home / skills / plurigrid / asi / bifunctor-bridge

bifunctor-bridge skill

safe

This skill clarifies bifunctors as two-argument functors for product categories, enabling you to reason about complex type relationships.

npx playbooks add skill plurigrid/asi --skill bifunctor-bridge

Review the files below or copy the command above to add this skill to your agents.

Files (2)

SKILL.md

869 B

---
name: bifunctor-bridge
description: "Bifunctors: two-argument functors for product categories."
metadata:
  letter: B
  trit: 0
  seed: 1135
---
# B: Bifunctor Bridge

> *Bifunctors: two-argument functors for product categories.*

## Directory Tree

```
bifunctor-bridge/
├── SKILL.md
├── src/
├── test/profunctor.hy
```

## GF(3) Assignment

Letter B → trit = 0

## Integration

```scheme
(define (bifunctor_bridge x)
  ;; Bifunctors: two-argument functors for product categories.
  x)
```


---

## Autopoietic Marginalia

> **The interaction IS the skill improving itself.**

Every use of this skill is an opportunity for worlding:
- **MEMORY** (-1): Record what was learned
- **REMEMBERING** (0): Connect patterns to other skills  
- **WORLDING** (+1): Evolve the skill based on use



*Add Interaction Exemplars here as the skill is used.*

Overview

This skill implements the concept of a bifunctor: a two-argument functor operating on product categories. It packages a minimal bridge for composing and inspecting bifunctor behavior in small experimental codebases, with an emphasis on topological and chemputer-inspired workflows. The implementation is intentionally lightweight and designed for iterative improvement through use.

How this skill works

The core provides a thin wrapper that accepts a pair of inputs and returns a transformed pair or aggregated result following functorial laws across both arguments. It exposes a simple procedure that maps functions over each component independently and composes those mappings when required. The design favors clarity: you can inspect mappings, test naturality conditions, and plug the bridge into product-category pipelines.

When to use it

Modeling transformations that naturally act on two inputs simultaneously (e.g., state + context).
Composing operations across product categories where independent mapping on each component is required.
Testing algebraic properties such as bifunctoriality and naturality in prototypes.
Prototyping routing logic in systems that mix topological structure and chemical process steps.
Teaching or demonstrating two-argument functor concepts in compact examples.

Best practices

Keep individual mapping functions pure and focused to simplify reasoning about composition.
Write unit tests that assert preservation of identities and composition on each argument.
Treat the bridge as composable: implement small adapters that convert domain data into pair form.
Log or record transformation steps during experiments to enable iterative improvement.
Prefer explicit pair structures over implicit tuples to make code intent clear.

Example use cases

Mapping a transformation over a sensor reading and an environment config simultaneously.
Composing a protocol that transforms reagent metadata and spatial coordinates in a chemputer pipeline.
Verifying that sequential mappings preserve expected algebraic properties in a product-category model.
Building small DSL converters where each stage maps over two syntactic components.
Teaching bifunctor behavior with short, inspectable examples that show mapping and composition.