Author:Leslie De Koninck, K.U. Leuven

This CLP(Q,R) system is a port of the CLP(Q,R) system of Sicstus
Prolog by Christian Holzbaur: Holzbaur C.: OFAI clp(q,r) Manual, Edition
1.3.3, Austrian Research Institute for Artificial Intelligence, Vienna,
TR-95-09, 1995.^{85http://www.ai.univie.ac.at/cgi-bin/tr-online?number+95-09}
This manual is roughly based on the manual of the above mentioned
CLP(Q,R) implementation.

The CLP(Q,R) system consists of two components: the CLP(Q) library for handling constraints over the rational numbers and the CLP(R) library for handling constraints over the real numbers (using floating point numbers as representation). Both libraries offer the same predicates (with exception of bb_inf/4 in CLP(Q) and bb_inf/5 in CLP(R)). It is allowed to use both libraries in one program, but using both CLP(Q) and CLP(R) constraints on the same variable will result in an exception.

Please note that the `library(clpqr)`

library is *not*
an
*autoload* library and therefore this library must be loaded
explicitely before using it:

:- use_module(library(clpq)).

or

:- use_module(library(clpr)).

**{}**(`+Constraints`)-
Adds the constraints given by
`Constraints`to the constraint store. **entailed**(`+Constraint`)-
Succeeds if
`Constraint`is necessarily true within the current constraint store. This means that adding the negation of the constraint to the store results in failure. **inf**(`+Expression, -Inf`)-
Computes the infimum of
`Expression`within the current state of the constraint store and returns that infimum in`Inf`. This predicate does not change the constraint store. **sup**(`+Expression, -Sup`)-
Computes the supremum of
`Expression`within the current state of the constraint store and returns that supremum in`Sup`. This predicate does not change the constraint store. **minimize**(`+Expression`)-
Minimizes
`Expression`within the current constraint store. This is the same as computing the infimum and equation the expression to that infimum. **maximize**(`+Expression`)-
Maximizes
`Expression`within the current constraint store. This is the same as computing the supremum and equating the expression to that supremum. **bb_inf**(`+Ints, +Expression, -Inf, -Vertex, +Eps`)-
This predicate is offered in CLP(R) only. It computes the infimum of
`Expression`within the current constraint store, with the additional constraint that in that infimum, all variables in`Ints`have integral values.`Vertex`will contain the values of`Ints`in the infimum.`Eps`denotes how much a value may differ from an integer to be considered an integer. E.g. when`Eps`= 0.001, then X = 4.999 will be considered as an integer (5 in this case).`Eps`should be between 0 and 0.5. **bb_inf**(`+Ints, +Expression, -Inf, -Vertex`)- This predicate is offered in CLP(Q) only. It behaves the same as bb_inf/5 but does not use an error margin.
**bb_inf**(`+ints, +Expression, -Inf`)- The same as bb_inf/5 or bb_inf/4 but without returning the values of the integers. In CLP(R), an error margin of 0.001 is used.
**dump**(`+Target, +Newvars, -CodedAnswer`)-
Returns the constraints on
`Target`in the list`CodedAnswer`where all variables of`Target`have veen replaced by`NewVars`. This operation does not change the constraint store. E.g. indump([X,Y,Z],[x,y,z],Cons)

Cons will contain the constraints on X, Y and Z where these variables have been replaced by atoms x, y and z.

<Constraints> | ::= | <Constraint> | single constraint |

| | <Constraint>
, <Constraints> | conjunction | |

| | <Constraint>
; <Constraints> | disjunction | |

<Constraint> | ::= | <Expression> `<` <Expression> | less than |

| | <Expression> `>` <Expression> | greater than | |

| | <Expression> `=<` <Expression> | less or equal | |

| | `<=` (<Expression>, <Expression>) | less or equal | |

| | <Expression> `>=` <Expression> | greater or equal | |

| | <Expression> `=\=` <Expression> | not equal | |

| | <Expression>
=:= <Expression> | equal | |

| | <Expression>
= <Expression> | equal | |

<Expression> | ::= | <Variable> | Prolog variable |

| | <Number> | Prolog number (float, integer) | |

| | +<Expression> | unary plus | |

| | -<Expression> | unary minus | |

| | <Expression>
+ <Expression> | addition | |

| | <Expression>
- <Expression> | substraction | |

| | <Expression>
* <Expression> | multiplication | |

| | <Expression>
/ <Expression> | division | |

| | abs(<Expression>) | absolute value | |

| | sin(<Expression>) | sine | |

| | cos(<Expression>) | cosine | |

| | tan(<Expression>) | tangent | |

| | exp(<Expression>) | exponent | |

| | pow(<Expression>) | exponent | |

| | <Expression> `^` <Expression> | exponent | |

| | min(<Expression>, <Expression>) | minimum | |

| | max(<Expression>, <Expression>) | maximum |

Table 9 : CLP(Q,R) constraint BNF |

Instead of using the {}/1 predicate, you can also use the standard unification mechanism to store constraints. The following code samples are equivalent:

*Unification with a variable*

{X =:= Y} {X = Y} X = Y

*Unification with a number*

{X =:= 5.0} {X = 5.0} X = 5.0

A = B * C | B or C is ground | A = 5 * C or A = B * 4 |

A and (B or C) are ground | 20 = 5 * C or 20 = B * 4 | |

A = B / C | C is ground | A = B / 3 |

A and B are ground | 4 = 12 / C | |

X = min(Y,Z) | Y and Z are ground | X = min(4,3) |

X = max(Y,Z) | Y and Z are ground | X = max(4,3) |

X = abs(Y) | Y is ground | X = abs(-7) |

X = pow(Y,Z) | X and Y are ground | 8
= 2 `^` Z |

X = exp(Y,Z) | X and Z are ground | 8
= Y `^` 3 |

X = Y `^` Z | Y and Z are ground | X = 2 `^` 3 |

X = sin(Y) | X is ground | 1 = sin(Y) |

X = cos(Y) | Y is ground | X = sin(1.5707) |

X = tan(Y) |

Table 10 : CLP(Q,R) isolating axioms |