Topic B: Backtracking and Lists

Transcription

1 Topic B: Backtracking and Lists 1 Recommended Exercises and Readings From Programming in Prolog (5 th Ed.) Readings: Chapter 3 2

2 Searching for the Answer In order for a Prolog program to report the correct result, it must be: Logically Correct Procedurally Correct Why is there a difference? In theory, the order in which clauses in a conjunction or disjunction are evaluated doesn t matter In practice, Prolog evaluates clauses in a defined order Impacts how quickly an answer is found Or even if it is ever found 3 Searching for the Answer Order Search order Prolog searches the knowledge base from top to bottom Left to right within each line Once a matching line is found, and the left most rule is satisfied, then the next rule on the line is attempted If a term fails, backtracking is performed Move back one level and try another value If all of the values have been tried, move back another level Until all combinations have been tested 4

3 Backtracking Example Consider the following knowledgebase: sings(alice). sings(bob). playsguitar(charles). playsguitar(bob). Consider the query: sings(x), playsguitar(x). How does Prolog satisfy this goal? 5 Watching Prolog Work Prolog includes a debugger Enable it with trace. Display it with notrace. Within the debugger <enter> creeps through each step s skips to the answer for the current call l leaps to the next answer a aborts debugging of the query 6

4 Backtracking Prolog uses brute force to check all possibilities Facts and rules are processed from top to bottom Clauses within a rule are satisfied from left to right When a failure occurs, backtracking undoes the most recent match and choses another value, or moves back one level if there are no further values This process repeats until an answer is found, or all possibilities have been exhausted 7 Recursion Recursion is critically important in logic programming Recursive rules use the same functor on both sides of the : symbol Recursive rules must have a base case, which is either: A version of the rule that is not recursive, or A smaller version of the problem results in failure 8

5 Recursion Example Recall our family tree knowledge base How do we define the grandparent relationship? How do we define the great grandparent relationship? How do we define the ancestor relationship? 9 Recursion Example Order matters! What happens if we place the base case after the recursive case? What happens if we make the recursive call first in the recursive case? 10

6 Routing Example Consider a transportation company that has the following routes between cities in Alberta Grand Prairie Edmonton Lloydminster Camrose Red Deer Banff Medicine Hat Calgary Lethbridge 11 Routing Example Create a Prolog knowledgebase that represents the routes 12

7 Routing Example Create a Prolog rule that allows one to identify a route form any city to any other city What are the challenges / limitations? 13 Lists Lists in Prolog: Similar to Haskell, both structurally and syntactically Represented as a head element followed by the tail of the list Elements are enclosed in square brackets [] represents the empty list [1, 2, 3] is a list of 3 integers [H T] is equivalent to (h : t) 14

8 Lists Matches are performed on Prolog lists like other variables List matching examples: [1, 2, 3] = [A, B, C]. [1, 2, 3] = [A, B C]. [1, 2, 3] = [A, B, C D]. [1, 2, 3] = [A B]. [1, 2, 3] = [A, B]. [A, 2] = [1, B]. [A, 2] = [1, B C]. [A, B] = [1, C D]. 15 List Functors Prolog includes numerous built in list predicates Exact list of predicates varies from implementation to implementation Some are more standard than others gprolog includes: length member reverse permutation sublist maplist 16

9 Length of a List The length/2 predicate determines how many atoms are in a list First parameter: A list Second parameter: A non negative integer length Common uses: First and second parameters are both instantiated The predicate succeeds when the second parameter is the length of the list The first parameter is a list and the second parameter is an uninstantiated variable The variable is instantiated to an integer equal to the length of the list Less common use: The first parameter is an uninstantiated variable and the second parameter is an integer The variable is instantiated to a list of the indicated length 17 List Membership The member/2 predicate determines whether or not a value is present in a list First parameter: A term Second parameter: A list of terms Common uses: The first parameter is a term, the second is a list Succeeds if and only if the term is present in the list The first parameter is an uninstantiated variable, the second is a list The variable is instantiated to each term in sequence (by backtracking) Less common uses: The first parameter is a term, the second is an uninstantiated variable The variable is instantiated with an infinite sequence of lists containing the value (by backtracking) 18

10 List Membership Write a predicate that provides the same functionality as member/2 It will be recursive 19 Negation How can we negate the outcome of a predicate? Specifically, how do we test if an element is not present in a list? The \+ predicate reverses the outcome of a predicate Failure is treated as success Examples: member(1, [1, 2, 3]). member(4, [1, 2, 3]). \+member(1, [1, 2, 3]). \+member(4, [1, 2, 3]). 20

11 Creating Bigger Lists One element, H, can be added to the front of an existing list, T NewList = [H T] Multiple items H1, H2, H3 can be added to the front of T NewList = [H1, H2, H3 T] Two lists can be concatenated with the append/3 predicate 21 Creating Bigger Lists Normal uses of the append/3 predicate: The first parameter is a list, the second parameter is a list, the third parameter is an uninstantiated variable The third parameter is an uninstantiated variable that is instantiated to a list containing all of the elements in first followed by all of the elements in second One of the first two parameters is a list, the other is an uninstantiated variable, the third is a list The uninstantiated variable is instantiated to a list containing the elements necessary to form the list provided as the third parameter The first two parameters are uninstantiated variables, the third parameter is a list All combinations of lists that can be concatenated to form the third list are generated in sequence (by backtracking) 22

12 Creating Bigger Lists Write a predicate that provides the same functionality as append/3 It will be recursive 23 Other Useful List Predicates permutation/2: Is one list a permutation of another Does it have the same elements but in a different order? Generate all permutations of a list (by backtracking) sublist/2: Is the first list a sublist of another? Are all elements in first found in second in the same order (possibly with other elements in between them)? Generate all sublists of a list (by backtracking) 24

13 Routing Example Create a Prolog rule that allows one to identify a route form any city to any other city Ensure that the route only includes each city once Record the route in a list 25 Summary Evaluation order is important A program can be logically correct while being procedurally incorrect Such a program will not return a correct result! Backtracking is performed when a failure occurs Order of facts, rules and clauses within a rule determine how quickly an answer is found (or if it is ever found) and the order in which the answers are found Lists can hold an arbitrary number of terms (including duplicates) Lists are represented as a head element, followed by a tail Predicates that operate on lists are often recursive 26