# Preliminaries

Before starting this part of the assignment:

1. Install `parsec3` via the command `cabal install parsec3`
2. Learn to read the documentation
3. Download the test files test.imp, fact.imp, abs.imp, times.imp.

# Submission Instructions

To complete this homework, download this file as plain text and answer each question, filling in code where noted (where it says “TBD”). Your code must typecheck against the given type signatures. Feel free to add your own tests to this file to exercise the functions you write. Submit your homework by sending this file, filled in appropriately, to `cse230@goto.ucsd.edu` with the subject “HW3”; you will receive a confirmation email after submitting. Please note that this address is unmonitored; if you have any questions about the assignment, email Pat at `prondon@cs.ucsd.edu`.

``> {-# LANGUAGE TypeSynonymInstances #-}> module Hw3 where> import Fal hiding (between, pball, walls, paddle)> import Animation (picToGraphic)> import qualified SOE as G> import Picture> import Data.Map> import Control.Monad.State hiding (when)> import Text.Parsec hiding (State, between)> import Text.Parsec.Combinator hiding (between)> import Text.Parsec.Char> import Text.Parsec.String``

# Problem 1 : Pong

For the first problem, extend the paddleball game we saw in class to a two player Pong.

Both players start with `0` points, and whenever a player misses the ball, the other player gets a point. When the game begins, and after each player wins a point, the score is shown and the game must continue after a key is pressed. The game must continue till a player reaches

``> maxscore = 5``

at which point she is declared the winner. The top level game is issued by the function

``> playPong = reactimate "pong" \$ pong 0 0 2.0``

which renders the behavior

``> pong ::  Integer -> Integer -> Float -> Behavior G.Graphic> pong p1score p2score vel =>   if p1score == maxscore then>     lift0 \$ G.text (0, 0) "Player 1 wins!">   else if p2score == maxscore then>     lift0 \$ G.text (0, 0) "Player 2 wins!">   else>     lift0 (G.text (0, 0) \$ show p1score ++ " vs. " ++ show p2score)>     `untilB` key ->> play p1score p2score vel``

Your task is to fill in the implementation of following function

``> play ::  Integer -> Integer -> Float -> Behavior G.Graphic> play p1score p2score vel = error "TBD"``

Use the same conditions as in `paddleball` to determine when the ball has hit the paddle. The ball can be said to have missed player 1’s paddle (ie player 2 scores a point) when the ball’s y-coordinate

``ypos <* -2.5``

dually, player 1 scores a point when

``ypos >* 2.5``

You may use the following behaviors to render the wall,

``> walls = left `over` right>   where left  = paint blue \$ translate (-2.2,0) (rec 0.05 3.4)>         right = paint blue \$ translate ( 2.2,0) (rec 0.05 3.4)``

the paddles for each player,

``> paddle1 ::  Behavior Picture> paddle1 = paddle (-1.7) red p1input> > paddle2 ::  Behavior Picture> paddle2 = paddle 1.7 green p2input> > paddle :: Behavior Float-> Behavior Color-> Behavior Float-> Behavior Picture> paddle y color pos = paint color \$ translate (pos, y) (rec 0.5 0.05)``

The positions of the paddles of each player are given by the following behaviors

``> p1input ::  Behavior Float> p1input = keyboardPos> p2input ::  Behavior Float> p2input = fst mouse``

which are generated thus (you can ignore this if you are not curious…)

``> keyUpE k = Event (\(uas,_) -> Prelude.map getkey uas)>   where getkey (Just (G.Key k' False)) | k' == k = Just ()>         getkey _                               = Nothing>         > kbSpeed = 2.5> > keyboardVel = lift0 0 `switch` key =>> \k ->>   case k of>     'a' -> lift0 (-kbSpeed) `untilB` (keyUpE 'a') ->> lift0 0>     'd' -> lift0 kbSpeed `untilB` (keyUpE 'd') ->> lift0 0>     _   -> lift0 0> > keyboardPos = integral keyboardVel``

# Problem 2: An Interpreter for WHILE

Next, you will use monads to build an evaluator for a simple WHILE language. In this language, we will represent different program variables as

``> type Variable = String``

Programs in the language are simply values of the type

``> data Statement =>     Assign Variable Expression          -- x = e>   | If Expression Statement Statement   -- if (e) {s1} else {s2}>   | While Expression Statement          -- while (e) {s}>   | Sequence Statement Statement        -- s1; s2>   | Skip                                -- no-op>   deriving (Show)``

where expressions are variables, constants or binary operators applied to sub-expressions

``> data Expression =>     Var Variable                        -- x>   | Val Value                           -- v >   | Op  Bop Expression Expression>   deriving (Show)``

and binary operators are simply two-ary functions

``> data Bop = >     Plus     -- +  :: Int  -> Int  -> Int>   | Minus    -- -  :: Int  -> Int  -> Int>   | Times    -- *  :: Int  -> Int  -> Int>   | Divide   -- /  :: Int  -> Int  -> Int>   | Gt       -- >  :: Int -> Int -> Bool >   | Ge       -- >= :: Int -> Int -> Bool>   | Lt       -- <  :: Int -> Int -> Bool>   | Le       -- <= :: Int -> Int -> Bool>   deriving (Show)``
``> data Value =>     IntVal Int>   | BoolVal Bool>   deriving (Show)``

We will represent the store i.e. the machine’s memory, as an associative map from `Variable` to `Value`

``> type Store = Map Variable Value``

Note: we don’t have exceptions (yet), so if a variable is not found (eg because it is not initialized) simply return the value `0`. In future assignments, we will add this as a case where exceptions are thrown (the other case being type errors.)

We will use the standard library’s `State` monad to represent the world-transformer. Intuitively, `State s a` is equivalent to the world-transformer `s -> (a, s)`. See the above documentation for more details. You can ignore the bits about `StateT` for now.

## Expression Evaluator

First, write a function

``> evalE :: Expression -> State Store Value``

that takes as input an expression and returns a world-transformer that returns a value. Yes, right now, the transformer doesnt really transform the world, but we will use the monad nevertheless as later, the world may change, when we add exceptions and such.

Hint: The value `get` is of type `State Store Store`. Thus, to extract the value of the “current store” in a variable `s` use `s <- get`.

``> evalE (Var x)      = error "TBD"> evalE (Val v)      = error "TBD" > evalE (Op o e1 e2) = error "TBD"``

## Statement Evaluator

Next, write a function

``> evalS :: Statement -> State Store ()``

that takes as input a statement and returns a world-transformer that returns a unit. Here, the world-transformer should in fact update the input store appropriately with the assignments executed in the course of evaluating the `Statement`.

Hint: The value `put` is of type `Store -> State Store ()`. Thus, to “update” the value of the store with the new store `s'` do `put s`.

``> evalS w@(While e s)    = error "TBD" > evalS Skip             = error "TBD"> evalS (Sequence s1 s2) = error "TBD"> evalS (Assign x e )    = error "TBD"> evalS (If e s1 s2)     = error "TBD" ``

In the `If` case, if `e` evaluates to a non-boolean value, just skip both the branches. (We will convert it into a type error in the next homework.) Finally, write a function

``> execS :: Statement -> Store -> Store> execS = error "TBD"``

such that `execS stmt store` returns the new `Store` that results from evaluating the command `stmt` from the world `store`. Hint: You may want to use the library function

``execState :: State s a -> s -> s``

When you are done with the above, the following function will “run” a statement starting with the `empty` store (where no variable is initialized). Running the program should print the value of all variables at the end of execution.

``> run :: Statement -> IO ()> run stmt = do putStrLn "Output Store:" >               putStrLn \$ show \$ execS stmt empty``

Here are a few “tests” that you can use to check your implementation.

``> w_test = (Sequence (Assign "X" (Op Plus (Op Minus (Op Plus (Val (IntVal 1)) (Val (IntVal 2))) (Val (IntVal 3))) (Op Plus (Val (IntVal 1)) (Val (IntVal 3))))) (Sequence (Assign "Y" (Val (IntVal 0))) (While (Op Gt (Var "X") (Val (IntVal 0))) (Sequence (Assign "Y" (Op Plus (Var "Y") (Var "X"))) (Assign "X" (Op Minus (Var "X") (Val (IntVal 1))))))))``
``> w_fact = (Sequence (Assign "N" (Val (IntVal 2))) (Sequence (Assign "F" (Val (IntVal 1))) (While (Op Gt (Var "N") (Val (IntVal 0))) (Sequence (Assign "X" (Var "N")) (Sequence (Assign "Z" (Var "F")) (Sequence (While (Op Gt (Var "X") (Val (IntVal 1))) (Sequence (Assign "F" (Op Plus (Var "Z") (Var "F"))) (Assign "X" (Op Minus (Var "X") (Val (IntVal 1)))))) (Assign "N" (Op Minus (Var "N") (Val (IntVal 1))))))))))``

As you can see, it is rather tedious to write the above tests! They correspond to the code in the files `test.imp` and `fact.imp`. When you are done, you should get

``ghci> run w_testOutput Store:fromList [("X",IntVal 0),("Y",IntVal 10)]ghci> run w_factOutput Store:fromList [("F",IntVal 2),("N",IntVal 0),("X",IntVal 1),("Z",IntVal 2)]``

# Problem 3: A Parser for WHILE

It is rather tedious to have to specify individual programs as Haskell values. For this problem, you will use parser combinators to build a parser for the WHILE language from the previous problem.

## Parsing Constants

First, we will write parsers for the `Value` type

``> valueP :: Parser Value> valueP = intP <|> boolP``

To do so, fill in the implementations of

``> intP :: Parser Value> intP = error "TBD" ``

Next, define a parser that will accept a particular string `s` as a given value `x`

``> constP :: String -> a -> Parser a> constP s x = error "TBD"``

and use the above to define a parser for boolean values where `"true"` and `"false"` should be parsed appropriately.

``> boolP :: Parser Value> boolP = error "TBD"``

Continue to use the above to parse the binary operators

``> opP :: Parser Bop > opP = error "TBD"``

## Parsing Expressions

Next, the following is a parser for variables, where each variable is one-or-more uppercase letters.

``> varP :: Parser Variable> varP = many1 upper``

Use the above to write a parser for `Expression` values

``> exprP :: Parser Expression> exprP = error "TBD"``

## Parsing Statements

Next, use the expression parsers to build a statement parser

``> statementP :: Parser Statement> statementP = error "TBD" ``

When you are done, we can put the parser and evaluator together in the end-to-end interpreter function

``> runFile s = do p <- parseFromFile statementP s>                case p of>                  Left err   -> print err>                  Right stmt -> run stmt``

When you are done you should see the following at the ghci prompt

``ghci> runFile "test.imp"Output Store:fromList [("X",IntVal 0),("Y",IntVal 10)]ghci> runFile "fact.imp" Output Store:fromList [("F",IntVal 2),("N",IntVal 0),("X",IntVal 1),("Z",IntVal 2)]``