Recursive Formation and First-Class Reuse of Compositional Capabilities

Hang Lin

cs.PLOct 14, 2026

Recursive Formation and First-Class Reuse of Compositional Capabilities

Authors: Hang Lin

Abstract

We introduce FormCraft, a framework for representing acquired operations as first-class capabilities that can be recursively composed, directly invoked, and selectively retained in a persistent library through domain-specific verification. The framework separates capability well-formedness and public callability from later admission to persistent storage while preserving formation provenance and operational identity. We formalize recursive compositional closure over a uniform capability space and show that formed composites can be reused through the same public interface without re-forming their historical derivation. Experiments across continuous, discrete, propositional, and sequence domains demonstrate instance-independent reuse, independent checking, persistent acquisition, and reduced reuse-time search work under first-class exposure.

Figures & tables

Panel of Figure 1 — Figure 1: Recursive formation and first-class reuse of an intermediate capability. All boxes denote generic capabilities $G\in\mathfrak{F}$ ; the orange styling only highlights the same $G_{5}$ across the two panels and does not denote a distinct operational type. In (a), compatible recursive composition forms $G_{5}$ and later continues to $G_{6}$ . In (b), the same $G_{5}$ is exposed directly in a later task: it can accept a new invocation $(X,\alpha)$ or participate in further compatible composition with $G_{7}$ to form $G_{8}$ , without re-forming its historical subgraph. The recorded formation DAG and provenance remain retained.

Capability-record field	Role in the lifecycle
Record identity	Distinguishes concrete records and serialized objects.
$\operatorname{opid}(G)$	Represents operational identity independently of a particular formation history.
Typed input/output ports	Declare the public contract used for invocation and compatibility checks.
External-parameter schema	Declares the form of invocation-specific $\alpha$ while keeping call-specific values external.
Executable body	Implements the observable operation $\llbracket G\rrbracket$ .
Parent references and wiring $\omega$	Record the static formation relation for a composite capability record.

Table 1: Core fields of an executable capability record. Composite-specific formation fields extend the record while preserving the same public call form.

Panel of Figure 2 — Figure 2: Formation–admission–reuse lifecycle used to organize the experimental evidence. Search or acquisition first produces a well-formed first-class capability $G\in\mathfrak{F}$ . Verification and admission determine persistent membership $G\in\mathcal{L}$ , while membership in $\mathfrak{F}$ remains a property of the capability representation. An admitted capability can later be retrieved through the same public interface for direct invocation or further composition. The applicable verification procedure is domain-dependent.

Measure	Result
Composite capabilities formed	5/5
Composite theorem reuses	10/10
Lean checks accepted (exit code 0)	10/10
Capability-record hash and formation provenance preserved	Yes

Table 2: Composite capability reuse in the Lean-checked propositional microdomain.

Stage	Start	Goals	Added $F$	End
Stage I: Example-driven acquisition	12	7	14	26
Stage II: Increasing-depth chain (D01–D12)	26	12	12	38

Table 3: Sequential persistent-store growth in the sequence-domain study. Start and End count persistent records; Added

F

counts new executable capabilities.

Search-work measure	Expanded	First-class	Reduction
Candidate attempts	16,570	144	99.1%
Composition expansions	37,300	0	100%
Intermediate materializations	16,778	0	100%
Verification batches	17,116	192	98.9%

Table 4: Paired reuse-time search-work counts over 12 goals. Outputs in both search views matched the frozen oracle on evaluated cases; the 12 main-chain acquisitions passed admission.

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

Snapshot	Persistent records	Executable capabilities	Auxiliary records
Initial seed	12	–	–
After Stage I	26	24	2
After Stage II	38	36	2

Appendix

Table 5: Persistent-record accounting for the sequence-domain acquisition stages.

Compositional Reasoning

Compositional reasoning studies how models combine facts, concepts, rules, and skills to solve tasks that require multiple structured steps.

See all 39 papers

Lingering Authority: Revocable Resource-and-Effect Capabilities for Coding Agents
Jun 21, 2026Igor Santos-GrueiroCoding Agents AI Agent Security
International University of La Rioja
EvoWeave: Composing Reusable Agent Experience through Operation Level Graphs
Oct 14, 2026Guanhua Zhu, Bo Shen, Lei Zhang +4Agent Memory LLM Agent Memory
Department of Informatics, New Jersey Institute of Technology · Department of Mechanical and Industrial Engineering, New Jersey Institute of Technology · Department of Computer Science, New Jersey Institute of Technology +1
Capability Safety as Datalog: A Foundational Equivalence
Mar 20, 2026Cosimo SperaCapability-Based Security
Minerva CQ, 114 Lester Ln, Los Gatos, CA 95032.

Jun 21, 2026J/K move · Enter open · S save

Lingering Authority: Revocable Resource-and-Effect Capabilities for Coding Agents

Igor Santos-Grueiro

International University of La Rioja

Coding Agents AI Agent Security Capability-Based Security Runtime Assurance

Open paper AskPDF arXiv

Coding agents often receive broad tool access for an entire task, even when a resource is needed only for one subgoal. We call this gap lingering authority: a temporary resource/effect capability remains exposed after the episode that justified it has closed. PORTICO is a reference monitor for revocable capabilities exposed to the planner. It compiles an explicit task contract into initial capabilities, grant rules, trusted closure predicates, and global deny rules. A request-grant-invoke lifecycle materializes expansions as opaque, epoch-bound handles. Closure removes those handles from the next planner interface and rejects stale replay before side effects. The monitor assumes mediated tools and a sound typed catalog. In controlled coding-agent tasks, PORTICO records no executed contract-forbidden effects in the evaluated runs, while controlled grants recover boundary work blocked by a fixed narrow envelope. A non-revoking comparator receives the same initial envelope and the same grants at the same turns. On the closure slice, both systems match task success, scope compliance, and all pre-closure decisions; PORTICO then rejects 10/10 post-closure reuses, while the comparator permits 10/10. A deterministic stale-write audit records 0/6 versus 6/6 executed forbidden effects. Scripted traces and six live model traces over file writes, git mutation, and network egress show the same split. In a four-episode same-policy diagnostic, broad request exposure preserves zero executed forbidden effects but raises blocked proposals from 67 to 84. Frozen real-repository runs, with commits and traces recorded, exercise the same lifecycle on real project layouts.

Abstract

Compositional Reasoning

Explore similar work

Lingering Authority: Revocable Resource-and-Effect Capabilities for Coding Agents

EvoWeave: Composing Reusable Agent Experience through Operation Level Graphs

Capability Safety as Datalog: A Foundational Equivalence