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


-- | A general framework to work with Symbolic Regression expression trees.
--   
--   A Symbolic Regression Tree data structure to work with mathematical
--   expressions with support to first order derivative and simplification;
@package srtree
@version 1.0.0.1

module Data.SRTree.Recursion
data ListF a b
NilF :: ListF a b
ConsF :: a -> b -> ListF a b
data NatF a
ZeroF :: NatF a
SuccF :: a -> NatF a
data StreamF a b
StreamF :: a -> b -> StreamF a b
data TreeF a b
LeafF :: TreeF a b
NodeF :: b -> a -> b -> TreeF a b
newtype Fix f
Fix :: f (Fix f) -> Fix f
[unfix] :: Fix f -> f (Fix f)
type Algebra f a = f a -> a
type CoAlgebra f a = a -> f a
data Cofree f a
(:<) :: a -> f (Cofree f a) -> Cofree f a
data Free f a
Ret :: a -> Free f a
Op :: f (Free f a) -> Free f a
extract :: Cofree f a -> a
unOp :: Free f a -> f (Free f a)
cata :: Functor f => (f a -> a) -> Fix f -> a
cataM :: (Functor f, Monad m) => (forall x. f (m x) -> m (f x)) -> (f a -> m a) -> Fix f -> m a
ana :: Functor f => (a -> f a) -> a -> Fix f
hylo :: Functor f => (f b -> b) -> (a -> f a) -> a -> b
para :: Functor f => (f (Fix f, a) -> a) -> Fix f -> a
mutu :: Functor f => (f (a, b) -> a) -> (f (a, b) -> b) -> (Fix f -> a, Fix f -> b)
apo :: Functor f => (a -> f (Either (Fix f) a)) -> a -> Fix f
accu :: Functor f => (forall x. f x -> p -> f (x, p)) -> (f a -> p -> a) -> Fix f -> p -> a
histo :: Functor f => (f (Cofree f a) -> a) -> Fix f -> a
futu :: Functor f => (a -> f (Free f a)) -> a -> Fix f
chrono :: Functor f => (f (Cofree f b) -> b) -> (a -> f (Free f a)) -> a -> b
fromList :: [a] -> Fix (ListF a)
toList :: Fix (ListF a) -> [a]
stream2list :: StreamF a [a] -> [a]
toNat :: Int -> Fix NatF
fromNat :: Fix NatF -> Int
instance GHC.Base.Functor (Data.SRTree.Recursion.ListF a)
instance GHC.Base.Functor Data.SRTree.Recursion.NatF
instance GHC.Base.Functor (Data.SRTree.Recursion.StreamF a)
instance GHC.Base.Functor (Data.SRTree.Recursion.TreeF a)


-- | Expression tree for Symbolic Regression
module Data.SRTree.Internal

-- | Tree structure to be used with Symbolic Regression algorithms. This
--   structure is a fixed point of a n-ary tree.
data SRTree val

-- | index of the variables
Var :: Int -> SRTree val

-- | index of the parameter
Param :: Int -> SRTree val

-- | constant value, can be converted to a parameter
Const :: Double -> SRTree val

-- | univariate function
Uni :: Function -> val -> SRTree val

-- | binary operator
Bin :: Op -> val -> val -> SRTree val

-- | Supported functions
data Function
Id :: Function
Abs :: Function
Sin :: Function
Cos :: Function
Tan :: Function
Sinh :: Function
Cosh :: Function
Tanh :: Function
ASin :: Function
ACos :: Function
ATan :: Function
ASinh :: Function
ACosh :: Function
ATanh :: Function
Sqrt :: Function
Cbrt :: Function
Square :: Function
Log :: Function
Exp :: Function

-- | Supported operators
data Op
Add :: Op
Sub :: Op
Mul :: Op
Div :: Op
Power :: Op

-- | create a tree with a single node representing a parameter
param :: Int -> Fix SRTree

-- | create a tree with a single node representing a variable
var :: Int -> Fix SRTree

-- | Arity of the current node
arity :: Fix SRTree -> Int

-- | Get the children of a node. Returns an empty list in case of a leaf
--   node.
getChildren :: Fix SRTree -> [Fix SRTree]

-- | Count the number of nodes in a tree.
countNodes :: Fix SRTree -> Int

-- | Count the number of <a>Var</a> nodes
countVarNodes :: Fix SRTree -> Int

-- | Count the number of const nodes
countConsts :: Fix SRTree -> Int

-- | Count the number of <a>Param</a> nodes
countParams :: Fix SRTree -> Int

-- | Count the occurrences of variable indexed as <tt>ix</tt>
countOccurrences :: Int -> Fix SRTree -> Int

-- | Creates the symbolic partial derivative of a tree by variable
--   <tt>dx</tt> (if <tt>p</tt> is <a>False</a>) or parameter <tt>dx</tt>
--   (if <tt>p</tt> is <a>True</a>).
deriveBy :: Bool -> Int -> Fix SRTree -> Fix SRTree

-- | Symbolic derivative by a variable
deriveByVar :: Int -> Fix SRTree -> Fix SRTree

-- | Symbolic derivative by a parameter
deriveByParam :: Int -> Fix SRTree -> Fix SRTree
derivative :: Floating a => Function -> a -> a

-- | Calculates the numerical derivative of a tree using forward mode
--   provided a vector of variable values <tt>xss</tt>, a vector of
--   parameter values <tt>theta</tt> and a function that changes a Double
--   value to the type of the variable values.
forwardMode :: (Show a, Num a, Floating a) => Vector a -> Vector Double -> (Double -> a) -> Fix SRTree -> [a]

-- | The function <a>gradParams</a> calculates the numerical gradient of
--   the tree and evaluates the tree at the same time. It assumes that each
--   parameter has a unique occurrence in the expression. This should be
--   significantly faster than <a>forwardMode</a>.
gradParams :: (Show a, Num a, Floating a) => Vector a -> Vector Double -> (Double -> a) -> Fix SRTree -> (a, [a])
evalFun :: Floating a => Function -> a -> a
evalOp :: Floating a => Op -> a -> a -> a

-- | Returns the inverse of a function. This is a partial function.
inverseFunc :: Function -> Function

-- | Evaluates the tree given a vector of variable values, a vector of
--   parameter values and a function that takes a Double and change to
--   whatever type the variables have. This is useful when working with
--   datasets of many values per variables.
evalTree :: (Num a, Floating a) => Vector a -> Vector Double -> (Double -> a) -> Fix SRTree -> a

-- | Relabel the parameters incrementaly starting from 0
relabelParams :: Fix SRTree -> Fix SRTree

-- | Change constant values to a parameter, returning the changed tree and
--   a list of parameter values
constsToParam :: Fix SRTree -> (Fix SRTree, [Double])

-- | Same as <a>constsToParam</a> but does not change constant values that
--   can be converted to integer without loss of precision
floatConstsToParam :: Fix SRTree -> (Fix SRTree, [Double])
instance GHC.Enum.Enum Data.SRTree.Internal.Op
instance GHC.Classes.Ord Data.SRTree.Internal.Op
instance GHC.Classes.Eq Data.SRTree.Internal.Op
instance GHC.Read.Read Data.SRTree.Internal.Op
instance GHC.Show.Show Data.SRTree.Internal.Op
instance GHC.Enum.Enum Data.SRTree.Internal.Function
instance GHC.Classes.Ord Data.SRTree.Internal.Function
instance GHC.Classes.Eq Data.SRTree.Internal.Function
instance GHC.Read.Read Data.SRTree.Internal.Function
instance GHC.Show.Show Data.SRTree.Internal.Function
instance GHC.Base.Functor Data.SRTree.Internal.SRTree
instance GHC.Classes.Ord val => GHC.Classes.Ord (Data.SRTree.Internal.SRTree val)
instance GHC.Classes.Eq val => GHC.Classes.Eq (Data.SRTree.Internal.SRTree val)
instance GHC.Show.Show val => GHC.Show.Show (Data.SRTree.Internal.SRTree val)
instance GHC.Base.Functor Data.SRTree.Internal.Tape
instance GHC.Show.Show a => GHC.Show.Show (Data.SRTree.Internal.Tape a)
instance GHC.Num.Num a => GHC.Num.Num (Data.SRTree.Internal.Tape a)
instance GHC.Float.Floating a => GHC.Float.Floating (Data.SRTree.Internal.Tape a)
instance GHC.Real.Fractional a => GHC.Real.Fractional (Data.SRTree.Internal.Tape a)
instance GHC.Num.Num (Data.SRTree.Recursion.Fix Data.SRTree.Internal.SRTree)
instance GHC.Real.Fractional (Data.SRTree.Recursion.Fix Data.SRTree.Internal.SRTree)
instance GHC.Float.Floating (Data.SRTree.Recursion.Fix Data.SRTree.Internal.SRTree)


-- | Functions to generate random trees and nodes.
module Data.SRTree.Random
class HasVars p
class HasVals p
class HasFuns p

-- | Constraint synonym for all properties.
type HasEverything p = (HasVars p, HasVals p, HasExps p, HasFuns p)

-- | A structure with every property
data FullParams
P :: [Int] -> (Double, Double) -> (Int, Int) -> [Function] -> FullParams

-- | RndTree is a Monad Transformer to generate random trees of type
--   `SRTree ix val` given the parameters `p ix val` using the random
--   number generator <a>StdGen</a>.
type RndTree p = ReaderT p (StateT StdGen IO) (Fix SRTree)

-- | Returns a random variable, the parameter <tt>p</tt> must have the
--   <a>HasVars</a> property
randomVar :: HasVars p => RndTree p

-- | Returns a random constant, the parameter <tt>p</tt> must have the
--   <tt>HasConst</tt> property
randomConst :: HasVals p => RndTree p

-- | Returns a random integer power node, the parameter <tt>p</tt> must
--   have the <a>HasExps</a> property
randomPow :: HasExps p => RndTree p

-- | Returns a random function, the parameter <tt>p</tt> must have the
--   <a>HasFuns</a> property
randomFunction :: HasFuns p => RndTree p

-- | Returns a random node, the parameter <tt>p</tt> must have every
--   property.
randomNode :: HasEverything p => RndTree p

-- | Returns a random non-terminal node, the parameter <tt>p</tt> must have
--   every property.
randomNonTerminal :: HasEverything p => RndTree p

-- | Returns a random tree with a limited budget, the parameter <tt>p</tt>
--   must have every property.
randomTree :: HasEverything p => Int -> RndTree p

-- | Returns a random tree with a approximately a number <tt>n</tt> of
--   nodes, the parameter <tt>p</tt> must have every property.
randomTreeBalanced :: HasEverything p => Int -> RndTree p
instance Data.SRTree.Random.HasVars Data.SRTree.Random.FullParams
instance Data.SRTree.Random.HasVals Data.SRTree.Random.FullParams
instance Data.SRTree.Random.HasExps Data.SRTree.Random.FullParams
instance Data.SRTree.Random.HasFuns Data.SRTree.Random.FullParams


-- | Conversion functions to display the expression trees in different
--   formats.
module Data.SRTree.Print
showExpr :: Fix SRTree -> String
printExpr :: Fix SRTree -> IO ()

-- | Displays a tree in Tikz format
showTikz :: Fix SRTree -> String
printTikz :: Fix SRTree -> IO ()

-- | Displays a tree as a numpy compatible expression.
showPython :: Fix SRTree -> String
printPython :: Fix SRTree -> IO ()

-- | Displays a tree as a sympy compatible expression.
showLatex :: Fix SRTree -> String
printLatex :: Fix SRTree -> IO ()


-- | Expression tree for Symbolic Regression
module Data.SRTree

-- | Tree structure to be used with Symbolic Regression algorithms. This
--   structure is a fixed point of a n-ary tree.
data SRTree val

-- | index of the variables
Var :: Int -> SRTree val

-- | index of the parameter
Param :: Int -> SRTree val

-- | constant value, can be converted to a parameter
Const :: Double -> SRTree val

-- | univariate function
Uni :: Function -> val -> SRTree val

-- | binary operator
Bin :: Op -> val -> val -> SRTree val

-- | Supported functions
data Function
Id :: Function
Abs :: Function
Sin :: Function
Cos :: Function
Tan :: Function
Sinh :: Function
Cosh :: Function
Tanh :: Function
ASin :: Function
ACos :: Function
ATan :: Function
ASinh :: Function
ACosh :: Function
ATanh :: Function
Sqrt :: Function
Cbrt :: Function
Square :: Function
Log :: Function
Exp :: Function

-- | Supported operators
data Op
Add :: Op
Sub :: Op
Mul :: Op
Div :: Op
Power :: Op

-- | create a tree with a single node representing a parameter
param :: Int -> Fix SRTree

-- | create a tree with a single node representing a variable
var :: Int -> Fix SRTree

-- | Arity of the current node
arity :: Fix SRTree -> Int

-- | Get the children of a node. Returns an empty list in case of a leaf
--   node.
getChildren :: Fix SRTree -> [Fix SRTree]

-- | Count the number of nodes in a tree.
countNodes :: Fix SRTree -> Int

-- | Count the number of <a>Var</a> nodes
countVarNodes :: Fix SRTree -> Int

-- | Count the number of const nodes
countConsts :: Fix SRTree -> Int

-- | Count the number of <a>Param</a> nodes
countParams :: Fix SRTree -> Int

-- | Count the occurrences of variable indexed as <tt>ix</tt>
countOccurrences :: Int -> Fix SRTree -> Int

-- | Creates the symbolic partial derivative of a tree by variable
--   <tt>dx</tt> (if <tt>p</tt> is <a>False</a>) or parameter <tt>dx</tt>
--   (if <tt>p</tt> is <a>True</a>).
deriveBy :: Bool -> Int -> Fix SRTree -> Fix SRTree

-- | Symbolic derivative by a variable
deriveByVar :: Int -> Fix SRTree -> Fix SRTree

-- | Symbolic derivative by a parameter
deriveByParam :: Int -> Fix SRTree -> Fix SRTree
derivative :: Floating a => Function -> a -> a

-- | Calculates the numerical derivative of a tree using forward mode
--   provided a vector of variable values <tt>xss</tt>, a vector of
--   parameter values <tt>theta</tt> and a function that changes a Double
--   value to the type of the variable values.
forwardMode :: (Show a, Num a, Floating a) => Vector a -> Vector Double -> (Double -> a) -> Fix SRTree -> [a]

-- | The function <a>gradParams</a> calculates the numerical gradient of
--   the tree and evaluates the tree at the same time. It assumes that each
--   parameter has a unique occurrence in the expression. This should be
--   significantly faster than <a>forwardMode</a>.
gradParams :: (Show a, Num a, Floating a) => Vector a -> Vector Double -> (Double -> a) -> Fix SRTree -> (a, [a])
evalFun :: Floating a => Function -> a -> a
evalOp :: Floating a => Op -> a -> a -> a

-- | Returns the inverse of a function. This is a partial function.
inverseFunc :: Function -> Function

-- | Evaluates the tree given a vector of variable values, a vector of
--   parameter values and a function that takes a Double and change to
--   whatever type the variables have. This is useful when working with
--   datasets of many values per variables.
evalTree :: (Num a, Floating a) => Vector a -> Vector Double -> (Double -> a) -> Fix SRTree -> a

-- | Relabel the parameters incrementaly starting from 0
relabelParams :: Fix SRTree -> Fix SRTree

-- | Change constant values to a parameter, returning the changed tree and
--   a list of parameter values
constsToParam :: Fix SRTree -> (Fix SRTree, [Double])

-- | Same as <a>constsToParam</a> but does not change constant values that
--   can be converted to integer without loss of precision
floatConstsToParam :: Fix SRTree -> (Fix SRTree, [Double])