7COM1023 Programming Paradigms

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1 7COM1023 Programming Paradigms Practical 7: The Logic Paradigm Tutorial: Exercises Propositional and Predicate Logic form the basis for logic programming. 1. Explain what is meant by propositional logic. How do we combine propositions? 2. What is meant by propositional calculus? 3. Explain what is meant by predicate logic. 4. List three tutorial resources for Prolog. (and three for Lisp and Haskell) 5. Construct a table of comparing directives from Lisp with their corresponding directives in Haskell. 6. What other logic programming languages could we have used? 7. The Horn Clause is said to be a particular variant of predicate logic that underlies the syntax of Prolog. Give a definition for a Horn Clause. Include an example of a Horn clause. 8. What is meant by resolution, instantiation and unification with Horn Clauses? 9. Prolog is said to be an example of a programming language supporting the Logic Paradigm. Explain what this means to you. How is it different to the imperative and functional paradigms? Research the following three questions: 10. Four disciplines under the umbrella of Artificial Intelligence were given as driving forces in the development of the functional paradigm. Give one example from each discipline that were felt to be better suited to a functional approach rather than an imperative approach. 11. Give two examples of problems that you consider better suited to solving via the logic paradigm. What areas do they belong (in the sense of question 10)? 12. What does it mean to be Turing Complete?

2 Tutorial: Prolog in the Lab We note that Prolog does not store changeable data values (unlike the imperative or OO paradigms) and does not have executable statements does not entertain a sequence of commands to change stored data vales form one state to another works with the idea of a set of facts and rules for determining facts rather than on a sequence of executable commands is derived from a form of mathematical logic and an associated concept of automatic proof Practical Start SWI-Prolog. You should obtain a window similar to the one given below: 1. Work through the Quick Introduction to Prolog found at : Make a note of anything (if at all) that doesn t quite work out in the quick introduction.

3 Once you have completed the quick introduction, proceed with the following: 2. Select New from the File drop down menu to obtain the following: 3. Type in < user.pl > under File name and select return. You should obtain: 4. Type in the following (and be careful to include the full stops or your program will not compile): supports(a,b). supports(a,c). supports(b,d). supports(c,e). Save your program and enter the following into SWI-Prolog: a)? - supports(a,c). b)? - supports(a,d). c)? - supports(d,a). d)? - supports(d,e). e)? - supports(a,e). f)?- supports(a,f). g)? - answer(a,c).

4 5. Create a new file called languages.pl and Type the following program into the file and save it. speaks(allen, russian). speaks(bob, english). speaks(mary, russian). speaks(mary, english). talkswith(person1, Person2) :-speaks(person1, L), speaks(person2, L), Person1 \= Person2. Write down what you think each part of the program could mean? 6. Load the program into SWI-Prolog using File, Consult in the pull down menu and try the following: (Note you may have to use the semicolon to obtain all of the possible solutions to your queries). a)?- speaks(allen, russian). b)?- speaks(allen, english). c)?- speaks(mary, russian). d)?- speaks(mary, english). e)?- speaks(mary, greek). f)?- speaks(who, english). g)?- speaks(mary, What). h)?- speaks(mary, X). i)?- talkswith(mary, bob). j)?- talkswith(mary, x). k)?- talkswith(mary, X). l)?- talkswith(x, Y).

5 Recursion 7. Consider the following Word Puzzle based problem: Baker, Cooper, Fletcher and Miller live in a five storey building. Baker does not live on the 5 th floor and Cooper doesn t live on the 1 st floor. Fletcher doesn t live on the top or the bottom floor and he is not on a floor adjacent to Smith or Cooper. Miller lives on a some floor above Cooper. Who lives on what floors? (Hint: floors([floor( _, 5), floor( _, 4), floor( _, 3), floor( _, 2), floor( _, 1)]). building(floors) :- floors(floors). member(floor(baker, B), Floors), B /= 5... ) Can we find any more information? 1. Using a search engine of your own choosing can you find an example of Prolog code that illustrates recursion? Does it work in SWI-Prolog? 2. Define a function that calculates factorials in Prolog where n! = n*(n-1)*(n-2).3*2*1. Test your function with factorial(2, X)., factorial(3, X)., factorial(4, X)., and so forth. 3. Use the trace predicate on your factorial function in finding the value of 4! (type trace(factorial/2).) 4. What does listing(factorial/2). produce? 5. Write a recursive function in Prolog that gives the nth Fibonacci number. Lists The fundamental data structure used when programming in Prolog is the list. Here we consider a selection of techniques employed with lists 1. The list format in prolog is the same as in Haskell. Square brackets with entries separated by commas. For example X = [1, 2, 3]. Type in the following lists: a) L = [my, dog, has, many, fleas]. b) M = [many, fleas, spoil, the, picnic]. Now type in c) member (dog, L). d) member(pic,m). e) prefix(answer, L). f) suffix(answer, L). g) suffix(answer, L). prefix(answer, L). Curious?

6 Trace,?- trace(factorial/2). % factorial/2: [call,redo,exit,fail] true. [debug]?- factorial(4,x). T Call: (6) factorial(4, _G8298) T Call: (7) factorial(3, _G8406) T Call: (8) factorial(2, _G8409) T Call: (9) factorial(1, _G8412) T Call: (10) factorial(0, _G8415) T Exit: (10) factorial(0, 1) T Exit: (9) factorial(1, 1) T Exit: (8) factorial(2, 2) T Exit: (7) factorial(3, 6) T Exit: (6) factorial(4, 24) X = 24.