# Stack Language Specification v0.3

## 1. Overview

A statically-typed, stack-based language with pure postfix notation combining the execution model of HP's RPL, the type system of C and Rust, and modern array operations from Uiua.

### Design Principles
- **Everything is postfix** - no exceptions
- Stack-based execution (no local variables)
- Static typing with type inference
- Manual heap memory management
- Types define what things **are**, traits define how things **act**
- All constructs are implicitly generic
- **Every operator is defined by a trait**

## 2. Lexical Structure

### 2.1 Comments
```
// Single-line comment
```

### 2.2 Identifiers
- Start with letter or underscore: `[a-zA-Z_][a-zA-Z0-9_]*`
- Case-sensitive
- Trait names prefixed with `::` (e.g., `::Addable`, `::Number`)

### 2.3 Literals

**Integer Literals**
```
42          // i32 (default)
42 i64      // Annotate as i64
0xFF        // hexadecimal
0b1010      // binary
```

**Floating Point Literals**
```
3.14        // f64 (default)
3.14 f32    // Annotate as f32
```

**String Literals**
```
"hello world"
"escape sequences: \n \t \\ \""
```

**Boolean Literals**
```
true
false
```

**Array Literals**
```
[1 2 3 4 5]              // array of i32
[1.0 2.0 3.0]            // array of f64
[[1 2] [3 4]]            // 2D array
```

## 3. Type System

### 3.1 Primitive Types
- `i8`, `i16`, `i32`, `i64` - Signed integers
- `u8`, `u16`, `u32`, `u64` - Unsigned integers
- `f32`, `f64` - Floating point
- `bool` - Boolean
- `char` - Single character (UTF-8)
- `ptr` - Raw pointer (generic over pointed type)

### 3.2 Types vs Traits

**Types** define the concrete structure and memory layout:
```
Point struct              // Point is a type
Rectangle struct          // Rectangle is a type
```

**Traits** define behavioral contracts - how things act:
```
::Drawable trait          // Drawable is a trait
::Addable trait          // Addable is a trait
```

**Key Distinction:**
- A value **has** a type (what it is structurally)
- A value **implements** a trait (how it behaves)
- Types are concrete; traits are interfaces
- Functions can be generic over both types and traits
- **Every operator must be backed by a trait**

### 3.3 All Constructs are Generic

Every function, struct, and union is implicitly generic. Constraints are specified via traits:

```
// Function generic over any type T
(T -- T) { dup * } square fn

// Function requiring T to implement Addable trait
(T T -- T) ::Addable { + } add_two fn

// Struct generic over field types
(T T --) { x: y: } Point struct

// Union generic over variant types
(T --) { Some(T) None } Option union
```

## 4. Base Traits (Non-Exhaustive)

### 4.1 Core Traits

**::Pushable** - Can be pushed onto the stack
```
{ (-- Self) push: } ::Pushable trait
```

**::ArrayOf** - Array container trait
```
{ (-- ArrayOf[T]) create: (ArrayOf[T] i32 -- T) at: } ::ArrayOf trait
```

**::Addable** - Supports addition and subtraction
```
{ (Self Self -- Self) +: (Self Self -- Self) -: } ::Addable trait
```

**::Number** - Numeric operations
```
// Number inherits from multiple traits
[ ::Addable ::Multiplyable ::Comparable ] ::Number inher
```

**::String** - String operations
```
{ (Self Self -- Self) concat: (Self -- i32) length: } ::String trait
```

**::Identifier** - Represents identifiers/symbols
```
{ (-- TokenString) name: } ::Identifier trait
```

**::Trait** - Meta-trait for trait operations
```
{ (TokenString Identifier --) trait: (Identifier TokenString Identifier --) impl: (ArrayOf[Identifier] Identifier --) inher: } ::Trait trait
```

### 4.2 Additional Core Traits

**::Multiplyable** - Multiplication and division
```
{ (Self Self -- Self) *: (Self Self -- Self) /: (Self Self -- Self) %: } ::Multiplyable trait
```

**::Comparable** - Comparison operations
```
{ (Self Self -- bool) >: (Self Self -- bool) >=: (Self Self -- bool) <: (Self Self -- bool) <=: (Self Self -- bool) ==: (Self Self -- bool) !=: } ::Comparable trait
```

**::Logical** - Logical operations
```
{ (Self Self -- Self) and: (Self Self -- Self) or: (Self -- Self) not: } ::Logical trait
```

**::Bitwise** - Bitwise operations
```
{ (Self Self -- Self) bitand: (Self Self -- Self) bitor: (Self Self -- Self) bitxor: (Self -- Self) bitnot: (Self i32 -- Self) shl: (Self i32 -- Self) shr: } ::Bitwise trait
```

**::Exponentiable** - Exponentiation
```
{ (Self Self -- Self) ^: } ::Exponentiable trait
```

## 5. Stack Operations

### 5.1 Stack Manipulation

All stack operations are backed by traits.

```
dup         // ( a -- a a ) Duplicate top [::Duplicable]
drop        // ( a -- ) Remove top [::Droppable]
swap        // ( a b -- b a ) Swap top two [::Swappable]
over        // ( a b -- a b a ) Copy second to top [::Overable]
rot         // ( a b c -- b c a ) Rotate three items [::Rotatable]
```

### 5.2 Stack Inspection
```
depth       // ( -- n ) Push stack depth [::Inspectable]
pick        // ( n -- x ) Copy nth item to top (0 = top) [::Pickable]
roll        // ( n times -- ) Rotate n items, times times [::Rollable]
```

**Roll Examples:**
```
// Stack: a b c d e
3 1 roll    // Rotate top 3 items once: a b d e c
3 2 roll    // Rotate top 3 items twice: a b e c d
5 1 roll    // Rotate all 5 items once: b c d e a
```

## 6. Operators (Postfix)

**Every operator is backed by a trait and must be implemented for types that use it.**

### 6.1 Arithmetic (::Addable, ::Multiplyable, ::Exponentiable)

```
3 4 +       // ( a b -- result ) Addition [::Addable]
10 3 -      // Subtraction [::Addable]
5 6 *       // Multiplication [::Multiplyable]
20 4 /      // Division [::Multiplyable]
17 5 %      // Modulo [::Multiplyable]
2 8 ^       // Exponentiation [::Exponentiable]
```

### 6.2 Comparison (::Comparable)
```
5 3 >       // Greater than [::Comparable]
5 3 >=      // Greater or equal [::Comparable]
5 3 <       // Less than [::Comparable]
5 3 <=      // Less or equal [::Comparable]
5 5 ==      // Equal [::Comparable]
5 3 !=      // Not equal [::Comparable]
```

### 6.3 Logical (::Logical)
```
true false and    // Logical AND [::Logical]
true false or     // Logical OR [::Logical]
true not          // Logical NOT [::Logical]
```

### 6.4 Bitwise (::Bitwise)
```
0xFF 0x0F bitand     // Bitwise AND [::Bitwise]
0xFF 0x0F bitor      // Bitwise OR [::Bitwise]
0xFF 0x0F bitxor     // Bitwise XOR [::Bitwise]
0xFF bitnot          // Bitwise NOT [::Bitwise]
8 2 shl              // Left shift [::Bitwise]
8 2 shr              // Right shift [::Bitwise]
```

## 7. Trait System

### 7.1 Trait Definition

**Syntax**: `{ function_signatures } ::name trait`

```
// Simple trait
{
    (Self -- ) draw:
} ::Drawable trait

// Trait with multiple methods
{
    (Self Self -- Self) add:
    (Self Self -- Self) sub:
    (Self -- Self) neg:
} ::Numeric trait

// The comprehensive Trait meta-trait
{
    (TokenString Identifier --) trait:
    (Identifier TokenString Identifier --) impl:
    (ArrayOf[Identifier] Identifier --) inher:
} ::Implementable trait
```

### 7.2 Trait Implementation

**Syntax**: `::type { method_implementations } ::trait impl`

```
// Implement Addable for i32
::i32 {
    (Self Self -- Self) {
        // Native addition implementation
    } +:
    
    (Self Self -- Self) {
        // Native subtraction implementation
    } -:
} ::Addable impl

// Implement Drawable for Rectangle
::Rectangle {
    (Rectangle -- ) {
        "Drawing rectangle" print
        dup width get print
        height get print
    } draw:
} ::Drawable impl
```

### 7.3 Trait Inheritance

**Syntax**: `[ ::trait1 ::trait2 ... ] ::derived_trait inher`

```
// Number inherits from Addable and Multiplyable
[ ::Addable ::Multiplyable ] ::Number inher

// Numeric inherits from Number, Comparable, and Exponentiable
[ ::Number ::Comparable ::Exponentiable ] ::Numeric inher

// Complex inheritance
[ ::Drawable ::Transformable ::Collidable ] ::GameObject inher
```

### 7.4 Using Traits in Functions

```
// Function requiring Drawable trait
(T -- ) ::Drawable {
    draw
} draw_twice fn

// Multiple trait requirements
(T -- T) ::Numeric ::Copyable {
    dup abs swap dup * +
} complex_calc fn
```

## 8. Functions (Postfix Definition)

Functions are defined in postfix notation. The signature and body come before the name.

### 8.1 Basic Function Definition

**Syntax**: `(inputs -- outputs) { body } name fn`

```
// Define a square function
(i32 -- i32) { dup * } square fn

// Use it
5 square      // 25

// Multiple inputs and outputs
(i32 i32 -- i32 i32) {
    2dup / swap %
} divmod fn

10 3 divmod   // 3 1 (quotient remainder)
```

### 8.2 Generic Functions with Trait Constraints

**Syntax**: `(type_sig) ::trait_constraints { body } name fn`

```
// Generic identity - works with any type
(T -- T) {} identity fn

// Requires T to be Addable
(T T -- T) ::Addable {
    +
} add_values fn

// Multiple trait constraints
(T U -- U T) ::Copyable ::Swappable {
    swap
} swap_generic fn

// Multiple type parameters with different traits
(T U -- T) ::Addable ::Numeric {
    dup U as +
} add_converted fn
```

## 9. Control Flow (Postfix)

### 9.1 Conditionals

**Syntax**: `condition { then-block } { else-block } if`

```
// if-then (else block is empty)
x 0 > { "positive" print } {} if

// if-then-else
x 0 > 
    { "positive" print } 
    { "non-positive" print } 
if

// The condition comes first, then both blocks, then 'if'
a b > 
    { a } 
    { b } 
if max set

// Nested
x 0 >
    {
        y 0 >
            { "both positive" print }
            { "x positive, y not" print }
        if
    }
    { "x not positive" print }
if
```

### 9.2 Loops

**While Loop**

**Syntax**: `{ condition-block } { body-block } while`

```
// Sum 1 to 10
0 1                              // sum counter
    { dup 10 <= }                // condition block
    {                            // body block
        over over +              // Add counter to sum
        swap 1 + swap            // Increment counter
    }
while
drop                             // Drop counter, leave sum

// Infinite loop with break
{ true } {
    // body
    condition { break } {} if
} while
```

**For Loop**

**Syntax**: `start end { body-with-counter } for`

```
// The loop variable is implicitly pushed to stack in each iteration
1 10 { 
    // Stack has loop counter on top
    dup print
} for

// More complex
1 100 {
    dup fizzbuzz
} for
```

### 9.3 Loop Control
```
break       // Exit loop
continue    // Skip to next iteration
```

### 9.4 Match/Pattern Matching

**Syntax**: `value { pattern => block ... } match`

```
value {
    Some(x) => { x print }
    None => { "Nothing" print }
} match

// With multiple patterns
status {
    Pending => { "Waiting" print }
    Active => { "Running" print }
    Complete => { "Done" print }
} match
```

## 10. Data Structures (Postfix)

### 10.1 Struct Definition

**Syntax**: `(field_types -- ) { field_names } name struct`

```
// Define Point struct - generic over coordinate types
(T T --) { x: y: } Point struct

// Use with specific types
3.0 4.0 Point       // Creates Point with f64 fields
3 4 Point           // Creates Point with i32 fields

// More complex struct
(T U V --) { 
    width: 
    height: 
    depth: 
} Box3D struct

10.0 20.0 30.0 Box3D
```

### 10.2 Struct Field Access

**Syntax (postfix)**: `struct field get` or `struct value field set`

```
point x get         // Get x field
point 15.0 x set    // Set x field to 15.0

// Chaining
point x get 2 * y get +     // (point.x * 2) + point.y
```

### 10.3 Union Definition

**Syntax**: `(variant_types -- ) { variants } name union`

```
// Option type - generic over T
(T --) { 
    Some(T) 
    None 
} Option union

// Result type - generic over T and E
(T E --) { 
    Ok(T) 
    Err(E) 
} Result union

// Create union values
42 Some             // Creates Option::Some(42)
None                // Creates Option::None
"success" Ok        // Creates Result::Ok("success")
"error" Err         // Creates Result::Err("error")
```

### 10.4 Enum Definition

**Syntax**: `() { variants } name enum`

```
() { 
    Pending 
    Active 
    Complete 
} Status enum

// Usage
Pending             // Creates Status::Pending
Active              // Creates Status::Active
```

## 11. Memory Management (Postfix)

### 11.1 Heap Operations

```
// Allocate
3.0 4.0 Point alloc     // ( Point -- ptr<Point> )

// Dereference
ptr deref               // ( ptr<T> -- T )

// Store (dereference and update)
new_value ptr store     // ( T ptr<T> -- )

// Free
ptr free                // ( ptr<T> -- )
```

### 11.2 Example

```
// Create heap-allocated point
3.0 4.0 Point alloc     // Returns ptr<Point>
dup x get print         // Dereference and print x
free                    // Clean up
```

## 12. Array Operations (Postfix)

### 12.1 Basic Array Operations

```
// Creation
1 10 range              // Create range array [1..10]

// Shape operations
arr shape               // Get shape
arr 2 3 reshape         // Reshape to 2x3

// Element access
arr 2 at                // Index access
arr 1 3 slice           // Slice array
```

### 12.2 Array Combinators

```
// Map - apply function to each element
[1 2 3 4] { 2 * } map        // [2 4 6 8]

// Filter - keep elements matching predicate
[1 2 3 4 5] { 2 % 0 == } filter   // [2 4]

// Reduce - fold with function
[1 2 3 4] 0 { + } reduce     // 10

// Each - apply to each element (side effects)
[[1 2] [3 4]] { sum print } each
```

### 12.3 Array Arithmetic

```
[1 2 3] [4 5 6] +.      // Element-wise add: [5 7 9]
[1 2 3] [4 5 6] *.      // Element-wise multiply: [4 10 18]
[1 2 3] 2 *.            // Scalar multiply: [2 4 6]
```

### 12.4 Array Manipulation

```
[1 2 3] [4 5 6] concat  // Concatenate: [1 2 3 4 5 6]
[1 2 3] reverse         // [3 2 1]
[[1 2] [3 4]] transpose // [[1 3] [2 4]]
[1 2 3 4] 2 window      // [[1 2] [2 3] [3 4]]
```

## 13. Eval Operator (Postfix)

Execute code dynamically at runtime.

```
// Evaluate string as code
"2 3 +" eval            // Pushes 5

// Build and execute code
"(i32 -- i32) { dup * } square fn" eval
5 square                // 25

// Dynamic dispatch
operation_name " get" concat eval
```

## 14. Standard Library Concepts

### 14.1 I/O

```
"Hello" print           // Print to stdout
"Enter name: " input    // Read from stdin
"file.txt" read         // Read file contents
"data" "file.txt" write // Write to file
```

### 14.2 String Operations

```
"hello" " world" concat     // Concatenate: "hello world"
"hello" length              // 5
"hello" 1 3 substr          // "el"
"a,b,c" "," split           // ["a" "b" "c"]
["a" "b"] "," join          // "a,b"
```

### 14.3 Type Conversion

```
42 f64 as               // Convert i32 to f64
"123" i32 parse         // Parse string to i32
3.14 str as             // Convert to string
```

## 15. Complete Examples

### 15.1 Trait Implementation Example

```
// Define the Addable trait
{
    (Self Self -- Self) +:
    (Self Self -- Self) -:
} ::Addable trait

// Implement for i32
::i32 {
    (Self Self -- Self) {
        // Native addition
    } +:
    
    (Self Self -- Self) {
        // Native subtraction
    } -:
} ::Addable impl

// Implement for Point
::Point {
    (Point Point -- Point) {
        over x get over x get +
        swap y get swap y get +
        Point
    } +:
    
    (Point Point -- Point) {
        over x get over x get -
        swap y get swap y get -
        Point
    } -:
} ::Addable impl
```

### 15.2 Trait Inheritance Example

```
// Define base traits
{ (Self Self -- Self) +: (Self Self -- Self) -: } ::Addable trait
{ (Self Self -- Self) *: (Self Self -- Self) /: } ::Multiplyable trait
{ (Self Self -- Self) ^: } ::Exponentiable trait

// Number inherits from multiple traits
[ ::Addable ::Multiplyable ] ::Number inher

// Numeric extends Number further
[ ::Number ::Exponentiable ] ::Numeric inher
```

### 15.3 Factorial

```
(i32 -- i32) {
    dup 1 
        { drop 1 } 
        { dup 1 - factorial * } 
    <= if
} factorial fn

5 factorial print       // 120
```

### 15.4 FizzBuzz

```
(i32 -- ) {
    dup 15 % 0 ==
        { drop "FizzBuzz" print }
        {
            dup 3 % 0 ==
                { drop "Fizz" print }
                {
                    dup 5 % 0 ==
                        { drop "Buzz" print }
                        { print }
                    if
                }
            if
        }
    if
} fizzbuzz fn

1 100 { fizzbuzz } for
```

### 15.5 Using Roll

```
// Stack: 1 2 3 4 5
3 1 roll    // Rotate top 3 once: 1 2 4 5 3
3 2 roll    // Rotate top 3 twice: 1 2 5 3 4

// More complex example
10 20 30 40 50
4 2 roll    // Rotate top 4, twice: 10 30 40 50 20
```

### 15.6 Array Processing

```
// Sum of squares of even numbers from 1 to 10
[1 2 3 4 5 6 7 8 9 10]
    { 2 % 0 == } filter     // Keep even numbers
    { dup * } map           // Square each
    0 { + } reduce          // Sum
print                       // 220
```

## 16. Syntax Summary

### Complete Grammar Patterns

**Functions**: `(in -- out) ::constraints { body } name fn`

**Structs**: `(types -- ) { fields: } name struct`

**Unions**: `(types -- ) { Variant(T) ... } name union`

**Enums**: `() { Variant ... } name enum`

**Traits**: `{ (sig) method: ... } ::name trait`

**Trait Impl**: `::Type { (sig) { body } method: ... } ::Trait impl`

**Trait Inheritance**: `[ ::Trait1 ::Trait2 ] ::NewTrait inher`

**If**: `condition { then } { else } if`

**While**: `{ condition } { body } while`

**For**: `start end { body } for`

**Match**: `value { pattern => block ... } match`

---

**Version**: 0.3  
**Status**: Draft Specification - Trait-Backed Operations Edition