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.^[1] Since the constraint propagation is performed on real interval values, it is possible to express and partially solve non-linear equations.^[2]

The simultaneous equations:

${\displaystyle \tan x=y}$

${\displaystyle x^{2}+y^{2}=5}$

are expressed in CLP(BNR) as:

?- {X>=0,Y>=0, tan(X)==Y, X**2 + Y**2 == 5}.

and a typical implementation's response would be:

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

• Comparison of Prolog implementations
• Prolog syntax and semantics

• 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.

• GitHub site for a 2018 re-implementation in SWI-Prolog

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