Prolog • Declarative/logic paradigm • Functional paradigm – No assignment statement • Declarative paradigm – No program! Specification without implementation.
Prolog • Declarative/logic paradigm • Functional paradigm – No assignment statement • Declarative paradigm – No program! Specification without implementation.
Prolog • Declarative/logic paradigm • Functional paradigm – No assignment statement • Declarative paradigm – No program! Specification without implementation.
Using Prolog • Two shells • vi to edit and save the database, or more to view it • Prolog to query the database
4 Chapter 1 lntroduction to Prolog The question ?- parent( tr, This time thel ,,t solution: ...: ,l ii X=ann 5: ã * We may now .â * find: ç 4 X=pat # ä â If we request f .æ ânn ã s the solutions . ã s Our progra ã ê * whom? That i .ë ,.Ê Find X and '9. * æ This is express e d ,* ?- parent( X, I Figure 1.1 A family tree. :t tí ç Prolog now flr t: t: displayed one This program consists of six clauses. Each of these clauses declares one fact about the solutions I the parent relation. For example, parent( tom, bob) is a particular instqnce of the x=pam parent relation. In general, a relation is defined as the set of all its instances. Y = bob; When this program has been communicated to the Prolog system, Prolog can X=tom be posed some questions about the parent relation. For example: Is Bob a parent Y = bob; of Pat? This question can be communicated to the Prolog system by typing: X=tom Y =liz; ?- parent( bob, pat). Having found this as an asserted fact in the program, Prolog will answer: We can alwa¡ semicolon. yes Our exampJ A further query can be: is a grandparr ?- parent( liz, pat), illustrated by ì t'îi (1) Who is a 1 answers: (2) Who is a I because the program does not mention anything aboutLiz being a parent of Pat. It also answers 'no' to the question: parent ?- parent( tom, ben). ì t More interesting questions can also be asked. For example: Who is Liz's parent? I I gr ?- parent( X, liz). parent Prolog will now tell us what is the value of X such that the above statement is true. So the answer is: X=tom Figure 1.2 The ¡
4 Chapter 1 lntroduction to Prolog The question Defining relations by facts ?- parent( tr, This time thel parent( pam, bob). ,,t solution: ...: ,l parent( tom, bob). ii X=ann parent( tom, liz). 5: ã * parent( bob, ann). We may now .â * find: parent( bob, pat). ç 4 X=pat parent( pat, jim). # ä â If we request f .æ ânn ã s the solutions . ã s Our progra ã ê * whom? That i .ë ,.Ê Find X and '9. * æ This is express e d ,* ?- parent( X, I Figure 1.1 A family tree. :t tí ç Prolog now flr t: t: displayed one This program consists of six clauses. Each of these clauses declares one fact about the solutions I the parent relation. For example, parent( tom, bob) is a particular instqnce of the x=pam parent relation. In general, a relation is defined as the set of all its instances. Y = bob; When this program has been communicated to the Prolog system, Prolog can X=tom be posed some questions about the parent relation. For example: Is Bob a parent Y = bob; of Pat? This question can be communicated to the Prolog system by typing: X=tom Y =liz; ?- parent( bob, pat). Having found this as an asserted fact in the program, Prolog will answer: We can alwa¡ semicolon. yes Our exampJ A further query can be: is a grandparr ?- parent( liz, pat), illustrated by ì t'îi (1) Who is a 1 answers: (2) Who is a I because the program does not mention anything aboutLiz being a parent of Pat. It also answers 'no' to the question: parent ?- parent( tom, ben). ì t More interesting questions can also be asked. For example: Who is Liz's parent? I I gr ?- parent( X, liz). parent Prolog will now tell us what is the value of X such that the above statement is true. So the answer is: X=tom Figure 1.2 The ¡
Demo • ?- consult( ‘ch1.pl’). • ?- halt. % to quit • ; % next solution • a % all solutions • <ret> % stop
1.1 Defining relations by facts 5 The question Who are Bob's children? can be communicated to Prolog as: ?- parent( bob, X). This time there is more than iust one possible answer. Prolog frrst answers with one solution: X=ann We may now request another solution (by Wping a semicolon), and Prolog will ñnd: X=pat If we request further solutions (semicolon again), Prolog will answer'no'because all the solutions have been exhausted. Our program can be asked an even broader question: Who is a parent of whom? That is: Find X and Y such that X is a parent of Y. This is expressed in Prolog by: ?- parent( X, Y). Prolog now finds all the parent-child pairs one after another. The solutions will be displayed one at a time as long as we tell Prolog we want more solutions, until all the solutions have been found. The answers are output as: auses declares one fact about is a particular instønce of the x=pam : set of all its instances. Y = bob; he Prolog system, Prolog can X=tom For example: Is Bob a parent Y = bob; rolog system by Çping: X=tom Y = liz; Prolog will answer: We can always stop the stream of solutions by typing a return instead of a semicolon. Our example program can be asked still more complicated questions like: Who is a grandparent of Jim? This query has to be broken down into two steps, as illustrated by Figure 1.2. (1) \Âfho is a parent of Jim? Assume that this is some Y. (2) Who is a parent of Y? Assume that this is some X. ut Liz being a parent of Pat. It parent I mple: Who is Liz's parent? I grandparent I I parent tt the above statement is true. Figure 1.2 The grandparent relation expressed as a composition of two parent relations. Who is a grandparent of jim? 1. Who is a parent of jim? Y 2. Who is a parent of Y ? X Query: ?- parent( Y, jim), parent( X, Y).
Who are tom’s grandchildren? ?- parent( tom, X), parent( X, Y).
Who are tom’s grandchildren? ?- parent( tom, X), parent( X, Y).
Demo trace | ?- parent( tom, X), parent( X, Y). 1 1 Call: parent(tom,_273) ? 1 1 Exit: parent(tom,bob) ? 2 1 Call: parent(bob,_277) ? 2 1 Exit: parent(bob,ann) ? X = bob Y = ann ? ; 2 1 Redo: parent(bob,ann) ? 2 1 Exit: parent(bob,pat) ? X = bob Y = pat ? ; 1 1 Redo: parent(tom,bob) ? 1 1 Exit: parent(tom,liz) ? 2 1 Call: parent(liz,_277) ? 2 1 Fail: parent(liz,_277) ? (1 ms) no
Demo trace | ?- parent( tom, X), parent( X, Y). 1 1 Call: parent(tom,_273) ? 1 1 Exit: parent(tom,bob) ? 2 1 Call: parent(bob,_277) ? 2 1 Exit: parent(bob,ann) ? Exits one goal, and calls the next goal. X = bob Y = ann ? ; Exit means “success”. 2 1 Redo: parent(bob,ann) ? 2 1 Exit: parent(bob,pat) ? X = bob Y = pat ? ; 1 1 Redo: parent(tom,bob) ? 1 1 Exit: parent(tom,liz) ? 2 1 Call: parent(liz,_277) ? 2 1 Fail: parent(liz,_277) ? (1 ms) no
Demo trace | ?- parent( tom, X), parent( X, Y). 1 1 Call: parent(tom,_273) ? 1 1 Exit: parent(tom,bob) ? 2 1 Call: parent(bob,_277) ? 2 1 Exit: parent(bob,ann) ? The invocation number. X = bob Y = ann ? ; Unique for every invocation. 2 1 Redo: parent(bob,ann) ? 2 1 Exit: parent(bob,pat) ? X = bob Y = pat ? ; 1 1 Redo: parent(tom,bob) ? 1 1 Exit: parent(tom,liz) ? 2 1 Call: parent(liz,_277) ? 2 1 Fail: parent(liz,_277) ? (1 ms) no
Demo trace | ?- parent( tom, X), parent( X, Y). 1 1 Call: parent(tom,_273) ? 1 1 Exit: parent(tom,bob) ? 2 1 Call: parent(bob,_277) ? 2 1 Exit: parent(bob,ann) ? The index number. X = bob Y = ann ? ; The number of direct ancestors of the goal, 2 1 Redo: parent(bob,ann) ? 2 1 Exit: parent(bob,pat) ? i.e., the current depth of the goal. X = bob Y = pat ? ; 1 1 Redo: parent(tom,bob) ? 1 1 Exit: parent(tom,liz) ? 2 1 Call: parent(liz,_277) ? 2 1 Fail: parent(liz,_277) ? (1 ms) no
Demo trace | ?- parent( tom, X), parent( X, Y). 1 1 Call: parent(tom,_273) ? 1 1 Exit: parent(tom,bob) ? 2 1 Call: parent(bob,_277) ? 2 1 Exit: parent(bob,ann) ? X = bob The invocation number increases. Y = ann ? ; 2 1 Redo: parent(bob,ann) ? Now working off of invocation 1 . 2 1 Exit: parent(bob,pat) ? X = bob Y = pat ? ; 1 1 Redo: parent(tom,bob) ? 1 1 Exit: parent(tom,liz) ? 2 1 Call: parent(liz,_277) ? 2 1 Fail: parent(liz,_277) ? (1 ms) no
Demo trace | ?- parent( tom, X), parent( X, Y). 1 1 Call: parent(tom,_273) ? 1 1 Exit: parent(tom,bob) ? 2 1 Call: parent(bob,_277) ? 2 1 Exit: parent(bob,ann) ? X = bob The index number remains 1 . Y = ann ? ; 2 1 Redo: parent(bob,ann) ? No direct ancestors of the goal, 2 1 Exit: parent(bob,pat) ? i.e., the current depth of the goal is 1 . X = bob Y = pat ? ; 1 1 Redo: parent(tom,bob) ? 1 1 Exit: parent(tom,liz) ? 2 1 Call: parent(liz,_277) ? 2 1 Fail: parent(liz,_277) ? (1 ms) no
Demo trace | ?- parent( tom, X), parent( X, Y). 1 1 Call: parent(tom,_273) ? 1 1 Exit: parent(tom,bob) ? 2 1 Call: parent(bob,_277) ? 2 1 Exit: parent(bob,ann) ? X = bob Y = ann ? ; 2 1 Redo: parent(bob,ann) ? 2 1 Exit: parent(bob,pat) ? X = bob Y = pat ? ; 1 1 Redo: parent(tom,bob) ? 1 1 Exit: parent(tom,liz) ? 2 1 Call: parent(liz,_277) ? 2 1 Fail: parent(liz,_277) ? (1 ms) no
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