Arithmetic

Author(s): Daniel Cabeza, Manuel Hermenegildo.

Arithmetic is performed by built-in predicates which take as arguments arithmetic expressions (see arithexpression/1) and evaluate them. Terms representing arithmetic expressions can be created dynamically, but at the time of evaluation, each variable in an arithmetic expression must be bound to a non-variable expression (the term must be ground). For example, given the code in the first line a possible shell interaction follows:

evaluate(Expression, Answer) :- Answer is Expression.

?- _X=24*9, evaluate(_X+6, Ans).

Ans = 222 ?

yes

Usage and interface

Library usage:
These predicates are builtin in Ciao, so nothing special has to be done to use them.
Exports:
- Predicates:
  is/2, </2, =</2, >/2, >=/2, =:=/2, =\=/2.
- Regular Types:
  arithexpression/1, intexpression/1.
- Multifiles:
  $internal_error_where_term/4.
Imports:
- System library modules:
  assertions/native_props.
- Packages:
  prelude, nonpure, assertions, nortchecks, nativeprops, isomodes.

Documentation on exports

PREDICATE

is/2:

ISOVal is Exp

The arithmetic expression Exp is evaluated and the result is unified with Val

(Trust) Usage 1:A is B

The following properties should hold at call time:
(term_typing:var/1)A is a free variable.
(term_typing:nonvar/1)B is currently a term which is not a free variable.
(term_typing:var/1)A is a free variable.
(arithmetic:arithexpression/1)B is an arithmetic expression.
The following properties hold upon exit:
(basic_props:num/1)A is a number.
(arithmetic:arithexpression/1)B is an arithmetic expression.
(native_props:size/2)int(B) is the size of argument A, for any approximation.
The following properties hold globally:
(native_props:not_fails/1)All the calls of the form A is B do not fail.
(basic_props:eval/1)A is B is evaluable at compile-time.

(Trust) Usage 2:A is B

The following properties should hold at call time:
(term_typing:var/1)A is a free variable.
(term_typing:nonvar/1)B is currently a term which is not a free variable.
(term_typing:var/1)A is a free variable.
(arithmetic:intexpression/1)B is an integer expression.
The following properties hold upon exit:
(basic_props:int/1)A is an integer.
(arithmetic:intexpression/1)B is an integer expression.
(native_props:size/2)int(B) is the size of argument A, for any approximation.
The following properties hold globally:
(native_props:not_fails/1)All the calls of the form A is B do not fail.
(basic_props:eval/1)A is B is evaluable at compile-time.

(Trust) Usage 3:A is B

The following properties should hold at call time:
(term_typing:nonvar/1)A is currently a term which is not a free variable.
(term_typing:nonvar/1)B is currently a term which is not a free variable.
(basic_props:num/1)A is a number.
(arithmetic:arithexpression/1)B is an arithmetic expression.
The following properties hold globally:
(native_props:test_type/2)Indicates the type of test that a predicate performs. Required by the nonfailure analyisis.

(Trust) Usage 4:A is B

The following properties should hold at call time:
(term_typing:nonvar/1)A is currently a term which is not a free variable.
(term_typing:nonvar/1)B is currently a term which is not a free variable.
(basic_props:int/1)A is an integer.
(arithmetic:intexpression/1)B is an integer expression.
The following properties hold globally:
(native_props:test_type/2)Indicates the type of test that a predicate performs. Required by the nonfailure analyisis.

General properties:

Test:X is Y

is/2, sqrt test

If the following properties should hold at call time:
(term_basic:= /2)term_basic:Y=sqrt(4)
then the following properties should hold upon exit:
(term_basic:= /2)term_basic:X=2.0

Trust:A is B

The following properties hold globally:
(native_props:size_metric/3)int is the metric of the variable A, for any approximation.
(native_props:size_metric/3)int is the metric of the variable B, for any approximation.

True:

The following properties hold globally:
(basic_props:native/1)This predicate is understood natively by CiaoPP.
(basic_props:sideff/2)Val is Exp is side-effect free.
(basic_props:bind_ins/1)Val is Exp is binding insensitive.
(native_props:is_det/1)All calls of the form Val is Exp are deterministic.
(native_props:relations/2)Goal Val is Exp produces inf solutions.

PREDICATE

</2:

ISOExp1<Exp2

The numeric value of Exp1 is less than the numeric value of Exp2 when both are evaluated as arithmetic expressions.

(Trust) Usage:A<B

The following properties should hold at call time:
(term_typing:nonvar/1)A is currently a term which is not a free variable.
(term_typing:nonvar/1)B is currently a term which is not a free variable.
(arithmetic:arithexpression/1)A is an arithmetic expression.
(arithmetic:arithexpression/1)B is an arithmetic expression.
The following properties hold globally:
(basic_props:eval/1)A<B is evaluable at compile-time.
(native_props:size_metric/3)int is the metric of the variable A, for any approximation.
(native_props:size_metric/3)int is the metric of the variable B, for any approximation.

General properties:

True:

The following properties hold globally:
(basic_props:native/1)This predicate is understood natively by CiaoPP.
(basic_props:sideff/2)Exp1<Exp2 is side-effect free.
(basic_props:bind_ins/1)Exp1<Exp2 is binding insensitive.
(native_props:is_det/1)All calls of the form Exp1<Exp2 are deterministic.
(native_props:relations/2)Goal Exp1<Exp2 produces inf solutions.
(native_props:test_type/2)Indicates the type of test that a predicate performs. Required by the nonfailure analyisis.

PREDICATE

=</2:

ISOExp1=<Exp2

The numeric value of Exp1 is less than or equal to the numeric value of Exp2 when both are evaluated as arithmetic expressions.

(Trust) Usage:A=<B

The following properties should hold at call time:
(term_typing:nonvar/1)A is currently a term which is not a free variable.
(term_typing:nonvar/1)B is currently a term which is not a free variable.
(arithmetic:arithexpression/1)A is an arithmetic expression.
(arithmetic:arithexpression/1)B is an arithmetic expression.
The following properties hold globally:
(basic_props:eval/1)A=<B is evaluable at compile-time.
(native_props:size_metric/3)int is the metric of the variable A, for any approximation.
(native_props:size_metric/3)int is the metric of the variable B, for any approximation.

General properties:

True:

The following properties hold globally:
(basic_props:native/1)This predicate is understood natively by CiaoPP.
(basic_props:sideff/2)Exp1=<Exp2 is side-effect free.
(basic_props:bind_ins/1)Exp1=<Exp2 is binding insensitive.
(native_props:is_det/1)All calls of the form Exp1=<Exp2 are deterministic.
(native_props:relations/2)Goal Exp1=<Exp2 produces inf solutions.
(native_props:test_type/2)Indicates the type of test that a predicate performs. Required by the nonfailure analyisis.

PREDICATE

>/2:

ISOExp1>Exp2

The numeric value of Exp1 is greater than the numeric value of Exp2 when both are evaluated as arithmetic expressions.

(Trust) Usage:A>B

The following properties should hold at call time:
(term_typing:nonvar/1)A is currently a term which is not a free variable.
(term_typing:nonvar/1)B is currently a term which is not a free variable.
(arithmetic:arithexpression/1)A is an arithmetic expression.
(arithmetic:arithexpression/1)B is an arithmetic expression.
The following properties hold globally:
(basic_props:eval/1)A>B is evaluable at compile-time.
(native_props:size_metric/3)int is the metric of the variable A, for any approximation.
(native_props:size_metric/3)int is the metric of the variable B, for any approximation.

General properties:

True:

The following properties hold globally:
(basic_props:native/1)This predicate is understood natively by CiaoPP.
(basic_props:sideff/2)Exp1>Exp2 is side-effect free.
(basic_props:bind_ins/1)Exp1>Exp2 is binding insensitive.
(native_props:is_det/1)All calls of the form Exp1>Exp2 are deterministic.
(native_props:relations/2)Goal Exp1>Exp2 produces inf solutions.
(native_props:test_type/2)Indicates the type of test that a predicate performs. Required by the nonfailure analyisis.

PREDICATE

>=/2:

ISOExp1>=Exp2

The numeric value of Exp1 is greater than or equal to the numeric value of Exp2 when both are evaluated as arithmetic expressions.

(Trust) Usage:A>=B

The following properties should hold at call time:
(term_typing:nonvar/1)A is currently a term which is not a free variable.
(term_typing:nonvar/1)B is currently a term which is not a free variable.
(arithmetic:arithexpression/1)A is an arithmetic expression.
(arithmetic:arithexpression/1)B is an arithmetic expression.
The following properties hold globally:
(basic_props:eval/1)A>=B is evaluable at compile-time.
(native_props:size_metric/3)int is the metric of the variable A, for any approximation.
(native_props:size_metric/3)int is the metric of the variable B, for any approximation.

General properties:

True:

The following properties hold globally:
(basic_props:native/1)This predicate is understood natively by CiaoPP.
(basic_props:sideff/2)Exp1>=Exp2 is side-effect free.
(basic_props:bind_ins/1)Exp1>=Exp2 is binding insensitive.
(native_props:is_det/1)All calls of the form Exp1>=Exp2 are deterministic.
(native_props:relations/2)Goal Exp1>=Exp2 produces inf solutions.
(native_props:test_type/2)Indicates the type of test that a predicate performs. Required by the nonfailure analyisis.

PREDICATE

=:=/2:

ISOExp1=:=Exp2

The numeric values of Exp1 and Exp2 are equal when both are evaluated as arithmetic expressions.

(Trust) Usage:A=:=B

The following properties should hold at call time:
(term_typing:nonvar/1)A is currently a term which is not a free variable.
(term_typing:nonvar/1)B is currently a term which is not a free variable.
(arithmetic:arithexpression/1)A is an arithmetic expression.
(arithmetic:arithexpression/1)B is an arithmetic expression.
The following properties hold globally:
(basic_props:eval/1)A=:=B is evaluable at compile-time.
(native_props:size_metric/3)int is the metric of the variable A, for any approximation.
(native_props:size_metric/3)int is the metric of the variable B, for any approximation.

General properties:

True:

The following properties hold globally:
(basic_props:native/1)This predicate is understood natively by CiaoPP.
(basic_props:sideff/2)Exp1=:=Exp2 is side-effect free.
(basic_props:bind_ins/1)Exp1=:=Exp2 is binding insensitive.
(native_props:is_det/1)All calls of the form Exp1=:=Exp2 are deterministic.
(native_props:relations/2)Goal Exp1=:=Exp2 produces inf solutions.
(native_props:test_type/2)Indicates the type of test that a predicate performs. Required by the nonfailure analyisis.

PREDICATE

=\=/2:

ISOExp1=\=Exp2

The numeric values of Exp1 and Exp2 are not equal when both are evaluated as arithmetic expressions.

(Trust) Usage:A=\=B

The following properties should hold at call time:
(term_typing:nonvar/1)A is currently a term which is not a free variable.
(term_typing:nonvar/1)B is currently a term which is not a free variable.
(arithmetic:arithexpression/1)A is an arithmetic expression.
(arithmetic:arithexpression/1)B is an arithmetic expression.
The following properties hold globally:
(basic_props:eval/1)A=\=B is evaluable at compile-time.
(native_props:size_metric/3)int is the metric of the variable A, for any approximation.
(native_props:size_metric/3)int is the metric of the variable B, for any approximation.

General properties:

True:

The following properties hold globally:
(basic_props:native/1)This predicate is understood natively by CiaoPP.
(basic_props:sideff/2)Exp1=\=Exp2 is side-effect free.
(basic_props:bind_ins/1)Exp1=\=Exp2 is binding insensitive.
(native_props:is_det/1)All calls of the form Exp1=\=Exp2 are deterministic.
(native_props:relations/2)Goal Exp1=\=Exp2 produces inf solutions.
(native_props:test_type/2)Indicates the type of test that a predicate performs. Required by the nonfailure analyisis.

REGTYPE

arithexpression/1:

An arithmetic expression is a term built from numbers and evaluable functors that represent arithmetic functions. An arithmetic expression evaluates to a number, which may be an integer (int/1) or a float (flt/1). The evaluable functors allowed in an arithmetic expression are listed below, together with an indication of the functions they represent. All evaluable functors defined in ISO-Prolog are implemented, as well as some other useful or traditional. Unless stated otherwise, an expression evaluates to a float if any of its arguments is a float, otherwise to an integer.

- /1: sign reversal. ISO
+ /1: identity.
-- /1: decrement by one.
++ /1: increment by one.
+ /2: addition. ISO
- /2: subtraction. ISO
* /2: multiplication. ISO
// /2: integer division. Float arguments are truncated to integers, result always integer. ISO
/ /2: division. Result always float. ISO
rem/2: integer remainder. The result is always an integer, its sign is the sign of the first argument. ISO
mod/2: modulo. The result is always a positive integer. ISO
abs/1: absolute value. ISO
sign/1: sign of. ISO
float_integer_part/1: float integer part. Result always float. ISO
float_fractional_part/1: float fractional part. Result always float. ISO
truncate/1: The result is the integer equal to the integer part of the argument. ISO
integer/1: same as truncate/1.
float/1: conversion to float. ISO
floor/1: largest integer not greater than. ISO
round/1: integer nearest to. ISO
ceiling/1: smallest integer not smaller than. ISO
** /2: exponentiation. Result always float. ISO
>> /2: integer bitwise right shift. ISO
<< /2: integer bitwise left shift. ISO
/\ /2: integer bitwise and. ISO
\/ /2: integer bitwise or. ISO
\ /1: integer bitwise complement. ISO
# /2: integer bitwise exclusive or (xor).
exp/1: exponential (e to the power of). Result always float. ISO
log/1: natural logarithm (base e). Result always float. ISO
sqrt/1: square root. Result always float. ISO
sin/1: sine. Result always float. ISO
cos/1: cosine. Result always float. ISO
atan/1: arc tangent. Result always float. ISO
gcd/2: Greatest common divisor. Arguments must evaluate to integers, result always integer.

In addition to these functors, a list of just a number evaluates to this number. Since a quoted string is just a list of integers, this allows a quoted character to be used in place of its ASCII code; e.g. "A" behaves within arithmetic expressions as the integer 65. Note that this is not ISO-compliant, and that can be achieved by using the ISO notation 0'A.

Arithmetic expressions, as described above, are just data structures. If you want one evaluated you must pass it as an argument to one of the arithmetic predicates defined in this library.

Usage:arithexpression(E)

E is an arithmetic expression.

General properties:

Trust:

The following properties hold globally:
(basic_props:sideff/2)arithexpression(Arg1) is side-effect free.

Trust:

If the following properties hold at call time:
(term_typing:nonvar/1)Arg1 is currently a term which is not a free variable.
then the following properties hold globally:
(native_props:is_det/1)All calls of the form arithexpression(Arg1) are deterministic.
(native_props:test_type/2)Indicates the type of test that a predicate performs. Required by the nonfailure analyisis.

REGTYPE

intexpression/1:

Usage:intexpression(E)

E is an integer expression.

General properties:

True:

The following properties hold globally:
(basic_props:sideff/2)intexpression(Arg1) is side-effect free.

Documentation on multifiles

PREDICATE

$internal_error_where_term/4:

No further documentation available for this predicate. The predicate is multifile.

Known bugs and planned improvements

Run-time checks have been reported not to work with this code. That means that either the assertions here, or the code that implements the run-time checks are erroneous.
We could improve the precision if we had (arithexpression,+intexpression) but we need a relational domain. -- EMM, JFMC

Arithmetic

Usage and interface

Documentation on exports

Documentation on multifiles

Known bugs and planned improvements

Module Sections

Global Links

Indices