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Commit 1166ca9a authored by ik1g19's avatar ik1g19
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finished challenge 4

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......@@ -7,7 +7,7 @@
-- DO NOT MODIFY THE FOLLOWING LINES OF CODE
module Challenges (WordSearchGrid,Placement,Posn,Orientation(..),solveWordSearch, createWordSearch,
LamMacroExpr(..),LamExpr(..),prettyPrint, parseLamMacro,
cpsTransform,innerRedn1,outerRedn1,compareInnerOuter) where
cpsTransform,innerRedn1,outerRedn1,compareInnerOuter,unique,macroName,closedParse,expr) where
-- Import standard library and parsing definitions from Hutton 2016, Chapter 13
-- We import System.Random - make sure that your installation has it installed - use stack ghci and stack ghc
......@@ -22,23 +22,26 @@ import System.Random
import Control.Applicative
instance NFData Orientation
instance NFData LamMacroExpr
instance NFData LamExpr
-- types for Part I
type WordSearchGrid = [[ Char ]]
type Placement = (Posn,Orientation)
type Posn = (Int,Int)
data Orientation = Forward | Back | Up | Down | UpForward | UpBack | DownForward | DownBack deriving (Eq,Ord,Show,Read)
data Orientation = Forward | Back | Up | Down | UpForward | UpBack | DownForward | DownBack deriving (Eq,Ord,Show,Read,Generic)
-- types for Parts II and III
data LamMacroExpr = LamDef [ (String,LamExpr) ] LamExpr deriving (Eq,Show,Read)
data LamMacroExpr = LamDef [ (String,LamExpr) ] LamExpr deriving (Eq,Show,Read,Generic)
data LamExpr = LamMacro String | LamApp LamExpr LamExpr |
LamAbs Int LamExpr | LamVar Int deriving (Eq,Show,Read)
LamAbs Int LamExpr | LamVar Int deriving (Eq,Show,Read,Generic)
-- END OF CODE YOU MUST NOT MODIFY
-- ADD YOUR OWN CODE HERE
-- Challenge 1 --
------------------------------------------Challenge 1------------------------------------------------- -- | inline comments
solveWordSearch :: [ String ] -> WordSearchGrid -> [ (String,Maybe Placement) ]
......@@ -49,8 +52,8 @@ findString :: WordSearchGrid -> String -> (String,Maybe Placement)
findString css s = (s,findLocation css (0,0) s)
--recursively searches grid for first char of word
--returns Nothing or Placement
{--| recursively searches grid for first char of word |--
--| returns Nothing or Placement |--}
findLocation :: WordSearchGrid -> Posn -> String -> Maybe Placement
findLocation css (x,y) s@(l:ls) | x > limit && y > limit = Nothing
| x > limit = findLocation css (0,y+1) s
......@@ -61,7 +64,7 @@ findLocation css (x,y) s@(l:ls) | x > limit && y > limit = N
limit = length css - 1
--checks for hidden word in possible directions
{--| checks for hidden word in possible directions |--}
findPlacement :: WordSearchGrid -> Posn -> String -> Maybe Placement
findPlacement css (x,y) s | checkWordDir css (x,y) Forward s = Just ((x,y),Forward)
| checkWordDir css (x,y) Back s = Just ((x,y),Back)
......@@ -81,10 +84,10 @@ checkWordDir css (x,y) dir (l:ls) | nextElem css (x,y) dir == Just l = checkWo
| otherwise = False
--------------------pattern matching for traversing the grid--------------------
--returns position of movement in a given direction
{--| returns position of movement in a given direction |--}
nextPos :: Orientation -> Posn -> Posn
nextPos Forward (x,y) = (x+1,y)
nextPos Back (x,y) = (x-1,y)
......@@ -97,80 +100,56 @@ nextPos DownBack (x,y) = (x-1,y+1)
elemAt :: [[a]] -> Posn -> a
elemAt ass (x,y) = (ass !! y) !! x --ass means list of list of a's,
--not associated with any other meaning
elemAt ass (x,y) = (ass !! y) !! x -- | ass means list of list of a's,
-- | not associated with any other meaning
--returns specified adjacent element in grid, relative to given position
{--| returns specified adjacent element in grid, |--
--| relative to given position |--}
nextElem :: [[a]] -> Posn -> Orientation -> Maybe a
nextElem css (x,y) dir | x' < 0 || y' < 0 ||
x' > length css - 1 || y' > length css - 1 = Nothing
| otherwise = Just (elemAt css (x',y'))
nextElem css (x,y) dir | x' < 0 || y' < 0 ||
x' > length css - 1 ||
y' > length css - 1 = Nothing
| otherwise = Just (elemAt css (x',y'))
where
(x',y') = nextPos dir (x,y)
-- Two examples for you to try out, the first of which is in the instructions
exGrid1'1 = ["HAGNIRTSH" , "SACAGETAK", "GCSTACKEL",
"MGHKMILKI", "EKNLETGCN", "TNIRTLETE",
"IRAAHCLSR", "MAMROSAGD", "GIZKDDNRG"]
exWords1'1 = [ "HASKELL","STRING","STACK","MAIN","METHOD"]
exGrid1'2 = ["ROBREUMBR","AURPEPSAN","UNLALMSEE",
"YGAUNPYYP","NLMNBGENA","NBLEALEOR",
"ALRYPBBLG","NREPBEBEP","YGAYAROMR"]
exWords1'2 = [ "BANANA", "ORANGE", "MELON", "RASPBERRY",
"APPLE", "PLUM", "GRAPE" ]
-- Challenge 2 --
------------------------------------------Challenge 2-------------------------------------------------
--internal grid values are either a character or a placeholder for a random letter
{--| internal grid values are either a character
--| or a placeholder for a random letter |--}
data GridVal = Letter Char | Rand deriving Eq
type RandGrid = [[GridVal]]
createWordSearch :: [ String ] -> Double -> IO WordSearchGrid
createWordSearch ss den = do gen <- newStdGen --initial generator
createWordSearch ss den = do gen <- newStdGen -- | initial generator
return (createGrid dim gen ss)
where
charInInput = fromIntegral $ sum $ map length ss :: Double
longestWordLen = fromIntegral $ foldl1 max $ map length ss :: Double
dim = floor $ head [x | x <- [0..], x^2 > (charInInput / den), x >= longestWordLen] --calculates needed dimension of grid according to the density
dim = floor $ head [x | x <- [0..], x^2 > (charInInput / den), x >= longestWordLen] -- | calculates needed dimension of grid according to the density
createGrid :: Int -> StdGen -> [String] -> WordSearchGrid
createGrid dim gen ss = randToWord (charsFromStrs ss) gen' finalGrid
where
tempGrid = replicate dim (replicate dim Rand) --fills grid with random values
(finalGrid,gen') = addStrsToGrid tempGrid gen ss --final grid after all strings added
tempGrid = replicate dim (replicate dim Rand) -- | fills grid with random values
(finalGrid,gen') = addStrsToGrid tempGrid gen ss -- | final grid after all strings added
charsFromStrs = rmdups . concat --list of chars used in given strings
charsFromStrs = rmdups . concat -- | list of chars used in given strings
--removes duplicates from a list
--code from https://stackoverflow.com/a/16109302/10218833
rmdups :: (Ord a) => [a] -> [a]
rmdups = map head . group . sort
----------------------------Primary Functions-----------------------------------
-- --converts RandGrid to WordSearchGrid
-- --replaces placeholder random values with actual random values
-- randToWord :: RandGrid -> [Char] -> StdGen -> WordSearchGrid
-- randToWord rg cs gen =
-- where
-- charStream :: [Char]
-- charStream = map (cs!!) $ randomRs (0,length cs - 1) g
-- replaceRands = map (\Rand -> head charStream)
randToWord :: [Char] -> StdGen -> RandGrid -> WordSearchGrid
randToWord cs gen [] = []
randToWord cs gen (row:rs) = let (newRow,newGen) = rowConvert cs gen row
in newRow : randToWord cs newGen rs
rowConvert :: [Char] -> StdGen -> [GridVal] -> ([Char],StdGen)
rowConvert cs gen [] = ([],gen)
rowConvert cs gen (Letter x:xs) = let (rows,gen') = rowConvert cs gen xs
......@@ -182,7 +161,7 @@ rowConvert cs gen (Rand:xs) = let (rows,gen') = rowConvert cs newGen xs
randChar = cs !! index
--adds list of strings to given grid one by one
{--| adds list of strings to given grid one by one |--}
addStrsToGrid :: RandGrid -> StdGen -> [String] -> (RandGrid,StdGen)
addStrsToGrid rg gen (s:[]) = insertString rg s gen
addStrsToGrid rg gen (s:ss) = addStrsToGrid newGrid newGen ss
......@@ -190,14 +169,22 @@ addStrsToGrid rg gen (s:ss) = addStrsToGrid newGrid newGen ss
(newGrid,newGen) = insertString rg s gen
--takes a grid, string and a position
--returns a list of valid orientations for the string at that position
{--| takes a grid, string and a position |--
--| returns a list of valid orientations for the |--
--| string at that position |--}
validDirs :: RandGrid -> String -> Posn -> [Orientation]
validDirs rg s (x,y) = map fst $ filter ( \(_,b) -> b == True ) (zip dirs (map ( checkDir rg s (x,y) ) dirs) )
validDirs rg s (x,y) = map fst $ filter (\b -> snd b == True) (zipF ( checkDir rg s (x,y) ) dirs)
where dirs = [Forward,Back,Up,Down,UpForward,UpBack,DownForward,DownBack]
--checks whether an orientation for a string at a given position in a grid is valid
{--| applies given func to list and zips result with |--
--| original list |--}
zipF :: (a -> b) -> [a] -> [(a,b)]
zipF f xs = zip xs $ map f xs
{--| checks whether an orientation for a string at a
--| given position in a grid is valid |--}
checkDir :: RandGrid -> String -> Posn -> Orientation -> Bool
checkDir rg s (x,y) dir | let (x',y') = posns !! (length s - 1),
x' < 0 || x' > length rg - 1 ||
......@@ -209,12 +196,12 @@ checkDir rg s (x,y) dir | let (x',y') = posns !! (length s - 1),
lettersGrid = take (length s) $ map (elemAt rg) posns
--adds an individual string to a given grid
--returns new grid and new generator
{--| adds an individual string to a given grid |--
--| returns new grid and new generator |--}
insertString :: RandGrid -> String -> StdGen -> (RandGrid,StdGen)
insertString rg s gen | elemAt rg (x,y) /= Rand &&
elemAt rg (x,y) /= Letter (head s) = insertString rg s newGen --guard:if position is invalid, generate new position
| length vDirs == 0 = insertString rg s newGen --guard:if no valid orientations exist, generate new position
elemAt rg (x,y) /= Letter (head s) = insertString rg s newGen -- | guard:if position is invalid, generate new position
| length vDirs == 0 = insertString rg s newGen -- | guard:if no valid orientations exist, generate new position
| otherwise = (addToGrid randomDir s rg (x,y),newGen)
where
( (x,y),newGen ) = generatePos gen (length rg)
......@@ -228,21 +215,6 @@ insertString rg s gen | elemAt rg (x,y) /= Rand &&
where
charAdded :: RandGrid
charAdded = insertAt2D (Letter c) (x',y') rg
--addToGrid dir = map (\(c,(m,n)) -> insertAt2D (Letter c) (m,n) rg) (zip s (take (length s) $ iterate (nextPos dir) (x,y)))
--inserts element at location in 2d array
insertAt2D :: a -> (Int,Int) -> [[a]] -> [[a]]
insertAt2D newElement (x,y) grid | y == 0 = insertAt newElement x (grid !! y) : drop 1 belowRows
| y == length grid - 1 = aboveRows ++ [insertAt newElement x (grid !! y)]
| otherwise = aboveRows ++ [insertAt newElement x (grid !! y)] ++ drop 1 belowRows
where
(aboveRows,belowRows) = splitAt y grid
--using code from https://stackoverflow.com/a/43291593/10218833
insertAt :: a -> Int -> [a] -> [a]
insertAt newElement 0 as = newElement : drop 1 as
insertAt newElement i (a:as) = a : insertAt newElement (i - 1) as
generatePos :: StdGen -> Int -> (Posn,StdGen)
......@@ -251,84 +223,81 @@ generatePos gen dim = let (x,gen') = randomR (0,dim - 1) gen :: (Int,StdGen)
in ((x,y),gen'')
----------------------------Utility Functions-----------------------------------
--- Convenience functions supplied for testing purposes
createAndSolve :: [ String ] -> Double -> IO [ (String, Maybe Placement) ]
createAndSolve words maxDensity = do g <- createWordSearch words maxDensity
let soln = solveWordSearch words g
printGrid g
return soln
printGrid :: WordSearchGrid -> IO ()
printGrid [] = return ()
printGrid (w:ws) = do putStrLn w
printGrid ws
{--| removes duplicates from a list |--
--| code from https://stackoverflow.com/a/16109302/10218833 |--}
rmdups :: (Ord a) => [a] -> [a]
rmdups = map head . group . sort
-- Challenge 3 --
{--| inserts element at location in 2d array |--}
insertAt2D :: a -> (Int,Int) -> [[a]] -> [[a]]
insertAt2D newElement (x,y) grid | y == 0 = insertAt newElement x (grid !! y) : drop 1 belowRows
| y == length grid - 1 = aboveRows ++ [insertAt newElement x (grid !! y)]
| otherwise = aboveRows ++ [insertAt newElement x (grid !! y)] ++ drop 1 belowRows
where
(aboveRows,belowRows) = splitAt y grid
-- data LamMacroExpr = LamDef [ (String,LamExpr) ] LamExpr deriving (Eq,Show,Read)
-- data LamExpr = LamMacro String | LamApp LamExpr LamExpr |
-- LamAbs Int LamExpr | LamVar Int deriving (Eq,Show,Read)
{--| inserts element at given index of list |--
--| using code from https://stackoverflow.com/a/43291593/10218833 |--}
insertAt :: a -> Int -> [a] -> [a]
insertAt newElement 0 as = newElement : drop 1 as
insertAt newElement i (a:as) = a : insertAt newElement (i - 1) as
prettyPrint :: LamMacroExpr -> String
prettyPrint (LamDef ms e) = exprBrackets e
------------------------------------------Challenge 3-------------------------------------------------
--applies brackets to expr if needed
exprBrackets :: LamExpr -> String
exprBrackets e | foldl1 (||) $ map (e==) parsed = str --omit brackets
| otherwise = "(" ++ str ++ ")" --include brackets
where
str = exprToStr e
parsed = map fst (parse expr str) --possible parsings of str
{--| Repeated for Clarity: |--
--| |--
--| data LamMacroExpr = LamDef [ (String,LamExpr) ] LamExpr deriving (Eq,Show,Read) |--
--| data LamExpr = LamMacro String | LamApp LamExpr LamExpr | |--
--| LamAbs Int LamExpr | LamVar Int deriving (Eq,Show,Read) |--}
prettyPrint :: LamMacroExpr -> String
prettyPrint (LamDef ms e) = macroDef ms ++ exprToStr ms e
--converts expr to string
exprToStr :: LamExpr -> String
exprToStr (LamApp e1 e2) = exprBrackets e1 ++ " " ++ exprBrackets e2
exprToStr (LamAbs x e) = "\\x" ++ show x ++ " -> " ++ exprBrackets e
exprToStr (LamVar x) = "x" ++ show x
exprToStr (LamMacro m) = m
macroDef :: [(String,LamExpr)] -> String
macroDef [] = ""
macroDef ( (name,expr):ms ) = foldl1 (++) ["def ",name," = ",exprToStr [] expr," in ",macroDef ms]
-- examples in the instructions
ex3'1 = LamDef [] (LamApp (LamAbs 1 (LamVar 1)) (LamAbs 1 (LamVar 1))) --"(\x1 -> x1) \x1 -> x1"
ex3'2 = LamDef [] (LamAbs 1 (LamApp (LamVar 1) (LamAbs 1 (LamVar 1)))) --"\x1 -> x1 \x1 -> x1"
ex3'3 = LamDef [ ("F", LamAbs 1 (LamVar 1) ) ] (LamAbs 2 (LamApp (LamVar 2) (LamMacro "F"))) --"def F = \x1-> x1 in \x2 -> x2 F"
ex3'4 = LamDef [ ("F", LamAbs 1 (LamVar 1) ) ] (LamAbs 2 (LamApp (LamAbs 1 (LamVar 1)) (LamVar 2))) --"def F = \x1-> x1 in \x2-> F x2"
{--| replaces a macro with its definition |--}
catchMacro :: [(String,LamExpr)] -> LamExpr -> String
catchMacro ms e | macros == [] = exprToStr ms e
| otherwise = fst $ head macros
where
macros = filter ( (e==) . snd ) ms
-- Challenge 4 --
exprToStr :: [(String,LamExpr)] -> LamExpr -> String
exprToStr ms (LamApp e1@(LamVar _) e2) = catchMacro ms e1 ++ " " ++ catchMacro ms e2
-- data LamMacroExpr = LamDef [ (String,LamExpr) ] LamExpr deriving (Eq,Show,Read)
-- data LamExpr = LamMacro String | LamApp LamExpr LamExpr |
-- LamAbs Int LamExpr | LamVar Int deriving (Eq,Show,Read)
exprToStr ms (LamApp e1 e2) | catchMacro ms e1 == exprToStr ms e1 = foldl1 (++) ["(",exprToStr ms e1,") ",catchMacro ms e2]
| otherwise = catchMacro ms e1 ++ " " ++ catchMacro ms e2
exprToStr ms (LamAbs x e ) = "\\x" ++ show x ++ " -> " ++ catchMacro ms e
exprToStr ms (LamVar x ) = "x" ++ show x
exprToStr ms (LamMacro m ) = m
--MacroExpr ::= "def" MacroName "=" Expr "in" MacroExpr | Expr
--Expr ::= Var | MacroName | Expr Expr | “\” Var “->” Expr | “(“ Expr “)”
--MacroName ::= UChar | UChar MacroName
--UChar ::= "A" | "B" | ... | "Z"
--Var ::= “x” Digits
--Digits ::= Digit | Digit Digits
--Digit ::= “0” | “1” | “2” | “3” | “4” | “5” | “6” | “7” | “8” | “9”
------------------------------------------Challenge 4-------------------------------------------------
--MacroExpr ::= "def" MacroName "=" Expr "in" MacroExpr | Expr
--Expr ::= Var | MacroName | Applicative | Function | Expression
--MacroName ::= UChar | UChar MacroName
--UChar ::= "A" | "B" | ... | "Z"
--Var ::= “x” Digits
--Digits ::= Digit | Digit Digits
--Digit ::= “0” | “1” | “2” | “3” | “4” | “5” | “6” | “7” | “8” | “9”
--Applicative ::= Expr Expr
--Function ::= “\” Var “->” Expr
--Expression ::= “(“ Expr “)”
{--| Corresponding Grammar: |--
--| |--
--| MacroExpr ::= "def" MacroName "=" Expr "in" MacroExpr | Expr |--
--| Expr ::= Var | MacroName | Expr Expr | “\” Var “->” Expr | “(“ Expr “)” |--
--| MacroName ::= UChar | UChar MacroName |--
--| UChar ::= "A" | "B" | ... | "Z" |--
--| Var ::= “x” Digits |--
--| Digits ::= Digit | Digit Digits |--
--| Digit ::= “0” | “1” | “2” | “3” | “4” | “5” | “6” | “7” | “8” | “9” |--}
parseLamMacro :: String -> Maybe LamMacroExpr
......@@ -336,14 +305,13 @@ parseLamMacro str | parsed == [] = Nothing
| otherwise = Just $ fstHead parsed
where
parsed = parse (macroExpr []) str
fstHead = fst . head
macroExpr :: [ (String,LamExpr) ] -> Parser LamMacroExpr
macroExpr ms = do string "def"
name <- token macroName
name <- unique (map fst ms) (token macroName)
symbol "="
e <- token expr
e <- closedParse expr
token $ string "in"
macros <- macroExpr $ ms ++ [(name,e)]
return $ macros
......@@ -352,6 +320,34 @@ macroExpr ms = do string "def"
return $ LamDef ms e
{--| parses an element only if it is unique to a |--
--| given list |--}
unique :: Eq a => [a] -> Parser a -> Parser a
unique xs p = do x <- p
if x `elem` xs then empty else return x
{--| parses an expr if it is closed |--}
closedParse :: Parser LamExpr -> Parser LamExpr
closedParse p = do e <- p
if free e then empty else return e
{--| finds if an expression contains free variables |--
--| |--}
free :: LamExpr -> Bool
free (LamVar _) = True
free (LamAbs x e ) = freeVar x e
free (LamApp e1 e2) = free e1 && free e2
{--| finds if a given variable is free in an expr |--
--| |--}
freeVar :: Int -> LamExpr -> Bool
freeVar x (LamVar y) = not $ x == y
freeVar x (LamAbs y e) | x == y = False
| otherwise = freeVar x e
freeVar x (LamApp e1 e2) = freeVar x e1 || freeVar x e2
expr :: Parser LamExpr
expr = do terms <- some (token term)
return $ foldl1 LamApp terms
......@@ -369,30 +365,9 @@ term = do char '('
e <- expr
return $ LamAbs x e
<|> do {x <- var; return $ LamVar x}
<|> do {name <- macroName;return $ LamMacro name}
-- expr :: Parser LamExpr
-- expr = do e1 <- expr
-- space
-- e2 <- expr
-- return $ LamApp e1 e2
<|> do {x <- var; return $ LamVar x}
-- <|> do {x <- var; return $ LamVar x}
-- <|> do {name <- macroName;return $ LamMacro name}
-- <|> do char '\\'
-- x <- var
-- symbol "->"
-- e <- expr
-- return $ LamAbs x e
-- <|> do char '('
-- e <- token expr
-- char ')'
-- return e
<|> do {name <- macroName; return $ LamMacro name}
macroName :: Parser String
......@@ -406,47 +381,8 @@ var = do char 'x'
return x
-- examples in the instructions
--Just (LamDef [] (LamApp (LamVar 1) (LamApp (LamVar 2) (LamVar 3)))) --"x1 (x2 x3)"
--Just (LamDef [] (LamApp (LamApp (LamVar 1) (LamVar 2)) (LamMacro"F"))) --"x1 x2 F"
--Just (LamDef [ ("F", LamAbs 1 (LamVar 1) ) ] (LamAbs 2 (LamApp (LamVar 2) (LamMacro "F")))) --"def F = \x1-> x1 in \x2 -> x2 F"
--Nothing -not in grammar --"def F = \x1 -> x1 (def G = \x1 -> x1 in x1)in \x2 -> x2"
--Nothing -repeated macro definition --"def F = \x1 -> x1 in def F = \x2 -> x2 x1 in x1"
--Nothing -macro body not closed --"def F = x1 in F"
--arithmetic expression examples
-- expr ::= term '+' expr ⏐ term
-- term ::= factor '*' term ⏐ factor
-- factor ::= nat ⏐ '(' expr ')‘
-- nat ::= digit | digit nat
-- digit ::= ’0’ ⏐ '1' ⏐ ... ⏐ '9'
-- expr :: Parser AETree
-- expr = do t ← term
-- char ‘+’
-- e ← expr
-- return (Add t e)
-- <|> term
-- term :: Parser AETree
-- term = do f ← factor
-- char ‘*’
-- t ← term
-- return (Mul f t)
-- <|> factor
-- factor :: Parser AETree
-- factor = nat <|> do char '('
-- e ← expr
-- char ')'
-- return e
-- nat :: Parser AETree
-- nat = do ds ← some digit
-- return (Lit (read ds))
fstHead :: [(a,b)] -> a
fstHead = fst . head
-- Challenge 5
......
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