Semantics-Complete Execution Paradigm

• The semantics-complete execution paradigm is an integrated framework where semantic state and operational behavior are mutually determining, ensuring runtime fidelity.
• Key architectural patterns include executable semantic carriers, persistent state updates, and the explicit separation of syntactic completion from semantic commitment.
• Applications in code generation and program repair demonstrate improved correctness by aligning execution traces with formal, behavior-supervisory objectives.

Searching arXiv for the cited works to ground the synthesis in current preprints. arxiv_search.query {"^^^^^^^^7search_query7 complete execution paradigm\"^^^^^^^^7 OR ti:\7^^^^^^^^"CodeRL+\" OR ti:\7^^^^^^^^"Executable Ontologies\"^^^^^^^^7 OR ti:\7^^^^^^^^"SemAgent\" OR ti:\7^^^^^^^^"Correct and Complete Symbolic Execution for Free\"^^^^^^^^7 OR ti:\7^^^^^^^^"Execution Semantics and Neuro-Neuromorphic Systems\"","start":^^^^7search_query7^^^^,"max_results":^^^^7all:\7search_query7 arxiv_search.query The semantics-complete execution paradigm is a cross-domain ideal in which semantic description and operational behavior are not separated into loosely connected layers but are made mutually determining. Taken together, the literature uses this idea in several closely related senses: as an executable ontology in which the semantic model is “the actual operational substrate,” as a reinforcement-learning regime that aligns code tokens with runtime behavior, as a symbolic semantics generated directly from language semantics, as a repair workflow that joins issue, code, and execution semantics, as a runtime model for brain digital twins that preserves execution semantics across sensing and actuation, and as a critique of protocols whose completion signals stop short of semantic commitment (&&&^^^^7search_query7^^^^&&&, &&&^^^^7all:\7^^^^&&&, &&&^^^^7 OR ti:\7^^^^&&&, &&&^^^^7 OR ti:\7^^^^&&&, &&&^^^^7 OR ti:\7^^^^&&&, &&&^^^^7 OR ti:\7^^^^&&&).

^^^^7all:\7^^^^. Semantic completeness as an execution criterion

A common thread across these works is that semantics-complete execution rejects the view that a system is adequately characterized by output labels, transport success, or static description alone. In boldsea, the claim is explicit: the ontology is not a passive RDF/OWL-style description but a “dynamic semantic structure that directly controls execution,” so the same formal artifact contains concepts and relations, actors and provenance, conditions for triggering actions, restrictions on values and access, system actions, temporal causality, and executable behavior (&&&^^^^7search_query7^^^^&&&). In symbolic SOS, the same idea appears in a proof-theoretic form: a suitably structured stateful SOS specification simultaneously induces a deterministic concrete semantics and a nondeterministic symbolic semantics, with correctness and completeness obtained “by construction” (&&&^^^^7 OR ti:\7^^^^&&&).

Other papers formulate the same criterion negatively, by identifying where semantic completeness fails. The RDMA critique argues that completion semantics commit a category mistake because they guarantee placement but not commitment: a completion queue entry may indicate only that transport-level placement has succeeded, not that the receiving application has validated and integrated the data into meaning-bearing state (&&&^^^^7 OR ti:\7^^^^&&&). The brain digital twin survey similarly argues that model accuracy is insufficient if execution semantics are not preserved across data acquisition, model state evolution, online assimilation, and physical interaction; a system becomes maximally executable only when biological and computational dynamics are co-executed under shared physical execution constraints (&&&^^^^7 OR ti:\7^^^^&&&).

This suggests that “semantics-complete” is less a single formal doctrine than a recurring systems principle: semantic information must be operationally sufficient to determine execution, and execution status must remain faithful to semantic state.

^^^^7 OR ti:\7^^^^. Why the paradigm emerges: recurrent semantic gaps

Several papers motivate the paradigm by diagnosing a semantic gap between what systems are optimized for and what correctness actually requires. In code generation, the gap is between autoregressive next-token prediction and functional correctness. CodeRL+ states that LLMs are trained on textual patterns, whereas correctness is governed by formal execution semantics; RLVR narrows the gap by using test execution, but binary pass/fail reward remains too sparse to teach actual runtime behavior, especially for subtle logical errors (&&&^^^^7all:\7^^^^&&&). The proposed remedy is to teach the model to infer variable-level execution trajectory, so that learning is tied not only to whether a program passes but also to how its state evolves at runtime.

Repository-level repair exposes a related gap. SemAgent argues that many APR and agentic systems “hyper-localize” on suspicious lines and patch them in isolation, without sufficient use of execution semantics, issue semantics, or code semantics. The resulting patches can overfit the particular issue example or remain incomplete by missing sibling branches, related conditions, or consistency updates elsewhere in the file (&&&^^^^7 OR ti:\7^^^^&&&). Here semantics-complete behavior is associated with “complete” patches that identify and fix all lines relevant to the issue.

Earlier work on Constraint Handling Rules framed the problem differently but reached an analogous conclusion. Analytical operational semantics such as PRESERVED_PLACEHOLDER_^^^^7search_query7^^^^ are mathematically elegant but non-executable because propagation rules can fire indefinitely on the same effective content. Pragmatic semantics such as token-based PRESERVED_PLACEHOLDER_^^^^7all:\7^^^^, refined PRESERVED_PLACEHOLDER_^^^^7 OR ti:\7^^^^, or priority-based PRESERVED_PLACEHOLDER_^^^^7 OR ti:\7^^^^ terminate, but do so by introducing a non-declarative propagation history (&&&^^^^7all:\7 OR ti:\7^^^^&&&). The proposed execution model seeks a terminating execution paradigm that remains faithful to the analytical semantics.

Across these cases, the recurring failure mode is the same: the system can manipulate surface artifacts—tokens, lines, transfers, simulations, or workflow steps—without directly representing the semantic state transitions that determine correctness.

^^^^7 OR ti:\7^^^^. Structural patterns of semantics-complete execution

The papers converge on a small set of architectural patterns. The first is the use of a semantic carrier that is itself executable. In boldsea, that carrier is an event-centric ontology interpreted directly by the boldsea-engine without compilation. The event structure is given as

PRESERVED_PLACEHOLDER_^^^^7 OR ti:\7^^^^

with Actor required for provenance and Cause forming a directed acyclic graph of events. Execution is declarative and dataflow-like: model events act like operators, reification events act like data, activation depends on Condition, and results propagate through subscriptions rather than imperative calls (&&&^^^^7search_query7^^^^&&&).

The second pattern is persistent state updated by semantically typed events. The brain digital twin survey defines a brain digital twin as a computational brain model that maintains a persistent execution state continuously aligned with neurobiological observations acquired through sensing interfaces. Its taxonomy distinguishes regimes by persistence of execution state, admissible event types, and degree of temporal and causal coupling; Level III permits simulation and measurement events to update persistent state, while Level IV adds actuation events and bidirectional coupling under latency, bandwidth, and actuation constraints (&&&^^^^7 OR ti:\7^^^^&&&).

The third pattern is explicit separation between syntactic completion and semantic commitment. The RDMA analysis decomposes a Write into seven stages—submission, placement, transmission, remote placement, completion, visibility, and semantic agreement—and insists that PRESERVED_PLACEHOLDER_^^^^7 OR ti:\7^^^^ is false. A semantics-complete architecture must therefore distinguish placement, visibility, and commitment, and must include a mandatory reflecting phase in which the receiver communicates semantic acceptance rather than mere transport success (&&&^^^^7 OR ti:\7^^^^&&&).

The following summary captures these recurring structures.

Domain	Semantic carrier	Execution criterion
Executable ontologies	Event-centric semantic model	Model directly controls runtime
Brain digital twins	Persistent execution state	Measurement and actuation preserve causal-temporal alignment
Interconnect protocols	Receiver semantic state	Completion requires commitment, not placement

These patterns suggest that semantic completeness is achieved when runtime control, state persistence, and acknowledgment all refer to meaning-bearing structures rather than to external surrogates.

^^^^7 OR ti:\7^^^^. Formalizations and proof obligations

The strongest versions of the paradigm are formalized through state-transition semantics and accompanying correctness or completeness results. CodeRL+ defines execution semantics as runtime behavior and formalizes a program PRESERVED_PLACEHOLDER_^^^^7 OR ti:\7^^^^ as a higher-order state transition function $\Phi_p$, composed of atomic transitions $\phi_t$. Starting from $S_0$, execution yields a trajectory

PRESERVED_PLACEHOLDER_^^^^7all:\7search_query7^^^^

and the paper states that “the execution semantics of a program under a given input” is its complete execution trajectory PRESERVED_PLACEHOLDER_^^^^7all:\7all:\7^^^^. Because full trajectories are expensive, the method approximates execution semantics by the final value of each variable at its last definition point and introduces a variable-level reward

PRESERVED_PLACEHOLDER_^^^^7all:\7 OR ti:\7^^^^

which augments the usual binary generation reward (&&&^^^^7all:\7^^^^&&&).

Symbolic SOS gives a more foundational account. A concrete state is a map PRESERVED_PLACEHOLDER_^^^^7all:\7 OR ti:\7^^^^, while a symbolic state is a map PRESERVED_PLACEHOLDER_^^^^7all:\7 OR ti:\7^^^^. The key interpretation is that a symbolic state is a concrete state transformer:

PRESERVED_PLACEHOLDER_^^^^7all:\7 OR ti:\7^^^^

From one symbolic SOS specification, the framework derives a deterministic concrete small-step semantics and a nondeterministic symbolic small-step semantics with path conditions. The central theorem states that the identity relation on programs is a syncrete bisimulation between the concrete and symbolic models, yielding the corollary that symbolic execution is correct and complete with respect to the concrete semantics (&&&^^^^7 OR ti:\7^^^^&&&).

The higher-order library setting reaches a similar endpoint through operational game semantics. “Symbolic Execution Game Semantics” models library-client interaction as a game of calls and returns, extends it with symbolic integers and path conditions, and proves that the symbolic semantics is sound and complete for library failures. Its bounded variant imposes limits on recursion depth and callbacks, producing a finite symbolic search space for open higher-order programs (&&&^^^^7all:\7^^^^8&&&).

The CHR execution model resolves the analytical/pragmatic split by introducing linear and persistent stores, an idempotence law for persistent constraints, and an irreflexive transition condition PRESERVED_PLACEHOLDER_^^^^7all:\7 OR ti:\7^^^^. The resulting semantics is sound and complete with respect to PRESERVED_PLACEHOLDER_^^^^7all:\77^^^^ while remaining terminating and executable (&&&^^^^7all:\7 OR ti:\7^^^^&&&).

In all four cases, semantic completeness is not merely rhetorical. It is tied to explicit proof obligations: preservation of concrete meaning under abstraction, exhaustive symbolic coverage of concrete behaviors, or termination without loss of analytical faithfulness.

^^^^7 OR ti:\7^^^^. Semantics-aware code generation and repair

In machine-generated software, the paradigm appears as a move from outcome supervision to behavior supervision. CodeRL+ uses a dual-objective training framework combining code generation optimization with execution semantics alignment. It constructs alignment data on the fly from failed on-policy rollouts, extracts ground-truth variable final values during execution, and prompts the model with program, input, and variable names to infer those values. The mixed batch is

PRESERVED_PLACEHOLDER_^^^^7all:\7^^^^8

and the objective combines code-generation and semantics-alignment terms in GRPO-style training (&&&^^^^7all:\7^^^^&&&). Experimentally, the paper reports HumanEval 9^^^^7search_query7^^^^.9, LeetCode ^^^^7 OR ti:\7 OR ti:\7^^^^.^^^^7 OR ti:\7^^^^, LiveCodeBench ^^^^7 OR ti:\7 OR ti:\7^^^^.9, average code generation pass@^^^^7all:\7^^^^ ^^^^7 OR ti:\7 OR ti:\7^^^^.7, Code Reasoning 8^^^^7 OR ti:\7^^^^.^^^^7search_query7^^^^, and Test Output Generation ^^^^7 OR ti:\7 OR ti:\7^^^^.^^^^7 OR ti:\7^^^^; it further reports a ^^^^7 OR ti:\7^^^^.^^^^7 OR ti:\7^^^^% average relative improvement in pass@^^^^7all:\7^^^^, ^^^^7all:\7 OR ti:\7^^^^.^^^^7 OR ti:\7^^^^% higher accuracy on code-reasoning, and ^^^^7 OR ti:\7^^^^.^^^^7 OR ti:\7^^^^% higher accuracy on test-output generation (&&&^^^^7all:\7^^^^&&&).

SemAgent adopts a workflow-based form of the same idea for automated program repair. Its front end uses execution semantics to retrieve context by improving the reproducer, extracting suspicious files from the execution trace, and triangulating crash reports, execution traces, and spectrum-based fault localization. It then computes issue semantics through generalized abstraction, isolates code semantics by constructing execution flows and mapping flow steps back to exact snippets, and uses a repair stage, reviewer agent, and patch aggregator to obtain a final patch (&&&^^^^7 OR ti:\7^^^^&&&). On SWE-Bench Lite, described as ^^^^7 OR ti:\7search_query7search_query7^^^^ real-world GitHub issues across ^^^^7all:\7all:\7^^^^ Python repositories under a single pass@^^^^7all:\7^^^^ setting, the methodology achieves a ^^^^7 OR ti:\7 OR ti:\7^^^^.^^^^7 OR ti:\7 OR ti:\7^^^^% solve rate, corresponding to ^^^^7all:\7 OR ti:\7 OR ti:\7^^^^ solved issues, an absolute improvement of 7.^^^^7 OR ti:\7 OR ti:\7^^^^ percentage points over a ^^^^7 OR ti:\77^^^^% baseline; the repair stage alone improves from ^^^^7 OR ti:\77^^^^% to ^^^^7 OR ti:\7 OR ti:\7^^^^%, and adding the reviewer yields the final ^^^^7 OR ti:\7 OR ti:\7^^^^.^^^^7 OR ti:\7 OR ti:\7^^^^% (&&&^^^^7 OR ti:\7^^^^&&&).

These systems are not identical. CodeRL+ uses reinforcement with execution-semantics alignment during post-training, whereas SemAgent is a staged repair workflow. A plausible implication is that both instantiate the same operational thesis: correctness improves when supervision targets runtime behavior, behavioral intent, and dependency structure rather than isolated surface outputs.

^^^^7 OR ti:\7^^^^. Scope, partial realizations, and contested boundaries

The literature also marks clear limits. CodeRL+ explicitly does not supervise every intermediate step of the full execution trace in practice; instead it uses the tractable approximation of final values of variables at their last definitions. For that reason, the paper concludes that it is not “complete” in the strictest sense of modeling every state transition step-by-step, even though it is “significantly more complete than binary RLVR” (&&&^^^^7all:\7^^^^&&&). SemAgent similarly assumes that execution traces, issue descriptions, and file-local semantic flows are sufficient for many tasks, but its current implementation is restricted to single-file fixes, and the authors state that scaling to repository-level call chains and broader context retrieval remains open; it also averages about $^^^^7 OR ti:\7^^^^.9 per issue with Claude Sonnet ^^^^7 OR ti:\7^^^^.7, though caching reduces that cost (&&&^^^^7 OR ti:\7^^^^&&&).

Foundational frameworks are also scoped. Symbolic SOS is developed for deterministic small-step semantics and leaves nondeterministic or concurrent languages for future work (&&&^^^^7 OR ti:\7^^^^&&&). The CHR model is defined for range-restricted programs, and its implementation theorem relies on non-pathological programs (&&&^^^^7all:\7 OR ti:\7^^^^&&&). The higher-order game-semantics framework is bounded by recursion depth and callback depth in order to obtain strong normalization of the labeled transition system (&&&^^^^7all:\7^^^^8&&&).

At the systems level, the brain digital twin survey presents semantics completeness as a graded notion rather than an all-or-nothing property. Level I isolated models and Level II co-simulation frameworks remain non-executable with respect to the living brain because they lack persistent cross-run alignment and causal coupling. Level III executable brain digital twins achieve persistent state and online assimilation, while Level IV neuro–neuromorphic physical systems realize the strongest form through bidirectional temporal and causal coupling under shared physical constraints (&&&^^^^7 OR ti:\7^^^^&&&). The RDMA paper sharpens the boundary from another direction: any architecture that equates completion with transport success remains semantically incomplete unless it includes semantic agreement and a reflecting phase (&&&^^^^7 OR ti:\7^^^^&&&).

Taken together, these limits clarify the term’s contemporary use. A semantics-complete execution paradigm is not simply any system with rich annotations or formal specifications. It is an execution regime in which semantic state, operational state, and correctness criteria are aligned tightly enough that execution can be said to preserve meaning rather than merely produce effects.