problems/path-dependent-composition.md

# Composing operations with obligations inherited from the route

How can a small model compose large programs by navigating compatible operations?

A small model is proposed to select prepared operations by intent, entering local subspaces that inherit compatibility requirements from the route used to reach them. Extending simple-code experiments to more general reasoning remains open.

Status: open problem. Formulation and comparisons: reconstruction. Development: active.

## Alternative representations

### Prepared operations with named interfaces

Affords: Reduces repeated code construction.

Limits or losses: A name does not establish compatibility or reveal all effects.

### A context carrying inherited constraints

Affords: Makes route-dependent obligations explicit.

Limits or losses: Compatible local steps may still produce a globally invalid program.

## Tension

Standardized composition may reduce effort while producing bulky code and needing revision when standards change.

## Challenge

How does the interface know which obligations from earlier operations still apply?

This challenge is an editorial prompt, not a claim that the evidence already resolved it.

## Proposed next move

Compare two identical local calls reached through different contexts and test whether incompatible continuations are rejected.

Status: new model-proposed experiment or extension; not a reported result.

## Related problems

- [Becoming neighbors through a change of representation](changing-neighborhoods.md) — is recalled in a concrete design (corpus_evidence). The compatible-operation proposal explicitly returns to location-dependent topology and neighborhoods.
- [Navigation as an action language](navigation-as-language.md) — specifies inherited constraints (retrospective_connection). The later compatible-operation proposal makes route history relevant to the available next actions.
- [Constituents, order, and path identity](order-sensitive-path-encoding.md) — makes route identity operational (retrospective_connection). Inherited compatibility can depend on the route; the right equivalence relation must preserve relevant obligations.

## Evidence anchors

- basis-path-dependent-composition: The proposal has a small model choose prepared functions through simple controls instead of reading or writing their code. Entering a subspace is said to inherit compatibility with the route already taken. Simple-code experiments are reported as successful, followed by a question about extending the approach to more general reasoning. [Editorial paraphrase; presence of a proposal does not verify its truth.]

Root evidence and private recovery mappings are not part of this public release.

[Open in the reader](../index.html#node=path-dependent-composition) · [All problems](../CATALOG.md)

## Research editions

- [Memory, Tokens, and Learning Geometry](../documents/memory-tokens-and-learning-geometry.md) (reconstruction).