b   

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 :: (a -> a -> Bool) -> [(a,b)] -> FM a b   

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 :: FM a b -> a -> b -> FM a b   

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

---

addListToFM :: FM a b -> [(a,b)] -> FM a b   

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

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addToFM_C :: (a -> a -> a) -> FM b a -> b -> a -> FM b a   

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

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addListToFM_C :: (a -> a -> a) -> FM b a -> [(b,a)] -> FM b a   

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

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delFromFM :: FM a b -> a -> FM a b   

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

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delListFromFM :: FM a b -> [a] -> FM a b   

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

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updFM :: FM a b -> a -> (b -> b) -> FM a b   

Applies a function to element bound to given key.

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splitFM :: FM a b -> a -> Maybe (FM a b,(a,b))   

Combines delFrom and lookup.

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plusFM :: FM a b -> FM a b -> FM a b   

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

---

plusFM_C :: (a -> a -> a) -> FM b a -> FM b a -> FM b a   

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

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minusFM :: FM a b -> FM a b -> FM a b   

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

---

intersectFM :: FM a b -> FM a b -> FM a b   

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

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intersectFM_C :: (a -> a -> b) -> FM c a -> FM c a -> FM c b   

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

---

foldFM :: (a -> b -> c -> c) -> c -> FM a b -> c   

Folds finite map by given function.

---

mapFM :: (a -> b -> c) -> FM a b -> FM a c   

Applies a given function on every element in the map.

---

filterFM :: (a -> b -> Bool) -> FM a b -> FM a b   

Yields a new finite map with only those key/element pairs matching the given predicate.

---

sizeFM :: FM a b -> Int   

How many elements does given map contain?

Further infos:

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

---

eqFM :: FM a b -> FM a b -> Bool   

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

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isEmptyFM :: FM a b -> Bool   

Is the given finite map empty?

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elemFM :: a -> FM a b -> Bool   

Does given map contain given key?

---

lookupFM :: FM a b -> a -> Maybe b   

Retrieves element bound to given key

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lookupWithDefaultFM :: FM a b -> b -> a -> b   

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

Further infos:

• incompletely defined

---

keyOrder :: FM a b -> a -> a -> Bool   

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

Further infos:

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

---

minFM :: FM a b -> Maybe (a,b)   

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

---

maxFM :: FM a b -> Maybe (a,b)   

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

---

fmToList :: FM a b -> [(a,b)]   

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

---

keysFM :: FM a b -> [a]   

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

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eltsFM :: FM a b -> [b]   

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

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fmToListPreOrder :: FM a b -> [(a,b)]   

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

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fmSortBy :: (a -> a -> Bool) -> [a] -> [a]   

Sorts a given list by inserting and retrieving from finite map. Duplicates are deleted.

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