3. (a) Convert the following function so that it is tail recursive, and give an expression...

  

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3. (a) Convert the following function so that it is tail recursive, and give an expression to compute the same output as list 10. Give the type of your function. list x = if x==0 then [] else x:list (x-1) In your answer, explain what it means for a function to be tail recursive. (b) Give ONE example of Haskell overloading, and ONE example of Java overloading. Give types of variable/expressions to illustrate your answer. (c) Using the following code, explain the concept of dynamic lookup. class Course ( void describe() { System.out.println("This is a general university course."); } } class MathsCourse extends Course [ void describe() { System.out.println("This is a mathematics course."); } } class History Course extends Course ( void describe() { } System.out.println("This is a history course."); } Write appropriate lines of code to illustrate the concept. To what extent is this related to overloading? (d) Write a function in Haskell called applyA11, which applies a given function to every element of a given list. Show how applyAll can be used to write a function that will produce the same result as this list comprehension: \1 -> [x*x | x <- 1] Your function should take two parameters: a list and a function (in that order). (e) Unification is used in type reconstruction for functional programming (the algorithm was defined in the lecture slides to unify types). The same concept was also used for computation in logic programming, where terms are unified. Explain how unification works in each case, using the following as examples: . The unification of two types: U(A → (D→D). (BC) → A) Show the disagreement pairs at each step. • The evaluation of the Prolog program: add (0, X, X). ?add (A,B, 8 (0)). Draw the SLD tree to show the substitutions. 3. (a) Convert the following function so that it is tail recursive, and give an expression to compute the same output as list 10. Give the type of your function. list x = if x==0 then [] else x:list (x-1) In your answer, explain what it means for a function to be tail recursive. (b) Give ONE example of Haskell overloading, and ONE example of Java overloading. Give types of variable/expressions to illustrate your answer. (c) Using the following code, explain the concept of dynamic lookup. class Course ( void describe() { System.out.println("This is a general university course."); } } class MathsCourse extends Course [ void describe() { System.out.println("This is a mathematics course."); } } class History Course extends Course ( void describe() { } System.out.println("This is a history course."); } Write appropriate lines of code to illustrate the concept. To what extent is this related to overloading? (d) Write a function in Haskell called applyA11, which applies a given function to every element of a given list. Show how applyAll can be used to write a function that will produce the same result as this list comprehension: \1 -> [x*x | x <- 1] Your function should take two parameters: a list and a function (in that order). (e) Unification is used in type reconstruction for functional programming (the algorithm was defined in the lecture slides to unify types). The same concept was also used for computation in logic programming, where terms are unified. Explain how unification works in each case, using the following as examples: . The unification of two types: U(A → (D→D). (BC) → A) Show the disagreement pairs at each step. • The evaluation of the Prolog program: add (0, X, X). ?add (A,B, 8 (0)). Draw the SLD tree to show the substitutions.

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