250 lines
10 KiB
Haskell
250 lines
10 KiB
Haskell
{-# LANGUAGE RecordWildCards #-}
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{-# LANGUAGE TypeApplications #-}
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module Environment where
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import Data.Functor ((<$>))
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import Control.Applicative ((<*>))
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import Control.Monad (forM_)
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import Control.Monad.Reader
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import Data.List (permutations, subsequences)
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import Numeric.LinearAlgebra
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import Text.Printf
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import System.Random
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type Probability = Double
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type Quantity = Int
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type Activation = Double
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type Amount = Double
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-- | Nutrients are the basis for any reaction and are found in the environment of the plant.
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data Nutrient = Sulfur
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| Phosphor
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| Nitrate
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| Photosynthesis
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deriving (Show, Enum, Bounded, Eq)
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-- | Fixed, non-generic Components
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data Component = PP
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| FPP
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deriving (Show, Enum, Bounded, Eq)
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-- | Compounds are either direct nutrients, already processed components or GenericEnzymes
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data Compound = Substrate Nutrient
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| Produced Component
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| GenericEnzyme Int
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deriving (Show, Eq)
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instance Enum Compound where
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toEnum x
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| x <= maxS = Substrate . toEnum $ x
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| x - (maxS+1) <= maxP = Produced . toEnum $ x - (maxS + 1)
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| otherwise = GenericEnzyme $ x - (maxS + 1) - (maxP + 1)
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where
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maxS = fromEnum (maxBound :: Nutrient)
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maxP = fromEnum (maxBound :: Component)
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fromEnum (Substrate x) = fromEnum x
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fromEnum (Produced x) = fromEnum x + maxS + 1
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where
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maxS = fromEnum (maxBound :: Nutrient)
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fromEnum (GenericEnzyme x) = x + maxS + maxP + 2
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where
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maxS = fromEnum (maxBound :: Nutrient)
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maxP = fromEnum (maxBound :: Component)
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-- | Enzymes are the main reaction-driver behind synthesis of intricate compounds.
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--
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-- They are assumed to be reversible.
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data Enzyme = Enzyme
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{ enzymeName :: String
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-- ^ Name of the Enzyme.
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, substrateRequirements :: [(Compound,Amount)]
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-- ^ needed for reaction to take place
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, synthesis :: ((Compound,Amount),(Compound,Amount))
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-- ^ given x in amount -a, this will produce y in amount b
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, dominance :: Maybe Amount
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-- ^ in case of competition for nutrients this denotes the priority
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-- Nothing = max possible
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}
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deriving (Show, Eq)
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-- | conviniently make an Enzyme using 1 of the first compund to produce 1 of the second
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makeSimpleEnzyme :: Compound -> Compound -> Enzyme
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makeSimpleEnzyme a b = Enzyme (show a ++ " -> " ++ show b) [] ((a,-1),(b,1)) Nothing
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-- Evironment
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-- ----------
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-- | In the environment we have predators that impact the fitness of our plants and
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-- may be resistant to some compounds the plant produces. They can also differ in
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-- their intensity.
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data Predator = Predator { resistance :: [Compound]
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-- ^ list of components this predator is resistant to
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, fitnessImpact :: Amount
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-- ^ impact on the fitness of a plant
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-- (~ agressiveness of the herbivore)
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} deriving (Show, Eq)
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-- The environment itself is just the soil and the predators. Extensions would be possible.
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data Environment =
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Environment
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{ soil :: [(Nutrient, Amount)]
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-- ^ soil is a list of nutrients available to the plant.
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, predators :: [(Predator, Probability)]
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-- ^ Predators with the probability of appearance in this generation.
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, metabolismIteration :: Int
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-- ^ Number of iterations for producing compounds
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, maxCompound :: Int
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-- ^ Number of possible Compounds
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-- 'maxCompound' should be greater than #Nutrient + #Products.
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-- Rest will get filled up with 'GenericEnzyme i'
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--
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-- To find the 'maxCompound' without 'GenericEnzyme' use
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-- 'maxComponent = fromEnum (maxBound :: Nutrient) + fromEnum (maxBound :: Component) + 1'
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, toxicCompounds :: [(Compound,Amount)]
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-- ^ Compounds considered to be toxic in this environment.
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-- Kills 100% of Predators above Amount.
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, possibleEnzymes :: [Enzyme]
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-- ^ All enzymes that can be created by genetic manipulation in this setting.
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} deriving (Show, Eq)
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-- helper function. Allows for [0..maxCompoundWithoutGeneric] :: [Compound] with all non-generic Compounds
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maxCompoundWithoutGeneric :: Int
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maxCompoundWithoutGeneric = fromEnum (maxBound :: Nutrient) + fromEnum (maxBound :: Component) + 1
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type World a = ReaderT Environment IO a
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-- Plants
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-- ------
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-- Plants consist of a Genome responsible for creation of the PSM and also an
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-- external state how many nutrients and compounds are currently inside the plant.
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type Genome = [(Enzyme, Quantity, Activation)]
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data Plant = Plant
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{ genome :: Genome
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-- ^ the genetic characteristic of the plant
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, absorbNutrients :: World [(Nutrient,Amount)]
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-- ^ the capability to absorb nutrients given an environment
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}
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instance Show Plant where
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show p = "Plant with Genome " ++ show (genome p)
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instance Eq Plant where
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a == b = genome a == genome b
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-- Fitness
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-- -------
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-- The fitness-measure is central for the generation of offspring and the
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-- simulation. It evaluates the probability for passing on genes given a plant in
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-- an environment.
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type Fitness = Double
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fitness :: Plant -> World Fitness
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fitness p = do
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nutrients <- absorbNutrients p -- absorb soil
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products <- produceCompounds p nutrients -- produce compounds
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survivalRate <- deterPredators products -- defeat predators with produced compounds
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let sumEnzymes = sum $ (\(_,q,a) -> (fromIntegral q)*a) <$> genome p -- amount of enzymes * activation = resources "wasted"
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costOfEnzymes = 0.95 ** sumEnzymes
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return $ survivalRate * costOfEnzymes
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-- can also be written as, but above is more clear.
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-- fitness p = absorbNutrients p >>= produceCompounds p >>= deterPredators
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produceCompounds :: Plant -> [(Nutrient, Amount)] -> World (Vector Amount)
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produceCompounds (Plant genes _) substrate = do
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numIter <- metabolismIteration <$> ask
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numCompounds <- maxCompound <$> ask
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let
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initialAmount = (assoc (numCompounds+1) 0 ((\(n,a) -> (fromEnum $ Substrate n,a)) <$> substrate)) :: Vector Amount
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enzymes = (\(e,q,a) -> (synthesis e,(fromIntegral q)*a)) <$> genes -- [(((Component,Amount),(Component,Amount)),q*a)], Amount got * by quantity & activation
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positions = concat $ (\(((i,ia),(o,oa)),f) -> [((fromEnum i,fromEnum i),f*ia),((fromEnum o,fromEnum o),f*ia),((fromEnum o,fromEnum i),f*oa),((fromEnum i,fromEnum o),f*oa)]) <$> enzymes -- [((row,column),amount)]
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mat = accum (konst 0 (numCompounds+1,numCompounds+1)) (+) positions --accumulate all entries into one matrix.
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-- mat is now the rate of change in u'(t) = A u(t)
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-- (l,v) = eig (ident (numCompounds+1) + ((*0.01) `cmap` mat)) -- use u(t+1) = u(t) + A u(t) = (E + A) u(t) for iteration
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-- final = (realPart `cmap` (v <> ((^numIter) `cmap` diag l) <> inv v)) #> initialAmount -- (E + A)^numIter * t_0 for numIter iterations.
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final = (realPart `cmap` matFunc (^numIter) (ident (numCompounds+1) + (((*0.01) . (:+ 0)) `cmap` mat))) #> initialAmount
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-- matFunc splits mat into UD(U^-1), applies function to diag-Elements in D, then multiplies togehter.
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-- faster, because no inversions and optimized eig.
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return final
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deterPredators :: Vector Amount -> World Probability
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deterPredators cs = do
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ps <- predators <$> ask
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ts <- toxicCompounds <$> ask
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let
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deter :: Predator -> Double
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-- multiply (toxicity of t with 100% effectiveness at l| for all toxins t | and t not in p's resistance-list)
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deter p = product [1 - min 1 (cs ! (fromEnum t) / l) | (t,l) <- ts, not (t `elem` resistance p)]
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-- multiply (probability of occurence * intensity of destruction / probability to deter predator | for all predators)
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return . product $ [min 1 ((1-prob) * fitnessImpact p / deter p) | (p,prob) <- ps]
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-- Mating & Creation of diversity
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-- ------------------------------
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-- | mate haploid
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haploMate :: Plant -> World Plant
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haploMate (Plant genes abs) = do
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--generate some random infinite uniform distributed lists of doubles in [0,1)
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r1 <- liftIO ((randoms <$> newStdGen) :: IO [Double])
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r2 <- liftIO ((randoms <$> newStdGen) :: IO [Double])
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r3 <- liftIO ((randoms <$> newStdGen) :: IO [Double])
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r4 <- liftIO ((randoms <$> newStdGen) :: IO [Double])
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r5 <- liftIO ((randoms <$> newStdGen) :: IO [Double])
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enzymes <- possibleEnzymes <$> ask
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re1 <- liftIO ((randomRs (0,length enzymes - 1) <$> newStdGen) :: IO [Int])
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re2 <- liftIO ((randomRs (0,length enzymes - 1) <$> newStdGen) :: IO [Int])
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let
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genes' = mutateGene r1 re1
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. noiseActivation r2
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. addGene r3 re2
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. duplicateGene r4
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. deleteGene r5
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$ genes
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deleteGene :: [Double] -> Genome -> Genome
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deleteGene (r:rs) ((e,1,a):gs) = if a < 0.1 && r < 0.5 then deleteGene rs gs else (e,1,a):deleteGene rs gs
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deleteGene (r:rs) ((e,q,a):gs) = if a < 0.1 && r < 0.5 then (e,q-1,a):deleteGene rs gs else (e,q,a):deleteGene rs gs
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deleteGene _ [] = []
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duplicateGene :: [Double] -> Genome -> Genome
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duplicateGene (r:rs) ((e,q,a):gs) = if r < 0.05 then (e,q+1,a):duplicateGene rs gs else (e,q,a):duplicateGene rs gs
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duplicateGene _ [] = []
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addGene :: [Double] -> [Int] -> Genome -> Genome
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addGene (r:rs) (s:ss) g = if r < 0.01 then ((enzymes !! s),1,1):g else g
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noiseActivation :: [Double] -> Genome -> Genome
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noiseActivation (r:rs) ((e,q,a):gs) = (e,q,max 0 $ min 1 $ a-0.01+0.02*r):noiseActivation rs gs
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noiseActivation _ [] = []
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mutateGene :: [Double] -> [Int] -> Genome -> Genome
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mutateGene (r:rs) (s:ss) ((e,1,a):gs) = if r < 0.05 then ((enzymes !! s),1,a):mutateGene rs ss gs
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else (e,1,a):mutateGene rs ss gs
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mutateGene (r:rs) (s:ss) ((e,q,a):gs) = if r < 0.05 then (e,q-1,a):((enzymes !! s),1,a):mutateGene rs ss gs
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else (e,q,a):mutateGene rs ss gs
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mutateGene (r:rs) (s:ss) [] = []
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return $ Plant genes' abs
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-- Utility Functions
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-- -----------------
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-- | Plant with no secondary metabolism with unlimited extraction from environment.
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emptyPlant :: Plant
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emptyPlant = Plant [] (soil <$> ask)
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getAmountOf :: Compound -> [(Compound, Amount)] -> Amount
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getAmountOf c = sum . fmap snd . filter ((== c) . fst)
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