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


-- | DisCoCat implementation.
--   
--   An educational implementation of the DisCoCat framework.
@package discokitty
@version 0.1.0


-- | An implementation of the cups of the category of matrices over an
--   arbitary semiring. In this module we call "vector space" to what would
--   be more generally a module over a semiring. The representation is done
--   using sparse vectors that do not include the elements of the basis
--   whose element is zero. |
module Discokitty.Models.Vectorspaces

-- | A vector is given internally by a map representing the coefficients of
--   each basis element.
data Vectorspace u m
Vector :: Map [u] m -> Vectorspace u m

-- | Creates a sparse vector from a list of basis elements multiplied by
--   scalars.
sparse :: (Ord u, Eq u, Semiring m) => [([u], m)] -> Vectorspace u m
fromList :: (Ord u, Eq u, Semiring m) => [([u], m)] -> Vectorspace u m

-- | Creates a sparse vector from a map assigning a scalar to each base
--   element.
fromMap :: Map [u] m -> Vectorspace u m

-- | Outputs a map assigning to each base element its coefficient.
toMap :: Vectorspace u m -> Map [u] m
class (Eq m, Ord m) => Semiring m
plus :: Semiring m => m -> m -> m
mult :: Semiring m => m -> m -> m
zero :: Semiring m => m
unit :: Semiring m => m
instance (GHC.Show.Show m, GHC.Show.Show u) => GHC.Show.Show (Discokitty.Models.Vectorspaces.Vectorspace u m)
instance Discokitty.Dimension.Dim (Discokitty.Models.Vectorspaces.Vectorspace u m)
instance (GHC.Classes.Ord u, GHC.Classes.Eq u, Discokitty.Models.Vectorspaces.Semiring m) => Discokitty.HasCups.HasCups (Discokitty.Models.Vectorspaces.Vectorspace u m)


-- | |
module Discokitty.Models.Rel

-- | A relation hom(1,a) is given by a subset of the universe with elements
--   in a. We model this using the Data.Set library.
data Rel u
relation :: Ord u => [[u]] -> Rel u
fromList :: Ord u => [[u]] -> Rel u
toList :: Rel u -> [[u]]
relCup :: Ord u => Int -> Rel u -> Rel u -> Rel u
agrees :: Eq u => Int -> ([u], [u]) -> Maybe [u]
instance GHC.Show.Show u => GHC.Show.Show (Discokitty.Models.Rel.Rel u)
instance Discokitty.Dimension.Dim (Discokitty.Models.Rel.Rel u)
instance GHC.Classes.Ord u => Discokitty.HasCups.HasCups (Discokitty.Models.Rel.Rel u)
instance Discokitty.Dimension.Dim (Discokitty.Words.Words (Discokitty.Models.Rel.Rel u))


-- | This module allows us to obtain diagrams for our sentences. In order
--   to obtain these, we define a monoidal category whose morphisms are
--   diagrams and then implement a cup operation on that category that
--   consists on wiring two of them together. We apply then the ideas of
--   DisCoCat to words whose meanings are themselves diagrams, and just
--   perform the necessary reductions. |
module Discokitty.Models.Diagrams
tikzDiagrams :: [Words m] -> String
instance GHC.Show.Show Discokitty.Models.Diagrams.Schema
instance GHC.Show.Show Discokitty.Models.Diagrams.Diagram
instance GHC.Show.Show Discokitty.Models.Diagrams.Wire
instance GHC.Show.Show Discokitty.Models.Diagrams.Node
instance Discokitty.HasCups.HasCups Discokitty.Models.Diagrams.Schema
instance GHC.Show.Show Discokitty.Models.Diagrams.Style


-- | This module exports all basic modules of the Discokitty library.
--   Please note that models and examples should be imported separately.
module Discokitty
class Dim a

-- | In the meaning space, states can have a given number of output wires.
--   This function takes an state and should output the number of output
--   wires it has.
dim :: Dim a => a -> Int
class HasCups m

-- | Given an integer, performs that number of cups between the two meaning
--   spaces. In a monoidal category, this should be the composition of the
--   tensor product of two states with a certain number of cups.
cup :: HasCups m => Int -> m -> m -> m

-- | Neutral element for the cup operation. This could be given by the
--   identity morphism (state).
cunit :: HasCups m => m

-- | Lambek basic grammatical types.
data Type
N :: Type
S :: Type
L :: Type -> Type
R :: Type -> Type

-- | A Lambek pregroup type.
type Lambek = [Type]

-- | Checks if two Lambek types can be reduced a given number of steps.
agreeOn :: Int -> Lambek -> Lambek -> Bool

-- | A word is given by a meaning and a grammatical type. The Words type is
--   parameterized over the meaning type.
data Words m
Words :: m -> Lambek -> String -> Words m
[meaning] :: Words m -> m
[grammar] :: Words m -> Lambek
[text] :: Words m -> String

-- | Concatenates a list of words outputting all possible grammatical
--   reductions.
sentence :: HasCups m => [Words m] -> [Words m]
concatenate :: HasCups m => Words m -> Words m -> [Words m]

-- | Empty word. Unit for concatenation of words.
emptyWord :: HasCups m => Words m

-- | Filters a list of words by grammatical type.
(@@@) :: [Words m] -> Lambek -> [Words m]

module Discokitty.Examples.LesJustesViterbi
newtype Viterbi
Viterbi :: Double -> Viterbi
v :: Multiword (Vectorspace u Double) -> Multiword (Vectorspace u Viterbi)
instance GHC.Classes.Ord Discokitty.Examples.LesJustesViterbi.Viterbi
instance GHC.Num.Num Discokitty.Examples.LesJustesViterbi.Viterbi
instance GHC.Show.Show Discokitty.Examples.LesJustesViterbi.Viterbi
instance GHC.Classes.Eq Discokitty.Examples.LesJustesViterbi.Viterbi
instance Discokitty.Models.Vectorspaces.Semiring Discokitty.Examples.LesJustesViterbi.Viterbi

module Discokitty.Examples.LesJustesUniverse
data Universe
Universe :: Universe
Yanek :: Universe
Dora :: Universe
Boris :: Universe
Duke :: Universe
Stepan :: Universe
Nephew :: Universe
Skouratov :: Universe
Poet :: Universe
Revolutionary :: Universe
Terrorist :: Universe
Saviour :: Universe
Innocent :: Universe
Tsarist :: Universe
Alive :: Universe
Life :: Universe
Poetry :: Universe
Chemistry :: Universe
Propaganda :: Universe
Bomb :: Universe
IsTrue :: Universe
IsFalse :: Universe
IsRighteous :: Universe
IsWrong :: Universe
IsPlot :: Universe
type UniverseN = [Universe]
universe :: [Universe]

-- | In the meaning space, states can have a given number of output wires.
--   This function takes an state and should output the number of output
--   wires it has.
dim :: Dim a => a -> Int
instance GHC.Classes.Ord Discokitty.Examples.LesJustesUniverse.Universe
instance GHC.Enum.Enum Discokitty.Examples.LesJustesUniverse.Universe
instance GHC.Enum.Bounded Discokitty.Examples.LesJustesUniverse.Universe
instance GHC.Show.Show Discokitty.Examples.LesJustesUniverse.Universe
instance GHC.Classes.Eq Discokitty.Examples.LesJustesUniverse.Universe
instance Discokitty.Dimension.Dim Discokitty.Examples.LesJustesUniverse.UniverseN

module Discokitty.Examples.LesJustesVector
yanek' :: Words (Vectorspace Universe Double)
dora' :: Words (Vectorspace Universe Double)
likes' :: Words (Vectorspace Universe Double)
combat' :: Words (Vectorspace Universe Double)
is' :: Words (Vectorspace Universe Double)
people' :: Semiring m => Words (Vectorspace Universe m)
yanek :: Multiword (Vectorspace Universe Double)
dora :: Multiword (Vectorspace Universe Double)
likes :: Multiword (Vectorspace Universe Double)
enjoy :: Multiword (Vectorspace Universe Double)
is :: Multiword (Vectorspace Universe Double)
people :: Multiword (Vectorspace Universe Double)
combat :: Multiword (Vectorspace Universe Double)
who :: Semiring m => Multiword (Vectorspace Universe m)
basis :: Semiring m => Universe -> Multiword (Vectorspace Universe m)
tsarist :: Semiring m => Multiword (Vectorspace Universe m)
life :: Semiring m => Multiword (Vectorspace Universe m)
propaganda :: Semiring m => Multiword (Vectorspace Universe m)
poetry :: Semiring m => Multiword (Vectorspace Universe m)
innocent :: Semiring m => Multiword (Vectorspace Universe m)
terrorist :: Semiring m => Multiword (Vectorspace Universe m)
revolutionary :: Semiring m => Multiword (Vectorspace Universe m)
tsarists :: Multiword (Vectorspace Universe Double)
revolutionaries :: Multiword (Vectorspace Universe Double)
that :: Multiword (Vectorspace Universe Double)
are :: Multiword (Vectorspace Universe Double)
newtype Tropical
Tropical :: Double -> Tropical
instance GHC.Classes.Ord Discokitty.Examples.LesJustesVector.Tropical
instance GHC.Num.Num Discokitty.Examples.LesJustesVector.Tropical
instance GHC.Show.Show Discokitty.Examples.LesJustesVector.Tropical
instance GHC.Classes.Eq Discokitty.Examples.LesJustesVector.Tropical
instance Discokitty.Models.Vectorspaces.Semiring Discokitty.Examples.LesJustesVector.Tropical
instance Discokitty.Models.Vectorspaces.Semiring GHC.Types.Double

module Discokitty.Examples.LesJustesMain
type RelU = Rel Universe
yanek :: Words RelU
attacks :: Words RelU
duke :: Words RelU
example2 :: [Words RelU]
lnot :: Universe -> Words RelU
rnot :: Universe -> Words RelU
cnst :: Universe -> Words RelU
kills :: Words RelU
example3 :: [Words RelU]
nephew :: Words RelU
bomb :: Words RelU
and' :: Words RelU
example4a :: [Words RelU]
using :: Words RelU
with :: Multiword RelU
yanek' :: Multiword RelU
duke' :: Multiword RelU
nephew' :: Multiword RelU
bomb' :: Multiword RelU
using' :: Multiword RelU
and'' :: Multiword RelU
attacks' :: Multiword RelU
example5a :: Multiword RelU
example5b :: Multiword RelU
becomes :: Words RelU
becomes' :: Multiword RelU
revolutionary :: Multiword RelU
kills''' :: Multiword RelU
discarding' :: Multiword RelU
he :: Multiword (Rel Universe)
saviour :: Multiword (Rel Universe)
terrorist :: Multiword (Rel Universe)
alive :: Multiword (Rel Universe)
is' :: Multiword (Rel Universe)
(?) :: Multiword (Rel Universe)
example6 :: Multiword RelU
example7 :: Multiword RelU
people :: Multiword RelU
combat :: Multiword RelU
enjoy :: Multiword RelU
is_ :: Multiword RelU
who :: Multiword RelU
tsarist :: Multiword RelU
tsarists :: Multiword RelU
revolutionaries :: Multiword RelU
example8 :: Multiword RelU
example9 :: Multiword RelU
life :: Multiword RelU
propaganda :: Multiword RelU
innocent :: Multiword RelU
poetry :: Multiword RelU
chemistry :: Multiword RelU
example10 :: Multiword RelU
example11 :: Multiword RelU

module Discokitty.Examples.AliceAndBob
data Universe
Alice :: Universe
Bob :: Universe
IsTrue :: Universe
IsFalse :: Universe
type Term = Words (Rel Universe)
alice :: Term
bob :: Term
loves :: Term
example :: [Term]
exampleDiagram :: String
instance GHC.Show.Show Discokitty.Examples.AliceAndBob.Universe
instance GHC.Classes.Ord Discokitty.Examples.AliceAndBob.Universe
instance GHC.Classes.Eq Discokitty.Examples.AliceAndBob.Universe