# Built-in Math Expressions

Adama lets you do math, and that's awesome! It has the typical operations that you would expect, and then some fun twists. So, let's get into it.

## Operators#

### Parentheses: ( expr )#

You can wrap any expression with parentheses, and parentheses will alter the precedence of evaluation. See operator precedence section for details about operator precedence.

Sample Code

public int z;
@construct {
z = (1 + 2) * 3;
}

Result

{"z":6}

Typing: The resulting type is the type of the sub-expression.

### Unary numeric negation: - expr#

When you want want to turn a positive into a negative, a negative into a positive, a smile into a frown, a frown upside down, or reflect a value over the y-axis.. This is done with the subtract symbol prefixing any expression.

Sample Code

public int z;
public formula neg_z = -z;
@construct {
z = 42;
}

Result

{"z":42,"neg_z":-42}

Typing: The sub-expression type must be an int, long, or double. The resulting type is the type of the sub-expression.

### Unary boolean negation / not / logical compliment: ! expr#

Turn false into true, and true into false. This is the power of the unary Not operator using the exclamation point !. Money back if it doesn't invert those boolean values!

Sample Code

public bool a;
public formula not_a = !a;
@construct {
a = true;
}

Result

{"a":true,"not_a":false}

Typing: The sub-expression type must be a bool, and the resulting type is also bool.

You'll need to use addition to count the phat stacks of money you'll earn with a computer science degree.

Sample Code

public int a;
public formula b = a + 10;
public formula c = b + 100;
@construct {
a = 1;
}

Result

{"a":1,"b":11,"c":111}

Typing: The addition operator commonly is used to add two numbers, but it can also be used with strings and lists. The following table summarizes the typing and behavior.

left typeright typeresult typebehavior
stringstringstringconcatenation
intstringstringconcatenation
longstringstringconcatenation
doublestringstringconcatenation
boolstringstringconcatenation
stringintstringconcatenation
stringlongstringconcatenation
stringdoublestringconcatenation
stringboolstringconcatenation
list<int>doublelist<double>floating point addition on each element
list<double>intlist<double>floating point addition on each element
list<double>doublelist<double>floating point addition on each element
list<string>intlist<string>concatenation on each element
list<string>longlist<string>concatenation on each element
list<string>doublelist<string>concatenation on each element
list<string>boollist<string>concatenation on each element

### Subtraction: expr - expr#

You'll need the subtract operator to remove taxes from your phat stack of dolla-bills.

Sample Code

public int a;
public formula b = a - 10;
public formula c = b - 100;
@construct {
a = 1000;
}

Result

{"a":1000,"b":990,"c":890}

Typing:

The subtraction operator commonly is used to subtract a number from another number, but it can also be used with lists. The following table summarizes the typing and behavior.

left typeright typeresult typebehavior
intintintinteger subtraction
intdoubledoublefloating point subtraction
doubledoubledoublefloating point subtraction
doubleintdoublefloating point subtraction
longintintinteger subtraction
longlonglonginteger subtraction
intlongintinteger subtraction
list<int>intlist<int>integer subtraction on each element
list<int>longlist<long>integer subtraction on each element
list<int>doublelist<double>floating point subtraction on each element
list<long>intlist<int>integer subtraction on each element
list<long>longlist<long>integer subtraction on each element
list<double>intlist<double>floating point subtraction on each element
list<double>doublelist<double>floating point subtraction on each element

### Multiplication: expr * expr#

Sample Code

public int a;
public formula b = a * 2;
public formula c = b * 3;
@construct {
a = 7;
}

Result

{"a":7,"b":14,"c":42}

Typing: TODO | int | int | int | integer subtraction | | int | double | double | floating point subtraction | | double | double | double | floating point subtraction | | double | int | double | floating point subtraction | | long | int | int | integer subtraction | | long | long | long | integer subtraction | | int | long | int | integer subtraction |

### Division: expr / expr#

Sample Code

public double a;
public formula b = a / 2;
public formula c = b / 10;
@construct {
a = 20;
}

Result

{"a":20.0,"b":10.0,"c":1.0}

Typing: TODO

### Modulus: expr % expr#

TODO: something pithy about Modulus and remainders.

Sample Code

public int a;
public formula b = a % 2;
public formula c = a % 4;
@construct {
a = 7;
}

Result

{"a":7,"b":1,"c":3}

Typing: The left and right side must be integral (i.e. int or long), and the result is integral as well. The following table summarizes the logic precisely.

left typeright typeresult type
intintint
longintint
intlongint
longlonglong

### Less than: expr < expr#

TODO: something pithy

Sample Code

public int a;
public int b;
public formula cmp1 = a < b;
public formula cmp2 = b < a;
@construct {
a = 1;
b = 2;
}

Result

{"a":1,"b":2,"cmp1":true,"cmp2":false}

Typing: The left and right must be comparable, and the resulting type is always bool. The following table outlines comparability

left typeright type
intint
intlong
intdouble
longint
longlong
longdouble
doubleint
doublelong
doubledouble
stringstring

TODO: do maybes play into this?

### Greater than: expr > expr#

TODO: something pithy

Sample Code

public int a;
public int b;
public formula cmp1 = a > b;
public formula cmp2 = b > a;
@construct {
a = 1;
b = 2;
}

Result

{"a":1,"b":2,"cmp1":false,"cmp2":true}

Typing: This has the same typing as <

### Less than or equal to: expr <= expr#

TODO: something pithy

Sample Code

public int a;
public int b;
public formula cmp1 = a <= b;
public formula cmp2 = b <= a;
public formula cmp3 = a + 1 <= b;
@construct {
a = 1;
b = 2;
}

Result

{"a":1,"b":2,"cmp1":true,"cmp2":false,"cmp3":true}

Typing: This has the same typing as <

### Greater than or equal to: expr >= expr#

TODO: something pithy

Sample Code

public int a;
public int b;
public formula cmp1 = a >= b;
public formula cmp2 = b >= a;
public formula cmp3 = a + 1 >= b;
@construct {
a = 1;
b = 2;
}

Typing: This has the same typing as <

Result

{"a":1,"b":2,"cmp1":false,"cmp2":true,"cmp3":true}

### Equality: expr == expr#

TODO: something pithy

Sample Code

public int a;
public int b;
public formula eq1 = a == b;
public formula eq2 = a + 1 == b;
@construct {
a = 1;
b = 2;
}

Result

{"a":1,"b":2,"eq1":false,"eq2":true}

Typing: If a left and right type are comparable (see table under <), then the types can be tested for equality. The resulting type is a bool. Beyond comparable left and right types, the following table

### Inequality: expr != expr#

TODO: something pithy

Sample Code

public int a;
public int b;
public formula neq1 = a != b;
public formula neq2 = a + 1 != b;
@construct {
a = 1;
b = 2;
}

Result

{"a":1,"b":2,"neq1":true,"neq2":false}

Typing: This has the same typing as =;

### Logical and: expr && expr#

TODO: something pithy

Truth Table

leftrightresult
falsefalsefalse
truefalsefalse
falsetruefalse
truetruetrue

Sample Code

public bool a;
public bool b;
public formula and = a && b;
@construct {
a = true;
b = false;
}

Result

{"a":true,"b":false,"and":false}

Typing: The left and right expressions must have a type of bool, and the resulting type is bool.

### Logical or: expr || expr#

TODO: something pithy

Truth Table

leftrightresult
falsefalsefalse
truefalsetrue
falsetruetrue
truetruetrue

Sample Code

public bool a;
public bool b;
public formula or = a || b;
@construct {
a = true;
b = false;
}

Result

{"a":true,"b":false,"or":true}

Typing: The left and right expressions must have a type of bool, and the resulting type is bool.

### Conditional / Ternary: expr ? expr : expr#

Sample Code

public bool cond;
public formula inline = a ? 5 : 10;
@construct {
cond = true;
}

Result

{"cond":true,"inline":5}

Typing: The first expression must have a type of bool, and the second and third type must be the compatible under type rectification. The result is the rectified type. For more information about type rectification, see anonymous messages and arrays.

## Operator precedence#

When multiple operators operate on different operands (i.e. things), the order of operators (or operator precedence) is used to break ambiguities such that the final result is deterministic. This avoids confusion, and operators with a higher level must evaluate first.

When there are multiple operators at the same level, then an associativity rule indicates how to evaluate those operations. Typically, this is left to right, but some operators may not be associative or be right to left.

leveloperator(s)descriptionassociativity
11expr.ident
_expr
[expr]
exprF(expr0,...,exprN)
(expr)
field dereference
index lookup
functional application
parentheses
left to right
10expr++
expr--
post-increment
post-decrement
not associative
9++expr
--expr
pre-increment
pre-decrement
not associative
8-expr
!expr
unary negationnot associative
7expr*expr
expr/expr
expr%expr
multiply
divide
modulo
left to right
6expr+expr
expr-expr
subtraction
left to right
5expr<expr
expr>expr
expr<=expr
expr>=expr
less than
greater than
less than or equal to
greater than or equal to
not associative
4expr==expr
expr!=expr
equality
inequality
not associative
3expr&&exprlogical andleft to right
2expr||exprlogical orleft to right
1expr?expr:_exprinline conditional / ternaryright to left