G6021: Comparative Programming Exam Practice 1. Consider the ¦Ë-term t = (¦Ëx.xx)(II), where I = ¦Ëx.x. (a) Give the definition of a ¦Â-reduction graph. (b) Draw the ¦Â-reduction graph of the term t. (c) Which reduction strategy gives the shortest reduction sequence for reducing t to normal form? 2. Give the types of the following: […]
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G6021: Comparative Programming Exam Practice 1. Consider the ¦Ë-term t = (¦Ëx.xx)(II), where I = ¦Ëx.x. (a) Give the definition of a ¦Â-reduction graph. Answer: A graph showing all the possible reductions starting from the initial term. (b) Draw the ¦Â-reduction graph of the term t. Answer: (¦Ëx.xx)(II) c (¦Ëx.xx)I E (II)(II) I(II) E II
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G6021: Comparative Programming Exam Practice 3 1. Given the ¦Ë-terms: I = ¦Ëx.x, T = ¦Ëx.xIII and U = ¦Ëzy.y(¦Ëx.xz): (a) (b) (c) (d) 2. (a) (b) (c) (d) (e) 3. (a) (b) (c) (d) Write the ¦Ë-term T U out in full (without abbreviations, and including ALL brackets). Draw the ¦Â-reduction graph of the
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G6021: Comparative Programming Exercise Sheet 10 1 Bits of past exam questions The following questions are parts of past exam questions (or very similar to them). You would have to answer these on paper, but for this exercise sheet, try to test your answers with the Haskell interpreter in the labs. 1. Give the output
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G6021: Comparative Programming Exam Practice 2 1. (a) Give an example for each of the following: i. a ¦Ë-term that is in normal form but does not have a type. ii. a ¦Ë-term that has a normal form but does not have a type. iii. a ¦Ë-term that has a normal form and does have
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1 1. 2. 3. G6021: Comparative Programming Exercise Sheet 6 Higher-Order functions on lists Write a function sumAll that returns the sum of all the elements of a list of numbers. Answer: sumAll [] = 0 sumAll (h:t) = h+sumAll t Write a function multAll that returns the product of all the elements of a
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1 Types G6021: Comparative Programming Exercise Sheet 7 What are the types of the following? In each case, try to work out the type first, then check with Haskell. (Note: at least one of these does not have a type!) ix=x kxy=x zero f x = x one f x = f x two f
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1 G6021: Comparative Programming Exercise Sheet 6 Higher-Order functions on lists Write a function sumAll that returns the sum of all the elements of a list of numbers. Write a function multAll that returns the product of all the elements of a list of numbers. The pattern of recursion should be the same in the
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G6021: Comparative Programming Exercise Sheet 4 1 Data Types In Haskell we can define our own types in two ways: • Renaming old types, for example: type Name = [Char]. • Constructing new types, for example: data MyBool = T | F. (Adding deriving (Show) means that Haskell will print these types.) When constructing new
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G6021: Comparative Programming Exam Practice 3 1. Given the λ-terms: I = λx.x, T = λx.xIII and U = λzy.y(λx.xz): (a) Write the λ-term T U out in full (without abbreviations, and including ALL brackets). Answer: ((λx.(((x(λx.x))(λx.x))(λx.x)))(λz.(λy.(y(λx.(xz)))))) (b) Draw the β-reduction graph of the λ-term TU. Answer: There is only one reduction at each step:
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