majiayu000/claude-arsenal
xiaohongshu
xiaohongshu
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Collimator Optics Quick Reference
collimator-optics
Use profunctor optics from the Collimator library for Lean 4. Use when working with lenses, prisms, traversals, or nested data access.
SKILL.md
Full skill instructions
Collimator Optics Quick Reference
Setup
import Collimator
import Collimator.Derive.Lenses
open Collimator.Derive
open scoped Collimator.Operators
Generate Lenses (Preferred)
-- In separate Optics.lean file (to avoid circular imports)
makeLenses Person -- Generates: personName, personAge, etc.
makeLenses Address -- Generates: addressCity, addressZip, etc.
Operators
| Op | Name | Example |
|---|---|---|
^. | view | person ^. personName |
^? | preview | val ^? _someVariant |
.~ | set | person & personAge .~ 30 |
%~ | over | person & personAge %~ (· + 1) |
& | pipe | x & lens .~ v |
∘ | compose | outer ∘ inner |
Prisms for Sum Types
def _left : Prism' (Either A B) A := ctorPrism% Either.left
def _right : Prism' (Either A B) B := ctorPrism% Either.right
-- Usage
either ^? _left -- Option A
either & _left %~ f -- modify if Left
Affine Traversals (0-or-1 Focus)
For HashMap/collection access where a key may or may not exist:
import Collimator.Indexed
import Collimator.Instances.Option
-- Compose: field lens → index lens → some prism
def itemAt (k : Key) : AffineTraversal' Container Item :=
containerItems ∘ Collimator.Indexed.atLens k ∘ Collimator.Instances.Option.somePrism' Item
-- Usage
container ^? itemAt key -- Option Item
(container ^? itemAt key).isSome -- exists check
Common Patterns
-- Nested access
employee ^. (employeeAddress ∘ addressCity)
-- Chained updates
config
& configHost .~ "localhost"
& configPort .~ 8080
-- Conditional via prism
if (val ^? _error).isSome then handleError else continue
File Organization
To avoid circular imports:
- Put structures in
Types.lean - Put
makeLensescalls inOptics.lean(imports Types) - Put methods in other files (import Optics)
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