Operators

Keel provides a rich set of operators for arithmetic, comparison, logical operations, and more.

Arithmetic Operators

Basic mathematical operations:

Operator	Description	Example
`+`	Addition	`1 + 2`
`-`	Subtraction	`5 - 3`
`*`	Multiplication	`4 * 2`
`/`	Division	`10 / 3`
`//`	Integer division	`10 // 3`
`%`	Modulo	`10 % 3`
`^`	Power	`2 ^ 8`

let addition = 5 + 3

let subtraction = 10 - 4

let multiply = 6 * 7

let divide = 15 / 3

let intDiv = 10 // 3

let modulo = 17 % 5

let power = 2 ^ 10

let negative = -42  -- -42 (negation)

power

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Integer vs Float Division

Division behavior:

let floatDiv = 10 / 3

let intDiv = 10 // 3

(floatDiv, intDiv)

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Numeric Type Promotion

When mixing Int and Float, Int is promoted to Float:

let x = 1 + 2.5

let y = 3 * 1.5

x + y

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Comparison Operators

Compare values and return Bool:

Operator	Description	Example
`==`	Equal	`a == b`
`!=`	Not equal	`a != b`
`<`	Less than	`a < b`
`<=`	Less than or equal	`a <= b`
`>`	Greater than	`a > b`
`>=`	Greater than or equal	`a >= b`

let eq = 5 == 5

let neq = 5 != 6

let lt = 3 < 5

let gt = 5 > 3

let lte = 3 <= 3

let gte = 5 >= 4

(eq, neq, lt, gt, lte, gte)

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== and != work on all scalar types (Int, Float, Decimal, Bool, String, Char, Symbol, Unit), Enum variants, and structural collections (Tuple, List, Record). They do not work on functions, DataFrames, Matrices, or open record types.

Logical Operators

Boolean logic operations:

Operator	Description	Example
`&&`	Logical AND	`a && b`
`\|\|`	Logical OR	`a \|\| b`
`not`	Logical NOT	`not a`

-- And (both must be True)
let and1 = True && True

let and2 = True && False

-- Or (at least one must be True)
let or1 = True || False

let or2 = False || False

-- Not (negation)
let not1 = not True  -- False

let not2 = not False  -- True

let not3 = not (1 > 2)

-- True
let not4 = not not True  -- True (double negation)

(and1, or1, not1, not3)

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Short-circuit Evaluation

Logical operators use short-circuit evaluation:

-- False && ... returns False immediately without evaluating the right side
let result = False && True

result  -- False

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Bitwise Operators

Bitwise operations on Int values (two's-complement 64-bit integers):

Operator	Description	Example
`~`	Bitwise NOT	`~n`

~n flips every bit of n. The result satisfies ~~n == n (double inversion is identity) and ~n == -(n + 1) for all Int values.

let n = 42

let inverted = ~n  -- -43 (two's-complement bitwise NOT)

let restored = ~inverted  -- 42 (double inversion is identity)

restored

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~ accepts only Int. Applying it to Float, Decimal, or Bool is a compile error.

String Operators

String manipulation:

"Hello, " ++ "World!"

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List Operators

Working with lists:

Operator	Description	Example
`::`	Cons (prepend)	`1 :: [2, 3]`
`++`	Concatenation	`[1, 2] ++ [3, 4]`

-- Cons (prepend element)
let consed1 = 1 :: [2, 3]

let consed2 : [Int] = 1 :: (2 :: [])

-- Concatenation
let joined = [1, 2] ++ [3, 4]

joined

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Pipe Operators

Chain function calls elegantly:

Operator	Description	Example
`\|>`	Pipe forward	`x \|> f`
`<\|`	Pipe backward	`f <\| x`

fn double : Int -> Int
fn double x =
    x * 2

fn addOne : Int -> Int
fn addOne x =
    x + 1

-- Forward pipe
5 |> double  -- Same as: double 5 = 10

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import List

-- Pipeline example
[1, 2, 3, 4, 5]
    |> List.filter (|x| x > 2)
    |> List.map (|x| x * 2)

-- [6, 8, 10]

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Function Composition

Compose functions into new functions:

Operator	Description	Example
`>>`	Compose (left to right)	`f >> g`
`<<`	Compose (right to left)	`g << f`

-- Forward composition (f first, then g)
let addOne = |x : Int| x + 1

let double = |x : Int| x * 2

let addThenDouble = addOne >> double

addThenDouble 5  -- 12 (5 + 1 = 6, 6 * 2 = 12)

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-- Backward composition (g first, then f)
let addOne = |x : Int| x + 1

let double = |x : Int| x * 2

let doubleThenAdd = addOne << double

doubleThenAdd 5  -- 11 (5 * 2 = 10, 10 + 1 = 11)

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Result Propagation Operator

The ? postfix operator works on Result values:

Operator	Description
`?`	Unwrap `Ok` value; short-circuit with `Err` if the result is an error

-- ? unwraps Ok values and short-circuits on Err
let addOne = |x: Int| Ok (x + 1)
let result = 5 |> addOne
result?

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If the expression is Ok v, ? evaluates to v. If it is Err e, the expression evaluates to Err e (the error is preserved). Applying ? to a non-Result type is a compile error.

Operators with DataFrame Expressions

Arithmetic (+, -, *, /, %, ^), comparison (==, !=, <, <=, >, >=), boolean (&&, ||), and unary (-, not) operators work directly on Expr values from the DataFrame.Expr module. When either operand is an Expr, scalars are automatically coerced to literal expressions:

-- Operators work directly on column references
import DataFrame
import Result

import DataFrame.Expr as Expr

let df =
    DataFrame.fromRecords
        [ { price = 10.0, quantity = 2, active = True }
        , { price = 20.0, quantity = 3, active = False }
        ]

-- Arithmetic: @col * scalar -> Expr
-- Comparison: @col >= scalar -> Expr (boolean)
-- Boolean: Expr && Expr -> Expr
let expr = @price * 1.1

df
    |> DataFrame.applyExprs [(@adjusted, expr)]
    |> Result.andThen (DataFrame.column @adjusted)
    |> Result.withDefault []

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See the DataFrame Expressions guide for full details.

Best Practices

Use parentheses when precedence is unclear
Prefer pipes (|>) for data transformation chains
Use composition (>>) to build reusable function pipelines
Use != for inequality (not /=)

Next Steps

Learn about functions to create reusable code.