Acorn Theorem Prover Verifier

---
name: acorn-theorem-prover-verifier
description: "Verify and write proofs using the Acorn theorem prover for mathematical and cryptographic formalization. Use when working with Acorn proof files (.ac), verifying theorems, formalizing mathematical or cryptographic protocols, or writing proofs in the Acorn language. Triggers on:…"
category: "Content & Writing"
author: community
version: "1.0.0"
icon: pencil
---

# Acorn Prover

## Setup (MUST DO WHEN RUNNING FIRST TIME)

If `config.env` does not exist in the skill directory:

1. **Ask the user** for the following paths:
   - `ACORN_LIB` - Path to acornlib (e.g., `/path/to/acornprover/acornlib`)
   - `ACORN_PROJECT` - Path to project directory for `.ac` files (e.g., `/path/to/acorn-playground`)

2. **Verify** the paths exist using `list_dir` or equivalent. If a path is invalid, inform the user and ask again.

3. **Run setup.sh** with the validated paths:

```bash
bash skills/acorn-prover/scripts/setup.sh "<ACORN_LIB>" "<ACORN_PROJECT>"
```

4. **Source the config** to get `ACORN_LIB`, `ACORN_PROJECT`, and `USE_MISE` variables:

```bash
source skills/acorn-prover/config.env
```

If any of the above are blank / not set, inform the user to set the variable manually.
If any of the above are changed, ask the user for new paths and run setup again.

## Configuration

Config values are stored in `skills/acorn-prover/config.env`:

| Variable        | Description                     |
| --------------- | ------------------------------- |
| `ACORN_LIB`     | Path to acornlib                |
| `ACORN_PROJECT` | Project directory for .ac files |
| `USE_MISE`      | `true` if mise is available     |

## Verify Proofs

If `USE_MISE=true`:

```bash
mise run acorn verify <filename>.ac
```

Otherwise, use the direct CLI:

```bash
acorn --lib "$ACORN_LIB" verify <filename>.ac
```

## Reverify Proofs (CI/CD)

Check that all proofs are cached with no AI searches required:

```bash
# With mise
mise run acorn reverify

# Or direct CLI
acorn --lib "$ACORN_LIB" reverify
```

Use for CI pipelines to ensure all proofs are complete.

## Training Data Generation

Generate training data (problem-proof pairs) for AI model development:

```bash
# With mise
mise run acorn training ./training_data

# Or direct CLI
acorn --lib "$ACORN_LIB" training ./training_data
```

Argument: `DIR` - Directory to output training data.

## Documentation Generation

Generate library reference documentation:

```bash
# With mise
mise run acorn docs ./docs/library

# Or direct CLI
acorn --lib "$ACORN_LIB" docs ./docs/library
```

Argument: `DIR` - Directory to output documentation.

## Workflow

1. Source config: `source skills/acorn-prover/config.env`
2. Write proof file in `$ACORN_PROJECT/`
3. Run the appropriate command (verify, reverify, training, docs)
4. **Always show the full command output to the user** (success or error)
5. Debug errors using the common errors table in [references/syntax.md](references/syntax.md)
6. Iterate until verification passes

## Quick Syntax Overview

```acorn
from nat import Nat
from add_comm_group import AddCommGroup

// Theorems - auto-proved or with hints
theorem example(a: Nat, b: Nat) {
    a < b implies a != b
}

// Typeclasses - axioms are named blocks, no "axiom" keyword
typeclass A: AddGroup extends Zero, Neg, Add {
    inverse_right(a: A) { a + -a = A.0 }
}

// Structures
structure Pair[T, U] { first: T  second: U }

// Inductive types - constructors MUST be lowercase
inductive MyBool { tru fls }
```

Key points:

- Built-in logic keywords (`not`, `and`, `or`, `implies`, `iff`, `true`, `false`) are reserved - do not redefine
- Constructor names must be lowercase
- Typeclass axioms use named blocks, not the `axiom` keyword

## Standard Library (`acornlib`)

Key modules in `$ACORN_LIB/src`:

| Module              | Contents                                   |
| ------------------- | ------------------------------------------ |
| `nat/`              | Natural number axioms, induction, addition |
| `add_group.ac`      | `AddGroup` with `a + -a = A.0`             |
| `add_comm_group.ac` | Abelian groups (`AddCommGroup`)            |

## References

- **Full syntax, error table, examples**: See [references/syntax.md](references/syntax.md)
- **Context7 docs**: Use `context7` MCP with `/acornprover/acorn` or `/acornprover/acornlib` for latest documentation