SUBJECT: GEOMETRY

It when applied to a function of x and y? [3 marks] 9 [TURN OVER CST.2004.13.10 10 Introduction to Functional Programming (a) Define a polymorphic datatype 'a tree to represent binary trees. [1 mark] (b) A breadth-first traversal of a tree walks over all the nodes at each level before proceeding to the next level. For example the breadth-first traversal of the tree: 1 2 3 4 5 6 7 visits the nodes in the order 1, 2, 3, 4, 5, 6, 7. Define a function breadth: 'a tree -> 'a list such that breadth(t) returns the nodes of tree t in breadth-first order. [10 marks] (c) Define a polymorphic datatype 'a seq to represent lazy lists. (b) Describe the Lappin and Leass algorithm for pronoun resolution, illustrating its operation on the text below. Exact weights for salience factors are not required. Owners love the new hybrid cars. Summarize any issues connected with left-or right-cooperative administrators in the two methods (in executing the parser and in developing the apparatus) you illustrated to some degree (e). 5 [TURN OVER CST.2004.13.6 6 Compiler Construction (a) Explain the differences (illustrating each with a small program) between (i) static and dynamic binding (scoping); [4 marks] (ii) static and dynamic typing. would execute C1 rather than C2 as the former was in scope at the raise point. By analogy with statically scoped variables, or otherwise, explain how such exceptions might be implemented on a stack. where the li denote vectors of desired outputs. Let E(w; (xi , li)) denote some measure of the error that N makes when applied to the ith labelled training example. Assuming that each node in the network computes a weighted summation of its inputs -

(b) Consider the use of a monad for input-output. For the purposes of this question, take the IO monad as including two operations readint and writeint which respectively read integers from stdin and write integers to stdout. Give the types of these operators. [2 marks] (c) Assume MLreadint and MLwriteint are primitives with side effects for inputoutput and consider the ML expression add1 of type int: let val x = MLreadint() in MLwriteint(x+1); x end (i) Give an equivalent expression which uses the IO monad instead of side-effects, and state its type. [3 marks] (ii) Give a function run2diff which can be applied to your answer to part (c)(i). When so applied it should give a value in the IO monad which corresponds to ML code that runs add1 twice and returns the difference between the values read.

Describe how the Lempel Ziv text compression algorithm works, illustrating your answer by deriving the sequence of numbers and corresponding bit patterns it would generate when applied to a string starting with the following 24 characters:4 Comparative Programming Languages (a) Discuss to what extent a programmer can expect a program that conforms to a standard to generate identical results when run under different conforming compilers on different machines. [6 marks] (b) ALGOL 60 provided call by value and call by name, Pascal provided call by value and call by reference, and ALGOL-W provided a variety of calling methods including call by result.