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Principles of Programming Languages 2013.07.24 Notes • Total available time: 2h. • You may use any written material you need. • You cannot use computers or phones during the exam. 1 Prolog (11 points) 1. Define the prefix predicate that holds iff its second argument is a prefix of the first argument. E.g. prefix("Hello world", "Hello") is true, while prefix("Hello world", "wor") is not. 2. Define an analogous predicate for suffixes. E.g. suffix("Hello world", "world") is true, while suffix("Hello world", "Hello") is not. 3. Define the infix predicate that holds iff its second argument is a substring of the first argument. (Hint: an infix is a prefix of a suffix.) 4. Define the overlap predicate that holds iff its two argument strings actually overlap, i.e. either one is an infix of the other, or one’s prefix is a suffix of the other. 2 Haskell (11 points) Consider an immutable doubly linked list datatype (DList), where each node has two pointers, one to the previous node (prev) and another to the next node ( next), together with its local datum. There is a special value Nil, denoting the empty DList. A well-formed DList has always the first node with prev set to Nil, and the last node with next set to Nil. 1. Define the DList datatype. DList must be an instance of the Eq class, and == must always terminate for every well-formed DList. 2. Define the car and cdr functions for DLists. The latter must return well-formed DLists, if not called on Nil. Errors must be managed in the Maybe monad. 3. Define the cons function for DLists. 3 Scheme/Ruby (10 points) Define a mutable variant of DList either in Scheme or in Ruby. You are requested to define the DList datatype; Dcar, Dcdr, and Dcons, i.e. car, cdr, cons variants for DLists; and DList=? that holds if both its arguments are equal. 1 Solutions…