Exercises part 1

In these exercises, you are going to implement some small command-line applications. Some of these will potentially run forever, as they will only stop when the user enters a keyword for quitting the application. Such programs are no longer provably total. If you added the %default total pragma at the top of your source file, you'll need to annotate these functions with covering, meaning that you covered all cases in all pattern matches but your program might still loop due to unrestricted recursion.

1. Implement function rep, which will read a line of input from the terminal, evaluate it using the given function, and print the result to standard output:

   rep : (String -> String) -> IO ()
   

2. Implement function repl, which behaves just like rep but will repeat itself forever (or until being forcefully terminated):

   covering
   repl : (String -> String) -> IO ()
   

3. Implement function replTill, which behaves just like repl but will only continue looping if the given function returns a Right. If it returns a Left, replTill should print the final message wrapped in the Left and then stop.

   covering
   replTill : (String -> Either String String) -> IO ()
   

4. Write a program, which reads arithmetic expressions from standard input, evaluates them using eval, and prints the result to standard output. The program should loop until users stops it by entering "done", in which case the program should terminate with a friendly greeting. Use replTill in your implementation.

5. Implement function replWith, which behaves just like repl but uses some internal state to accumulate values. At each iteration (including the very first one!), the current state should be printed to standard output using function dispState, and the next state should be computed using function next. The loop should terminate in case of a Left and print a final message using dispResult:

   covering
   replWith :  (state      : s)
            -> (next       : s -> String -> Either res s)
            -> (dispState  : s -> String)
            -> (dispResult : res -> s -> String)
            -> IO ()
   

6. Use replWith from Exercise 5 to write a program for reading natural numbers from standard input and printing the accumulated sum of these numbers. The program should terminate in case of invalid input and if a user enters "done".