2.15.1.6 Rational number syntax
As of version 8.1.22, SWI-Prolog supports rational numbers as a
primary citizen atomic data type if SWI-Prolog is compiled with the GMP
library. This can be tested using the bounded
Prolog flag. An atomic type also requires a syntax. Unfortunately there
are few options for adding rational numbers without breaking the ISO
standard.30ECLiPSe uses numerator_denominator.
This syntax conflicts with SWI-Prolog digit groups (see section
2.15.1.5) and does not have a recognised link to rational numbers.
The notation 1/3r
and 1/3R
have also been
proposed. The 1/3r
is compatible to Ruby, but is hard to
parse due to the required look-ahead and not very natural. See also https://en.wikipedia.org/wiki/Rational_data_type.
ECLiPSe and SWI-Prolog have agreed to define the canonical syntax for
rational numbers to be e.g., 1r3
. In addition, ECLiPSe
accepts
1_3
and SWI-Prolog can be asked to accept 1/3
using the module sensitive Prolog flag rational_syntax,
which has the values below. Note that write_canonical/1
always uses the compatible
1r3
syntax.
- natural
- This is the default mode where we ignore the ambiguity issue and follow
the most natural <integer>/<nonneg>
alternative. Here, <integer> follows the normal rules
for Prolog decimal integers and <nonneg> does the same,
but does not allows for a sign. Note that the parser translates a
rational number to its canonical form which implies there are no common
divisors in the resulting numerator and denominator. Examples of ration
numbers are:
1/2 1/2 2/4 1/2 1 000 000/33 000 1000/33 -3/5 -3/5 We expect very few programs to have text parsed into a rational number while a term was expected. Note that for rationals appearing in an arithmetic expression the only difference is that evaluation moves from runtime to compiletime. The utility list_rationals/0 may be used on a loaded program to check whether the program contains rational numbers inside clauses and thus may be subject to compatibility issues. If a term is intended this can be written as
/(1,2)
,(1)/2
,1 / 2
or some variation thereof. - compatibility
- Read and write rational numbers as e.g.,
1r3
. In other words, this adheres to the same rules asnatural
above, but using the‘r
’instead of‘
’. Note that this may conflict with traditional Prolog as‘/
r
’can be defined as an infix operator. The same argument holds for0x23
and similar syntax for numbers that are part of the ISO standard.
While the syntax is controlled by the flag rational_syntax, behavior on integer division and exponentiation is controlled by the flag prefer_rationals. See section section 4.27.2.2 for arithmetic on rational numbers.