-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Context Algebra
--   
@package ContextAlgebra
@version 0.1.0.0


-- | models a Lattice for a context type, the top of the lattice is
--   represented by One and inherits a list of all subcontexts, the bottom
--   of the lattice is represented by Zero. To inherit the contextlattice
--   to a new data type the data type has to instanciate: Enumerable c, Eq
--   c, Ord c, Show c
module ContextLattice

-- | data type to represent a lattice structure, the actual context is the
--   type variable <tt>c</tt>
data Context c

-- | constructor represents the One element of the lattice, all contexts
--   are included in this constructor, for this constructor the model
--   includes all contexts
One :: [Context c] -> Context c

-- | constructor for one context
Ctx :: [c] -> Context c

-- | constructor represents the bottom element of the lattice, without any
--   context
Zero :: Context c

-- | takes a context and returns all finer
getFinerContexts :: (Eq c, Enumerable c, Enumerable (Context c)) => Context c -> [Context c]

-- | extracts a context list of contexts from the element, needed for the
--   One wrapper constructor
extractContext :: Context c -> [[c]]

-- | test for commutativity
--   
--   <pre>
--   &gt;&gt;&gt; (Ctx [Walking]) `propCommutative` One [Ctx [Walking],Ctx [Driving],Ctx [Walking,Driving],Ctx [Uphill],Ctx [Walking,Uphill],Ctx [Driving,Uphill],Ctx [Walking,Driving,Uphill]] = (Ctx [Walking]) `meet` One [Ctx [Walking],Ctx [Driving],Ctx [Walking,Driving],Ctx [Uphill],Ctx [Walking,Uphill],Ctx [Driving,Uphill],Ctx [Walking,Driving,Uphill]] == One [Ctx [Walking],Ctx [Driving],Ctx [Walking,Driving],Ctx [Uphill],Ctx [Walking,Uphill],Ctx [Driving,Uphill],Ctx [Walking,Driving,Uphill]] `meet` (Ctx [Walking])
--   true
--   </pre>
propCommutative :: (Eq c, Enumerable c, Enumerable (Context c)) => Context c -> Context c -> Bool

-- | test for idempotency
--   
--   <pre>
--   &gt;&gt;&gt; propIdempotent (Ctx [Walking]) = (Ctx [Walking]) `meet` (Ctx [Walking]) == (Ctx [Walking])
--   true
--   </pre>
propIdempotent :: (Eq c, Enumerable c, Enumerable (Context c)) => Context c -> Bool

-- | test for associativity
--   
--   <pre>
--   &gt;&gt;&gt; propAssociative (Ctx [Walking]) (Ctx [Driving]) (Ctx [Uphill]) =  (Ctx [Walking]) `meet` ((Ctx [Driving]) `meet` (Ctx [Uphill])) == ((Ctx [Walking]) `meet` (Ctx [Driving])) `meet` (Ctx [Uphill])
--   true
--   </pre>
propAssociative :: (Eq c, Enumerable c, Enumerable (Context c)) => Context c -> Context c -> Context c -> Bool
instance Show c => Show (Context c)
instance Eq c => Eq (Context c)
instance Ord c => Ord (Context c)
instance (Enumerable c, Eq c, Enumerable (Context c)) => MeetSemiLattice (Context c)


-- | This module implements the necessary functions to model a concept and
--   the context influence. The concept is represented by several
--   exemplars. For each influencing context the exemplars have different
--   observation frequency. This conncetion is modeled here by a multiset.
module Model

-- | Each experience is formed by a exemplar of type e and a context c this
--   exemplar was observed at.
data Experience c e

-- | constructor; establishes an experience from a context and an exemplar
Exp :: c -> e -> Experience c e

-- | All experiences are hold in a multiset
type Experiences c e = MultiSet (Experience c e)

-- | type synonym for better readability
type Probability = Float

-- | the class defines the necessary functions needed for the context
--   algebra
class (Ord c, Ord e, Show c, Show e) => InterpretationModel c e

-- | combines the observation amount of exemplars for one context
createExperiencesForContext :: (Show c, Ord c, Show e, Ord e) => c -> [e] -> [Int] -> Experiences c e

-- | If an experience is made several times the amount can be specified by
--   the <tt>amount</tt>
manyfoldExperiences :: (Ord c, Show c, Ord e, Show e) => Experience c e -> Occur -> Experiences c e

-- | calculates the amount of experiences that are present
amountExperiences :: Experiences (Context c) e -> Int

-- | filters experiences for a context, gets experiences for a finer
--   context, the context c has to be more finer than the context that are
--   included in the experiences
lambda :: (Enumerable c, Enumerable (Context c), Ord e, Eq c, Ord c) => Context c -> Experiences (Context c) e -> Experiences (Context c) e

-- | returns a probability of an exemplar observed in a context for the
--   given experiences
mu :: (Enumerable c, Enumerable (Context c), Ord e, Ord c) => Experience (Context c) e -> Experiences (Context c) e -> Probability

-- | returns experiences for the exemplar given in the first argument
--   <tt>e</tt> in quantum mechanics called projector
filterExemplars :: (Ord c, Ord e) => e -> Experiences c e -> Experiences c e

-- | returns the observation distribution for the context c, the type e is
--   only used as type parameter
probAllExemplars4Context :: (Ord c, Ord e, Enum e, Bounded e, Enumerable c, Enumerable (Context c)) => Context c -> e -> Experiences (Context c) e -> [(e, Probability)]

-- | returns the most probable exemplar given by the list of tuples of
--   (Exemplar, Probability)
getMostProbableExemplar :: Ord e => [(e, Probability)] -> (e, Probability)

-- | converts the experiences type to a IO()
printExperiences :: (Show e, Show c) => Experiences c e -> IO ()

-- | adds the <tt>new</tt> experience to the given experiences
addExperience :: (Ord c, Ord e) => Experience c e -> Experiences c e -> Experiences c e
instance (Ord c, Ord e) => Ord (Experience c e)
instance (Show c, Show e) => Show (Experience c e)
instance (Eq c, Eq e) => Eq (Experience c e)