From 1166ca9a0fb0a9aae7a22ae56cd65a47e5dd17c7 Mon Sep 17 00:00:00 2001
From: ik1g19 <ik1g19@soton.ac.uk>
Date: Fri, 8 Jan 2021 19:51:09 +0000
Subject: [PATCH] finished challenge 4
---
cw/src/Challenges.hs | 332 +++++++++++++++++--------------------------
1 file changed, 134 insertions(+), 198 deletions(-)
diff --git a/cw/src/Challenges.hs b/cw/src/Challenges.hs
index 295d931..f5ff8e1 100644
--- a/cw/src/Challenges.hs
+++ b/cw/src/Challenges.hs
@@ -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
--
GitLab