agda — consolidated language guide — DedSec Project

Agda

Typical use: Proof assistants and dependent types.

Suggested file extension: .agda.

How to run / environment: Typecheck with agda (not a standalone executable example).

Starter example

module Hello where
open import Agda.Builtin.Nat
answer : Nat
answer = 42

How to read it

This is a minimal typechecking example rather than console I/O.

Common pitfall

This is a minimal typechecking example rather than console I/O.

Agda — Expanded practice workbook

Inspect the smallest source

module Hello where
open import Agda.Builtin.Nat
answer : Nat
answer = 42

Run or compilation context: Typecheck with agda (not a standalone executable example).. Treat this as a baseline: save a copy, confirm the toolchain version and note whether the example merely evaluates a value, prints text, or creates external effects. Production accounts, datasets and hardware must not be used for first attempts.

Work through the actual mechanism

Define a length-indexed vector function and write a type that forbids an out-of-bounds index. Check a proof by removing one constructor case.

Diagnose the sharp edge

A type hole is an unfinished proof, not evidence. Universe levels and termination checking require a specific Agda version.

Agda — Focused mastery pathway

Applied exercises

1. State a small proposition and list its assumptions.
2. Reconstruct a short proof using only trusted inference rules.
3. Try removing one assumption and determine whether the proof still works.

• Is the goal an executable value or a checked proposition?
• Which exact runtime, compiler, host, and version does the reference need?
• What is the smallest working program and what side effects does it have?
• How do syntax, logic, and environment errors differ?
• How can invalid inputs be tested without modifying real user files?