haga/src/LambdaCalculus.hs

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2024-02-23 17:12:27 +01:00
{-# LANGUAGE GADTs #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE Trustworthy #-}
{-# LANGUAGE TypeApplications #-}
{-# LANGUAGE NoImplicitPrelude #-}
module LambdaCalculus where
import Data.Dynamic
import Data.List (foldr1, last, lookup, zipWith3, (!!), (\\))
import Data.List.Extra (delete, nubOrd, nubOrdOn)
import qualified Data.List.NonEmpty as NE
import qualified Data.Map.Strict as Map
import Data.Maybe
import Data.Random
import qualified Data.Text as T
import Data.Typeable
import GA
import Pretty
import Protolude
import Test.QuickCheck hiding (sample, shuffle)
import Test.QuickCheck.Monadic (assert, monadicIO)
import qualified Type.Reflection as Ref
data ExpressionWeights = ExpressionWeights
{ lambdaSpucker :: Int,
lambdaSchlucker :: Int,
symbol :: Int,
variable :: Int,
constant :: Int
}
data LambdaEnviroment = LambdaEnviroment
{ functions :: (Map TypeRep [ConVal]),
constants :: (Map TypeRep [RVar ConVal]),
targetType :: TypeRep,
maxDepth :: Int,
weights :: ExpressionWeights
}
showSanifid:: Show a => a -> Text
showSanifid var = T.replace " -> " "To" (show var)
exampleLE :: LambdaEnviroment
exampleLE =
LambdaEnviroment
{ functions =
Map.fromList
[ ((Ref.SomeTypeRep (Ref.TypeRep @(Int -> Int -> Int))), ["(+)", "(-)", "(*)", "mod"]),
((Ref.SomeTypeRep (Ref.TypeRep @(Int -> Int -> Bool))), ["(>)", "(==)", "(>=)"]),
((Ref.SomeTypeRep (Ref.TypeRep @(Bool -> Int -> Int -> Int))), ["if'"])
],
constants =
Map.fromList
[ ((Ref.SomeTypeRep (Ref.TypeRep @(Int))), [(fmap show (uniform 0 10000 :: RVar Int))]),
((Ref.SomeTypeRep (Ref.TypeRep @(Bool))), [(fmap show (uniform True False :: RVar Bool))])
],
targetType = (Ref.SomeTypeRep (Ref.TypeRep @(Int -> Int -> Int))),
maxDepth = 10,
weights =
ExpressionWeights
{ lambdaSpucker = 1,
lambdaSchlucker = 1,
symbol = 1,
variable = 1,
constant = 1
}
}
type BoundVars = [TypeRep]
-- we need a dynamic typ with a concept of equality here, should we want to interpret the result, instead of compiling it...
type ConVal = Text
-- LambdaSpucker - adds TypeRequester#1 as bound var and returns the result of TypeRequester#2
data LambdaExpression = LambdaSpucker TypeRequester TypeRequester BoundVars | LambdaSchlucker TypeRequester BoundVars | Symbol ConVal [TypeRequester] BoundVars | Var TypeRep Int [TypeRequester] BoundVars | Constan ConVal deriving (Eq)
asList :: LambdaExpression -> [TypeRequester]
asList (LambdaSpucker tr1 tr2 _) = [tr1, tr2]
asList (LambdaSchlucker tr _) = [tr]
asList (Symbol _ trs _) = trs
asList (Var _ _ trs _) = trs
asList (Constan _) = []
data TypeRequester = TR TypeRep (Maybe LambdaExpression) BoundVars deriving (Eq)
toLambdaExpressionS :: TypeRequester -> Text
toLambdaExpressionS (TR typeRep (Just lambdaExpression) boundVars) = "((" <> eToLambdaExpressionS lambdaExpression <> ") :: (" <> show typeRep <> "))"
toLambdaExpressionS (TR _ (Nothing) _) = "Invalid Lambda Epr"
-- data LambdaExpression = LambdaSpucker TypeRequester TypeRequester BoundVars | LambdaSchlucker TypeRequester BoundVars | Symbol ConVal [TypeRequester] BoundVars | Var TypeRep Int | Constan ConVal
eToLambdaExpressionS :: LambdaExpression -> Text
eToLambdaExpressionS (LambdaSpucker typeRequester1 typeRequester2 boundVars) = "(\\l" <> showSanifid (last boundVars) <> show (count boundVars (last boundVars) - 1) <> " -> " <> toLambdaExpressionS typeRequester2 <> ") " <> toLambdaExpressionS typeRequester1
eToLambdaExpressionS (LambdaSchlucker typeRequester boundVars) = "\\l" <> showSanifid (last boundVars) <> show (count boundVars (last boundVars) - 1) <> " -> " <> toLambdaExpressionS typeRequester
eToLambdaExpressionS (Symbol (valS) typeRequesters _) = valS <> " " <> (unwords (map toLambdaExpressionS typeRequesters))
eToLambdaExpressionS (Var typeRep int typeRequesters _) = "l" <> showSanifid typeRep <> show int <> " " <> (unwords (map toLambdaExpressionS typeRequesters))
eToLambdaExpressionS (Constan (valS)) = valS
instance Pretty TypeRequester where
pretty = toLambdaExpressionShort
instance Individual TypeRequester
instance Pretty LambdaEnviroment where
pretty (LambdaEnviroment functions constants target _ _) = "Functions: " <> show functions <> " Constants: " <> show (Map.keys constants) <> " Target is a function: " <> show target
genTypeRequester :: LambdaEnviroment -> Int -> TypeRep -> BoundVars -> RVar TypeRequester
genTypeRequester env depthLeft target boundVars = do
le <- genLambdaExpression env (depthLeft - 1) target boundVars
return (TR target (Just le) boundVars)
genLambdaExpression :: LambdaEnviroment -> Int -> TypeRep -> BoundVars -> RVar LambdaExpression
genLambdaExpression env@(LambdaEnviroment functions constants _ _ weights) depthLeft target boundVar = do
let weightMap =
( if not (canGenSchlucker target)
then [(constant weights, genLambdaConst env depthLeft target boundVar)]
else []
)
<> ( if depthLeft > 0
then [(lambdaSpucker weights, genLambdaSpucker env depthLeft target boundVar)]
else []
)
<> ( if canGenSchlucker target
then [(lambdaSchlucker weights, genLambdaSchlucker env depthLeft target boundVar)]
else []
)
<> ( if depthLeft > 0 && doAnyMatchThatType target (Map.keys functions)
then [(symbol weights, genLambdaSymbol env depthLeft target boundVar)]
else []
)
<> ( if depthLeft > 0 && doAnyMatchThatType target boundVar
then [(variable weights, genLambdaVar env depthLeft target boundVar)]
else []
)
expres <- selectWeighted weightMap
res <- expres
return res
selectWeighted :: [(Int, a)] -> RVar a
selectWeighted x = do
let total = sum (map fst x)
selection <- uniform 1 total
return $ selectAtWeight selection (NE.fromList x)
selectAtWeight :: Int -> NonEmpty (Int, a) -> a
selectAtWeight _ (x :| []) = snd x
selectAtWeight w (x :| xs)
| fst x >= w = snd x
| otherwise = selectAtWeight (w - fst x) (NE.fromList xs)
canGenSchlucker :: TypeRep -> Bool
canGenSchlucker t = (typeRepTyCon t) == (typeRepTyCon (Ref.SomeTypeRep (Ref.TypeRep @(->))))
doAnyMatchThatType :: TypeRep -> [TypeRep] -> Bool
doAnyMatchThatType toGen available = any (doTypesMatch toGen) available
doTypesMatch :: TypeRep -> TypeRep -> Bool
doTypesMatch toGen available = elem toGen (available : (repeatedly (lastMay . typeRepArgs) available))
genLambdaSpucker :: LambdaEnviroment -> Int -> TypeRep -> BoundVars -> RVar LambdaExpression
genLambdaSpucker env@(LambdaEnviroment functions constants _ _ weights) depthLeft target boundVar = do
lamdaTypeLength <- uniform 1 3
lambaTypes <- replicateM lamdaTypeLength (randomElement (Map.keys constants))
let lambaType = foldr1 mkFunTy lambaTypes
lamdaVarTypeRequester <- genTypeRequester env depthLeft lambaType boundVar
typeRequester <- genTypeRequester env depthLeft target (boundVar ++ [lambaType])
return (LambdaSpucker lamdaVarTypeRequester typeRequester (boundVar ++ [lambaType]))
genLambdaSchlucker :: LambdaEnviroment -> Int -> TypeRep -> BoundVars -> RVar LambdaExpression
genLambdaSchlucker env@(LambdaEnviroment functions constants _ _ weights) depthLeft target boundVar = do
let args = typeRepArgs target
let lambaType = fromJust (head args)
let toFind = last args
typeRequester <- genTypeRequester env depthLeft toFind (boundVar ++ [lambaType])
return (LambdaSchlucker typeRequester (boundVar ++ [lambaType]))
genLambdaConst :: LambdaEnviroment -> Int -> TypeRep -> BoundVars -> RVar LambdaExpression
genLambdaConst env@(LambdaEnviroment functions constants _ _ weights) depthLeft target boundVar = do
elm <- randomElement $ fromJust (Map.lookup target constants)
res <- elm
return $ Constan res
genLambdaSymbol :: LambdaEnviroment -> Int -> TypeRep -> BoundVars -> RVar LambdaExpression
genLambdaSymbol env@(LambdaEnviroment functions constants _ _ weights) depthLeft target boundVar = do
let availFunTypes = filter (doTypesMatch target) (Map.keys functions)
(tr, fun) <- randomElement $ concatMap (\l -> zip (repeat l) (fromMaybe [] (Map.lookup l functions))) availFunTypes
ret <- genLambdaSymbol' tr fun [] env depthLeft target boundVar
return ret
genLambdaSymbol' :: TypeRep -> ConVal -> [TypeRequester] -> LambdaEnviroment -> Int -> TypeRep -> BoundVars -> RVar LambdaExpression
genLambdaSymbol' tr v trs env@(LambdaEnviroment functions constants _ _ weights) depthLeft target boundVar
| tr == target = do
return $ Symbol v trs boundVar
| otherwise = do
let args = typeRepArgs tr
let param = fromJust (head args)
let rest = last args
newTypeRequ <- genTypeRequester env depthLeft param boundVar
ret <- genLambdaSymbol' rest v (trs ++ [newTypeRequ]) env depthLeft target boundVar
return ret
genLambdaVar :: LambdaEnviroment -> Int -> TypeRep -> BoundVars -> RVar LambdaExpression
genLambdaVar env@(LambdaEnviroment functions constants _ _ weights) depthLeft target boundVar = do
let availTypes = filter (doTypesMatch target) boundVar
choosenType <- randomElement $ availTypes
let tCount = count boundVar choosenType
indexV <- uniform 0 (tCount-1)
ret <- genLambdaVar' choosenType choosenType indexV [] env depthLeft target boundVar
return ret
genLambdaVar' :: TypeRep -> TypeRep -> Int -> [TypeRequester] -> LambdaEnviroment -> Int -> TypeRep -> BoundVars -> RVar LambdaExpression
genLambdaVar' tr varType varNumber trs env@(LambdaEnviroment functions constants _ _ weights) depthLeft target boundVar
| tr == target = do
return $ Var varType varNumber trs boundVar
| otherwise = do
let args = typeRepArgs tr
let param = fromJust (head args)
let rest = last args
newTypeRequ <- genTypeRequester env depthLeft param boundVar
ret <- genLambdaVar' rest varType varNumber (trs ++ [newTypeRequ]) env depthLeft target boundVar
return ret
instance Environment TypeRequester LambdaEnviroment where
new env@(LambdaEnviroment _ _ target maxDepth _) = do
tr <- genTypeRequester env maxDepth target []
return tr
mutate env@(LambdaEnviroment _ _ _ maxDepth _) tr = do
let trCount = countTrsR(tr)
selectedTR <- uniform 1 trCount
let (depthAt,(TR trep _ bound)) = depthLeftAndTypeAtR tr selectedTR maxDepth
res <- genTypeRequester env depthAt trep bound
return $ replaceAtR selectedTR tr res
crossover1 env@(LambdaEnviroment _ _ _ maxDepth _) tr1 tr2 = do
let trCount = countTrsR tr1
selectedIndex1 <- uniform 1 trCount
let (depthAt, selectedTr1@(TR trep _ bound)) = depthLeftAndTypeAtR tr selectedTR maxDepth
let indexes = findIndicesWhere tr2 ( == trep)
if length indexes == 0 then return Nothing else (do
(selectedTr2,selectedIndex2) <- randomElement indexes
)
-- helper
findIndicesWhere:: TypeRequester -> (TypeRep -> Bool) -> Int -> [(TypeRequester, Int)]
findIndicesWhere tr@(TR t lE _) filte indx = case lE of
Just le -> (tr, indx+1):(findIndicesWhere' (asList le) filte (indx+1))
Nothing -> undefined
findIndicesWhere':: [TypeRequester] -> (TypeRep -> Bool) -> Int -> [(TypeRequester, Int)]
findIndicesWhere' (tr:trs) f indx = (findIndicesWhere tr f indx) ++ (findIndicesWhere' trs f (indx + countTrsR tr))
depthLeftAndTypeInSubtreeWithIndex :: [TypeRequester] -> Int -> Int -> (Int, TypeRequester)
depthLeftAndTypeInSubtreeWithIndex (tr:trs) indexLeft depthLeft = if countTrsR tr >= indexLeft then depthLeftAndTypeAtR tr indexLeft depthLeft else depthLeftAndTypeInSubtreeWithIndex trs (indexLeft - countTrsR tr) depthLeft
depthLeftAndTypeInSubtreeWithIndex [] indexLeft depthLeft = undefined
replaceAtR:: Int -> TypeRequester -> TypeRequester -> TypeRequester
replaceAtR 0 _ with = with
replaceAtR i (TR tm (Just le) bV) with = TR tm (Just (replaceAt (i-1) le with)) bV
replaceAtR _ (TR _ Nothing _) _ = undefined
-- LambdaSpucker TypeRequester TypeRequester BoundVars | LambdaSchlucker TypeRequester BoundVars | Symbol ConVal [TypeRequester] BoundVars | Var TypeRep Int [TypeRequester] BoundVars | Constan ConVal
replaceAt:: Int -> LambdaExpression -> TypeRequester -> LambdaExpression
replaceAt i le@(LambdaSpucker _ _ bv) with = LambdaSpucker (fromJust (head trs)) (last trs) bv where trs = replaceInSubtreeWithIndex i (asList le) with
replaceAt i (LambdaSchlucker tr bv) with = LambdaSchlucker (replaceAtR i tr with) bv
replaceAt i le@(Symbol cv _ bv) with = Symbol cv trs bv where trs = replaceInSubtreeWithIndex i (asList le) with
replaceAt i le@(Var tr ix _ bv) with = Var tr ix trs bv where trs = replaceInSubtreeWithIndex i (asList le) with
replaceAt _ (Constan _) _ = undefined
replaceInSubtreeWithIndex :: Int -> [TypeRequester] -> TypeRequester -> [TypeRequester]
replaceInSubtreeWithIndex indexLeft (tr:trs) with = if countTrsR tr >= indexLeft then (replaceAtR indexLeft tr with):trs else tr:(replaceInSubtreeWithIndex (indexLeft - countTrsR tr) trs with)
replaceInSubtreeWithIndex _ [] _ = undefined
depthLeftAndTypeAtR::TypeRequester -> Int -> Int -> (Int, TypeRequester)
depthLeftAndTypeAtR t 0 depthLeft = ((depthLeft - 1), t)
depthLeftAndTypeAtR (TR _ (Just le) _) indexLeft depthLeft = depthLeftAndTypeAt le (indexLeft - 1) (depthLeft - 1)
depthLeftAndTypeAtR (TR _ Nothing _) indexLeft depthLeft = undefined
depthLeftAndTypeAt :: LambdaExpression -> Int -> Int -> (Int, TypeRequester)
depthLeftAndTypeAt le indexLeft depthLeft = depthLeftAndTypeInSubtreeWithIndex (asList le) indexLeft depthLeft
depthLeftAndTypeInSubtreeWithIndex :: [TypeRequester] -> Int -> Int -> (Int, TypeRequester)
depthLeftAndTypeInSubtreeWithIndex (tr:trs) indexLeft depthLeft = if countTrsR tr >= indexLeft then depthLeftAndTypeAtR tr indexLeft depthLeft else depthLeftAndTypeInSubtreeWithIndex trs (indexLeft - countTrsR tr) depthLeft
depthLeftAndTypeInSubtreeWithIndex [] indexLeft depthLeft = undefined
countTrsR:: TypeRequester -> Int
countTrsR tr@(TR t lE _) = case lE of
Just le -> countTrs le + 1
Nothing -> 1
countTrs:: LambdaExpression -> Int
countTrs le = sum (map countTrsR (asList le))
repeatedly :: (a -> Maybe a) -> a -> [a]
repeatedly f x = case f x of
Nothing -> []
Just y -> y : repeatedly f y
count :: (Eq a) => [a] -> a -> Int
count [] find = 0
count ys find = length xs
where
xs = [xs | xs <- ys, xs == find]
-- Test Stuff
testConstInt :: TypeRequester
testConstInt = TR (Ref.SomeTypeRep (Ref.TypeRep @Int)) (Just (Symbol ("5") [] [])) []
testIntToClassCons :: TypeRequester
testIntToClassCons = TR (Ref.SomeTypeRep (Ref.TypeRep @(Int -> ResClass))) (Just (Symbol ("Class1") [] [])) []
testIntToClassCorrect :: TypeRequester
testIntToClassCorrect =
TR
(Ref.SomeTypeRep (Ref.TypeRep @(Int -> ResClass)))
( Just
( LambdaSchlucker
( TR
(Ref.SomeTypeRep (Ref.TypeRep @(ResClass)))
( Just
( Symbol
("iteClass")
[ ( TR
(Ref.SomeTypeRep (Ref.TypeRep @(Bool)))
( Just
( Symbol
("eqInt")
[ ( TR
(Ref.SomeTypeRep (Ref.TypeRep @(Int)))
(Just (Var (Ref.SomeTypeRep (Ref.TypeRep @(Int))) 0 [] []))
[(Ref.SomeTypeRep (Ref.TypeRep @(Int)))]
),
( TR
(Ref.SomeTypeRep (Ref.TypeRep @(Int)))
(Just (Constan ("1")))
[(Ref.SomeTypeRep (Ref.TypeRep @(Int)))]
)
]
[(Ref.SomeTypeRep (Ref.TypeRep @(Int)))]
)
)
[(Ref.SomeTypeRep (Ref.TypeRep @(Int)))]
),
( TR
(Ref.SomeTypeRep (Ref.TypeRep @(ResClass)))
(Just (Constan ("Class1")))
[(Ref.SomeTypeRep (Ref.TypeRep @(Int)))]
),
( TR
(Ref.SomeTypeRep (Ref.TypeRep @(ResClass)))
( Just
( Symbol
("iteClass")
[ ( TR
(Ref.SomeTypeRep (Ref.TypeRep @(Bool)))
( Just
( Symbol
("eqInt")
[ ( TR
(Ref.SomeTypeRep (Ref.TypeRep @(Int)))
(Just (Var (Ref.SomeTypeRep (Ref.TypeRep @(Int))) 0 [] []))
[(Ref.SomeTypeRep (Ref.TypeRep @(Int)))]
),
( TR
(Ref.SomeTypeRep (Ref.TypeRep @(Int)))
(Just (Constan ("2")))
[(Ref.SomeTypeRep (Ref.TypeRep @(Int)))]
)
]
[(Ref.SomeTypeRep (Ref.TypeRep @(Int)))]
)
)
[(Ref.SomeTypeRep (Ref.TypeRep @(Int)))]
),
( TR
(Ref.SomeTypeRep (Ref.TypeRep @(ResClass)))
(Just (Constan ("Class2")))
[(Ref.SomeTypeRep (Ref.TypeRep @(Int)))]
),
( TR
(Ref.SomeTypeRep (Ref.TypeRep @(ResClass)))
( Just
( Symbol
("iteClass")
[ ( TR
(Ref.SomeTypeRep (Ref.TypeRep @(Bool)))
( Just
( Symbol
("eqInt")
[ ( TR
(Ref.SomeTypeRep (Ref.TypeRep @(Int)))
(Just (Var (Ref.SomeTypeRep (Ref.TypeRep @(Int))) 0 [] []))
[(Ref.SomeTypeRep (Ref.TypeRep @(Int)))]
),
( TR
(Ref.SomeTypeRep (Ref.TypeRep @(Int)))
(Just (Constan ("3")))
[(Ref.SomeTypeRep (Ref.TypeRep @(Int)))]
)
]
[(Ref.SomeTypeRep (Ref.TypeRep @(Int)))]
)
)
[(Ref.SomeTypeRep (Ref.TypeRep @(Int)))]
),
( TR
(Ref.SomeTypeRep (Ref.TypeRep @(ResClass)))
(Just (Constan ("Class3")))
[(Ref.SomeTypeRep (Ref.TypeRep @(Int)))]
),
( TR
(Ref.SomeTypeRep (Ref.TypeRep @(ResClass)))
(Just (Constan ("Class3")))
[(Ref.SomeTypeRep (Ref.TypeRep @(Int)))]
)
]
[(Ref.SomeTypeRep (Ref.TypeRep @(Int)))]
)
)
[(Ref.SomeTypeRep (Ref.TypeRep @(Int)))]
)
]
[(Ref.SomeTypeRep (Ref.TypeRep @(Int)))]
)
)
[(Ref.SomeTypeRep (Ref.TypeRep @(Int)))]
)
]
[(Ref.SomeTypeRep (Ref.TypeRep @(Int)))]
)
)
[(Ref.SomeTypeRep (Ref.TypeRep @(Int)))]
)
[(Ref.SomeTypeRep (Ref.TypeRep @(Int)))]
)
)
[]
data ResClass = Class1 | Class2 | Class3 deriving (Enum, Show)
eqInt :: Int -> Int -> Bool
eqInt a b = a == b
iteClass :: Bool -> ResClass -> ResClass -> ResClass
iteClass True c _ = c
iteClass False _ c = c
toLambdaExpressionShort :: TypeRequester -> Text
toLambdaExpressionShort (TR _ (Just lambdaExpression) _) = "(" <> eToLambdaExpressionShort lambdaExpression <> ")"
toLambdaExpressionShort (TR _ (Nothing) _) = "Invalid Lambda Epr"
-- data LambdaExpression = LambdaSpucker TypeRequester TypeRequester BoundVars | LambdaSchlucker TypeRequester BoundVars | Symbol ConVal [TypeRequester] BoundVars | Var TypeRep Int | Constan ConVal
eToLambdaExpressionShort :: LambdaExpression -> Text
eToLambdaExpressionShort (LambdaSpucker typeRequester1 typeRequester2 boundVars) = "(\\l" <> showSanifid (last boundVars) <> show (count boundVars (last boundVars) - 1) <> " -> " <> toLambdaExpressionShort typeRequester2 <> ") " <> toLambdaExpressionShort typeRequester1
eToLambdaExpressionShort (LambdaSchlucker typeRequester boundVars) = "()\\l" <> showSanifid (last boundVars) <> show (count boundVars (last boundVars) - 1) <> " -> " <> toLambdaExpressionShort typeRequester <> ")"
eToLambdaExpressionShort (Symbol (valS) typeRequesters _) = valS <> " " <> (unwords (map toLambdaExpressionShort typeRequesters))
eToLambdaExpressionShort (Var typeRep int typeRequesters _) = "l" <> showSanifid typeRep <> show int <> " " <> (unwords (map toLambdaExpressionShort typeRequesters))
eToLambdaExpressionShort (Constan (valS)) = valS
res :: Int -> ResClass
res = ((\lInt0 -> ((iteClass ((eqInt ((lInt0) :: (Int)) ((1) :: (Int))) :: (Bool)) ((Class1) :: (ResClass)) ((iteClass ((eqInt ((lInt0) :: (Int)) ((2) :: (Int))) :: (Bool)) ((Class2) :: (ResClass)) ((iteClass ((eqInt ((lInt0) :: (Int)) ((3) :: (Int))) :: (Bool)) ((Class3) :: (ResClass)) ((Class3) :: (ResClass))) :: (ResClass))) :: (ResClass))) :: (ResClass))) :: (Int -> ResClass))