G6021 Comparative Programming Part 4 – Types Part 4 – Types G6021 Comparative Programming 1/63 Typed λ-calculus There are many variants of the λ-calculus (applied λ-calculi). Here we briefly outline the simply typed λ-calculus; and a minimal functional programming language. Definition: Types: type variables: σ, τ,… and function types: σ → τ Typed terms: terms […]
G6021 Comparative Programming Part 5 – Logic Programming (Prolog) Part 5 – Logic Programming (Prolog) G6021 Comparative Programming 1/22 Logic Programming Languages Use logic to express knowledge, describe a problem. Use inference to compute, manipulate knowledge, obtain a solution to a problem. Based on this idea, several programming languages have been developed. The most popular
1 1. 2. 3. G6021: Comparative Programming Exercise Sheet 3 Functions on lists Write a function addOneToAll that will add one to all the elements of a list. Write this two ways, first using pattern matching, then using list comprehensions. Answer: addOneToAll [] = [] addOneToAll (h:t) = (h+1):addOneToAll t addOneToAllLC l = [x+1 |
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G6021 Comparative Programming Reduction and reduction graphs: functional expressions A reduction graph simply shows all the different ways that an expression can be reduced. In this work we use three words interchangeably: reduce, simplify, and evaluate. We introduce some more terminology: • A reducible expression (abbreviated to redex) is an expression that can be simplified.
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G6021: Comparative Programming Exercise Sheet 2 1 Function arguments If a function needs two arguments, it can take them one at a time or both together, as illustrated by the following functions: f x y = x+y g (x,y) = x+y We say that f is a curried version of g. 1. What are the
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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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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 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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