a7P1.ml
a7P2.ml

Exercise 2.1.1 b, d, f, h.

Exercise 2.1.2 b, d, f, h

Exercise 2.2.2 b, f, g.

Exercise 2.3.2

Exercise 2.4.2 b, d, f, h.

Exercise 2.4.3 b, d.

Exercise 2.4.5 b, d.

Exercise 3.1.3 b, f

Exercise 3.2.1 b, e.

Exercise 3.2.3 b, d.

Exercise 3.3.1 b, c.

Exercise 3.3.2.

Exercise 3.3.5 b.

1. (20 points) Define a function Encipher k plainText that takes an integer k, returning a function that then takes a string of characters and replaces each character by another which is obtained by going k positions further into the 8-bit ASCII character set and wrapping from chr(255) to chr(0). For example

   - encipher 25 "Madam I'm Adam!" ;
   val it = "fz}z\1349b@\1349Z}z\134:" : string
   

   You may define any helping functions needed.
    
   
2. (Optional for 5 points of extra credit) Define a function Verify(propFormula) that takes a string in the propositional formula language described below and tells whether it is a tautology, contradiction, underDetermined, or poorlyFormed (if it's not a legal formula). Your function should return values of a new type tval defined as follows.

   - datatype tval = tautology | contradiction | underDetermined | poorlyFormed ;
   

   - Verify("t") ;
   val it = tautology : tval
   - Verify("~t v ~t") ;
   val it = contradiction : tval
   - Verify("~t v f v f") ;
   val it = contradiction : tval
   - Verify("~t v f v ~f") ;
   val it = tautology : tval
   

   In this exercise, you can assume that each formula is well-formed and uses only the symbols f, t, ~, v, . Assume that "v" is a binary operator, and that "~" is unary negation. These formulas are clauses involving only the possible literals f, t, ~f, and ~t. Here f means false and t means true. (This problem may offer ideas for solving a problem in Assignment 8.)
    
   
3. (Optional for 5 points of extra credit) Given a definition of the function ngrams, described below, using a functional programming approach. The function should be defined in curried form, with an argument n that tells how long each n-gram should be. Then there is a list argument which is the source for constructing the n-grams. An n-gram is a list of n consecutive elements from the source list.

   - ngrams 3 [0,1,2,3,4] ;
   val it = [[0,1,2],[1,2,3],[2,3,4]] : int list list