Raising rational number to integer exponent yields floating-point result

[dcnorris]

?- R is 1 rdiv 5, R2 is R^2.
   R = 1 rdiv 5, R2 = 0.04000000000000001.

Cf. #2752 (comment)

[UWN]

9.3.1.2 Template and modes

'**'(int-exp, int-exp) = float
'**'(float-exp, int-exp) = float
'**'(int-exp, float-exp) = float
'**'(float-exp, float-exp) = float

?- X is 2**1.
   X = 2.0.

So (**)/2 produces always floats.

However, the situation is different for (^)/2.

[UWN]

What do you expect in stead of:

?- X is 2 ^ (1 rdiv 2).
   X = 1.4142135623730951. % not sure about this

So far, (^)/2 is about integer exponentiation as long as the arguments are all integers. And in cases where integers would produce a non-integer value we get:

?- X is 2^ -1.
   error(type_error(float,2),(^)/2).
?- X is 2.0^ -1.
   X = 0.5.

It is not clear what your use case is. Maybe you need an entirely new function/evaluable functor.

[dcnorris]

I've corrected the original now, to omit the irrelevant (**)/2.
The point is that (^)/2 does not yield a rational when expected.

[UWN]

Again, what about 2 ^ (1 rdiv 2)?

[dcnorris]

Only non-negative integer exponents are needed for my use-case, which involves computing the joint probability $\prod_{i=1}^k p_i^{n_i}$ of one permutation of $n_1, n_2, ..., n_k$ occurrences each of events with probabilities $p_1, p_2, ..., p_k$. I'm looking for confirmation that a probability sums to exactly 1, as an indication that a DCG has indeed accounted for every possible outcome, as in:
https://github.com/Precisfice/DEDUCTION/blob/ca1dba28100ceaaae673b782cf76cb87a42b5a6d/catform.pl#L665-L675

FWIW, doing this check did alert me to some missing sequences the DCG neglected to describe.

[UWN]

Probabilities and exact sums? Sounds unusual to me. It seems you could live with a type error as shown above for integers, this time only for rationals that result in non-rational value.

[dcnorris]

With an arbitrary vector of rational toxicity-probabilities, one can rather easily assign an exact probability of occurrence to each possible trial realization described by declarative code (here, a DCG). The sum of these probabilities then gives a convenient check that all possibilities considered by the [relatively easy] probability calculation are accounted-for by the [more difficult] code. (I will even venture that the Girsanov theorem lends some justification to such arbitrary probability choices.)

At any rate, here's the result; it is at least much tidier now; floating-point is so gauche! ;)
https://github.com/Precisfice/DEDUCTION/blob/78434ed53bebc7b2420bed74a208bb9c513845d9/catform.pl#L634-L714