Lambda the Ultimate

The Cat language has a primitive called while. The while construct takes two functions as argument, an invariant and a variant. Both functions consume the same number of elements from the stack. The variant (loop body) produces the same number and type of elements that it consumes. The invariant produces the same types as the variant, plus it leaves a boolean value on top of the stack. The while loop terminates when the evaluation of the invariant leaves the value false on top of the stack. The while loop pops the value false, before exiting.

So the question is: how should one express this in the type system?

Here is my current proposal:

define while : 
( 
  a:A=any* 
  variant:(b:A)->(c:A) 
  invariant:(d:A)->(d:A continue:bool)
)
  -> 
(
  result:A
)

What is good or bad about this notation? What other possibilities should I consider?