BNR Prolog

BNR Prolog, also known as CLP(BNR), is a declarative constraint logic programming language based on relational interval arithmetic developed at Bell-Northern Research in the 1980s and 1990s. Embedding relational interval arithmetic in a logic programming language differs from other constraint logic programming (CLP) systems like CLP(R) or Prolog-III in that it does not perform any symbolic processing. BNR Prolog was the first such implementation of interval arithmetic in a logic programming language. Since the constraint propagation is performed on real interval values, it is possible to express and partially solve non-linear equations.

Example rule
The simultaneous equations:



\tan x = y $$

x^2 + y^2 = 5 $$

are expressed in CLP(BNR) as:

and a typical implementation's response would be:

X = _58::real(1.0966681287054703,1.0966681287054718), Y = _106::real(1.9486710896099515,1.9486710896099542). Yes

General references

 * J. G. Cleary, "Logical Arithmetic", Future Computing Systems, Vol 2, No 2, pp. 125–149, 1987.
 * W. Older and A. Vellino, "Extending Prolog with Constraint Arithmetic on Real Intervals", in Proc. of the Canadian Conf. on Electrical and Computer Engineering, 1990.
 * Older, W., and Benhamou, F., Programming in CLP(BNR), in: 1st Workshop on Principles and Practice of Constraint Programming, 1993.