Abstract Language Tree (ALT) Framework

Updated 22 December 2025

Abstract Language Tree (ALT) is a semantically-grounded, hierarchical data structure that abstracts program logic and query intent from concrete syntax.
ALTs, exemplified by SALT for binary decompilation and ARC for relational query analysis, organize logic into rooted trees with explicit control flow and quantification.
This formalism enables precise reasoning, program transformation, and deep learning applications by decoupling syntax from semantics with measurable evaluation metrics.

An Abstract Language Tree (ALT) is an explicit, semantically-grounded, hierarchical data structure for representing the logic, intent, and structure of programs or queries independently of any surface syntax. ALTs serve as canonical machine-interpretable forms that abstract away from linear or ad-hoc code presentations, instead organizing constructs such as control flow (in programs) or logical quantification and grouping (in queries) as rooted, labeled trees (sometimes with cross-links or annotations for non-tree references). Recent deployments of ALT formalism include the Source-level Abstract Logic Tree (SALT) for lifting binary code to high-level representations (Wang et al., 18 Sep 2025), and as the semantic backbone of Abstract Relational Query Language (ARQL) and Abstract Relational Calculus (ARC) in the context of database queries (Gatterbauer et al., 15 Dec 2025). The ALT paradigm enables precise reasoning, program transformation, and learning tasks by decoupling logic structure from concrete language artifacts.

1. Formalization and Core Semantics

An ALT is a rooted, ordered tree (or, more generally, a hierarchical graph with cross-links) whose nodes represent abstract syntactic or logical constructs. The specific node types and labeling functions depend on the semantic domain:

For binary decompilation (SALT (Wang et al., 18 Sep 2025)):

$T = (V, E, \ell)$ , where $V$ is the set of logic blocks (function, loops, flat regions), $E \subseteq V \times V$ encodes parent–child nesting, and $\ell : V \to L$ maps each node to a normalized instruction sequence or a special marker (e.g., $\mathtt{<<LOOP_i>>}$ ). Each $v \in V$ also carries metadata for nesting depth and covered address ranges.

For relational query logic (ARC (Gatterbauer et al., 15 Dec 2025)):

An ALT encodes the parsed, name-resolved abstract syntax of a comprehension query as a tree with nodes: Query, Head, Assign, Quantifier, Grouping, Conjunction, Disjunction, Negation, Comparison, Aggregation, RelationRef, etc. Cross-links explicitly tie variable usages in assignments or predicates to their binding quantifiers. This representation makes quantifier nesting, grouping keys, and assignments explicit, supporting well-founded semantic evaluation.

Key properties enforced by ALT definitions include:

Coverage: All primitive instructions or logical operations are present.
Disjointness/Nesting: Instruction ranges or variable scopes are non-overlapping except by tree containment.
Soundness: Parent–child relations in the tree reflect structural or logical containment and correct output flow.

2. Construction Algorithms and Node Typology

ALT construction follows deterministic algorithms that enforce semantic faithfulness:

In SALT4Decompile (Wang et al., 18 Sep 2025):

Extract the control-flow graph (CFG) via binary disassembly.
Normalize assembly instructions (e.g., convert jumps to relative offsets, extract data references).
Detect jump-units (loops) as strongly connected subgraphs containing back-edges.
Traverse the CFG recursively, partitioning basic blocks into logic blocks and loop markers, constructing the logic tree rooted at the function entry. Pseudocode is provided for explicit tree construction with loop handling, subloop extraction, and exit block identification.

In ARC (Gatterbauer et al., 15 Dec 2025):

Parse the query into a comprehension-style syntax tree.
Perform name-resolution, binding each variable occurrence to its quantifier.
Build the ALT as a rooted tree where nodes correspond to grammar nonterminals. Cross-links are built for each variable use.
Annotate quantifier nodes with grouping keys, aggregation or external relations as appropriate.

Node types are strictly domain-specific but obey certain universals: roots (function, query), structural groupings (loop, quantifier), leaves (instructions, tuples), and operational markers (loop markers, group-by keys, assignment predicates).

3. Illustrative Examples

SALT: Hierarchical Logic Extraction from Assembly

For a function with nested loops, such as:

int foo(int n) {
  int sum = 0;
  for (i=0; i<n; i++) {
    for (j=0; j<i; j++) {
      sum += j;
    }
  }
  return sum;
}

A typical SALT organizes logic as a tree whose nodes represent initialization blocks, outer loop (with marker

\mathtt{<<LOOP_0>>}

), inner loop (

\mathtt{<<LOOP_1>>}

), and flat leaf blocks for straight-line code. Each marker denotes a loop boundary, with nesting captured by tree structure. See Table 1 for a concise summary.

Node	Type	Contents/Marker
foo	Function	entry instructions
LOOP_0	Loop	$\mathtt{<<LOOP_0>>}$ , sub-blocks
LOOP_1	Loop	$\mathtt{<<LOOP_1>>}$ , sub-blocks

ARC: Relational Query Logic as Tree

For the SQL:

1
2
3

SELECT R.A FROM R WHERE EXISTS (
  SELECT 1 FROM S WHERE S.B = R.B AND S.C = 0
);

ARC comprehension and its ALT encode:

Query root with Head (assignment $Q.A = r.A$ )
Body with nested Quantifiers $(\exists r~R), (\exists s~S)$
Conjunction node incorporating comparisons $r.B = s.B$ , $s.C = 0$
Binding cross-links from variable uses to their quantifier introductions

4. Role in Machine Reasoning and Program Transformation

ALTs enable lossless machine reasoning and program manipulation because each logical or structural step is explicit:

For deep learning (SALT4Decompile):

ALT (specifically SALT) provides the left-hand input for seq2seq fine-tuning. A transformer receives a flattened logic tree, with block and loop markers embedded to bias attention toward intra-block reasoning. Additional attention biasing using tree distance further encourages local context exploitation.

Formally, attention between positions $i$ , $j$ can be modulated by:

$\mathrm{score}(i, j) = \frac{Q_i \cdot K_j}{\sqrt{d} + \alpha\,d_T(v_i, v_j)}$

where $d_T(v_i, v_j)$ is the tree distance in the ALT (Wang et al., 18 Sep 2025).

For query analysis (ARC):

Algorithms can walk the ALT to check that all variables are bound, validate scoping, push down predicates, flatten nested comprehensions, identify reusable subquery blocks, and compare queries for semantic equivalence by tree isomorphism. The canonical representation removes syntactic ambiguity and facilitates both optimization and explainability.

5. Empirical Benefits and Evaluation Metrics

Structured ALT representations yield measurable improvements in downstream tasks:

SALT4Decompile (Wang et al., 18 Sep 2025):
- On the Decompile-Eval benchmark, achieves Re-Compilation Rate ( $RC$ ) 96.8%, Re-Execution Rate ( $RE$ ) 58.7%, Test-Case-Pass Rate ( $TCP$ ) 70.4%.
- Outperforms prior state-of-the-art decompilers by $+10.6\%$ absolute TCP.
- Demonstrates $5$– $8\%$ TCP improvement on other benchmarks (MBPP, Exebench).
- Robustness to common obfuscations confirmed.
ARC and relational query reasoning (Gatterbauer et al., 15 Dec 2025):
- ALT modality exposes the relational core, groupings, and variable bindings, enabling language-agnostic transformations and deep analysis.
- Semantics-first design with convention-orthogonality supports modular, cross-language reasoning.

6. Limitations and Directions for Generalization

Identified limitations in current ALT instantiations include:

SALT (Wang et al., 18 Sep 2025):
- Only abstracts loops and flat blocks; if-else, switch-case structures are not directly represented.
- Loop unrolling and aggressive optimization may obscure recoverable structure.
- Functions without loops collapse to flat sequences, reducing abstraction value.
- Fidelity depends on the accuracy of CFG extraction; analysis errors propagate.

Potential extensions: - Add structural nodes for conditionals (if-else, switch-case) by detecting multi-exit subgraphs. - Incorporate data-dependency to allow for DAGs instead of strict trees. - Annotate nodes with inferred types and signatures. - Extend to recursive calls and architectures beyond x86.

ARC ALT (Gatterbauer et al., 15 Dec 2025):
- Verbosity is a trade-off for explicitness; surface-syntax features like ORDER BY and window functions require further node types.
- Requires correct lowering from user syntax (e.g., SQL) to ALT; errors in transformation affect ALT soundness.

7. Significance and Broader Implications

The Abstract Language Tree formalism introduces an explicit, semantics-centric representation for program logic, bridging the gap between low-level, implementation-specific artifacts and high-level, intention-driven reasoning. By making structural features such as control regions or logical quantification explicit, ALTs serve as foundational building blocks for decompilation, reverse engineering, querying, and code analysis tasks. In both binary decompilation and relational query domains, ALTs operationalize intent over syntax, offer a pathway for cross-domain abstraction, and enable flexible, modular, and explainable program and query transformations (Wang et al., 18 Sep 2025, Gatterbauer et al., 15 Dec 2025). A plausible implication is that generalized ALT frameworks can play a central role in future human–machine language interfaces, unified program IRs, and LLM-based toolchains.