using throw(cut) and catch() to implement the cut in a meta-interpreter

Question

I have previously asked about implementing the cut in a simple prolog meta-interpreter: handling the cut with a simple meta-interpreter

A comment pointed me to using the throw(cut)/catch combination: Implementing cut in tracing meta interpreter prolog

This is a simpler program to minimise distraction and help focus on the issue:

fruit(apple).
fruit(orange) :- !.
fruit(banana).

% meta-interpreter
prove(true) :- !.
prove(!) :- !, ( true ; throw(cut) ).
prove((A,B)):- !, prove(A), prove(B).
prove(H) :- clause(H,B),
    catch(prove(B), cut, fail),
    write(H), write(" <- "), writeln(B).

The desired behaviour is this:

?- fruit(X)

X = apple
X = orange

When using the meta-interpreter, it seem the cut is not implemented correctly:

?- prove(fruit(X)).

fruit(apple) <- true
X = apple ;

fruit(orange) <- !
X = orange ;

fruit(banana) <- true
X = banana.

Question: Why isn't the meta-interpreter implementation of cut working as expected?

---

I have traced the query (removing the lines related to write/1). The traces for the three fruit appear the same suggesting the prove(!) is not throwing cut.

Call:prove(fruit(_6416))
 Call:clause(fruit(_504),_722)
 Exit:clause(fruit(apple),true)
 Call:catch(prove(true),cut,fail)
 Exit:catch('5afa3202-4e65-4ba4-b81d-893043450958' :prove(true),cut,'5afa3202-4e65-4ba4-b81d-893043450958' :fail)
 Exit:prove(fruit(apple))
X = apple

 Redo:clause(fruit(_504),_720)
 Exit:clause(fruit(orange),!)
 Call:catch(prove(!),cut,fail)
 Exit:catch('5afa3202-4e65-4ba4-b81d-893043450958' :prove(!),cut,'5afa3202-4e65-4ba4-b81d-893043450958' :fail)
 Exit:prove(fruit(orange))
X = orange

 Redo:catch('5afa3202-4e65-4ba4-b81d-893043450958' :prove(!),cut,'5afa3202-4e65-4ba4-b81d-893043450958' :fail)
 Exit:clause(fruit(banana),true)
 Call:catch(prove(true),cut,fail)
 Exit:catch('5afa3202-4e65-4ba4-b81d-893043450958' :prove(true),cut,'5afa3202-4e65-4ba4-b81d-893043450958' :fail)
 Exit:prove(fruit(banana))
X = banana

Answer 1

Your problem is that you are catching just one clause at a time instead of the whole rule. You are backtracking over the alternatives given by clause/2.

So your last clause of prove/1 may be written:

prove(H) :- 
    catch(
           (clause(H,B), 
            prove(B)
           ), cut, fail),
    write(H), write(" <- "), writeln(B).