I am reading joy of clojure. In the "forward to second edition" William E 
Byrd and Daniel P Firedman says :



*As with recursion, the art of defining little languages encourages—and 
rewards—wishful thinking. You might think to yourself, “If only I had a 
language for expressing the rules for legal passwords for my login system.” 
A more involved example—a story, really—started several years ago, when we 
thought to ourselves, “If only we had the right relational language, we 
could write a Lisp interpreter that runs backward.”[2] 
<http://www-legacy.manning.com/fogus2/excerpt_foreword2ed.html#footnote-2> 
What does this mean? *


*An interpreter can be thought of as a function that maps an input 
expression, such as (+ 5 1), onto a value—in this case, 6. We wanted to 
write an interpreter in the style of a relational database, in which either 
the expression being interpreted or the value of that expression, or both, 
can be treated as unknown variables. We can run the interpreter forward 
using the query (interpret ‘(+ 5 1) x), which associates the query variable 
x with the value 6. Better yet, we can run the interpreter backward with 
the query (interpret x 6), which associates x with an infinite stream of 
expressions that evaluate to 6, including (+ 5 1) and ((lambda (n) (* n 2)) 
3). (Brainteaser: determine the behavior of the query (interpret x x).)*

Although the writer gave an example of `*(interpret x 6)*` i could not 
imagine the use case of `*lisp interpreter running backwards*` ?
I am not even sure what he meant exactly.

Thinking on it, i could only relate this to *theorem prover*s where you run 
backwards from the result.
Can somebody explain this ?

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