!Z3      !"#$%&'()*+,-./012 3gERP, 2010All Rights Reserved Patrick BahrunknownunknownNone@AH equivalencenThis is the top-level data structure that represents an equivalence relation. An equivalence relation of type  s c a% lives in the state space indexed by s1, contains equivalence class descriptors of type c and has elements of type a. 3 equivalence7maps elements to their entry in the tree data structure4 equivalence@constructs an equivalence class descriptor for a singleton class5 equivalence[combines the equivalence class descriptor of two classes which are meant to be combined.6 equivalenceTThis type represents entries (nodes) in the tree data structure. Entry data of type 6 s c a% lives in the state space indexed by s1, contains equivalence class descriptors of type c and has elements of type a. 7 equivalenceZThis type represents a reference to an entry in the tree data structure. An entry of type 7 s c a% lives in the state space indexed by s1, contains equivalence class descriptors of type c and has elements of type a. equivalenceThis function constructs the initial data structure for maintaining an equivalence relation. That is it represents, the fines (or least) equivalence class (of the set of all elements of type aE). The arguments are used to maintain equivalence class descriptors. 8 equivalencerThis function returns the representative entry of the argument's equivalence class (i.e. the root of its tree) or Nothing$ if it is the representative itself.*This function performs path compression. 9 equivalenceoThis function returns the representative entry of the argument's equivalence class (i.e. the root of its tree).*This function performs path compression. : equivalenceyThis function provides the representative entry of the given equivalence class. This function performs path compression. ; equivalenceThis function constructs a new (root) entry containing the given entry's value, inserts it into the lookup table (thereby removing any existing entry). < equivalenceThis function constructs a new (root) entry containing the given value, inserts it into the lookup table (thereby removing any existing entry).  equivalencePThis function provides the equivalence class the given element is contained in. = equivalencejThis function looks up the entry of the given element in the given equivalence relation representation or Nothing if there is none, yet. > equivalenceThis function equates the two given elements. That is, it unions the equivalence classes of the two elements and combines their descriptor. The returned entry is the representative of the new equivalence class  equivalenceThis function combines all equivalence classes in the given list. Afterwards all elements in the argument list represent the same equivalence class!  equivalenceThis function combines the two given equivalence classes. Afterwards both arguments represent the same equivalence class! One of it is returned in order to represent the new combined equivalence class.  equivalenceThis function equates the element in the given list. That is, it unions the equivalence classes of the elements and combines their descriptor.  equivalenceThis function equates the two given elements. That is, it unions the equivalence classes of the two elements and combines their descriptor.  equivalenceEThis function returns the descriptor of the given equivalence class.  equivalenceOThis function returns the descriptor of the given element's equivalence class.  equivalenceNThis function decides whether the two given equivalence classes are the same.  equivalenceThis function decides whether the two given elements are in the same equivalence class according to the given equivalence relation representation. ? equivalence7This function modifies the content of a reference cell.@ equivalence6This function marks the given root entry as deleted.  equivalencedThis function removes the given equivalence class. If the equivalence class does not exists anymore False is returned; otherwise True.  equivalencerThis function removes the equivalence class of the given element. If there is no corresponding equivalence class, False is returned; otherwise True.  equivalenceGused to construct an equivalence class descriptor for a singleton class equivalencebused to combine the equivalence class descriptor of two classes which are meant to be combined.; equivalencethe constructed entry< equivalencethe constructed entry    Patrick Bahr, 2010All Rights Reserved Patrick BahrunknownunknownNone =>?@ACSX equivalencefThis class specifies the interface for a monadic computation that maintains an equivalence relation.  equivalencepThis function decides whether the two given elements are equivalent in the current equivalence relation  equivalenceWThis function obtains the descriptor of the given element's equivalence class.  equivalenceThis function equates the element in the given list. That is, it unions the equivalence classes of the elements and combines their descriptor.  equivalenceuThis function equates the given two elements. That is it unions the equivalence classes of the two elements.  equivalencexThis function removes the equivalence class of the given element. If there is no corresponding equivalence class, False is returned; otherwise True.  equivalenceVThis function provides the equivalence class the given element is contained in.  equivalenceThis function combines all equivalence classes in the given list. Afterwards all elements in the argument list represent the same equivalence class!  equivalenceThis function combines the two given equivalence classes. Afterwards both arguments represent the same equivalence class! One of it is returned in order to represent the new combined equivalence class.  equivalenceTThis function decides whether the two given equivalence classes are the same.  equivalenceKThis function returns the descriptor of the given equivalence class.  equivalencejThis function removes the given equivalence class. If the equivalence class does not exists anymore False is returned; otherwise True.  equivalence This monad is a special case of C that only maintains trivial equivalence class descriptors of type ().  equivalencehThis monad encapsulates computations maintaining an equivalence relation. A monadic computation of type  s c v a) maintains a state space indexed by type s:, maintains an equivalence relation over elements of type v, with equivalence class descriptors of type c and returns a value of type a.  equivalence,This monad transformer is a special case of C that only maintains trivial equivalence class descriptors of type ().  equivalencetThis monad transformer encapsulates computations maintaining an equivalence relation. A monadic computation of type   s c v m a) maintains a state space indexed by type s:, maintains an equivalence relation over elements of type v, with equivalence class descriptors of type c6 and contains an internal monadic computation of type m a.  equivalenceThis function runs a monadic computation that maintains an equivalence relation. The first tow arguments specify how to construct an equivalence class descriptor for a singleton class and how to combine two equivalence class descriptors. ! equivalence#This function is a special case of  C that only maintains trivial equivalence class descriptors of type (). " equivalenceThis function runs a monadic computation that maintains an equivalence relation. The first tow arguments specify how to construct an equivalence class descriptor for a singleton class and how to combine two equivalence class descriptors. # equivalence#This function is a special case of "C that only maintains trivial equivalence class descriptors of type ().   equivalenceGused to construct an equivalence class descriptor for a singleton class equivalencebused to combine the equivalence class descriptor of two classes which are meant to be combined." equivalenceGused to construct an equivalence class descriptor for a singleton class equivalencebused to combine the equivalence class descriptor of two classes which are meant to be combined. !"# !"#A          !"#$%&'()*+,-./0123456789(equivalence-0.3.4-BTEoqVfdcFlEKfMwLQj2tYData.Equivalence.STTData.Equivalence.MonadEquivClass leastEquivgetClass combineAllcombine equateAllequatedesc classDescsame equivalentremove removeClass MonadEquiv===EquivM'EquivMEquivT'EquivTunEquivT runEquivT runEquivT' runEquivM runEquivM'$fMonadErroreEquivT$fMonadStatestEquivT$fMonadWriterwEquivT$fMonadReaderrEquivT$fMonadFailEquivT$fMonadTransEquivT $fMonadEquivT$fApplicativeEquivT$fFunctorEquivT$fMonadEquivcvdReaderT$fMonadEquivcvdStateT$fMonadEquivcvdExceptT$fMonadEquivcvdErrorT$fMonadEquivcvdWriterT$fMonadEquivClassvdEquivTentries singleDesccombDesc EntryDataEntryrepresentative'representativeclassRepmkEntry'mkEntrygetEntry equateEntry modifySTRef removeEntry