torsional parse trees and non-commutative syntax

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Comprehensive Research Probe: Torsional Parse Trees & Non-Commutative Syntax

Primary Search Anchors

Core Concept Queries

"non-commutative parsing" OR "parse tree with memory" OR "history-dependent parsing"
"asymmetric parse tree" OR "directional syntax tree" OR "parse tree with state"
"topological parsing" OR "winding number computation" OR "parse tree topology"
"self-modifying parse tree" OR "reflexive parsing" OR "parse tree with feedback"

Mathematical/Theoretical Foundations

("parse tree" OR "syntax tree" OR "AST") AND ("torsion" OR "twist" OR "chirality")
("context-sensitive grammar" OR "ordered grammar") AND ("non-associative" OR "path-dependent")
"monoidal category" AND "parsing" AND ("trace" OR "feedback" OR "recursion")
("winding number" OR "topological invariant") AND ("computation" OR "evaluation")

Related Formal Systems

"ordered context-free grammar" AND ("accumulator" OR "history" OR "state")
"parsing expression grammar" AND "side effects" AND "evaluation order"
"attribute grammar" AND ("circular" OR "self-referential" OR "fixed-point")
"van Wijngaarden grammar" AND ("two-level" OR "affix") AND "computation"

Interdisciplinary Connections

Consciousness & Computation

("self-aware computation" OR "reflective programming") AND ("parse" OR "syntax")
"strange loop" AND "formal grammar" AND ("consciousness" OR "self-reference")
"metacircular evaluator" AND ("non-commutative" OR "history" OR "trace")

Physics/Topology Inspired

("geometric phase" OR "Berry phase") AND ("computation" OR "programming language")
"holonomy" AND "parse tree" 
"parallel transport" AND ("syntax" OR "semantics" OR "evaluation")
("spin" OR "angular momentum") AND "abstract syntax tree"

Quantum/Non-Classical Computation

"quantum programming language" AND ("measurement" OR "collapse") AND "syntax"
"non-commutative computation" AND ("grammar" OR "parsing" OR "evaluation order")
"contextual semantics" AND "path-dependent" AND ("parse" OR "evaluation")

Specific Technical Features

Implementation Approaches

"colored parentheses" OR "chromatic syntax" OR "directional brackets"
"parse tree annotation" AND ("flow" OR "direction" OR "orientation")
"syntax-directed" AND "accumulator" AND ("torsion" OR "phase" OR "history")
"zipper" AND "parse tree" AND ("context" OR "history" OR "trace")

Error Handling & Debugging

"topological debugging" OR "non-local error" OR "path-dependent error"
"error" AND "parse tree" AND ("winding" OR "cycle" OR "loop")
"contractible error" OR "error topology" OR "error homotopy"

Extended Search Strategies

Author/Group Searches

author:"Conor McBride" AND ("ornament" OR "structure" OR "dependent type")
author:"Tarmo Uustalu" AND ("comonad" OR "dataflow" OR "circular")
author:"Olivier Danvy" AND ("delimited continuation" OR "context")
"INRIA" AND "geometric" AND ("syntax" OR "semantics")

Conference/Journal Venues

source:("ICFP" OR "POPL" OR "LICS") AND ("non-commutative" OR "path-dependent" OR "contextual")
source:("Topology and Computation" OR "Applied Categorical Structures")
source:"Journal of Functional Programming" AND ("circular" OR "self-referential")

Patent Searches

"parse tree" AND "state accumulation" AND (patent OR application)
"non-commutative evaluation" AND "programming language" 
"directional syntax" OR "asymmetric parsing"

Semantic Variations

Alternative Terminology

"anisotropic parsing" | "chiral syntax" | "handed evaluation"
"parse dag" AND ("cycle" OR "feedback" OR "non-tree")
"syntax graph" AND ("directed" OR "weighted" OR "attributed")
"evaluation trace" AND ("non-linear" OR "branching" OR "merging")

Metaphorical Descriptions

"Möbius parse" | "twisted syntax" | "helical evaluation"
"parse spiral" | "syntactic vortex" | "computational winding"
"strange loop" AND ("grammar" OR "syntax" OR "parsing")

Boolean Query Combinations

Comprehensive Academic Search

(("parse tree" OR "abstract syntax tree" OR "syntax tree" OR AST) 
AND ("non-commutative" OR "non-associative" OR "path-dependent" OR "history-dependent" OR "context-sensitive")
AND ("torsion" OR "twist" OR "winding" OR "chirality" OR "handedness" OR "orientation")
NOT ("natural language" OR "NLP"))

Patent/Technical Report Search

(("parsing method" OR "syntax analysis" OR "program analysis")
NEAR/5 ("accumulator" OR "state" OR "history" OR "context")
AND ("order-dependent" OR "evaluation order" OR "traversal order")
AND (CLASS:G06F OR IPC:G06F9/45))

Recommended Search Procedure

1. Start broad: Use core concept queries in Google Scholar, arXiv, Semantic Scholar
2. Check citations: Look for papers citing "Ordered Context-Free Grammars" (van der Merwe)
3. Explore tangential: Search quantum programming languages, topological computation
4. Industry check: Patent databases, technical reports from IBM, Microsoft Research
5. Interdisciplinary: Check cognitive science, consciousness studies journals
6. Recent preprints: bioRxiv, PsyArXiv for consciousness/computation connections
7. Specialized venues: SPLASH, Onward!, Strange Loop conference proceedings

Key Discriminating Features to Verify

If similar work exists, it should exhibit:

• Parse trees where traversal order affects final result
• Syntax elements that distinguish forward/backward evaluation
• Accumulation of some quantity during parsing that affects semantics
• Non-commutativity at the syntactic (not just semantic) level
• Self-referential parsing creating observable effects
• Topological language for describing computational phenomena

This probe should uncover any prior work on parse trees with memory, non-commutative syntax, or topologically-inspired computational models.