A Typed Algebra for Agent Skills
The typed skill algebra turns a directory of prompts into a composable system. Skills are categorized by what they do, checked by a linter, and routed by type compatibility so chains can be reasoned about before execution.
Paper workspace
Live draft structure
Artifacts
System source mapped
This is currently a running-system page, not a rendered paper.
source-only
Editable source
Running system summary. No standalone manuscript found in this pass; this should become a technical note with evidence from the skills corpus and linter.
Source anchors
Codex/Claude skills corpus
skill linter and typed skill registry
blog/type-system-for-skills
Method tags
Ingest intersections
Status
Running; 99.7% of the library typed, linter enforced.
Key claims
01
A skill library without types is hard to compose safely.
02
Generators, transformers, reducers, distributors, effectors, and auditors form a practical operational algebra.
03
Linting skill composition prevents some classes of agent drift.
Public reading note
System summary public; exact internal skill corpus is private.
Standard skeleton
What this paper must keep proving
problem
A large skill library becomes ungovernable if every skill is just text with trigger phrases.
method
Assign operational types to skills and check composition before routing or chaining.
implementation
Generator, transformer, reducer, distributor, effector, and auditor categories plus linter/router enforcement.
data
The internal skill corpus and routing outcomes; public release should summarize counts and examples without leaking private operations.
evaluation
Type coverage, linter rejection quality, routing success, and failure reduction in composed workflows.
references
Typed workflow systems, category-inspired composition, tool-use agents, skill libraries.
openQuestions
The next step is a concise technical note with measured linter and routing outcomes.
Checkpoints and references
Proof chain
Claim checkpoint
central-claim slot
Every central claim must point to a proof anchor or remain labeled as speculative.
Implementation checkpoint
implementation-map slot
Every method should identify the code path, harness, schema, or protocol that embodies it.
Evidence checkpoint
evidence-manifest slot
Every reported result should point to run IDs, packet IDs, data snapshots, commits, or review artifacts.
Reference checkpoint
references slot
Every external claim should resolve to a cited paper, benchmark, standard, or documented prior system.
Release checkpoint
release-gate slot
Every PDF needs a named condition before it can move from draft to citation-ready.