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| 1 | +# lens (Template Morphism) |
| 2 | + |
| 3 | +## ΠΠ½ΡΠ΅Π½ΡΡΡ |
| 4 | + |
| 5 | +**Π‘ΡΠ²ΠΎΡΠΈΡΠΈ getter/setter ΠΏΠ°ΡΡ Π΄Π»Ρ immutable field access/update**. ΠΠ΅ΡΡΠΈΠΉ template morphism β domain-specific generator, ΡΠΎ Π²ΠΈΠΊΠΎΡΠΈΡΡΠΎΠ²ΡΡ `make` ΡΠΊ ΠΏΡΠΈΠΌΡΡΠΈΠ². |
| 6 | + |
| 7 | +**Π€ΡΠ»ΠΎΡΠΎΡΡΡΠΊΠ° ΡΡΡΡ**: Lens Π΄ΠΎΠ·Π²ΠΎΠ»ΡΡ **ΡΠΎΠΊΡΡΡΠ²Π°ΡΠΈΡΡ** Π½Π° ΡΠ°ΡΡΠΈΠ½Ρ ΡΡΡΡΠΊΡΡΡΠΈ, Π·Π±Π΅ΡΡΠ³Π°ΡΡΠΈ immutability. |
| 8 | + |
| 9 | +**Type signature**: |
| 10 | +``` |
| 11 | +lens :: String β { get: (a β b), set: (b β a β a) } |
| 12 | +``` |
| 13 | + |
| 14 | +## Π€ΠΎΡΠΌΠ° (Template) |
| 15 | + |
| 16 | +Lens Π½Π΅ ΠΌΠ°Ρ Platonic .Ξ» ΡΠΎΡΠΌΠΈ, Π±ΠΎ ΡΠ΅ **template** β Π²ΡΠ½ Π³Π΅Π½Π΅ΡΡΡ morphisms ΡΠ΅ΡΠ΅Π· `make`. |
| 17 | + |
| 18 | +**Template definition**: |
| 19 | +```javascript |
| 20 | +lens = Ξ»field. { |
| 21 | + get: Ξ»obj. obj[field], |
| 22 | + set: Ξ»value. Ξ»obj. { ...obj, [field]: value } |
| 23 | +} |
| 24 | +``` |
| 25 | + |
| 26 | +**Built on**: `make` primitives (partial application patterns) |
| 27 | + |
| 28 | +## ΠΡΠΎΡΠΊΡΡΡ |
| 29 | + |
| 30 | +**TypeScript**: [projections/ts.js](./projections/ts.js) |
| 31 | + |
| 32 | +```js |
| 33 | +export const lens = field => ({ |
| 34 | + get: obj => obj[field], |
| 35 | + set: value => obj => ({ ...obj, [field]: value }) |
| 36 | +}); |
| 37 | +``` |
| 38 | + |
| 39 | +## ΠΠΈΠΊΠΎΡΠΈΡΡΠ°Π½Π½Ρ |
| 40 | + |
| 41 | +```js |
| 42 | +import { lens } from '@lambda-foundation/morphisms'; |
| 43 | + |
| 44 | +const obj = { name: 'Alice', age: 30, city: 'Kyiv' }; |
| 45 | + |
| 46 | +// Create lenses |
| 47 | +const nameLens = lens('name'); |
| 48 | +const ageLens = lens('age'); |
| 49 | + |
| 50 | +// Get |
| 51 | +nameLens.get(obj); // β 'Alice' |
| 52 | +ageLens.get(obj); // β 30 |
| 53 | + |
| 54 | +// Set (immutable) |
| 55 | +const obj2 = nameLens.set('Bob')(obj); |
| 56 | +// obj2 = { name: 'Bob', age: 30, city: 'Kyiv' } |
| 57 | +// obj unchanged |
| 58 | + |
| 59 | +// Composition |
| 60 | +const updatedObj = ageLens.set(31)(nameLens.set('Carol')(obj)); |
| 61 | +// { name: 'Carol', age: 31, city: 'Kyiv' } |
| 62 | +``` |
| 63 | + |
| 64 | +## Significance |
| 65 | + |
| 66 | +**First template morphism** β demonstrates how domain knowledge (field access) can generate morphisms via make-style patterns. |
| 67 | + |
| 68 | +**Foundation for**: |
| 69 | +- Nested lenses |
| 70 | +- Reactive systems |
| 71 | +- State management |
| 72 | +- Immutable updates |
| 73 | + |
| 74 | +--- |
| 75 | + |
| 76 | +**Event**: 007 - Template Morphisms (proof-of-concept) |
| 77 | +**Type**: Domain-specific generator |
| 78 | +**Built on**: Event 006 (make patterns) |
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