4.2.1.1. Built-in functions and operators
These functions and operators provide the core of the MiniZinc expression language.
Comparison Builtins
These builtins implement comparison operations.
In this section: ‘!=’, ‘<’, ‘<=’, ‘=’, ‘>’, ‘>=’, ~!=, ~=.
‘!=’
1. test '!='($T: x, $T: y)
2. test '!='(opt $T: x, opt $T: y)
3. predicate '!='(any $T: x, any $T: y)
4. test '!='(array [$U] of $T: x, array [$U] of $T: y)
5. test '!='(array [$U] of opt $T: x, array [$U] of opt $T: y)
6. predicate '!='(array [$U] of var $T: x, array [$U] of var $T: y)
7. predicate '!='(array [$U] of var opt $T: x,
array [$U] of var opt $T: y)
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‘<’
1. test '<'($T: x, $T: y)
2. predicate '<'(var $T: x, var $T: y)
3. predicate '<'(var opt int: x, var opt int: y)
4. test '<'(opt int: x, opt int: y)
5. predicate '<'(var opt float: x, var opt float: y)
6. test '<'(opt float: x, opt float: y)
7. test '<'(array [$U] of $T: x, array [$U] of $T: y)
8. predicate '<'(array [$U] of var int: x, array [$U] of var int: y)
9. predicate '<'(array [$U] of var bool: x, array [$U] of var bool: y)
10. predicate '<'(array [$U] of var float: x, array [$U] of var float: y)
11. predicate '<'(array [$U] of var set of int: x,
array [$U] of var set of int: y)
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‘<=’
1. test '<='($T: x, $T: y)
2. predicate '<='(var $T: x, var $T: y)
3. predicate '<='(var opt int: x, var opt int: y)
4. test '<='(opt int: x, opt int: y)
5. predicate '<='(var opt float: x, var opt float: y)
6. test '<='(opt float: x, opt float: y)
7. test '<='(array [$U] of $T: x, array [$U] of $T: y)
8. predicate '<='(array [$U] of var int: x, array [$U] of var int: y)
9. predicate '<='(array [$U] of var bool: x, array [$U] of var bool: y)
10. predicate '<='(array [$U] of var float: x, array [$U] of var float: y)
11. predicate '<='(array [$U] of var set of int: x,
array [$U] of var set of int: y)
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‘=’
1. test '='($T: x, $T: y)
2. test '='(opt $T: x, opt $T: y)
3. predicate '='(any $T: x, any $T: y)
4. test '='(array [$U] of $T: x, array [$U] of $T: y)
5. test '='(array [$U] of opt $T: x, array [$U] of opt $T: y)
6. predicate '='(array [$U] of var $T: x, array [$U] of var $T: y)
7. predicate '='(array [$U] of var opt $T: x, array [$U] of var opt $T: y)
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‘>’
1. test '>'($T: x, $T: y)
2. predicate '>'(var $T: x, var $T: y)
3. predicate '>'(var opt int: x, var opt int: y)
4. test '>'(opt int: x, opt int: y)
5. predicate '>'(var opt float: x, var opt float: y)
6. test '>'(opt float: x, opt float: y)
7. test '>'(array [$U] of $T: x, array [$U] of $T: y)
8. predicate '>'(array [$U] of var int: x, array [$U] of var int: y)
9. predicate '>'(array [$U] of var bool: x, array [$U] of var bool: y)
10. predicate '>'(array [$U] of var float: x, array [$U] of var float: y)
11. predicate '>'(array [$U] of var set of int: x,
array [$U] of var set of int: y)
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‘>=’
1. test '>='($T: x, $T: y)
2. predicate '>='(var $T: x, var $T: y)
3. predicate '>='(var opt int: x, var opt int: y)
4. test '>='(opt int: x, opt int: y)
5. predicate '>='(var opt float: x, var opt float: y)
6. test '>='(opt float: x, opt float: y)
7. test '>='(array [$U] of $T: x, array [$U] of $T: y)
8. predicate '>='(array [$U] of var int: x, array [$U] of var int: y)
9. predicate '>='(array [$U] of var bool: x, array [$U] of var bool: y)
10. predicate '>='(array [$U] of var float: x, array [$U] of var float: y)
11. predicate '>='(array [$U] of var set of int: x,
array [$U] of var set of int: y)
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~!=
predicate '~!='(var opt bool: x, var opt bool: y)
predicate '~!='(var opt int: x, var opt int: y)
predicate '~!='(var opt float: x, var opt float: y)
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Weak disequality. True if either x or y are absent, or present and not equal. |
~=
predicate '~='(var opt bool: x, var opt bool: y)
predicate '~='(var opt int: x, var opt int: y)
predicate '~='(var opt float: x, var opt float: y)
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Weak equality. True if either x or y are absent, or present and equal. |
Arithmetic Builtins
These builtins implement arithmetic operations.
In this section: ‘*’, ‘+’, ‘-’, ‘/’, ‘^’, ‘div’, ‘mod’, abs, arg_max, arg_min, count, max, max_weak, min, min_weak, pow, product, sqrt, sum, ~*, ~+, ~-, ~/, ~div.
‘*’
1. function int: '*'(int: x, int: y)
2. function var int: '*'(var int: x, var int: y)
3. function var int: '*'(var opt int: x, var opt int: y)
4. function int: '*'(opt int: x, opt int: y)
5. function var float: '*'(var opt float: x, var opt float: y)
6. function float: '*'(opt float: x, opt float: y)
7. function float: '*'(float: x, float: y)
8. function var float: '*'(var float: x, var float: y)
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‘+’
1. function int: '+'(int: x, int: y)
2. function var int: '+'(var int: x, var int: y)
3. function float: '+'(float: x, float: y)
4. function var float: '+'(var float: x, var float: y)
5. function var int: '+'(var opt int: x, var opt int: y)
6. function int: '+'(opt int: x, opt int: y)
7. function var float: '+'(var opt float: x, var opt float: y)
8. function float: '+'(opt float: x, opt float: y)
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‘-’
1. function int: '-'(int: x, int: y)
2. function var int: '-'(var int: x, var int: y)
3. function float: '-'(float: x, float: y)
4. function var float: '-'(var float: x, var float: y)
5. function var opt int: '-'(var opt int: x, var opt int: y)
6. function var opt float: '-'(var opt float: x, var opt float: y)
7. function opt int: '-'(opt int: x, opt int: y)
8. function opt float: '-'(opt float: x, opt float: y)
9. function int: '-'(int: x)
10. function var int: '-'(var int: x)
11. function float: '-'(float: x)
12. function var float: '-'(var float: x)
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‘/’
1. function float: '/'(float: x, float: y)
2. function var float: '/'(var float: x, var float: y)
3. function var opt float: '/'(var opt float: x, var opt float: y)
4. function opt float: '/'(opt float: x, opt float: y)
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‘^’
function int: '^'(int: x, int: y)
function var int: '^'(var int: x, var int: y)
function float: '^'(float: x, float: y)
function var float: '^'(var float: x, var float: y)
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Return \({\bf x} ^ {{\bf y}}\) Usage: x ^ y |
‘div’
1. function int: 'div'(int: x, int: y)
2. function var int: 'div'(var int: x, var int: y)
3. function var opt int: 'div'(var opt int: x, var opt int: y)
4. function opt int: 'div'(opt int: x, opt int: y)
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‘mod’
1. function int: 'mod'(int: x, int: y)
2. function var int: 'mod'(var int: x, var int: y)
3. function var opt int: 'mod'(var opt int: x, var opt int: y)
4. function opt int: 'mod'(opt int: x, opt int: y)
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abs
function int: abs(int: x)
function var int: abs(var int: x)
function float: abs(float: x)
function var float: abs(var float: x)
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Return absolute value of x |
arg_max
function $$E: arg_max(array [$$E] of bool: x)
function $$E: arg_max(array [$$E] of int: x)
function $$E: arg_max(array [$$E] of float: x)
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Returns the index of the maximum value in the array x. When breaking ties the least index is returned. |
arg_min
function $$E: arg_min(array [$$E] of bool: x)
function $$E: arg_min(array [$$E] of int: x)
function $$E: arg_min(array [$$E] of float: x)
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Returns the index of the minimum value in the array x. When breaking ties the least index is returned. |
count
function int: count(array [$T] of bool: x)
function var int: count(array [$T] of var bool: x)
function var int: count(array [$T] of var opt bool: x)
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Return number of true elments in array x |
max
1. function $T: max($T: x, $T: y)
2. function var int: max(var int: x, var int: y)
3. function var float: max(var float: x, var float: y)
4. function $T: max(array [$U] of $T: x)
5. function var int: max(array [$U] of var int: x)
6. function var float: max(array [$U] of var float: x)
7. function var int: max(array [$X] of var opt int: x)
8. function var float: max(array [$X] of var opt float: x)
9. function $$E: max(set of $$E: x)
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max_weak
function var opt int: max_weak(array [$X] of var opt int: x)
function var opt float: max_weak(array [$X] of var opt float: x)
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Return maximum of elements in x that are not absent. Result is absent when all values are absent. |
min
1. function $T: min($T: x, $T: y)
2. function var int: min(var int: x, var int: y)
3. function var float: min(var float: x, var float: y)
4. function $T: min(array [$U] of $T: x)
5. function var int: min(array [$U] of var int: x)
6. function var float: min(array [$U] of var float: x)
7. function var int: min(array [$X] of var opt int: x)
8. function var float: min(array [$X] of var opt float: x)
9. function $$E: min(set of $$E: x)
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min_weak
function var opt int: min_weak(array [$X] of var opt int: x)
function var opt float: min_weak(array [$X] of var opt float: x)
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Return minimum of elements in x that are not absent. Result is absent when all values are absent. |
pow
1. function int: pow(int: x, int: y)
2. function var int: pow(var int: x, int: y)
3. function var int: pow(var int: x, var int: y)
4. function float: pow(float: x, float: y)
5. function var float: pow(var float: x, var float: y)
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product
1. function int: product(array [$T] of int: x)
2. function var int: product(array [$T] of var int: x)
3. function float: product(array [$T] of float: x)
4. function var float: product(array [$T] of var float: x)
5. function int: product(array [$T] of opt int: x)
6. function var int: product(array [$T] of var opt int: x)
7. function float: product(array [$T] of opt float: x)
8. function var float: product(array [$T] of var opt float: x)
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sqrt
function float: sqrt(float: x)
function var float: sqrt(var float: x)
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Return \(\sqrt{{\bf x}}\) |
sum
1. function int: sum(array [$T] of int: x)
2. function var int: sum(array [$T] of var int: x)
3. function float: sum(array [$T] of float: x)
4. function var float: sum(array [$T] of var float: x)
5. function var int: sum(array [int] of var opt int: x)
6. function int: sum(array [int] of opt int: x)
7. function var float: sum(array [int] of var opt float: x)
8. function float: sum(array [int] of opt float: x)
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~*
function var opt int: '~*'(var opt int: x, var opt int: y)
function opt int: '~*'(opt int: x, opt int: y)
function var opt float: '~*'(var opt float: x, var opt float: y)
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Weak multiplication. Return product of x and y if both are present, otherwise return absent. |
~+
function var opt int: '~+'(var opt int: x, var opt int: y)
function opt int: '~+'(opt int: x, opt int: y)
function var opt float: '~+'(var opt float: x, var opt float: y)
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Weak addition. Return sum of x and y if both are present, otherwise return absent. |
~-
function var opt int: '~-'(var opt int: x, var opt int: y)
function opt int: '~-'(opt int: x, opt int: y)
function var opt float: '~-'(var opt float: x, var opt float: y)
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Weak subtraction. Return difference of x and y if both are present, otherwise return absent. |
~/
function var opt float: '~/'(var opt float: x, var opt float: y)
function opt float: '~/'(opt float: x, opt float: y)
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Weal optional division. Return absent if x or y is absent, x divided by y if both are present. |
~div
function var opt int: '~div'(var opt int: x, var opt int: y)
function opt int: '~div'(opt int: x, opt int: y)
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Weak optional division. Return absent if x or y is absent, x divided by y if both are present. |
Exponential and logarithmic builtins
These builtins implement exponential and logarithmic functions.
In this section: exp, ln, log, log10, log2.
exp
function float: exp(float: x)
function var float: exp(var float: x)
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Return \(e ^ {{\bf x}}\) |
ln
function float: ln(float: x)
function var float: ln(var float: x)
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Return \(\ln {\bf x}\) |
log
function float: log(float: x, float: y)
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Return \(\log_{{\bf x}} {\bf y}\) |
log10
function float: log10(float: x)
function var float: log10(var float: x)
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Return \(\log_{10} {\bf x}\) |
log2
function float: log2(float: x)
function var float: log2(var float: x)
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Return \(\log_{2} {\bf x}\) |
Trigonometric functions
These builtins implement the standard trigonometric functions.
In this section: acos, acosh, asin, asinh, atan, atanh, cos, cosh, sin, sinh, tan, tanh.
acos
function float: acos(float: x)
function var float: acos(var float: x)
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Return \(\mbox{acos}\ {\bf x}\) |
acosh
function float: acosh(float: x)
function var float: acosh(var float: x)
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Return \(\mbox{acosh}\ {\bf x}\) |
asin
function float: asin(float: x)
function var float: asin(var float: x)
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Return \(\mbox{asin}\ {\bf x}\) |
asinh
function float: asinh(float: x)
function var float: asinh(var float: x)
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Return \(\mbox{asinh}\ {\bf x}\) |
atan
function float: atan(float: x)
function var float: atan(var float: x)
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Return \(\mbox{atan}\ {\bf x}\) |
atanh
function float: atanh(float: x)
function var float: atanh(var float: x)
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Return \(\mbox{atanh}\ {\bf x}\) |
cos
function float: cos(float: x)
function var float: cos(var float: x)
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Return \(\cos {\bf x}\) |
cosh
function float: cosh(float: x)
function var float: cosh(var float: x)
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Return \(\cosh {\bf x}\) |
sin
function float: sin(float: x)
function var float: sin(var float: x)
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Return \(\sin {\bf x}\) |
sinh
function float: sinh(float: x)
function var float: sinh(var float: x)
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Return \(\sinh {\bf x}\) |
tan
function float: tan(float: x)
function var float: tan(var float: x)
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Return \(\tan {\bf x}\) |
tanh
function float: tanh(float: x)
function var float: tanh(var float: x)
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Return \(\tanh {\bf x}\) |
Coercions
These functions implement coercions, or channeling, between different types.
In this section: bool2float, bool2int, ceil, floor, int2float, round, set2array.
bool2float
1. function float: bool2float(bool: b)
2. function opt float: bool2float(opt bool: b)
3. function array [$T] of float: bool2float(array [$T] of bool: x)
4. function array [$T] of var float: bool2float(array [$T] of var bool: x)
5. function var float: bool2float(var bool: b)
6. function var opt float: bool2float(var opt bool: x)
7. function array [$T] of opt float: bool2float(array [$T] of opt bool: x)
8. function array [$T] of var opt float: bool2float(array [$T] of var opt bool: x)
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bool2int
1. function int: bool2int(bool: b)
2. function opt int: bool2int(opt bool: b)
3. function var opt int: bool2int(var opt bool: x)
4. function var int: bool2int(var bool: b)
5. function array [$T] of var int: bool2int(array [$T] of var bool: b)
6. function array [$T] of int: bool2int(array [$T] of bool: x)
7. function array [$T] of set of int: bool2int(array [$T] of set of bool: x)
8. function array [$T] of var int: bool2int(array [$T] of var bool: x)
9. function array [$T] of opt int: bool2int(array [$T] of opt bool: x)
10. function array [$T] of var opt int: bool2int(array [$T] of var opt bool: x)
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ceil
function int: ceil(float: x)
function var int: ceil(var float: x)
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Return \(\lceil{ {\bf x}} \rceil\) |
floor
function int: floor(float: x)
function var int: floor(var float: x)
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Return \(\lfloor{ {\bf x}} \rfloor\) |
int2float
1. function float: int2float(int: x)
2. function opt float: int2float(opt int: x)
3. function var float: int2float(var int: x)
4. function var opt float: int2float(var opt int: x)
5. function array [$T] of float: int2float(array [$T] of int: x)
6. function array [$T] of opt float: int2float(array [$T] of opt int: x)
7. function array [$T] of var float: int2float(array [$T] of var int: x)
8. function array [$T] of var opt float: int2float(array [$T] of var opt int: x)
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round
function int: round(float: x)
function var int: round(var float: x)
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Return x rounded to nearest integer |
set2array
function array [int] of $$E: set2array(set of $$E: x)
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Return a set of integers x coerced to an array of integers |
Array operations
These functions implement the basic operations on arrays.
In this section: ‘++’, ‘in’, array1d, array2d, array2set, array3d, array4d, array5d, array6d, arrayXd, col, has_element, has_index, index_set, index_set_1of2, index_set_1of3, index_set_1of4, index_set_1of5, index_set_1of6, index_set_2of2, index_set_2of3, index_set_2of4, index_set_2of5, index_set_2of6, index_set_3of3, index_set_3of4, index_set_3of5, index_set_3of6, index_set_4of4, index_set_4of5, index_set_4of6, index_set_5of5, index_set_5of6, index_set_6of6, index_sets_agree, length, reverse, row, slice_1d, slice_2d, slice_3d, slice_4d, slice_5d, slice_6d, array_check_form.
Functions and Predicates
‘++’
function array [int] of any $T: '++'(array [int] of any $T: x,
array [int] of any $T: y)
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Return the concatenation of arrays x and y Usage: x ++ y |
‘in’
test 'in'($X: x, array [$T] of $X: y)
test 'in'(opt $X: x, array [$T] of opt $X: y)
predicate 'in'(var $X: x, array [$T] of var $X: y)
predicate 'in'(var opt $X: x, array [$T] of var opt $X: y)
test 'in'(set of $X: x, array [$T] of set of $X: y)
predicate 'in'(var set of $X: x, array [$T] of var set of $X: y)
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Return if y contains x Usage: x in y |
array1d
1. function array [int] of any $V: array1d(array [$U] of any $V: x)
2. function array [$$E] of any $V: array1d(set of $$E: S,
array [$U] of any $V: x)
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array2d
function array [$$E,$$F] of any $V: array2d(set of $$E: S1,
set of $$F: S2,
array [$U] of any $V: x)
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Return array x coerced to two-dimensional array with index sets S1 and S2. Coercions are performed by considering the array x in row-major order. |
array2set
function var set of $$T: array2set(array [int] of var $$T: x)
function set of $$T: array2set(array [int] of $$T: x)
function set of $$T: array2set(array [int] of opt $$T: x)
function set of bool: array2set(array [int] of bool: x)
function set of float: array2set(array [int] of float: x)
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Return the set containing the elements of x |
array3d
function array [$$E,$$F,$$G] of any $V: array3d(set of $$E: S1,
set of $$F: S2,
set of $$G: S3,
array [$U] of any $V: x)
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Return array x coerced to three-dimensional array with index sets S1, S2 and S3. Coercions are performed by considering the array x in row-major order. |
array4d
function array [$$E,$$F,$$G,$$H] of any $V: array4d(set of $$E: S1,
set of $$F: S2,
set of $$G: S3,
set of $$H: S4,
array [$U] of any $V: x)
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Return array x coerced to 4-dimensional array with index sets S1, S2, S3 and S4. Coercions are performed by considering the array x in row-major order. |
array5d
function array [$$E,$$F,$$G,$$H,$$I] of any $V: array5d(set of $$E: S1,
set of $$F: S2,
set of $$G: S3,
set of $$H: S4,
set of $$I: S5,
array [$U] of any $V: x)
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Return array x coerced to 5-dimensional array with index sets S1, S2, S3, S4 and S5. Coercions are performed by considering the array x in row-major order. |
array6d
function array [$$E,$$F,$$G,$$H,$$I,$$J] of any $V: array6d(set of $$E: S1,
set of $$F: S2,
set of $$G: S3,
set of $$H: S4,
set of $$I: S5,
set of $$J: S6,
array [$U] of any $V: x)
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Return array x coerced to 6-dimensional array with index sets S1, S2, S3, S4, S5 and S6. Coercions are performed by considering the array x in row-major order. |
arrayXd
function array [$T] of any $V: arrayXd(array [$T] of any $X: x,
array [$U] of any $V: y)
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Return array y coerced to array with same number of dimensions and same index sets as array x. Coercions are performed by considering the array y in row-major order. |
col
function array [$$E] of any $T: col(array [$$E,int] of any $T: x,
int: c)
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Return column c of array x |
has_element
test has_element($T: e, array [int] of $T: x)
test has_element($T: e, array [int] of opt $T: x)
predicate has_element($T: e, array [$$E] of any $T: x)
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Test if e is an element of array x |
has_index
test has_index(int: i, array [int] of any $T: x)
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Test if i is in the index set of x |
index_set
function set of $$E: index_set(array [$$E] of any $U: x)
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Return index set of one-dimensional array x |
index_set_1of2
function set of $$E: index_set_1of2(array [$$E,int] of any $U: x)
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Return index set of first dimension of two-dimensional array x |
index_set_1of3
function set of $$E: index_set_1of3(array [$$E,int,int] of any $U: x)
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Return index set of first dimension of 3-dimensional array x |
index_set_1of4
function set of $$E: index_set_1of4(array [$$E,int,int,int] of any $U: x)
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Return index set of first dimension of 4-dimensional array x |
index_set_1of5
function set of $$E: index_set_1of5(array [$$E,int,int,int,int] of any $U: x)
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Return index set of first dimension of 5-dimensional array x |
index_set_1of6
function set of $$E: index_set_1of6(array [$$E,int,int,int,int,int] of any $U: x)
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Return index set of first dimension of 6-dimensional array x |
index_set_2of2
function set of $$E: index_set_2of2(array [int,$$E] of any $U: x)
|
Return index set of second dimension of two-dimensional array x |
index_set_2of3
function set of $$E: index_set_2of3(array [int,$$E,int] of any $U: x)
|
Return index set of second dimension of 3-dimensional array x |
index_set_2of4
function set of $$E: index_set_2of4(array [int,$$E,int,int] of any $U: x)
|
Return index set of second dimension of 4-dimensional array x |
index_set_2of5
function set of $$E: index_set_2of5(array [int,$$E,int,int,int] of any $U: x)
|
Return index set of second dimension of 5-dimensional array x |
index_set_2of6
function set of $$E: index_set_2of6(array [int,$$E,int,int,int,int] of any $U: x)
|
Return index set of second dimension of 6-dimensional array x |
index_set_3of3
function set of $$E: index_set_3of3(array [int,int,$$E] of any $U: x)
|
Return index set of third dimension of 3-dimensional array x |
index_set_3of4
function set of $$E: index_set_3of4(array [int,int,$$E,int] of any $U: x)
|
Return index set of third dimension of 4-dimensional array x |
index_set_3of5
function set of $$E: index_set_3of5(array [int,int,$$E,int,int] of any $U: x)
|
Return index set of third dimension of 5-dimensional array x |
index_set_3of6
function set of $$E: index_set_3of6(array [int,int,$$E,int,int,int] of any $U: x)
|
Return index set of third dimension of 6-dimensional array x |
index_set_4of4
function set of $$E: index_set_4of4(array [int,int,int,$$E] of any $U: x)
|
Return index set of fourth dimension of 4-dimensional array x |
index_set_4of5
function set of $$E: index_set_4of5(array [int,int,int,$$E,int] of any $U: x)
|
Return index set of fourth dimension of 5-dimensional array x |
index_set_4of6
function set of $$E: index_set_4of6(array [int,int,int,$$E,int,int] of any $U: x)
|
Return index set of fourth dimension of 6-dimensional array x |
index_set_5of5
function set of $$E: index_set_5of5(array [int,int,int,int,$$E] of any $U: x)
|
Return index set of fifth dimension of 5-dimensional array x |
index_set_5of6
function set of $$E: index_set_5of6(array [int,int,int,int,$$E,int] of any $U: x)
|
Return index set of fifth dimension of 6-dimensional array x |
index_set_6of6
function set of $$E: index_set_6of6(array [int,int,int,int,int,$$E] of any $U: x)
|
Return index set of sixth dimension of 6-dimensional array x |
index_sets_agree
test index_sets_agree(array [$T] of any $U: x, array [$T] of any $W: y)
|
Test if x and y have the same index sets |
length
function int: length(array [$T] of any $U: x)
|
Return the length of array x Note that the length is defined as the number of elements in the array, regardless of its dimensionality. |
reverse
function array [$$E] of $T: reverse(array [$$E] of $T: x)
function array [$$E] of opt $T: reverse(array [$$E] of opt $T: x)
function array [$$E] of any $T: reverse(array [$$E] of any $T: x)
|
Return the array x in reverse order The resulting array has the same index set as x. |
row
function array [$$E] of any $T: row(array [int,$$E] of any $T: x,
int: r)
|
Return row r of array x |
slice_1d
function array [$$F] of any $T: slice_1d(array [$E] of any $T: x,
array [int] of set of int: s,
set of $$F: dims1)
|
Return slice of array x specified by sets s, coerced to new 1d array with index set dims1 |
slice_2d
function array [$$F,$$G] of any $T: slice_2d(array [$E] of any $T: x,
array [int] of set of int: s,
set of $$F: dims1,
set of $$G: dims2)
|
Return slice of array x specified by sets s, coerced to new 2d array with index sets dims1 and dims2 |
slice_3d
function array [$$F,$$G,$$H] of any $T: slice_3d(array [$E] of any $T: x,
array [int] of set of int: s,
set of $$F: dims1,
set of $$G: dims2,
set of $$H: dims3)
|
Return slice of array x specified by sets s, coerced to new 3d array with index sets dims1, dims2 and dims3 |
slice_4d
function array [$$F,$$G,$$H,$$I] of any $T: slice_4d(array [$E] of any $T: x,
array [int] of set of int: s,
set of $$F: dims1,
set of $$G: dims2,
set of $$H: dims3,
set of $$I: dims4)
|
Return slice of array x specified by sets s, coerced to new 4d array with index sets dims1, dims2, dims3, dims4 |
slice_5d
function array [$$F,$$G,$$H,$$I,$$J] of any $T: slice_5d(array [$E] of any $T: x,
array [int] of set of int: s,
set of $$F: dims1,
set of $$G: dims2,
set of $$H: dims3,
set of $$I: dims4,
set of $$J: dims5)
|
Return slice of array x specified by sets s, coerced to new 5d array with index sets dims1, dims2, dims3, dims4, dims5 |
slice_6d
function array [$$F,$$G,$$H,$$I,$$J,$$K] of any $T: slice_6d(array [$E] of any $T: x,
array [int] of set of int: s,
set of $$F: dims1,
set of $$G: dims2,
set of $$H: dims3,
set of $$I: dims4,
set of $$J: dims5,
set of $$K: dims6)
|
Return slice of array x specified by sets s, coerced to new 6d array with index sets dims1, dims2, dims3, dims4, dims5, dims6 |
Annotations
array_check_form
annotation array_check_form
|
Forces a arrayNd call to throw an error if the new index sets are offsets of the current index sets. |
Logical operations
Logical operations are the standard operators of Boolean logic.
In this section: ‘->’, ‘/’, ‘<-’, ‘<->’, ‘\/’, ‘not’, ‘xor’, bool_not, clause, exists, forall, iffall, xorall.
‘->’
test '->'(bool: x, bool: y)
test '->'(opt bool: x, opt bool: y)
predicate '->'(var bool: x, var bool: y)
predicate '->'(var opt bool: x, var opt bool: y)
|
Return truth value of x implies y Usage: x -> y |
‘/'
1. test '/\'(bool: x, bool: y)
2. test '/\'(opt bool: x, opt bool: y)
3. predicate '/\'(var bool: x, var bool: y)
4. predicate '/\'(var opt bool: x, var opt bool: y)
|
|
‘<-’
test '<-'(bool: x, bool: y)
test '<-'(opt bool: x, opt bool: y)
predicate '<-'(var bool: x, var bool: y)
predicate '<-'(var opt bool: x, var opt bool: y)
|
Return truth value of y implies x Usage: x <- y |
‘<->’
test '<->'(bool: x, bool: y)
test '<->'(opt bool: x, opt bool: y)
predicate '<->'(var bool: x, var bool: y)
predicate '<->'(var opt bool: x, var opt bool: y)
|
Return truth value of x if-and-only-if y Usage: x <-> y |
‘/’
1. test '\/'(bool: x, bool: y)
2. test '\/'(opt bool: x, opt bool: y)
3. predicate '\/'(var bool: x, var bool: y)
4. predicate '\/'(var opt bool: x, var opt bool: y)
|
|
‘not’
1. test 'not'(bool: x)
2. function opt bool: 'not'(opt bool: x)
3. predicate 'not'(var bool: x)
4. function var opt bool: 'not'(var opt bool: x)
|
|
‘xor’
test 'xor'(bool: x, bool: y)
test 'xor'(opt bool: x, opt bool: y)
predicate 'xor'(var bool: x, var bool: y)
predicate 'xor'(var opt bool: x, var opt bool: y)
|
Return truth value of x xor y Usage: x xor y |
bool_not
predicate bool_not(var bool: b)
|
Return negation of b |
clause
test clause(array [$T] of bool: x, array [$T] of bool: y)
test clause(array [$T] of opt bool: x, array [$T] of opt bool: y)
predicate clause(array [$T] of var bool: x, array [$T] of var bool: y)
predicate clause(array [$T] of var opt bool: x,
array [$T] of var opt bool: y)
|
Return truth value of \((\bigvee_i {\bf x}[i]) \lor (\bigvee_j \lnot {\bf y}[j])\) |
exists
1. test exists(array [$T] of bool: x)
2. predicate exists(array [$T] of var bool: x)
3. predicate exists(array [int] of var opt bool: x)
|
|
forall
1. test forall(array [$T] of bool: x)
2. predicate forall(array [$T] of var bool: x)
3. predicate forall(array [int] of var opt bool: x)
|
|
iffall
test iffall(array [$T] of bool: x)
test iffall(array [$T] of opt bool: x)
predicate iffall(array [$T] of var bool: x)
predicate iffall(array [$T] of var opt bool: x)
|
Return truth value of \(\text{true}\oplus (\oplus_i {\bf x}[i])\) |
xorall
test xorall(array [$T] of bool: x)
test xorall(array [$T] of opt bool: x)
predicate xorall(array [$T] of var bool: x)
predicate xorall(array [$T] of var opt bool: x)
|
Return truth value of \(\oplus_i {\bf x}[i]\) |
Set operations
These functions implement the basic operations on sets.
In this section: ‘..’, ‘..<’, ‘<..’, ‘<..<’, ‘diff’, ‘in’, ‘intersect’, ‘subset’, ‘superset’, ‘symdiff’, ‘union’, ..<o, ..o, <..<o, <..o, array_intersect, array_union, card, max, min, o.., o..<, o<.., o<..<, set_to_ranges.
‘..’
function set of $$E: '..'($$E: a, $$E: b)
function set of float: '..'(float: a, float: b)
function set of bool: '..'(bool: a, bool: b)
|
Return the set \(\{{\bf a},\ldots,{\bf b}\}\) Usage: a .. b |
‘..<’
function set of $$E: '..<'($$E: a, $$E: b)
|
Return the set \(\{{\bf a},\ldots,{\bf b}-1\}\) Usage: a ..< b |
‘<..’
function set of $$E: '<..'($$E: a, $$E: b)
|
Return the set \(\{{\bf a}+1,\ldots,{\bf b}\}\) Usage: a <.. b |
‘<..<’
function set of $$E: '<..<'($$E: a, $$E: b)
|
Return the set \(\{{\bf a}+1,\ldots,{\bf b}-1\}\) Usage: a <..< b |
‘diff’
function set of $T: 'diff'(set of $T: x, set of $T: y)
function var set of $$T: 'diff'(var set of $$T: x, var set of $$T: y)
|
Return the set difference of sets \({\bf x} \setminus {\bf y}\) Usage: x diff y |
‘in’
1. test 'in'(int: x, set of int: y)
2. predicate 'in'(var int: x, var set of int: y)
3. predicate 'in'(var opt int: x, set of int: y)
4. test 'in'(opt int: x, set of int: y)
5. predicate 'in'(var opt int: x, var set of int: y)
6. test 'in'(float: x, set of float: y)
7. predicate 'in'(var float: x, set of float: y)
8. test 'in'(opt float: x, set of float: y)
9. predicate 'in'(var opt float: x, set of float: y)
|
|
‘intersect’
function set of $T: 'intersect'(set of $T: x, set of $T: y)
function var set of $$T: 'intersect'(var set of $$T: x,
var set of $$T: y)
|
Return the intersection of sets x and y Usage: x intersect y |
‘subset’
1. test 'subset'(set of $T: x, set of $T: y)
2. predicate 'subset'(var set of int: x, var set of int: y)
|
|
‘superset’
1. test 'superset'(set of $T: x, set of $T: y)
2. predicate 'superset'(var set of int: x, var set of int: y)
|
|
‘symdiff’
function set of $T: 'symdiff'(set of $T: x, set of $T: y)
function var set of $$T: 'symdiff'(var set of $$T: x,
var set of $$T: y)
|
Return the symmetric set difference of sets x and y Usage: x symdiff y |
‘union’
function set of $T: 'union'(set of $T: x, set of $T: y)
function var set of $$T: 'union'(var set of $$T: x, var set of $$T: y)
|
Return the union of sets x and y Usage: x union y |
..<o
function set of $$E: '..<o'($$E: a)
|
Return the set \(\{{\bf a},\ldots,{\bf b}-1\}\) |
..o
function set of $$E: '..o'($$E: a)
|
Return the set \(\{{\bf a},\ldots,{\bf b}-1\}\) |
<..<o
function set of $$E: '<..<o'($$E: a)
|
Return the set \(\{{\bf a}+1,\ldots,{\bf b}-1\}\) |
<..o
function set of $$E: '<..o'($$E: a)
|
Return the set \(\{{\bf a}+1,\ldots,{\bf b}\}\) |
array_intersect
1. function set of $U: array_intersect(array [$T] of set of $U: x)
2. function var set of int: array_intersect(array [int] of var set of int: x)
|
|
array_union
function set of $U: array_union(array [$T] of set of $U: x)
function var set of int: array_union(array [int] of var set of int: x)
|
Return the union of the sets in array x |
card
function int: card(set of $T: x)
function var int: card(var set of int: x)
|
Return the cardinality of the set x |
max
function var $$E: max(var set of $$E: s)
|
Return the maximum of the set s |
min
function var $$E: min(var set of $$E: s)
|
Return the minimum of the set s |
o..
function set of $$E: 'o..'($$E: a)
|
Return the set \(\{{\bf a},\ldots,{\bf b}-1\}\) |
o..<
function set of $$E: 'o..<'($$E: a)
|
Return the set \(\{{\bf a},\ldots,{\bf b}-1\}\) |
o<..
function set of $$E: 'o<..'($$E: a)
|
Return the set \(\{{\bf a}+1,\ldots,{\bf b}\}\) |
o<..<
function set of $$E: 'o<..<'($$E: a)
|
Return the set \(\{{\bf a}+1,\ldots,{\bf b}-1\}\) |
set_to_ranges
function array [int] of int: set_to_ranges(set of int: S)
function array [int] of float: set_to_ranges(set of float: S)
function array [int] of bool: set_to_ranges(set of bool: S)
|
Return a sorted list of the non-overlapping ranges in S |
String operations
These functions implement operations on strings.
In this section: ‘++’, concat, file_path, format, format_justify_string, join, json_array, json_object, outputJSON, outputJSONParameters, output_to_json_section, output_to_section, show, show2d, show2d_indexed, show3d, showJSON, show_float, show_int, string_length.
‘++’
function string: '++'(string: s1, string: s2)
|
Return concatenation of s1 and s2 Usage: s1 ++ s2 |
concat
function string: concat(array [$T] of string: s)
|
Return concatenation of strings in array s |
file_path
function string: file_path()
|
Return path of file where this function is called |
format
1. function string: format(any $T: x)
2. function string: format(array [$U] of any $T: x)
3. function string: format(int: w, int: p, any $T: x)
4. function string: format(int: w, int: p, array [$U] of any $T: x)
5. function string: format(int: w, any $T: x)
6. function string: format(int: w, array [$U] of any $T: x)
|
|
format_justify_string
function string: format_justify_string(int: w, string: x)
|
String justification Returns the string x right justified by the number of characters given by w, or left justified if w is negative. |
join
function string: join(string: d, array [$T] of string: s)
|
Join string in array s using delimiter d |
json_array
function string: json_array(array [int] of string: arr)
|
Create a JSON array from an array of JSON strings arr. The elements are assumed to be strings already in JSON format (usually generated using showJSON) |
json_object
function string: json_object(array [int,1..2] of string: obj)
|
Create a JSON object from an array of key-value pairs obj. obj[i, 1] is the key name for the i-th entry obj[i, 2] is the JSON value for the o i-th entry (usually generated using showJSON) |
outputJSON
1. function array [int] of string: outputJSON()
2. function array [int] of string: outputJSON(bool: b)
|
|
outputJSONParameters
function array [int] of string: outputJSONParameters()
|
Return array for output of all parameters in JSON format |
output_to_json_section
test output_to_json_section(string: s, any $T: o)
test output_to_json_section(string: s, array [$U] of any $T: o)
|
Output o to the JSON section s |
output_to_section
test output_to_section(string: s, string: o)
|
Add o to the output section s |
show
function string: show(any $T: x)
function string: show(array [$U] of any $T: x)
|
Convert x into a string |
show2d
function string: show2d(array [$$E,$$F] of any $T: x)
|
Convert two-dimensional array x into a string |
show2d_indexed
function string: show2d_indexed(array [int] of string: row_hdr,
array [int] of string: col_hdr,
array [int,int] of string: vs)
|
Convert two-dimensional array vs into a string with row and column headers row_hdr and col_hdr |
show3d
function string: show3d(array [int,int,int] of any $T: x)
|
Convert three-dimensional array x into a string |
showJSON
function string: showJSON(any $T: x)
function string: showJSON(array [$U] of any $T: x)
|
Convert x into JSON string |
show_float
function string: show_float(int: w, int: p, var float: x)
|
Formatted to-string conversion for floats. Converts the float x into a string right justified by the number of characters given by w, or left justified if w is negative. The number of digits to appear after the decimal point is given by p. It is a run-time error for p to be negative. |
show_int
function string: show_int(int: w, var int: x)
|
Formatted to-string conversion for integers Converts the integer x into a string right justified by the number of characters given by w, or left justified if w is negative. |
string_length
function int: string_length(string: s)
|
Return length of s |
Functions for enums
In this section: enum_next, enum_of, enum_prev, to_enum.
enum_next
1. function $$E: enum_next($$E: x)
2. function opt $$E: enum_next(opt $$E: x)
3. function var $$E: enum_next(var $$E: x)
4. function var opt $$E: enum_next(var opt $$E: x)
5. function $$E: enum_next(set of $$E: e, $$E: x)
6. function opt $$E: enum_next(set of $$E: e, opt $$E: x)
7. function var $$E: enum_next(set of $$E: e, var $$E: x)
8. function var opt $$E: enum_next(set of $$E: e, var opt $$E: x)
|
|
enum_of
function set of $$E: enum_of(var opt $$E: x)
function set of $$E: enum_of(var set of $$E: x)
function set of $$E: enum_of(array [$T] of var opt $$E: x)
function set of $$E: enum_of(array [$T] of var set of $$E: x)
|
Return enum set of x |
enum_prev
1. function $$E: enum_prev($$E: x)
2. function opt $$E: enum_prev(opt $$E: x)
3. function var $$E: enum_prev(var $$E: x)
4. function var opt $$E: enum_prev(var opt $$E: x)
5. function $$E: enum_prev(set of $$E: e, $$E: x)
6. function opt $$E: enum_prev(set of $$E: e, opt $$E: x)
7. function var $$E: enum_prev(set of $$E: e, var $$E: x)
8. function var opt $$E: enum_prev(set of $$E: e, var opt $$E: x)
|
|
to_enum
function $$E: to_enum(set of $$E: X, int: x)
function opt $$E: to_enum(set of $$E: X, opt int: x)
function var $$E: to_enum(set of $$E: X, var int: x)
function var opt $$E: to_enum(set of $$E: X, var opt int: x)
function array [$U] of $$E: to_enum(set of $$E: X,
array [$U] of int: x)
function array [$U] of opt $$E: to_enum(set of $$E: X,
array [$U] of opt int: x)
function array [$U] of var $$E: to_enum(set of $$E: X,
array [$U] of var int: x)
function array [$U] of var opt $$E: to_enum(set of $$E: X,
array [$U] of var opt int: x)
function set of $$E: to_enum(set of $$E: X, set of int: x)
function array [$U] of set of $$E: to_enum(set of $$E: X,
array [$U] of set of int: x)
function array [$U] of var set of $$E: to_enum(set of $$E: X,
array [$U] of var set of int: x)
|
Convert x to enum type X |