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


-- | Library for using Mixed Integer Programming (MIP)
--   
--   Please see the README on GitHub at
--   <a>https://github.com/msakai/haskell-MIP/tree/master/MIP#readme</a>
@package MIP
@version 0.1.2.0


-- | Mixed-Integer Programming Problems with some commmonly used extensions
module Numeric.Optimization.MIP.Base

-- | Problem
data Problem c
Problem :: Maybe Text -> ObjectiveFunction c -> [Constraint c] -> [SOSConstraint c] -> [Constraint c] -> Map Var VarType -> Map Var (Bounds c) -> Problem c
[name] :: Problem c -> Maybe Text
[objectiveFunction] :: Problem c -> ObjectiveFunction c
[constraints] :: Problem c -> [Constraint c]
[sosConstraints] :: Problem c -> [SOSConstraint c]
[userCuts] :: Problem c -> [Constraint c]
[varType] :: Problem c -> Map Var VarType
[varBounds] :: Problem c -> Map Var (Bounds c)

-- | label
type Label = Text

-- | variable
type Var = InternedText

-- | convert a string into a variable
toVar :: String -> Var

-- | convert a variable into a string
fromVar :: Var -> String
data VarType
ContinuousVariable :: VarType
IntegerVariable :: VarType
SemiContinuousVariable :: VarType
SemiIntegerVariable :: VarType

-- | looking up bounds for a variable
getVarType :: Problem c -> Var -> VarType

-- | type for representing lower/upper bound of variables
type BoundExpr c = Extended c

-- | <tt>Extended r</tt> is an extension of <i>r</i> with positive/negative
--   infinity (±∞).
data () => Extended r

-- | negative infinity (-∞)
NegInf :: Extended r

-- | finite value
Finite :: !r -> Extended r

-- | positive infinity (+∞)
PosInf :: Extended r

-- | type for representing lower/upper bound of variables
type Bounds c = (BoundExpr c, BoundExpr c)

-- | default bounds
defaultBounds :: Num c => Bounds c

-- | default lower bound (0)
defaultLB :: Num c => BoundExpr c

-- | default upper bound (+∞)
defaultUB :: BoundExpr c

-- | looking up bounds for a variable
getBounds :: Num c => Problem c -> Var -> Bounds c
variables :: Problem c -> Set Var
integerVariables :: Problem c -> Set Var
semiContinuousVariables :: Problem c -> Set Var
semiIntegerVariables :: Problem c -> Set Var

-- | expressions
newtype Expr c
Expr :: [Term c] -> Expr c
varExpr :: Num c => Var -> Expr c
constExpr :: (Eq c, Num c) => c -> Expr c
terms :: Expr c -> [Term c]

-- | terms
data Term c
Term :: c -> [Var] -> Term c

-- | The <a>OptDir</a> type represents optimization directions.
data () => OptDir

-- | minimization
OptMin :: OptDir

-- | maximization
OptMax :: OptDir

-- | objective function
data ObjectiveFunction c
ObjectiveFunction :: Maybe Label -> OptDir -> Expr c -> ObjectiveFunction c
[objLabel] :: ObjectiveFunction c -> Maybe Label
[objDir] :: ObjectiveFunction c -> OptDir
[objExpr] :: ObjectiveFunction c -> Expr c

-- | constraint
data Constraint c
Constraint :: Maybe Label -> Maybe (Var, c) -> Expr c -> BoundExpr c -> BoundExpr c -> Bool -> Constraint c
[constrLabel] :: Constraint c -> Maybe Label
[constrIndicator] :: Constraint c -> Maybe (Var, c)
[constrExpr] :: Constraint c -> Expr c
[constrLB] :: Constraint c -> BoundExpr c
[constrUB] :: Constraint c -> BoundExpr c
[constrIsLazy] :: Constraint c -> Bool

-- | Equality constraint.
(.==.) :: Num c => Expr c -> Expr c -> Constraint c
infix 4 .==.

-- | Inequality constraint (≤).
(.<=.) :: Num c => Expr c -> Expr c -> Constraint c
infix 4 .<=.

-- | Inequality constraint (≥).
(.>=.) :: Num c => Expr c -> Expr c -> Constraint c
infix 4 .>=.

-- | relational operators
data RelOp
Le :: RelOp
Ge :: RelOp
Eql :: RelOp

-- | types of SOS (special ordered sets) constraints
data SOSType

-- | Type 1 SOS constraint
S1 :: SOSType

-- | Type 2 SOS constraint
S2 :: SOSType

-- | SOS (special ordered sets) constraints
data SOSConstraint c
SOSConstraint :: Maybe Label -> SOSType -> [(Var, c)] -> SOSConstraint c
[sosLabel] :: SOSConstraint c -> Maybe Label
[sosType] :: SOSConstraint c -> SOSType
[sosBody] :: SOSConstraint c -> [(Var, c)]

-- | Type for representing a solution of MIP problem.
data Solution r
Solution :: Status -> Maybe r -> Map Var r -> Solution r
[solStatus] :: Solution r -> Status
[solObjectiveValue] :: Solution r -> Maybe r
[solVariables] :: Solution r -> Map Var r

-- | MIP status with the following partial order:
--   
data Status
StatusUnknown :: Status
StatusFeasible :: Status
StatusOptimal :: Status
StatusInfeasibleOrUnbounded :: Status
StatusInfeasible :: Status
StatusUnbounded :: Status

-- | <i>meet</i> (greatest lower bound) operator of the partial order of
--   <a>Status</a> type.
--   
--   If the version of <tt>lattices</tt> is &lt;2, then
--   <tt>MeetSemiLattice</tt> instance can also be used.
meetStatus :: Status -> Status -> Status
data FileOptions
FileOptions :: Maybe TextEncoding -> FileOptions
[optFileEncoding] :: FileOptions -> Maybe TextEncoding

-- | A class for types with a default value.
class () => Default a

-- | The default value for this type.
def :: Default a => a
class Variables a
vars :: Variables a => a -> Set Var
intersectBounds :: Ord c => Bounds c -> Bounds c -> Bounds c
instance GHC.Show.Show Numeric.Optimization.MIP.Base.VarType
instance GHC.Classes.Ord Numeric.Optimization.MIP.Base.VarType
instance GHC.Classes.Eq Numeric.Optimization.MIP.Base.VarType
instance GHC.Show.Show c => GHC.Show.Show (Numeric.Optimization.MIP.Base.Term c)
instance GHC.Classes.Ord c => GHC.Classes.Ord (Numeric.Optimization.MIP.Base.Term c)
instance GHC.Classes.Eq c => GHC.Classes.Eq (Numeric.Optimization.MIP.Base.Term c)
instance GHC.Show.Show c => GHC.Show.Show (Numeric.Optimization.MIP.Base.Expr c)
instance GHC.Classes.Ord c => GHC.Classes.Ord (Numeric.Optimization.MIP.Base.Expr c)
instance GHC.Classes.Eq c => GHC.Classes.Eq (Numeric.Optimization.MIP.Base.Expr c)
instance GHC.Show.Show c => GHC.Show.Show (Numeric.Optimization.MIP.Base.ObjectiveFunction c)
instance GHC.Classes.Ord c => GHC.Classes.Ord (Numeric.Optimization.MIP.Base.ObjectiveFunction c)
instance GHC.Classes.Eq c => GHC.Classes.Eq (Numeric.Optimization.MIP.Base.ObjectiveFunction c)
instance GHC.Show.Show c => GHC.Show.Show (Numeric.Optimization.MIP.Base.Constraint c)
instance GHC.Classes.Ord c => GHC.Classes.Ord (Numeric.Optimization.MIP.Base.Constraint c)
instance GHC.Classes.Eq c => GHC.Classes.Eq (Numeric.Optimization.MIP.Base.Constraint c)
instance GHC.Show.Show Numeric.Optimization.MIP.Base.RelOp
instance GHC.Enum.Enum Numeric.Optimization.MIP.Base.RelOp
instance GHC.Classes.Ord Numeric.Optimization.MIP.Base.RelOp
instance GHC.Classes.Eq Numeric.Optimization.MIP.Base.RelOp
instance GHC.Read.Read Numeric.Optimization.MIP.Base.SOSType
instance GHC.Show.Show Numeric.Optimization.MIP.Base.SOSType
instance GHC.Enum.Enum Numeric.Optimization.MIP.Base.SOSType
instance GHC.Classes.Ord Numeric.Optimization.MIP.Base.SOSType
instance GHC.Classes.Eq Numeric.Optimization.MIP.Base.SOSType
instance GHC.Show.Show c => GHC.Show.Show (Numeric.Optimization.MIP.Base.SOSConstraint c)
instance GHC.Classes.Ord c => GHC.Classes.Ord (Numeric.Optimization.MIP.Base.SOSConstraint c)
instance GHC.Classes.Eq c => GHC.Classes.Eq (Numeric.Optimization.MIP.Base.SOSConstraint c)
instance GHC.Classes.Ord c => GHC.Classes.Ord (Numeric.Optimization.MIP.Base.Problem c)
instance GHC.Classes.Eq c => GHC.Classes.Eq (Numeric.Optimization.MIP.Base.Problem c)
instance GHC.Show.Show c => GHC.Show.Show (Numeric.Optimization.MIP.Base.Problem c)
instance GHC.Show.Show Numeric.Optimization.MIP.Base.Status
instance GHC.Enum.Bounded Numeric.Optimization.MIP.Base.Status
instance GHC.Enum.Enum Numeric.Optimization.MIP.Base.Status
instance GHC.Classes.Ord Numeric.Optimization.MIP.Base.Status
instance GHC.Classes.Eq Numeric.Optimization.MIP.Base.Status
instance GHC.Show.Show r => GHC.Show.Show (Numeric.Optimization.MIP.Base.Solution r)
instance GHC.Classes.Ord r => GHC.Classes.Ord (Numeric.Optimization.MIP.Base.Solution r)
instance GHC.Classes.Eq r => GHC.Classes.Eq (Numeric.Optimization.MIP.Base.Solution r)
instance GHC.Show.Show Numeric.Optimization.MIP.Base.FileOptions
instance Data.Default.Class.Default Numeric.Optimization.MIP.Base.FileOptions
instance Numeric.Optimization.MIP.Base.Variables a => Numeric.Optimization.MIP.Base.Variables [a]
instance (Numeric.Optimization.MIP.Base.Variables a, Numeric.Optimization.MIP.Base.Variables b) => Numeric.Optimization.MIP.Base.Variables (Data.Either.Either a b)
instance Numeric.Optimization.MIP.Base.Variables (Numeric.Optimization.MIP.Base.Problem c)
instance Numeric.Optimization.MIP.Base.Variables (Numeric.Optimization.MIP.Base.Expr c)
instance Numeric.Optimization.MIP.Base.Variables (Numeric.Optimization.MIP.Base.Term c)
instance Numeric.Optimization.MIP.Base.Variables (Numeric.Optimization.MIP.Base.ObjectiveFunction c)
instance Numeric.Optimization.MIP.Base.Variables (Numeric.Optimization.MIP.Base.Constraint c)
instance Numeric.Optimization.MIP.Base.Variables (Numeric.Optimization.MIP.Base.SOSConstraint c)
instance GHC.Base.Functor Numeric.Optimization.MIP.Base.Solution
instance Data.Default.Class.Default (Numeric.Optimization.MIP.Base.Solution r)
instance Algebra.PartialOrd.PartialOrd Numeric.Optimization.MIP.Base.Status
instance Data.Default.Class.Default (Numeric.Optimization.MIP.Base.Problem c)
instance GHC.Base.Functor Numeric.Optimization.MIP.Base.Problem
instance GHC.Base.Functor Numeric.Optimization.MIP.Base.SOSConstraint
instance Data.Default.Class.Default (Numeric.Optimization.MIP.Base.Constraint c)
instance GHC.Base.Functor Numeric.Optimization.MIP.Base.Constraint
instance Data.Default.Class.Default (Numeric.Optimization.MIP.Base.ObjectiveFunction c)
instance GHC.Base.Functor Numeric.Optimization.MIP.Base.ObjectiveFunction
instance GHC.Num.Num c => GHC.Num.Num (Numeric.Optimization.MIP.Base.Expr c)
instance GHC.Base.Functor Numeric.Optimization.MIP.Base.Expr
instance GHC.Base.Functor Numeric.Optimization.MIP.Base.Term
instance Data.Default.Class.Default Numeric.Optimization.MIP.Base.VarType


module Numeric.Optimization.MIP.FileUtils

-- | Error type for parsing.
--   
--   The definition is slightly different based on the <tt>megaparsec</tt>
--   version.
type ParseError s = ParseErrorBundle s Void


-- | A CPLEX <tt>.lp</tt> format parser library.
--   
--   References:
--   
--   <ul>
--   
--   <li><a>http://publib.boulder.ibm.com/infocenter/cosinfoc/v12r2/index.jsp?topic=/ilog.odms.cplex.help/Content/Optimization/Documentation/CPLEX/_pubskel/CPLEX880.html</a></li>
--   <li><a>http://www.gurobi.com/doc/45/refman/node589.html</a></li>
--   <li><a>http://lpsolve.sourceforge.net/5.5/CPLEX-format.htm</a></li>
--   </ul>
module Numeric.Optimization.MIP.LPFile

-- | Parse a string containing LP file data. The source name is only used
--   in error messages and may be the empty string.
parseString :: (Stream s, Token s ~ Char, IsString (Tokens s)) => FileOptions -> String -> s -> Either (ParseError s) (Problem Scientific)

-- | Parse a file containing LP file data.
parseFile :: FileOptions -> FilePath -> IO (Problem Scientific)

-- | Error type for parsing.
--   
--   The definition is slightly different based on the <tt>megaparsec</tt>
--   version.
type ParseError s = ParseErrorBundle s Void

-- | LP file parser
parser :: (MonadParsec e s m, Token s ~ Char, IsString (Tokens s)) => m (Problem Scientific)

-- | Render a problem into a <a>Text</a> containing LP file data.
render :: FileOptions -> Problem Scientific -> Either String Text


-- | A <tt>.mps</tt> format parser library.
--   
--   References:
--   
--   <ul>
--   
--   <li><a>http://pic.dhe.ibm.com/infocenter/cosinfoc/v12r4/topic/ilog.odms.cplex.help/CPLEX/File_formats_reference/topics/MPS_synopsis.html</a></li>
--   
--   <li><a>http://pic.dhe.ibm.com/infocenter/cosinfoc/v12r4/topic/ilog.odms.cplex.help/CPLEX/File_formats_reference/topics/MPS_ext_synopsis.html</a></li>
--   
--   <li><a>http://www.gurobi.com/documentation/5.0/reference-manual/node744</a></li>
--   <li><a>http://en.wikipedia.org/wiki/MPS_(format)</a></li>
--   </ul>
module Numeric.Optimization.MIP.MPSFile

-- | Parse a string containing MPS file data. The source name is only used
--   in error messages and may be the empty string.
parseString :: (Stream s, Token s ~ Char, IsString (Tokens s)) => FileOptions -> String -> s -> Either (ParseError s) (Problem Scientific)

-- | Parse a file containing MPS file data.
parseFile :: FileOptions -> FilePath -> IO (Problem Scientific)

-- | Error type for parsing.
--   
--   The definition is slightly different based on the <tt>megaparsec</tt>
--   version.
type ParseError s = ParseErrorBundle s Void

-- | MPS file parser
parser :: (MonadParsec e s m, Token s ~ Char, IsString (Tokens s)) => m (Problem Scientific)

-- | Render a problem into a <a>Text</a> containing MPS file data.
render :: FileOptions -> Problem Scientific -> Either String Text
instance GHC.Enum.Bounded Numeric.Optimization.MIP.MPSFile.BoundType
instance GHC.Enum.Enum Numeric.Optimization.MIP.MPSFile.BoundType
instance GHC.Read.Read Numeric.Optimization.MIP.MPSFile.BoundType
instance GHC.Show.Show Numeric.Optimization.MIP.MPSFile.BoundType
instance GHC.Classes.Ord Numeric.Optimization.MIP.MPSFile.BoundType
instance GHC.Classes.Eq Numeric.Optimization.MIP.MPSFile.BoundType


-- | Mixed-Integer Programming Problems with some commmonly used extensions
module Numeric.Optimization.MIP

-- | Parse LP or MPS file based on file extension.
readFile :: FileOptions -> FilePath -> IO (Problem Scientific)

-- | Parse a file containing LP file data.
readLPFile :: FileOptions -> FilePath -> IO (Problem Scientific)

-- | Parse a file containing MPS file data.
readMPSFile :: FileOptions -> FilePath -> IO (Problem Scientific)

-- | Parse a string containing LP file data.
parseLPString :: (Stream s, Token s ~ Char, IsString (Tokens s)) => FileOptions -> String -> s -> Either (ParseError s) (Problem Scientific)

-- | Parse a string containing MPS file data.
parseMPSString :: (Stream s, Token s ~ Char, IsString (Tokens s)) => FileOptions -> String -> s -> Either (ParseError s) (Problem Scientific)

-- | Error type for parsing.
--   
--   The definition is slightly different based on the <tt>megaparsec</tt>
--   version.
type ParseError s = ParseErrorBundle s Void

-- | Generate LP file or MPS file based on file extension.
writeFile :: FileOptions -> FilePath -> Problem Scientific -> IO ()

-- | Generate LP file.
writeLPFile :: FileOptions -> FilePath -> Problem Scientific -> IO ()

-- | Generate MPS file.
writeMPSFile :: FileOptions -> FilePath -> Problem Scientific -> IO ()

-- | Generate a <a>Text</a> containing LP file data.
toLPString :: FileOptions -> Problem Scientific -> Either String Text

-- | Generate a <a>Text</a> containing MPS file data.
toMPSString :: FileOptions -> Problem Scientific -> Either String Text


module Numeric.Optimization.MIP.Solution.CBC

-- | Type for representing a solution of MIP problem.
data Solution r
Solution :: Status -> Maybe r -> Map Var r -> Solution r
[solStatus] :: Solution r -> Status
[solObjectiveValue] :: Solution r -> Maybe r
[solVariables] :: Solution r -> Map Var r
parse :: Text -> Solution Scientific
readFile :: FilePath -> IO (Solution Scientific)


module Numeric.Optimization.MIP.Solution.CPLEX

-- | Type for representing a solution of MIP problem.
data Solution r
Solution :: Status -> Maybe r -> Map Var r -> Solution r
[solStatus] :: Solution r -> Status
[solObjectiveValue] :: Solution r -> Maybe r
[solVariables] :: Solution r -> Map Var r
parse :: Text -> Solution Scientific
readFile :: FilePath -> IO (Solution Scientific)


module Numeric.Optimization.MIP.Solution.GLPK

-- | Type for representing a solution of MIP problem.
data Solution r
Solution :: Status -> Maybe r -> Map Var r -> Solution r
[solStatus] :: Solution r -> Status
[solObjectiveValue] :: Solution r -> Maybe r
[solVariables] :: Solution r -> Map Var r
parse :: Text -> Solution Scientific
readFile :: FilePath -> IO (Solution Scientific)


module Numeric.Optimization.MIP.Solution.Gurobi

-- | Type for representing a solution of MIP problem.
data Solution r
Solution :: Status -> Maybe r -> Map Var r -> Solution r
[solStatus] :: Solution r -> Status
[solObjectiveValue] :: Solution r -> Maybe r
[solVariables] :: Solution r -> Map Var r
render :: Solution Scientific -> Text
writeFile :: FilePath -> Solution Scientific -> IO ()
parse :: Text -> Solution Scientific
readFile :: FilePath -> IO (Solution Scientific)


module Numeric.Optimization.MIP.Solution.SCIP

-- | Type for representing a solution of MIP problem.
data Solution r
Solution :: Status -> Maybe r -> Map Var r -> Solution r
[solStatus] :: Solution r -> Status
[solObjectiveValue] :: Solution r -> Maybe r
[solVariables] :: Solution r -> Map Var r
parse :: Text -> Solution Scientific
readFile :: FilePath -> IO (Solution Scientific)


module Numeric.Optimization.MIP.Solver.Base
data SolveOptions
SolveOptions :: Maybe Double -> (String -> IO ()) -> (String -> IO ()) -> SolveOptions

-- | time limit in seconds
[solveTimeLimit] :: SolveOptions -> Maybe Double

-- | invoked when a solver output a line
[solveLogger] :: SolveOptions -> String -> IO ()

-- | invoked when a solver output a line to stderr
[solveErrorLogger] :: SolveOptions -> String -> IO ()

-- | A class for types with a default value.
class () => Default a

-- | The default value for this type.
def :: Default a => a
class Monad m => IsSolver s m | s -> m
solve :: IsSolver s m => s -> SolveOptions -> Problem Scientific -> m (Solution Scientific)
instance Data.Default.Class.Default Numeric.Optimization.MIP.Solver.Base.SolveOptions


module Numeric.Optimization.MIP.Solver.CBC
data CBC
CBC :: String -> CBC
[cbcPath] :: CBC -> String
cbc :: CBC
instance Data.Default.Class.Default Numeric.Optimization.MIP.Solver.CBC.CBC
instance Numeric.Optimization.MIP.Solver.Base.IsSolver Numeric.Optimization.MIP.Solver.CBC.CBC GHC.Types.IO


module Numeric.Optimization.MIP.Solver.CPLEX
data CPLEX
CPLEX :: String -> CPLEX
[cplexPath] :: CPLEX -> String
cplex :: CPLEX
instance Data.Default.Class.Default Numeric.Optimization.MIP.Solver.CPLEX.CPLEX
instance Numeric.Optimization.MIP.Solver.Base.IsSolver Numeric.Optimization.MIP.Solver.CPLEX.CPLEX GHC.Types.IO


module Numeric.Optimization.MIP.Solver.Glpsol
data Glpsol
Glpsol :: String -> Glpsol
[glpsolPath] :: Glpsol -> String
glpsol :: Glpsol
instance Data.Default.Class.Default Numeric.Optimization.MIP.Solver.Glpsol.Glpsol
instance Numeric.Optimization.MIP.Solver.Base.IsSolver Numeric.Optimization.MIP.Solver.Glpsol.Glpsol GHC.Types.IO


module Numeric.Optimization.MIP.Solver.GurobiCl
data GurobiCl
GurobiCl :: String -> GurobiCl
[gurobiClPath] :: GurobiCl -> String
gurobiCl :: GurobiCl
instance Data.Default.Class.Default Numeric.Optimization.MIP.Solver.GurobiCl.GurobiCl
instance Numeric.Optimization.MIP.Solver.Base.IsSolver Numeric.Optimization.MIP.Solver.GurobiCl.GurobiCl GHC.Types.IO


module Numeric.Optimization.MIP.Solver.LPSolve
data LPSolve
LPSolve :: String -> LPSolve
[lpSolvePath] :: LPSolve -> String
lpSolve :: LPSolve
instance Data.Default.Class.Default Numeric.Optimization.MIP.Solver.LPSolve.LPSolve
instance Numeric.Optimization.MIP.Solver.Base.IsSolver Numeric.Optimization.MIP.Solver.LPSolve.LPSolve GHC.Types.IO


module Numeric.Optimization.MIP.Solver.SCIP
data SCIP
SCIP :: String -> SCIP
[scipPath] :: SCIP -> String
scip :: SCIP
instance Data.Default.Class.Default Numeric.Optimization.MIP.Solver.SCIP.SCIP
instance Numeric.Optimization.MIP.Solver.Base.IsSolver Numeric.Optimization.MIP.Solver.SCIP.SCIP GHC.Types.IO


module Numeric.Optimization.MIP.Solver