# VM Function Values and Closures

Domain: VM closures and function values
Function: normative

This chapter defines how the PVM models first-class function values.

## 1 First-Class Function Model

The PVM treats user function values as closures.

This means:

- functions can be stored in variables;
- functions can be passed as arguments;
- functions can be returned from other functions;
- function values carry explicit runtime representation.

Even functions without captures may be represented as closures with an empty capture set.

## 2 Closure Layout

Closures are heap objects.

Conceptual layout:

```
Closure {
    func_id
    captures[]
}
```

Captures may be:

- copied values;
- handles to heap objects.

Closure environments are part of the GC root graph as long as the closure remains reachable.

## 3 Direct and Indirect Calls

The PVM supports two forms of invocation:

| Opcode         | Description                            |
| -------------- | -------------------------------------- |
| `CALL`         | Direct call by function id             |
| `CALL_CLOSURE` | Indirect call through a closure handle |

For `CALL_CLOSURE`:

1. the closure handle is read from the stack;
2. the VM resolves the target function;
3. captured environment state becomes available to the callee according to the closure calling convention.

## 4 Verification and Safety

The verifier ensures, at minimum:

- closure call sites have coherent arity;
- invalid closure call shapes are rejected or trapped according to the verifier/runtime boundary;
- return-slot contracts remain valid.

Handle validity, heap reachability, and dynamic misuse remain subject to runtime checks where static proof is not possible.

## 5 Relationship to Memory and GC

- Closure objects live in heap memory, so their object model is constrained by [`03-memory-stack-heap-and-allocation.md`](03-memory-stack-heap-and-allocation.md).
- Captured heap references participate in the GC root graph.
- Closures are function values, not syscalls; syscall calls remain a separate non-first-class boundary defined in [`16-host-abi-and-syscalls.md`](16-host-abi-and-syscalls.md).