6 Conjunctions and Disjunctions

▼ |  | Racklog: Prolog-Style Logic Programming

1 | Simple Goals and Queries
2 | Predicates
3 | Using Conventional Racket Expressions in Racklog
4 | Backtracking
5 | Unification
6 | Conjunctions and Disjunctions
7 | Manipulating Racklog Variables
8 | The Cut (!)
9 | Set Predicates
10 | Higher-order Predicates
11 | Racklog Module Language
12 | Glossary of Racklog Primitives
| Bibliography

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### 6`` Conjunctions and Disjunctions🔗ℹ

Goals may be combined using the forms %and and %or to form compound goals. (For %not, see Negation as Failure.) Eg,

> > (%which (x)
> (%and (%member x '(1 2 3))
> (%< x 3)))
> '((x . 1))

gives solutions for x that satisfy both the argument goals of the %and. Ie, x should both be a member of '(1 2 3) and be less than 3. Typing (%more) gives another solution:

> > (%more)
> '((x . 2))
> > (%more)
> #f

There are no more solutions, because [x 3] satisfies the first but not the second goal.

Similarly, the query

> > (%which (x)
> (%or (%member x '(1 2 3))
> (%member x '(3 4 5))))
> '((x . 1))

lists all x that are members of either list.

> > (%more)
> '((x . 2))
> > (%more)
> '((x . 3))
> > (%more)
> '((x . 3))
> > (%more)
> '((x . 4))
> > (%more)
> '((x . 5))

(Yes, ([x 3]) is listed twice.)

We can rewrite the predicate %computer-literate from Predicates with Rules using %and and %or:

> (define %computer-literate
> (%rel (person)
> [(person)
> (%or
> (%and (%knows person
> 'TeX)
> (%knows person
> 'Racket))
> (%and (%knows person
> 'TeX)
> (%knows person
> 'Prolog)))]))

Or, more succinctly:

> (define %computer-literate
> (%rel (person)
> [(person)
> (%and (%knows person
> 'TeX)
> (%or (%knows person
> 'Racket)
> (%knows person
> 'Prolog)))]))

We can even dispense with the %rel altogether:

> (define %computer-literate
> (lambda (person)
> (%and (%knows person
> 'TeX)
> (%or (%knows person
> 'Racket)
> (%knows person
> 'Prolog)))))

This last looks like a conventional Racket predicate definition, and is arguably the most readable format for a Racket programmer.

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