Library of Composable Objects (LOCO)

• LOCO is a framework of modular, reusable objects composed via formal methods and declarative specifications that ensure finite, verifiable system configurations.
• It supports diverse methodologies—from logic-based modeling and distributed regression to autonomous agent design and quantum simulation—offering scalable and interpretable solutions.
• LOCO frameworks facilitate algebraic composition, constrained coding, and formally verified distributed systems, enhancing performance and reliability across multiple domains.

A Library of Composable Objects (LOCO) is a generic term denoting a collection of modular, reusable components whose composition, interaction, and verification are governed by formal methods, declarative specifications, or algorithmic design patterns. Depending on context—ranging from declarative logic-based modeling (Aschinger et al., 2011), distributed regression (Heinze et al., 2014), autonomous agent design (Kappé et al., 2017), constrained coding (Hareedy et al., 2019), quantum workflows (Nguyen et al., 2021), to formally verified distributed object systems for RDMA (Ambal et al., 12 Oct 2025)—LOCO frameworks provide systematic means for constructing large systems from smaller, well-defined objects, with special emphasis on composability, resource management, finite or verifiable models, and algebraic reasoning.

1. Formal Declarative Modeling of Composable Objects

In logic-based configuration systems (Aschinger et al., 2011), LOCO is instantiated as a high-level declarative language (LoCo) for specifying composable components, their connections, and constraints. Components are encoded as n-ary predicates (e.g., Module(id, version, ...)), distinguished by unique identifiers and attribute vectors. Connections and composition are encoded via logical formulas using counting quantifiers: $$(\forall id_{Module}, attr)\ [Module(id_{Module}, attr) \rightarrow (\exists^{1}_{1}\ id_{Adapter})\ (Module2Adapter(id_{Module}, id_{Adapter}) \wedge Adapter(id_{Adapter}, ...))]$$ Bounding the minimal and maximal relations via connection axioms ensures all valid configurations are finite models; dynamic generation of instances (for example, new object instances or submodules) is tightly controlled by logic, making model construction a tractable reasoning task for compositional libraries.

Declarative composition and resource bounds are algorithmically propagated: $$LB = \left\lceil\frac{l_1 \cdot |\text{Module}|}{u_2}\right\rceil,\quad UB = \left\lfloor\frac{u_1 \cdot |\text{Module}|}{l_2}\right\rfloor$$ where $l_1$, $u_1$ are lower and upper bounds per connection. This supports automated synthesis and verification of finite compositional object libraries, foundational for tool support.

2. Distributed Algorithms and Modularity

In the context of large-scale optimization (Heinze et al., 2014), LOCO refers to modular distribution of feature-wise computation for ridge regression. The framework partitions feature space into $K$ nonoverlapping blocks, employing one-shot structured random projections (SRHT) per node to maintain feature dependencies across worker boundaries: $$\hat{X}_k' = X_k' \cdot \Pi_k',\quad \bar{X}_k = [X_k, \tilde{V}_k]$$ where $\Pi_k'$ is a randomized Hadamard projection and $\tilde{V}_k$ aggregates compressed representations from other nodes.

Objects in this LOCO are the modular computational units:

• Feature partitioners,
• Random projection compressors,
• Ridge regression solvers per block,
• Coefficient aggregators.

This design yields scalability (linear speedups for large $p$), interpretability (raw coefficients preserved), and minimal communication, encapsulating each unit as a composable object suitable for distributed frameworks (e.g., Spark).

3. Object-Oriented and Algebraic Composition

LOCO may manifest as an object-oriented combinator library (Kosarev et al., 2021), particularly in generic programming for languages such as OCaml. Here each algebraic data type generates:

• A generic traversal function ("gcata"),
• A virtual transformation class (per constructor),
• Concrete or compositional transformation objects via late binding.

Polymorphic variant support and fix-point combinators enable recursive and extensible data types and transformations. Transformations are expressed as: $\iota \rightarrow t \rightarrow \sigma$ where $\iota$ and $\sigma$ are inherited/synthesized attributes (attribute grammar formalism).

Composability is achieved through object inheritance, dynamic dispatch, and method-combinator composition, supporting domain-specific languages, code analysis, and transformation pipelines.

4. Formal Verification and Distributed System Libraries

In high-performance distributed settings with RDMA (Ambal et al., 12 Oct 2025), LOCO is a formally verified library of composable objects—barriers, shared variables, ring buffers, and mixed-size writes—built atop RDMA’s weak memory model. Each object is encapsulated and operations are specified as precise methods. Verification leverages the MOWGLI modular declarative framework:

• Abstract executions: $G' = \langle E', po' \rangle$ (library-level methods).
• Implementation executions: $G = \langle E, po, \gamma, so, hb \rangle$ (RDMA-level events/stamps).
• Refinement via surjective abstraction functions $\alpha: E \to E'$ and ordering consistency requirements, e.g.: $\alpha(po) \subseteq (po')^*$ Consistency predicates ($C$) are proved monotonic and decomposable, ensuring that modular proofs about individual objects can be composed for larger systems. Libraries are specified as triples $\langle M, \gamma, C \rangle$ (methods, stamps, consistency), and objects such as ring buffers and barriers are implemented and verified modularly.

A central formula: $$hb = (ppo \cup so)^+\quad ppo = \{(e_1, e_2) \mid (e_1, e_2) \in po,~\forall a_1 \in \gamma(e_1),~a_2 \in \gamma(e_2) : (a_1, a_2) \in to \}$$ underpins the event ordering assumptions and the verification process.

5. Compositional Semantics for Autonomous Systems

Within component-oriented autonomous agent frameworks (Kappé et al., 2017), LOCO is realized via Soft Component Automata (SCAs), where each object is a finite-state automaton labeled by actions and preference values (from a c-semiring):

• Actions: $\Sigma$ (CAS).
• Preferences: $E$ (c-semiring, $\otimes$).
• Composition: actions via $\circ$, preferences via $\otimes$.

Composed systems are represented by parallel product automata: $$A_0 \boxtimes A_1 = (Q_0 \times Q_1, \Sigma, E, \rightarrow, (q_0^0, q_1^0), t_0 \otimes t_1)$$ along with compositional LTL extensions (“capture” and “composable” operators) that enable diagnosis and system-level verification.

Diagnostic preference tracing and threshold tuning support verifiable fault isolation and behavioral guarantees. This modular synthesis of agent behaviors and preferences is directly germane to robotics, sensor networks, and distributed autonomous control.

6. Coding Theory and Constrained Code Libraries

LOCO also refers to codebooks of composable constrained codes in data transmission and storage (Hareedy et al., 2019). Asymmetric LOCO (A-LOCO) codes expand the library by forbidding only physically detrimental patterns specific to flash memory devices, maximizing code rate at finite length: $$N(m, x) = 2N(m - 1, x) - N(m - 2, x) + N(m - x - 2, x)$$ with lexicographic indexing and streamlined encoding/decoding procedures. These are objects in the form of codewords and encoding functions. The significant increase in allowed codewords and rate (e.g., for $m=5$, $x=1$; $N=21$ for A-LOCO vs $N=16$ for symmetric LOCO) provides empirical justification for this compositional code library approach in flash memories and communication systems.

7. Compositional Workflows for Quantum Simulation

In quantum simulation (Nguyen et al., 2021), LOCO consists of abstracted workflow objects encapsulating quantum simulation steps—model instantiation, circuit construction, execution, result validation—across hardware backends and simulators. Key objects are:

• QuantumSimulationModel (Hamiltonian, observable),
• QuantumSimulationWorkflow (execution logic),
• AnsatzGenerator, CostFunctionEvaluator (circuit, measurement abstraction),
• Plugin system for workflow specialization and dynamic customization.

Composability is achieved through extension and interchange of workflow plugins (VQE, QAOA, QITE), runtime swapping of circuit generators and optimizers, and polymorphic model builders. This design enables rapid adaptation, benchmarking, and integration with third-party quantum software, establishing a modular LOCO foundation for future quantum simulation research.

8. Implications and Applications

Library of Composable Objects frameworks universally support:

• Declarative specification and automated synthesis of modular systems (Aschinger et al., 2011),
• Model construction and resource analysis under compositional constraints,
• Scalable, interpretable distributed optimization via compositional computational units (Heinze et al., 2014),
• Algebraic, formally verified object design for distributed memory architectures (Ambal et al., 12 Oct 2025),
• Efficient encoding libraries in error-prone transmission/storage settings (Hareedy et al., 2019),
• Extensible transformation frameworks for typed programming languages (Kosarev et al., 2021),
• Autonomous systems with compositional preference reasoning and diagnosable logic (Kappé et al., 2017),
• Composable hybrid workflows for quantum simulation (Nguyen et al., 2021).

Formal compositional verification, modular object design, and declarative or algebraic modeling collectively distinguish LOCO approaches in both theory and implementation.

References

• (Aschinger et al., 2011) Introducing LoCo, a Logic for Configuration Problems
• (Heinze et al., 2014) LOCO: Distributing Ridge Regression with Random Projections
• (Kappé et al., 2017) A Component-oriented Framework for Autonomous Agents
• (Hareedy et al., 2019) Asymmetric LOCO Codes: Constrained Codes for Flash Memories
• (Nguyen et al., 2021) QuaSiMo: A Composable Library to Program Hybrid Workflows for Quantum Simulation
• (Kosarev et al., 2021) Generic Programming with Combinators and Objects
• (Ambal et al., 12 Oct 2025) A Verified High-Performance Composable Object Library for Remote Direct Memory Access (Extended Version)