Programming in Logic Prologs Declarative Procedural Semantics Readings

Programming in Logic: Prolog’s Declarative & Procedural Semantics Readings: Sections 2. 3 - 2. 7 MB: 2 March 2001 CS 360 Lecture 3 1

Where is the Prolog Program? When one talks about Prolog programs, one is referring to the Knowledge base. n The definitions of the relations in the Knowledge base is the Prolog code. n MB: 2 March 2001 CS 360 Lecture 3 2

Goals are the terms that Prolog attempts to match against the clause heads in its Knowledge base. n The top level terms in a query are all goals: n – n ? : a(4, x), b(Y, 7). The top level terms in the body of a clause are all goals: – p(X) : - q(X, a), r(3, X). MB: 2 March 2001 CS 360 Lecture 3 3

Goals and Data Structures Prolog goals look exactly like Prolog data structures. n In other words, Prolog code looks just like Prolog data. This is intentional! n A Prolog program can modify itself as it is running. n A Prolog program can create new queries & pose them to the Prolog interpreter. n MB: 2 March 2001 CS 360 Lecture 3 4

Prolog’s Declarative Semantics The prolog we have seen so far is called pure Prolog, i. e. , everything can be expressed in FOPC. n For example: ancestor(A, P) : - parent(A, X), ancestor(X, P). can be translated into the logical expression: A P(ancestor(A, P) n parent(A, X) ancestor(X, P)) MB: 2 March 2001 CS 360 Lecture 3 5

Translating Prolog clauses into FOPC n The clauses : ancestor(A, P) : - parent(A, P). ancestor (A, P): - parent(A, X), ancestor(X, P). Translates into FOPC as: A P( ancestor(A, P) parent(A, P) ( parent(A, X) ancestor(X, P))) MB: 2 March 2001 CS 360 Lecture 3 6

Prolog Declarative Semantics In the body of the clause, the commas separating the top-level terms are understood to be conjunctions (and’s). n There are two ways to specify disjunctions (or’s): n – – Write separate clauses (as done for ancestor) Use a semicolon (“; ”) MB: 2 March 2001 CS 360 Lecture 3 7

Disjunctions in Prolog n We could rewrite the ancestor example in Prolog as follows: ancestor(A, P) : - parent(A, P) ; parent(A, X), ancestor(X, P). MB: 2 March 2001 CS 360 Lecture 3 8

Negation in Pure Prolog n We cannot express negation in the clause body in pure prolog: – For example, we can’t express in pure Prolog the following FOPC expression H W( husband(H, W) married(H, W) male(H) divorced(H, W) ) MB: 2 March 2001 CS 360 Lecture 3 9

Negation in Pure Prolog cont’d Likewise, Prolog can’t tell us something is false rather it tells us that it can’t prove something is true. n For example, given the Knowledge base: n – – n man(socrates). mortal(X) : - man(X). The answer to mortal(mike) would be no, not because it isn’t true, but because Prolog can’t prove it’s true using that KB. MB: 2 March 2001 CS 360 Lecture 3 10

Prolog’s Procedural Semantics I Prolog’s control flow different from languages like Java. n In Prolog no distinction between statements & method calls - all goals recursively matched against KB (system defined relations (write/1) have own definitions). n Goal parameters can be unbound variables. n Goals succeed or they fail. n MB: 2 March 2001 CS 360 Lecture 3 11

Prolog Control Flow Example KB 1. a(X) : - b(X). n n n b(2). Given the query a(2), Prolog 2. Execution scans thetrace KB of forquery the first claus If it finds a match then it recurses on the goals in the clause b [a(2)] (goal stack) Query succeeded here. 1. X = 2 (which clause [b(2)] matched & bindings) 2. [] MB: 2 March 2001 CS 360 Lecture 3 12

Prolog Control Flow Example KB 1. a(X) : - b(X). n n 2. b(2). Execution trace of query Query: a(2) [a(2)] (goal stack) Notice that after the query goal matched the clause head, the 1. X = 2 (which clause [b(2)] matched & bindings) 2. [] MB: 2 March 2001 CS 360 Lecture 3 13

Prolog Control Flow Example KB 1. a(X) : - b(X). n n Query: a(3), Prolog scans the KB for first clause head match 2. b(2). of query If it fails to find a match then. Execution it tries totrace backtrack its matches [a(3)] There are no other possible matches. 1. X = 3 Query fails. [b(3)] MB: 2 March 2001 CS 360 Lecture 3 14

Backtracking KB : 1. a(X) : - b(X). 2. a(3). 3. b(2). n n Execution tracebacktracks of query to last Query: a(3), from point of failure, Prolog Matches clause 2 and succeeds. [a(3)] 1. X = 3 [b(3)] 2. [] MB: 2 March 2001 CS 360 Lecture 3 15

Flow of Control with Conjunctions [a(X)] Query: a(X). KB: 1. a(X) : - b(X), c(X). 2. b(2). 3. c(2). Response: X=2? 1. X = X’ Note renaming of variables in matched clause, X replaced by X’. I[b(X’), c(X’)]Goal query is replaced by first clause body goal 2. X’ = 2 and rest of clause body goals are pushed onto [c(2)] goal stack. 3. [] MB: 2 March 2001 CS 360 Lecture 3 16

Flow of Control with Conjunctions [a(X)] Query: a(X). KB: 1. a(X) : - b(X), c(X). 2. b(2). 3. b(3) 4. c(3). Notice unbinding 1. X = X’ of variable (X’) when backtrack [b(X’), c(X’)] over binding point. 2. X’ = 2 3. X’ = 3 [c(2)] Response: X=3? [c(3)] 4. [] MB: 2 March 2001 CS 360 Lecture 3 17

Prolog Procedural Semantics II When goal fails, control undoes any bindings done at that step & backs up to previous step. n It continues scan of KB for clause heads matching current goal. n If none found then continues to backtrack. n MB: 2 March 2001 CS 360 Lecture 3 18

Flow of Control with Conjunctions [a(X)] Query: a(X). KB: 1. a(X) : - b(X), c(X). 2. b(Y) : - d(Z), e(Y, Z). 3. b(3) 4. c(3). 5. d(5). 6. e(3, 5). Response: X=3? MB: 2 March 2001 1. X = X’ [b(X’), c(X’)] 2. X’ = Y [d(Z), e(Y, Z), c(Y)] 5. Z = 5 [e(Y, 5), c(Y)] 6. Y = 3 [c(3)] 4. [] CS 360 Lecture 3 19

Flow of Control with Conjunctions Query: a(X). KB: 1. a(X) : - b(X), c(X). 2. b(Y) : - d(Z), e(Y, Z). 3. b(3) 4. c(4). 5. d(5). 6. e(3, 5). 7. e(4, 5). Response: X=4? MB: 2 March 2001 [a(X)] 1. X = X’ [b(X’), c(X’)] 2. X’ = Y [d(Z), e(Y, Z), c(Y)] 5. Z = 5 [e(Y, 5), c(Y)] 6. Y = 3 [c(3)] 7. Y = 4 [c(4)] 4. [] CS 360 Lecture 3 20

Additional Answers What happens when Prolog returns an answer and prompts you with “? ”? n Since an answer was returned, the trace ended with a true and an empty goal stack. n If you type in “; ” then Prolog will, in effect, change that true to fails and backtrack. n MB: 2 March 2001 CS 360 Lecture 3 21

Effects of Clause/Goal Ordering A Prolog program can be declaratively correct, but procedurally inadequate (may recurse forever (p : - p. ), or simply be inefficient). n The program’s behavior is determined by the order of the clauses in the KB and the order of the goals in the clauses. n Changing either can dramatically affect the behavior of the program. n MB: 2 March 2001 CS 360 Lecture 3 22

Example: Parental Fact KB parent(pam, bob). n parent(tom, liz). n parent(bob, ann). n parent(bob, pat). n parent(pat, jim). n MB: 2 March 2001 CS 360 Lecture 3 23

Predecessor Relation Variations pred 1(X, Z) : - parent(X, Z). pred 1(X, Z) : - parent(X, Y), pred 1(Y, Z). pred 2(X, Z) : - parent(X, Y), pred 2(Y, Z). pred 2(X, Z) : - parent(X, Z). pred 3(X, Z) : - pred 3(Y, Z), parent(X, Y). pred 4(X, Z) : - pred 4(Y, Z), parent(X, Y). pred 4(X, Z) : - parent(X, Z). MB: 2 March 2001 CS 360 Lecture 3 24

Computing predn(tom, pat) For n from 1 to 3, Prolog returns yes. n For pred 4(tom, pat), Prolog loops forever. n While the first 3 preds find an answer they do so with different amounts of computation. n MB: 2 March 2001 CS 360 Lecture 3 25

Trace of pred 1(tom, pat) [pred 1(tom, pat)] 7. X=tom, Z=pat 8. X=tom, Z=pat KB: 1. parent(pam, bob). [parent(tom, pat)] [parent(tom, Y), pred 1(Y, pat)] 2. Y=bob 2. parent(tom, bob). 3. parent(tom, liz). [pred 1(bob, pat)] 4. parent(bob, ann). 7. X’=bob, Z’=pat 5. parent(bob, pat). [parent(bob, pat)] 6. parent(pat, jim). 7. pred 1(X, Z) : - parent(X, Z). 5. 8. pred 1(X, Z) : - parent(X, Y), pred 1(Y, Z). [] MB: 2 March 2001 CS 360 Lecture 3 26

Exercises n Try doing the execution traces of pred 2(tom, pat), pred 3(tom, pat), and pred 4(tom, pat) MB: 2 March 2001 CS 360 Lecture 3 27

Quick Quiz What is the difference between the structure of Prolog code and Prolog data? n What is a goal and how is it different from structured data? n How do you express a negated goal? n What does it mean when Prolog answers no n MB: 2 March 2001 CS 360 Lecture 3 28

Quick Quiz cont’d In pure Prolog, does changing the order of the clauses or of the goals in the clauses change the declarative meaning? n What about the procedural meaning? n Is there anything declaratively wrong with: n – – n ancestor(A, P) : - ancestor(X, P), parent(A, X). ancestor(A, P) : - parent(A, P). Is there anything procedurally wrong? MB: 2 March 2001 CS 360 Lecture 3 29

Summary Declarative semantics of pure Prolog program defines when a goal is true and for what instantiation of variables. n Commas between goals mean and, semicolons mean or. n Procedural semantics are determined by clause and goal ordering. n Goal failure causes backtracking and unbinding of affected variables. n MB: 2 March 2001 CS 360 Lecture 3 30