module Main where

import Prelude hiding (catch)
import Control.Exception ( AsyncException(..), catch )
import Control.Monad.Error

import Data.Version
import Data.List

import System.IO
import System.Environment
import System.Directory (getHomeDirectory)
import System.FilePath ((</>))
import System.Console.Haskeline hiding (handle, catch, throwTo)
import System.Console.GetOpt
import System.Exit (ExitCode (..), exitWith, exitFailure)

import Language.Egison
import Language.Egison.Util
import qualified Paths_egison_tutorial as P

main :: IO ()
main = do args <- getArgs
          let (actions, nonOpts, _) = getOpt Permute options args
          let opts = foldl (flip id) defaultOptions actions
          case opts of
            Options {optShowSections = True} -> putStrLn $ show tutorial
            Options {optSection = Just sn, optSubSection = Just ssn} -> do
              let sn' = (read sn) :: Int
              let ssn' = (read ssn) :: Int
              let ret = case tutorial of
                          Tutorial ss ->
                            if 0 < sn' && sn' <= length ss
                              then case nth sn' ss of
                                     Section _ cs ->
                                       if 0 < ssn' && ssn' <= length cs
                                         then showContent $ nth ssn' cs
                                         else "error: content out of range"
                              else "error: section out of range"
              putStrLn ret
            Options {optShowHelp = True} -> printHelp
            Options {optShowVersion = True} -> printVersionNumber
            Options {optPrompt = prompt} -> do
                env <- initialEnv
                case nonOpts of
                    [] -> showBanner >> repl env prompt
                    _ -> printHelp

data Options = Options {
    optShowVersion :: Bool,
    optShowHelp :: Bool,
    optPrompt :: String,
    optShowSections :: Bool,
    optSection :: Maybe String,
    optSubSection :: Maybe String
    }

defaultOptions :: Options
defaultOptions = Options {
    optShowVersion = False,
    optShowHelp = False,
    optPrompt = "> ",
    optShowSections = False,
    optSection = Nothing,
    optSubSection = Nothing
    }

options :: [OptDescr (Options -> Options)]
options = [
  Option ['v', 'V'] ["version"]
    (NoArg (\opts -> opts {optShowVersion = True}))
    "show version number",
  Option ['h', '?'] ["help"]
    (NoArg (\opts -> opts {optShowHelp = True}))
    "show usage information",
  Option ['p'] ["prompt"]
    (ReqArg (\prompt opts -> opts {optPrompt = prompt})
            "String")
    "set prompt string",
  Option ['l'] ["list"]
    (NoArg (\opts -> opts {optShowSections = True}))
    "show section list",
  Option ['s'] ["section"]
    (ReqArg (\sn opts -> opts {optSection = Just sn})
            "String")
    "set section number",
  Option ['c'] ["subsection"]
    (ReqArg (\ssn opts -> opts {optSubSection = Just ssn})
            "String")
    "set subsection number"
  ]

printHelp :: IO ()
printHelp = do
  putStrLn "Usage: egison-tutorial [options]"
  putStrLn ""
  putStrLn "Options:"
  putStrLn "  --help                Display this information"
  putStrLn "  --version             Display egison version information"
  putStrLn "  --prompt string       Set prompt of the interpreter"
  putStrLn ""
  exitWith ExitSuccess

printVersionNumber :: IO ()
printVersionNumber = do
  putStrLn $ showVersion P.version
  exitWith ExitSuccess

showBanner :: IO ()
showBanner = do
  putStrLn $ "Egison Tutorial Version " ++ showVersion P.version ++ " (C) 2013-2017 Satoshi Egi"
  putStrLn $ "Welcome to Egison Tutorial!"
  putStrLn $ "** Information **"
  putStrLn $ "We can use a \"Tab\" key to complete keywords on the interpreter."
  putStrLn $ "If we type a \"Tab\" key after a closed parenthesis, the next closed parenthesis will be completed."
  putStrLn $ "*****************"

showFinishMessage :: IO ()
showFinishMessage = do
  putStrLn $ "You have finished this section."
  putStrLn $ "Thank you!"

showByebyeMessage :: IO ()
showByebyeMessage = do
  putStrLn $ "Leaving Egison Tutorial.\nByebye."

yesOrNo :: String -> IO Bool
yesOrNo question = do
  input <- liftIO $ runInputT (Settings noCompletion Nothing False) $ getInputLine $ question ++ " (Y/n): "
  case input of
   Nothing -> return True
   (Just "") -> return True
   (Just "y") -> return True
   (Just "Y") -> return True
   (Just "n") -> return False
   (Just "N") -> return False
   _ -> yesOrNo question

nth n = head . drop (n - 1)

selectSection :: Tutorial -> IO Section
selectSection tutorial@(Tutorial sections) = do
  putStrLn $ take 30 $ repeat '='
  putStrLn $ "List of sections in the tutorial."
  putStrLn $ show tutorial
  putStrLn $ take 30 $ repeat '='
  putStrLn $ "Choose a section to learn."
  n <- getNumber (length sections)
  return $ nth n sections

getNumber :: Int -> IO Int
getNumber n = do
  input <- liftIO $ runInputT (Settings noCompletion Nothing False) $ getInputLine $ "(1-" ++ show n  ++ "): "
  case input of
    (Just "1") -> return 1
    (Just "2") -> return 2
    (Just "3") -> return 3
    (Just "4") -> return 4
    (Just "5") -> return 5
    (Just "6") -> return 6
    (Just "7") -> return 7
    _ -> do
      putStrLn "Invalid input!"
      getNumber n

repl :: Env -> String -> IO ()
repl env prompt = do
  section <- selectSection tutorial
  case section of
    Section _ cs -> loop env cs True
 where
  settings :: MonadIO m => FilePath -> Settings m
  settings home = setComplete completeEgison $ defaultSettings { historyFile = Just (home </> ".egison_history") }

  loop :: Env -> [Content] -> Bool -> IO ()
  loop env [] _ = do
--    liftIO $ showFinishMessage
    liftIO $ repl env prompt
  loop env (content:contents) b = (do
    if b
      then liftIO $ putStrLn $ show content
      else return ()
    home <- getHomeDirectory
    input <- liftIO $ runInputT (settings home) $ getEgisonExprOrNewLine prompt
    case input of
      Left Nothing -> do
        b <- yesOrNo "Do you want to quit?"
        if b
          then return ()
          else do
            b <- yesOrNo "Do you want to procced next?"
            if b
              then loop env contents True
              else loop env (content:contents) False
      Left (Just "") -> do
        b <- yesOrNo "Do you want to procced next?"
        if b
          then loop env contents True
          else loop env (content:contents) False
      Right (topExpr, _) -> do
        result <- liftIO $ runEgisonTopExpr True env topExpr
        case result of
          Left err -> do
            liftIO $ putStrLn $ show err
            loop env (content:contents) False
          Right env' -> loop env' (content:contents) False)
    `catch`
    (\e -> case e of
             UserInterrupt -> putStrLn "" >> loop env (content:contents) False
             StackOverflow -> putStrLn "Stack over flow!" >> loop env (content:contents) False
             HeapOverflow -> putStrLn "Heap over flow!" >> loop env (content:contents) False
             _ -> putStrLn "error!" >> loop env (content:contents) False
     )

data Tutorial = Tutorial [Section]

-- |title and contents
data Section = Section String [Content]

-- |explanation, examples, and exercises
data Content = Content String [String] [String]

instance Show Tutorial where
  show = showTutorial

instance Show Section where
  show = showSection

instance Show Content where
  show = showContent

showTutorial :: Tutorial -> String
showTutorial (Tutorial sections) =
  let n = length sections in
  intercalate "\n" $ map (\(n, section) -> show n ++ ": " ++ show section) $ zip [1..n] sections

showSection :: Section -> String
showSection (Section title _) = title

showContent :: Content -> String
showContent (Content msg examples exercises) =
  "====================\n" ++
  msg ++ "\n" ++
  (case examples of
     [] -> ""
     _ -> "\nExamples:\n" ++ (intercalate "\n" (map (\example -> "  " ++ example) examples)) ++ "\n") ++
  (case exercises of
     [] -> ""
     _ -> "\nExercises:\n" ++ (intercalate "\n" (map (\exercise -> "  " ++ exercise) exercises)) ++ "\n") ++
  "===================="

tutorial :: Tutorial
tutorial = Tutorial
 [Section "Arithmetic"
   [
    Content "We can do arithmetic operations with \"+\", \"-\", \"*\", \"/\", \"modulo\" and \"power\"."
     ["(+ 1 2)", "(- 30 15)", "(* 10 20)", "(/ 20 5)", "(modulo 17 4)", "(power 2 10)"]
     [],
    Content "We can write nested expressions."
     ["(+ (* 10 20) 2)", "(/ (* 10 20) (+ 10 20))"]
     ["Try to calculate \"(100 - 1) * (100 + 1)\"."],
    Content "We are supporting rational numbers."
     ["(+ (/ 2 3) (/ 1 5))", "(/ 42 84)"]
     [],
    Content "We are supporting floats, too."
     ["(f.+ 10.2 1.3)", "(f.* 10.2 1.3)"]
     [],
    Content "We can convert a rational number to a float number with \"rtof\"."
     ["(rtof (/ 1 5))", "(rtof (/ 1 100))"]
     [],
    Content "We can handle collections of numbers.\nWe construct collections with \"{}\"."
     ["{}", "{10}", "{1 2 3 4 5}"]
     [],
    Content "We can decompose a collection using the \"car\" and \"cdr\" function."
     ["(car {1 2 3 4 5})", "(cdr {1 2 3 4 5})", "(car (cdr {1 2 3 4 5}))"]
     ["Try to extract the third element of the collection \"{1 2 3 4 5}\" with \"car\" and \"cdr\"."],
    Content "With the \"take\" function, we can extract a head part of a collection."
     ["(take 0 {1 2 3 4 5})", "(take 3 {1 2 3 4 5})"]
     [],
    Content "We can handle infinite lists.\nFor example, \"nats\" and \"primes\" are an infinite list that contains all natural numbers and prime numbers respectively.\nTry to extract a head part from them."
     ["(take 10 nats)", "(take 30 nats)", "(take 10 primes)", "(take 30 primes)"]
     ["What is the 100th prime number."],
    Content "We can create a partially applied function using \"$\" as an argument."
     ["((* $ 2) 10)", "((modulo $ 3) 10)"]
     [],
    Content "With the \"map\" function, we can operate each element of the collection at once."
     ["(take 100 (map (* $ 2) nats))", "(take 100 (map (modulo $ 3) nats))"]
     [],
    Content "With the \"foldl\" function, we can gather together all elements of the collection using an operator you like."
     ["(foldl + 0 {1 2 3 4 5})", "(foldl * 1 {1 2 3 4 5})"]
     ["Try to get the sum of from 1 to 100."],
    Content "Try to create a sequence of numbers \"{1 1/2 1/3 1/4 ... 1/100}\"."
     []
     [],
    Content "Try to calculate \"1 + 1/2 + 1/3 + 1/4 + ... + 1/100\".\nRemember that we can convert a rational number to a float number with \"rtof\"."
     ["(rtof (/ 2 3))"]
     [],
    Content "Try to calculate \"1 + (1/2)^2 + (1/3)^2 + (1/4)^2 + ... + (1/100)^2\".\nIn fact, \"1 + (1/2)^2 + (1/3)^2 + (1/4)^2 + ...\" converges to \"(f./ (f.* f.pi f.pi) 6.0)\"."
     []
     [],
    Content "This is the end of this section.\nPlease play freely or proceed to the next section.\nThank you for enjoying our tutorial!"
     []
     []
    ],
  Section "Basics of functional programming"
   [
    Content "We can bind a value to a variable with a \"define\" expression.\nWe can easily get the value we bound to a variable."
     ["(define $x 10)", "x", "(define $y (+ 1 x))", "y"]
     [],
    Content "We support recursive definitions. It enables us to define an collection with infinite elements.\nNote that \"@\" expands the collection placed after \"@\" as a subcollection of the outer collection."
     ["(define $ones {1 @ones})", "(take 100 ones)", "(define $nats {1 @(map (+ $ 1) nats)})", "(take 100 nats)", "(define $odds {1 @(map (+ $ 2) odds)})", "(take 100 odds)"]
     ["Try to define the infinite list of even numbers that is like {2 4 6 8 10 ...}."],
    Content "We can create a function with a \"lambda\" expression. Let's define functions and test them."
     ["(define $increment (lambda [$x] (+ x 1)))", "(increment 10)", "(define $multiply (lambda [$x $y] (* x y)))", "(multiply 10 20)", "(define $sum (lambda [$n] (foldl + 0 (take n nats))))", "(sum 10)"]
     ["Try to define a \"fact\" function, which obtains an natural number \"n\" and returns \"n * (n - 1) * ... * 2 * 1\"."],
    Content "We can compare numbers using functions that return \"#t\" or \"#f\".\n\"#t\" means the true.\n\"#f\" means the false.\nFunctions that return \"#t\" or \"#f\" are called \"predicates\"."
     ["(eq? 1 1)", "(gt? 1 1)", "(lt? 1 1)",  "(gte? 1 1)", "(lte? 1 1)"]
     [],
    Content "With the \"take-while\" function, we can extract all head elements that satisfy the predicate.\n\"primes\" is a infinite list that contains all prime numbers."
     ["(take-while (lt? $ 100) primes)", "(take-while (lt? $ 1000) primes)"]
     [],
    Content "With the \"filter\" function, we can extract all elements that satisfy the predicate."
     ["(take 100 (filter even? nats))", "(take 100 (filter prime? nats))", "(take 100 (filter (lambda [$p] (eq? (modulo p 4) 1)) primes))"]
     ["Try to enumerate the first 100 primes that are congruent to 3 modulo 4."],
    Content "We combine numbers using \"[]\".\nThese things are called \"tuples\"."
     ["[1 2]", "[1 2 3]"]
     [],
    Content "Note that a tuple that consists of only one element is equal with that element itself."
     ["[1]", "[[[1]]]"]
     [],
    Content "With the \"zip\" function, we can combine two lists as follows."
     ["(take 100 (zip nats nats))", "(take 100 (zip primes primes))"]
     ["Try to generate the prime table as \"{[1 2] [2 3] [3 5] [4 7] [5 11] ...}\""],
    Content "Try to create a Fibonacci sequence \"{1 1 2 3 5 8 13 21 34 55 ...}\".\n\nHint:\n  Replace \"???\" in the following expression to a proper function.\n  (define $fibs {1 1 @(map ??? (zip fibs (cdr fibs)))})"
     []
     [],
    Content "This is the end of this section.\nPlease play freely or proceed to the next section.\nThank you for enjoying our tutorial!"
     []
     []
    ],
  Section "Basics of pattern matching"
   [
    Content "Let's try pattern-matching against a collection.\nThe \"join\" pattern divides a collection into two collections.\nPlease note that the \"match-all\" expression enumerates all results of pattern matching."
     ["(match-all {1 2 3}     (list integer) [<join $hs $ts> [hs ts]])",
      "(match-all {1 2 3 4 5} (list integer) [<join $hs $ts> [hs ts]])"]
     [],
    Content "Try another pattern constructor \"cons\".\nThe \"cons\" pattern divides a collection into the head element and the rest collection.\n"
     ["(match-all {1 2 3}     (list integer) [<cons $x $xs> [x xs]])",
      "(match-all {1 2 3 4 5} (list integer) [<cons $x $xs> [x xs]])"]
     [],
    Content "\"_\" is a wildcard and matches with any objects."
     ["(match-all {1 2 3}     (list integer) [<cons $x  _>  x])",
      "(match-all {1 2 3 4 5} (list integer) [<join $hs _> hs])"]
     [],
    Content "We can write non-linear patterns.\nA non-linear pattern is a pattern that allows multiple occurrences of the same variables in a pattern.\nA pattern that begins with \",\" matches the object when it is equal with the expression after \",\"."
     ["(match-all {1 1 2 3 3 2} (list integer) [<join _ <cons $x <cons ,x _>>> x])",
      "(match-all {1 1 2 3 3 2} (list integer) [<join _ <cons $x <cons ,(+ x 1) _>>> x])"]
     [],
    Content "Egison can handle pattern matching with infinite search space.\nFor example, we can enumerate twin primes using pattern matching as follows."
     ["(take 10 (match-all primes (list integer) [<join _ <cons $p <cons ,(+ p 2) _>>> [p (+ p 2)]]))"]
     ["What is the 100th twin prime?"],
    Content "Try to enumerate the first 10 prime pairs whose form is (p, p+6) like \"{{[5 11] [7 13] [11 17] [13 19] [17 23] ...}\"."
     []
     [],
    Content "A pattern that has \"!\" ahead of which is called a not-pattern.\nA not-pattern matches when the target does not match against the pattern."
     ["(match-all {1 1 2 2 3 4 4 5} (list integer) [<join _ <cons $x <cons  ,x _>>> x])",
      "(match-all {1 1 2 2 3 4 4 5} (list integer) [<join _ <cons $x <cons !,x _>>> x])"]
     [],
    Content "A pattern whose form is \"(& p1 p2 ...)\" is called an and-pattern.\nAn and-pattern is a pattern that matches the object, if and only if all the patterns are matched.\nThe and-pattern is used like an as-pattern in the following sample."
     ["(match-all {1 2 4 5 6 8 9} (list integer) [<join _ <cons $x <cons (& !,(+ x 1) $y) _>>> [x y]])"]
     [],
    Content "A pattern whose form is \"(| p1 p2 ...)\" is called an or-pattern.\nAn or-pattern matches with the object, if the object matches one of the given patterns.\nIn the following sample, we enumerate prime triplets using it."
     ["(take 10 (match-all primes (list integer) [<join _ <cons $p <cons (& $m (| ,(+ p 2) ,(+ p 4))) <cons ,(+ p 6) _>>>> [p m (+ p 6)]]))"]
     ["What is the 20th prime triplet?"],
    Content "Try to enumerate the first 8 prime quadruples whose form is (p, p+2, p+6, p+8) like \"{{[5 7 11 13] [11 13 17 19] ...}\"."
     []
     [],
    Content "This is the end of this section.\nPlease play freely or proceed to the next section.\nThank you for enjoying our tutorial!"
     []
     []
    ],
  Section "Pattern matching against various data types"
   [
    Content "We can pattern-match also against multisets and sets.\nWe can change the interpretation of patterns by changing a matcher (the second argument of the match-all expression).The meaning of the cons pattern is generalized to divide a collection into \"an\" element and the rest."
     ["(match-all {1 2 3} (list integer)     [<cons $x $xs> [x xs]])",
      "(match-all {1 2 3} (multiset integer) [<cons $x $xs> [x xs]])",
      "(match-all {1 2 3} (set integer)      [<cons $x $xs> [x xs]])"]
     [],
    Content "Try another pattern constructor \"join\".\nThe \"join\" pattern divides a collection into two collections."
     ["(match-all {1 2 3 4 5} (list integer)     [<join $xs $ys> [xs ys]])",
      "(match-all {1 2 3 4 5} (multiset integer) [<join $xs $ys> [xs ys]])",
      "(match-all {1 2 3 4 5} (set integer)      [<join $xs $ys> [xs ys]])"]
     [],
    Content "Try non-linear pattern matching against multiset."
     ["(match-all {1 1 2 3 2} (multiset integer) [<cons $x <cons ,x       _>> x])",
      "(match-all {1 1 2 3 2} (multiset integer) [<cons $x <cons ,(+ x 2) _>> x])",
      "(match-all {1 2 1 3 2} (multiset integer) [<cons $x !<cons ,x _>> x])"]
     [],
    Content "Pattern matching of Egison efficiently backtracks for non-linear patterns.\nFor example, all the following pattern-matching expressions are processed in O(n^2)."
     ["(match-all (between 1 100) (multiset integer) [<cons $x <cons ,x _>> x])",
      "(match-all (between 1 100) (multiset integer) [<cons $x <cons ,x <cons ,x _>>> x])",
      "(match-all (between 1 100) (multiset integer) [<cons $x <cons ,x <cons ,x <cons ,x _>>>> x])"]
     [],
    Content "The following samples enumerate pairs and triplets of natural numbers.\nNote that Egison really enumerates all the results."
     ["(take 10 (match-all nats (set integer) [<cons $x <cons $y _>>           [x y]]))",
      "(take 10 (match-all nats (set integer) [<cons $x <cons $y <cons $z _>>> [x y z]]))"]
     [],
    Content "This is the end of this section.\nPlease play freely or proceed to the next section.\nThank you for enjoying our tutorial!"
     []
     []
    ],
  Section "Symbolic computation"
   [
    Content "Egison treats unbound variables as a symbol."
     ["(+ x 1)",
      "(+ x x)",
      "(+ (* 2 x) y)"]
     [],
    Content "Egison automatically expands an expression to the canonical form."
     ["(* (+ x y) (+ x y))",
      "(** (+ x y) 2)",
      "(** (+ x y) 3)"]
     [],
    Content "Egison can handle complex numbers.\n\"i\" represents the imaginary unit."
     ["(* i i)",
      "(** (+ 1 i) 2)",
      "(** (+ 1 i) 4)"]
     [],
    Content "Egison can handle algebraic numbers such as \"(sqrt 2)\" and \"(sqrt 3)\"."
     ["(sqrt 12)",
      "(* (sqrt 2) (sqrt 2))",
      "(* (sqrt 2) (sqrt 3))",
      "(** (rt 3 2) 3)"]
     [],
    Content "Egison can handle the trigonometric functions such as \"(cos θ)\" and \"(sin θ)\"."
     ["(+ (cos θ)^2 (sin θ)^2)"]
     [],
    Content "Here are several samples for symbolic computation in Egison.\nPlease visit the link!\nhttps://www.egison.org/math/"
     [
      ]
     [],
    Content "This is the end of this section.\nPlease play freely or proceed to the next section.\nThank you for enjoying our tutorial!"
     []
     []
    ],
  Section "Differential geometry: tensor analysis"
   [
    Content "We can handle vectors.\nWe construct vectors with \"[| |]\"."
     ["[| 1 2 3 |]",
      "(+ [| 1 2 3 |] [| 1 2 3 |])"
      ]
     [],
    Content "We can append an index to a vector."
     ["(+ [| 1 2 3 |]_i [| 1 2 3 |]_i)",
      "(+ [| 1 2 3 |]_i [| 1 2 3 |]_j)"
      ]
     [],
    Content "The \".\" function is a function for multiplying tensors."
     ["(. [| 1 2 3 |]_i [| 1 2 3 |]_i)",
      "(. [| 1 2 3 |]_i [| 1 2 3 |]_j)"
      ]
     [],
    Content "We can handle both of superscripts (~) and subscripts(_).\nThe \".\" function supports Einstein summation notation."
     ["(. [| 1 2 3 |]~i [| 1 2 3 |]_i)"
      ]
     [],
    Content "Matrix is represented as a vector of vectors."
     ["[| [| 1 2 |] [| 10 20 30 |] |]"
      ]
     [],
    Content "Matrix multiplication is represented as follows using tensor index notation."
     ["(. [| [| a b |] [| c d |] |]~i_j [| [| x y |] [| z w |] |]~j_k)"
      ]
     [],
    Content "The function defined using scalar parameters (prepended by \"$\") are automatically mapped to each component of tensors."
     ["(define $min (lambda [$x $y] (if (lt? x y) x y)))",
      "(min [| 1 2 3 |]_i [| 10 20 30 |]_i)",
      "(min [| 1 2 3 |]_i [| 10 20 30 |]_j)"
      ]
     [],
    Content "The function defined using tensor parameters (prepended by \"%\") treats a tensor as a whole."
     ["(define $det2 (lambda [%X] (- (* X_1_1 X_2_2) (* X_1_2 X_2_1))))",
      "(det2 [| [| 2 1 |] [| 1 2 |] |])",
      "(det2 [| [| a b |] [| c d |] |])"
      ]
     [],
    Content "Here are several samples of tensor analysis in programming.\nPlease visit the link!\nhttps://www.egison.org/math/"
     [
      ]
     [],
    Content "This is the end of this section.\nPlease play freely or proceed to the next section.\nThank you for enjoying our tutorial!"
     []
     []
    ],
  Section "Differential geometry: differential forms"
   [
    Content "By default, the same indices are completed to each tensor of the arguments."
     ["(+ [| 1 2 3 |] [| 1 2 3 |]) ;=> (+ [| 1 2 3 |]_t1 [| 1 2 3 |]_t1)"
      ]
     [],
    Content "When “!” is prepended to the function application, the different indices are completed to each tensor of the arguments."
     ["!(+ [| 1 2 3 |] [| 1 2 3 |]) ;=> (+ [| 1 2 3 |]_t1 [| 1 2 3 |]_t2)"
      ]
     [],
    Content "1-forms on Euclid space and Wedge product are represented as follows.\n\"!\" is effectively used in the definition of Wedge product."
     ["(define $dx [| 1 0 0 |])",
      "(define $dy [| 0 1 0 |])",
      "(define $dz [| 0 0 1 |])",
      "(define $wedge (lambda [%A %B] !(. A B)))",
      "(wedge dx dy)"
      ]
     [],
    Content "The \"df-normalize\" function converts a differential form to the antisymmetric tensor."
     ["(wedge dx dy)",
      "(df-normalize (wedge dx dy))"
      ]
     [],
    Content "Exterior derivative is defined as follows.\n\"!\" is effectively used in the definition of exterior derivative."
     ["(define $params [| x y z |])",
      "(define $d (lambda [%A] !((flip ∂/∂) params A)))",
      "(d (f x y z))",
      "(d (d (f x y z)))",
      "(df-normalize (d (d (f x y z))))"
      ]
     [],
    Content "Here are several samples for representing differential forms in programming.\nPlease visit the link!\nhttps://www.egison.org/math/"
     [
      ]
     [],
    Content "This is the end of our tutorial.\nThank you for enjoying our tutorial!\nPlease check our paper, manual and code for further reference!"
     []
     []
    ]

  ]
--  Section "Define your own functions"
--   [
--    Content "Did we think how about \"n\" combinations of the elements of the collection?\nWe already have a solution.\nWe can write a pattern that include \"...\" as the following demonstrations."
--     ["(match-all {1 2 3 4 5} (list integer) [(loop $i [1 3] <join _ <cons $a_i ...>> _) a])", "(match-all {1 2 3 4 5} (list integer) [(loop $i [1 4] <join _ <cons $a_i ...>> _) a])"]
--     [],
--    Content "Let's try \"if\" expressions."
--     ["(if #t 1 2)", "(if #f 1 2)", "(let {[$x 10]} (if (eq? x 10) 1 2))"]
--     [],
--    Content "Using \"define\" and \"if\", we can write recursive functions as follows."
--     ["(define $your-take (lambda [$n $xs] (if (eq? n 0) {} {(car xs) @(your-take (- n 1) (cdr xs))})))", "(your-take 10 nats)"]
--     ["Try to write a \"your-while\" function."],
--    Content "Try to write a \"your-map\" function.\nWe may need \"empty?\" function inside \"your-map\" function."
--     ["(empty? {})", "(empty? {1 2 3})"]
--     []
--  Section "Writing scripts in Egison"
--   [
--    Content "Let's write a famous Hello world program in Egison.\nTry the following expression.\nIt is evaluated to the \"io-function\".\nTo execute an io-function, we use \"io\" primitive as follows."
--     ["(io (print \"Hello, world!\"))"]
--     [],
--    Content "We can execute multiple io-functions in sequence as follows.\nThe io-functions is executed from the head."
--     ["(io (do {[(print \"a\")] [(print \"b\")] [(print \"c\")]} []))", "(io (do {[(write-string \"Type your name: \")] [(flush)] [$name (read-line)] [(print {@\"Hello, \" @name @\"!\"})]} []))"]
--     [],
--    Content "The following is a hello world program in Egison.\nTry to create a file with the following content and save it as \"hello.egi\", and execute it in the terminal as \"% egison hello.egi\"\n"
--     ["(define $main (lambda [$args] (print \"Hello, world!\")))"]
--     [],
--    Content "That's all. Thank you for finishing our tutorail! Did you enjoy it?\nIf you got into Egison programming. I'd like you to try Rosseta Code.\nThere are a lot of interesting problems.\n\n  http://rosettacode.org/wiki/Category:Egison"
--     []
--     []
--    ]
--  ]