h&%$s2      !"#$%&'()*+,-./01Patrick Bahr, 2010 BSD-3-ClausePatrick Bahr, Andreas Abelstablenon-portable (MPTC) Safe-Inferred equivalenceThis 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. 2 equivalence8Maps elements to their entry in the tree data structure.3 equivalenceConstructs an equivalence class descriptor for a singleton class.4 equivalenceCombines the equivalence class descriptor of two classes which are meant to be combined.5 equivalenceThis type represents entries (nodes) in the tree data structure. Entry data of type 5 s c a% lives in the state space indexed by s1, contains equivalence class descriptors of type c and has elements of type a. 6 equivalenceThis type represents a reference to an entry in the tree data structure. An entry 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. equivalence1Abstract representation of an equivalence class.  equivalenceThis function constructs the initial data structure for maintaining an equivalence relation. That is, it represents the finest (or least) equivalence class (of the set of all elements of type a). The arguments are used to maintain equivalence class descriptors. 7 equivalenceThis 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. 8 equivalenceThis function returns the representative entry of the argument's equivalence class (i.e. the root of its tree).*This function performs path compression. 9 equivalenceThis 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).  equivalenceThis function provides the equivalence class the given element is contained in. < equivalenceThis 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 (representative) 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.  equivalenceThis function returns the descriptor of the given equivalence class.  equivalenceThis function returns the descriptor of the given element's equivalence class.  equivalenceThis 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.  equivalenceThis function removes the given equivalence class. If the equivalence class does not exist anymore, False is returned; otherwise True.  equivalenceThis function removes the equivalence class of the given element. If there is no corresponding equivalence class, False is returned; otherwise True.  equivalenceUsed to construct an equivalence class descriptor for a singleton class. equivalenceUsed to combine the equivalence class descriptor of two classes which are meant to be combined.: equivalencethe constructed entry; equivalencethe constructed entry    Patrick Bahr, 2010 BSD-3-ClausePatrick Bahr, Andreas Abelstablenon-portable (MPTC with FD) Safe-Inferred;$C equivalenceThis class specifies the interface for a monadic computation that maintains an equivalence relation.  equivalenceThis function decides whether the two given elements are equivalent in the current equivalence relation.  equivalenceThis 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.  equivalenceThis function equates the given two elements. That is it unions the equivalence classes of the two elements.  equivalenceThis function removes the equivalence class of the given element. If there is no corresponding equivalence class, False is returned; otherwise True.  equivalenceThis function provides the equivalence class of the given element.  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 decides whether the two given equivalence classes are the same.  equivalenceThis function returns the descriptor of the given equivalence class.  equivalenceThis function removes the given equivalence class. If the equivalence class does not exist anymore, False is returned; otherwise True.  equivalence This monad is a special case of  that only maintains trivial equivalence class descriptors of type ().  equivalenceThis 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  that only maintains trivial equivalence class descriptors of type ().  equivalenceThis 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 two 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   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 " that only maintains trivial equivalence class descriptors of type ().   equivalenceUsed to construct an equivalence class descriptor for a singleton class. equivalenceUsed to combine the equivalence class descriptor of two classes which are meant to be combined." equivalenceUsed to construct an equivalence class descriptor for a singleton class. equivalenceUsed to combine the equivalence class descriptor of two classes which are meant to be combined. !"# !"#          !"#$%&'()*+,-./012345678equivalence-0.4-inplaceData.Equivalence.STTData.Equivalence.MonadEquivClass leastEquivgetClass combineAllcombine equateAllequatedesc classDescsame equivalentremove removeClass MonadEquiv===EquivM'EquivMEquivT'EquivTunEquivT runEquivT runEquivT' runEquivM runEquivM'$fMonadReaderrEquivT$fMonadFailEquivT$fMonadTransEquivT$fMonadEquivcvdReaderT$fMonadEquivcvdStateT$fMonadEquivcvdExceptT$fMonadEquivcvdWriterT$fMonadEquivClassvdEquivT$fFunctorEquivT$fApplicativeEquivT $fMonadEquivT$fMonadErroreEquivT$fMonadStatestEquivT$fMonadWriterwEquivTentries singleDesccombDesc EntryDataEntryrepresentative'representativeclassRepmkEntry'mkEntrygetEntry equateEntry modifySTRef removeEntry