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# Type System
Types are optional. If a type is declared, assignments are checked at runtime.
## Declaring Types
```baba
// Type declaration (name Type)
myValue Int;
// Assignment must match declared type
myValue : 10; // OK (Int)
// myValue : "x"; // Error: expected Int
```
## Runtime Type Inference
Without declarations, values carry runtime type tags used by pattern matching:
- Numbers are tagged as `Int` or `Float`; `Number` is a supertype accepted in validation where numeric values are allowed
- Strings as `String`, Booleans as `Bool`
- Lists and Tables have `List`/`Table` tags
## Runtime Type Validation Semantics
- Parameter validation happens at call time for parameters with annotations only.
- Return type validation happens after body evaluation when a return type is declared.
- Untyped parameters are accepted as-is and are not validated.
## Function Return Types
```baba
add : (x: Int, y: Int) -> Int -> x + y;
```
## Typed Locals with `with`
Locals in a header can be typed exactly like globals using a declaration followed by assignment.
```baba
sumNext : (x: Int, y: Int) -> Int ->
with (nx Int; ny Int; nx : x + 1; ny : y + 1;) -> nx + ny;
```
## Numeric Type Lattice and Widening
The numeric types form a simple lattice:
```
Int ⊂ Float ⊂ Number
```
- When a parameter expects `Float`, an `Int` is accepted (widened) implicitly.
- When a parameter expects `Number`, either `Int` or `Float` are accepted.
- When a parameter expects `Int`, `Float` is rejected.
- Many `math.` functions return `Float` for predictability.
## Typed Functions
Typed functions annotate parameters and the return value. At runtime, arguments and returns are validated.
### Multi-Parameter Typed Functions
```baba
// Parameter types and return type
add : (x: Int, y: Int) -> Int -> x + y;
// Using typed functions
result1 : add 2 3; // OK => 5
// result2 : add 2 "3"; // Runtime error: parameter type mismatch
// Multi-parameter function takes all arguments at once
multiply : (x: Float, y: Float) -> Float -> x * y;
result : multiply 2.0 3.0; // 6.0
```
### Curried Typed Functions
Curried functions take one parameter at a time and return functions for partial application:
```baba
// Curried function with typed first parameter and function return type
mul : (x: Float) -> (Float -> Float) -> y -> x * y;
double : mul 2.0; // Partial application: double : (Float -> Float)
result : double 3.5; // 7.0
// Three-parameter curried function
add3 : (x: Int) -> (Int -> (Int -> Int)) -> y -> z -> x + y + z;
add5 : add3 5; // add5 : (Int -> (Int -> Int))
add5and3 : add5 3; // add5and3 : (Int -> Int)
result : add5and3 2; // 10
```
### Function Type Syntax
Function types use the syntax `(ParamType -> ReturnType)`:
```baba
// Simple function type
transform : (x: Int) -> (Int -> Int) -> y -> x + y;
// Function that returns another function
makeAdder : (x: Int) -> (Int -> Int) -> y -> x + y;
add5 : makeAdder 5; // add5 : (Int -> Int)
result : add5 3; // 8
```
Heads up! Complex nested parameter types like (f: (Int -> Int)) aren't implemented. The first parameter must use simple types like Int, Float, String, or Bool.
### Mixed Typed/Untyped Functions
```baba
// Mixed typed/untyped parameters (untyped are not validated)
concatIf : (flag: Bool, x, y) -> String ->
when flag is
true then x .. y
_ then y .. x;
// Return type enforcement
// This will raise a runtime error if the body evaluates to a non-String
greet : (name: String) -> String -> "Hello " .. name;
```
### Backward Compatibility
All existing function syntax continues to work:
```baba
// Untyped curried function (existing)
multiply : x -> y -> x * y;
// Multi-parameter typed function (existing)
add : (x: Float, y: Float) -> Float -> x + y;
// New: Typed curried function
multiply : (x: Float) -> (Float -> Float) -> y -> x * y;
```
## Typed Tables
Table values carry the `Table` tag and can be typed via variable declarations. Currently, there is no way to create complex types that totally model the typing of the values contained within a table data structure.
```baba
// Variable type declaration (applies to subsequent assignments)
user Table;
user : { name: "Alice", age: 30 };
// Access remains the same
userName : user.name; // "Alice"
userAge : user.age; // 30
```
## Result Type
`Result` encodes success (`Ok value`) or failure (`Err message`).
```baba
divide : x y ->
when y is
0 then Err "Division by zero"
_ then Ok (x / y);
useDivide : when (divide 10 2) is
Ok val then val
Err _ then 0;
```
Pattern matching binds inner values:
```baba
// Function returning a Result
parseIntOrErr : (s: String) -> Result ->
when (str.trim s) is
"" then Err "Empty"
_ then Ok 42; // placeholder
// Consuming Result
answer : when (parseIntOrErr " 10 ") is
Ok v then v
Err e then 0;
```
## Error messages
All runtime errors are thrown as plain `Error` with messages:
```
Type mismatch in function 'add': Expected Int for parameter 'y', but got String (value: "3")
Return type mismatch in function 'greet': Expected String, but got Int (value: 42)
Type mismatch for myValue: expected Int but got String (value: "x")
Division by zero
Index out of bounds: 5
Undefined variable: foo
Undefined property: age of person
Unknown operator: ^
Unexpected token: RPAREN ()) at 12:17
```
When a location is available, the CLI/REPL shows a code frame indicating `line:column`.
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