Pattern Abstract Grammar

Keyword Semanticsα

Each keyword carries specific semantic meaning:

Preposition Slotsβ

Prepositions establish relationships between keywords and operands:

Input Patternsγ

Patterns for acquiring data from sources:

Input Patterns
READ file FROM path INTO variable
LOAD config FROM "settings.json"
EXTRACT fields FROM response INTO data
WEB_FETCH resource FROM url INTO response

Output Patternsδ

Patterns for producing results:

Output Patterns
WRITE content TO file
CREATE report FROM data USING template
APPEND item TO collection
REPORT status_message

Transform Patternsε

Patterns for data transformation:

Transform Patterns
CONVERT data TO format
FILTER items TO filtered_items WHERE condition
MERGE sources INTO target
SPLIT data BY delimiter INTO segments

Validation Patternsζ

Patterns for verification and validation:

Validation Patterns
VALIDATE data AGAINST schema
VERIFY condition
VALIDATION GATE:
    ✅ condition_1 met
    ✅ condition_2 met
ANALYZE state FOR errors INTO error_list
COMPARE actual AGAINST expected INTO diff_result

Search Patternsη

Patterns for finding and discovering:

Search Patterns
FIND pattern IN scope INTO found_items
GLOB "**/*.js" INTO file_list
GREP "pattern" IN path INTO matches
WEB_SEARCH query INTO search_results

Control Patternsθ

Patterns for execution control:

Control Patterns
EXECUTE command WITH params
EXECUTE Task(subagent_type = agent_name, prompt = task_description)
DELEGATE task TO agent
SEND message TO recipient
AWAIT response INTO result

Pattern Typesι

Each pattern type maps trigger phrases to VERB chain templates:

Cognitive Pattern Exampleκ

For analyzing codebase patterns:

Cognitive Pattern Example
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Intent: "Analyze codebase for duplicated logic and create report"

Pattern matched: Cognitive (trigger: "analyze")

# PHASE 1: Filter Scope
    FILTER codebase TO target_files

# PHASE 2: Read Content
    FOR EACH file IN target_files:
        READ content FROM file

# PHASE 3: Find Patterns
    FIND duplicated_logic IN content

# PHASE 4: Link Context
    LINK patterns TO source_locations

# PHASE 5: Create Report
    CREATE report FROM linked_patterns

# PHASE 6: Analyze Quality
    ANALYZE report AGAINST quality_threshold

# PHASE 7: Write Output
    WRITE report TO output

Decision Pattern Exampleλ

For selecting between options:

Decision Pattern Example
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Intent: "Choose the best database for our requirements"

Pattern matched: Decision (trigger: "choose")

# PHASE 1: Create Options
    CREATE candidate_list FROM available_databases

# PHASE 2: Filter Requirements
    FILTER candidate_list BY must_have_requirements

# PHASE 3: Find Matches
    FIND matching_databases IN filtered_candidates

# PHASE 4: Filter Ranking
    FILTER matches BY performance_criteria INTO ranked_options

# PHASE 5: Execute Selection
    EXECUTE selection_decision WITH ranked_options

Hypothesis Pattern Exampleμ

For debugging and investigation:

Hypothesis Pattern Example
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Intent: "Debug the authentication failure"

Pattern matched: Hypothesis (trigger: "debug")

# PHASE 1: Create Hypotheses
    CREATE hypothesis_list FROM error_symptoms
    SET hypothesis_list[0] = "Token expired"
    SET hypothesis_list[1] = "Invalid credentials"
    SET hypothesis_list[2] = "Network timeout"

# PHASE 2: Rank Likelihood
    RANK hypothesis_list BY evidence_strength

# PHASE 3: Attempt Verification
    FOR EACH hypothesis IN ranked_hypotheses:
        ATTEMPT verify_hypothesis WITH test_case

# PHASE 4: Analyze Results
    ANALYZE verification_results AGAINST expected_outcomes

# PHASE 5: Execute Fix
    EXECUTE remediation FOR confirmed_hypothesis

Construction Pattern Exampleν

For building artifacts:

Construction Pattern Example
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Intent: "Generate API documentation from source code"

Pattern matched: Construction (trigger: "generate")

# PHASE 1: Extract Sources
    EXTRACT source_files FROM codebase WHERE api_endpoints

# PHASE 2: Read Definitions
    FOR EACH file IN source_files:
        READ endpoint_definitions FROM file

# PHASE 3: Create Structure
    CREATE documentation_structure FROM endpoint_definitions

# PHASE 4: Find Examples
    FIND usage_examples IN test_files

# PHASE 5: Write Documentation
    WRITE documentation TO output_path

# PHASE 6: Analyze Completeness
    ANALYZE documentation AGAINST coverage_threshold

Choosing the Right Patternξ

Loop Classification & Analysis Loopsο

Algorithm loops are classified by their primary operational category. Analysis loops (Perceptual, Cognitive) focus on understanding and pattern detection:

Loop Classification & Analysis Loops
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# PERCEPTUAL LOOPS - React to signals in input streams

[Signal-Analysis-Loop]
FIND<Signal> → ANALYZE<Signal> → EXTRACT<Analysis> → WRITE<Response> → SET<State> → ITERATE<Cycle>

[Reactive-Execution-Loop]
FIND<Trigger> → EXTRACT<Context> → CREATE<Response> → EXECUTE<Tools> → ANALYZE<Results> → ITERATE<Cycle>

[Deep-Focus-Loop]
FIND<Target> → FILTER<Distractions> → ANALYZE<Target> → CREATE<Insights> → ITERATE<Cycle>

# COGNITIVE LOOPS - Process information to build understanding

[Knowledge-Construction-Loop]
FILTER<Domain> → READ<Information> → FIND<Patterns> → LINK<Elements> → CREATE<Representations> → WRITE<Structures>

[Domain-Investigation-Loop]
READ<Domain> → FIND<Patterns> → ANALYZE<Patterns> → CREATE<Hypotheses> → ANALYZE<Hypotheses> → WRITE<Findings>

[Source-To-Sink-Tracing-Loop]
READ<Source> → FIND<Data-Flow> → INVESTIGATE<Path> → ANALYZE<Transformations> → WRITE<Trace>

Decision & Construction Loopsπ

Decision loops evaluate options and select actions. Construction loops build artifacts from specifications:

Decision & Construction Loops
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# DECISION LOOPS - Evaluate options and select actions

[Option-Selection-Loop]
CREATE<Options> → FILTER<Options> → FIND<Criteria> → FILTER<By-Criteria> → EXECUTE<Selection>

[Problem-Solving-Chain]
READ<Problem> → ANALYZE<Requirements> → CREATE<Solutions> → ANALYZE<Solutions> → FILTER<Feasible> → EXECUTE<Best-Solution>

[Severity-Hierarchical-Prioritization-Loop]
MARK<Severity> → COLLECT<By-Severity> → SET<Priority> → CREATE<Dependency-Graph> → DETERMINE<Execution-Order>

# CONSTRUCTION LOOPS - Build artifacts from specifications

[Artifact-Generation-Loop]
READ<Specifications> → EXTRACT<Requirements> → CREATE<Artifact> → ANALYZE<Artifact> → WRITE<Artifact>

[Multi-Artifact-Generation-Loop]
READ<Meta-Specification> → EXTRACT<Artifact-Types> → CREATE<Artifacts> → FIND<Dependencies> → CREATE<Dependency-Graph> → WRITE<Artifacts>

[Template-Instantiation-With-Calculated-Metrics-Loop]
READ<Template> → READ<Data> → DETERMINE<Metrics> → CREATE<Template-Parameters> → EXECUTE<Template-Instantiation> → WRITE<Instantiated-Artifact>

Meta, Adaptive & Hypothesis Loopsρ

Meta loops monitor and refine execution strategy. Adaptive and Hypothesis loops handle uncertainty and environmental change:

Meta, Adaptive & Hypothesis Loops
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# META LOOPS - Monitor and refine execution strategy

[Strategy-Refinement-Loop]
FIND<Failure> → ANALYZE<Root-Cause> → CREATE<Alternatives> → ANALYZE<Alternatives> → SET<Strategy> → EXECUTE<Strategy>

[Multi-Agent-Orchestration-Loop]
READ<Task> → EXTRACT<Subtasks> → CREATE<Agent-Assignments> → EXECUTE<Agents> → ANALYZE<Outputs> → COLLECT<Results>

[Two-Phase-Detection-Correction-Loop]
EXECUTE<Detection-Phase> → ANALYZE<Detection-Results> → CREATE<Correction-Plan> → EXECUTE<Correction-Phase> → ANALYZE<Corrections>

# ADAPTIVE & HYPOTHESIS LOOPS - Handle uncertainty

[Investigate-Action-Loop]
FIND<Uncertainty> → ANALYZE<Context> → CREATE<Investigation-Plan> → EXECUTE<Investigation> → ANALYZE<Findings> → WRITE<Knowledge>

[Parallel-Hypothesis-Tracking-With-Conditional-Pivot-Loop]
CREATE<Multiple-Hypotheses> → RANK<By-Confidence> → ATTEMPT<Top-Hypothesis> → ANALYZE<Failure> → EXECUTE<Pivot-Or-Return>

[Self-Calibration-Testing-Loop]
CREATE<Test-Cases> → EXECUTE<Tests-On-Self> → ANALYZE<Test-Results> → FIND<Calibration-Drift> → SET<Self-Parameters>

Analysis Examples: Cognitive & Decisionσ

Cognitive loops process information to build understanding. Decision loops evaluate and select from options:

Analysis Examples: Cognitive & Decision
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# COGNITIVE: Code-AST-Analysis-Data-Extraction-Loop
# Extracts structural information from source code using AST parsing

GLOB<Code-Files> → READ<Code-Content> → ANALYZE<AST> → EXTRACT<Symbols> → SET<Analysis-Entry> → WRITE<Analysis>

# PHASE 1: Locate Sources
    GLOB file_pattern IN workspace_root COLLECT code_files

# PHASE 2: Read & Parse
    FOR EACH code_file IN code_files:
        READ code_file INTO code_content
        ANALYZE code_content INTO ast USING parser

# PHASE 3: Extract & Build
    EXTRACT exported_symbols FROM ast
    EXTRACT imported_symbols FROM ast
    SET analysis_entry.file = code_file
    SET analysis_entry.exports = exported_symbols

# PHASE 4: Write Output
    APPEND analysis_entry TO ast_analysis
    WRITE ast_analysis TO analysis_output_path AS json

VALIDATION GATE:
    ✅ All files processed
    ✅ AST parse successful
    ✅ Output written

---

# DECISION: Pattern-Based-Risk-Classification-Loop
# Classifies patterns by risk level and generates recommendations

FIND<Patterns> → ANALYZE<Risk-Indicators> → DETERMINE<Risk-Score> → MARK<Risk-Level> → CREATE<Recommendations>

# PHASE 1: Detect & Analyze
    FIND patterns IN target_source USING pattern_detection
    FOR EACH pattern IN patterns:
        ANALYZE pattern FOR risk_indicators
        EXTRACT severity, likelihood, impact FROM risk_indicators

# PHASE 2: Score & Classify
    DETERMINE risk_score FROM indicators BASED_ON risk_formula
    MARK risk_level BASED_ON risk_score:
        IF risk_score >= 0.8: SET risk_level = "critical"
        IF risk_score >= 0.5: SET risk_level = "high"
        ELSE: SET risk_level = "medium/low"

# PHASE 3: Generate Output
    CREATE recommendations FROM risk_classification
    WRITE risk_report TO output_path

VALIDATION GATE:
    ✅ All patterns classified
    ✅ Risk scores in valid range [0, 1]
    ✅ Recommendations generated

Build Examples: Construction & Metaτ

Construction loops generate artifacts from specifications. Meta loops monitor and refine execution strategy:

Build Examples: Construction & Meta
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# CONSTRUCTION: Multi-Artifact-Generation-Loop
# Generates multiple artifacts with dependency tracking

READ<Meta-Specification> → EXTRACT<Artifact-Types> → CREATE<Artifacts> → FIND<Dependencies> → WRITE<Artifacts>

# PHASE 1: Load & Extract
    READ meta_specification FROM input_path
    EXTRACT artifact_type_list FROM meta_specification
    SET artifact_types = ["schema", "validator", "documentation", "tests"]

# PHASE 2: Generate with Validation
    FOR EACH artifact_type IN artifact_types:
        CREATE artifact FROM meta_specification USING generation_rules[artifact_type]
        ANALYZE artifact AGAINST type_specification
        VALIDATION GATE:
            ✅ Artifact conforms to type schema

# PHASE 3: Dependency Analysis
    FIND dependencies BETWEEN artifacts
    FOR EACH artifact_a, artifact_b IN artifacts:
        IF artifact_a.outputs INTERSECTS artifact_b.inputs:
            APPEND (artifact_a, artifact_b) TO dependency_edges
    CREATE dependency_graph FROM dependency_edges
    ANALYZE dependency_graph FOR cycles

# PHASE 4: Write Output
    WRITE artifacts TO artifact_repository
    WRITE dependency_graph TO graph_output_path

VALIDATION GATE:
    ✅ All artifact types generated
    ✅ No circular dependencies

---

# META: Strategy-Refinement-Loop
# Self-corrects strategy when failures are detected

FIND<Failure> → ANALYZE<Root-Cause> → CREATE<Alternatives> → SET<Strategy> → EXECUTE<Strategy>

# PHASE 1: Detect Failure
    FIND failure_pattern IN execution_results
    IF NOT failure_detected: STOP

# PHASE 2: Root Cause Analysis
    ANALYZE failure_context FOR causal_factors
    EXTRACT primary_cause FROM causal_factors
    SET root_cause_report = { primary: primary_cause, severity: failure_severity }

# PHASE 3: Generate & Evaluate Alternatives
    CREATE alternative_strategies FROM root_cause_report
    FOR EACH alternative IN alternatives:
        ANALYZE alternative AGAINST constraints
        DETERMINE feasibility_score FROM constraint_satisfaction
    RANK alternatives BY feasibility_score DESC

# PHASE 4: Update & Execute
    SET current_strategy = alternatives[0]
    WRITE strategy_change_log TO audit_trail
    EXECUTE current_strategy ON target
    IF NOT success: ITERATE Strategy-Refinement-Loop

VALIDATION GATE:
    ✅ Root cause identified
    ✅ Viable alternative generated
    ✅ Strategy update logged

Uncertainty Examples: Hypothesis & Perceptualυ

Hypothesis loops test multiple theories with confidence-based pivoting. Perceptual loops react to signals with state-based response:

Uncertainty Examples: Hypothesis & Perceptual
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# HYPOTHESIS: Parallel-Hypothesis-Tracking-With-Conditional-Pivot-Loop
# Tests multiple hypotheses with confidence-based pivot

CREATE<Multiple-Hypotheses> → RANK<By-Confidence> → ATTEMPT<Top-Hypothesis> → ANALYZE<Failure> → EXECUTE<Pivot-Or-Return>

# PHASE 1: Generate & Rank
    CREATE n_hypotheses FROM evidence
    FOR EACH symptom IN observed_symptoms:
        CREATE hypothesis THAT EXPLAINS symptom
        DETERMINE confidence_score FROM evidence_strength
        SET hypothesis.confidence = confidence_score
    RANK hypotheses BY confidence DESC
    SET H1 = hypotheses[0], H2 = hypotheses[1]
    SET secondary_threshold = 0.6

# PHASE 2: Test Top Hypothesis
    ATTEMPT fix_for_H1
    EXECUTE minimal_change FOR H1.remediation
    ANALYZE outcome AGAINST expected_resolution
    IF H1_fix_succeeded: REPORT "H1 confirmed" AND STOP

# PHASE 3: Pivot or Return
    IF H1_fix_failed:
        ANALYZE failure_mode FOR new_evidence
        COMPARE H2.confidence AGAINST secondary_threshold
        IF H2.confidence >= threshold: ATTEMPT fix_for_H2
        ELSE: RETURN TO investigation_phase WITH updated_evidence

VALIDATION GATE:
    ✅ At least 2 hypotheses generated
    ✅ Confidence scores assigned
    ✅ Resolution achieved OR investigation restarted

---

# PERCEPTUAL: Signal-Analysis-Loop
# Continuous monitoring with state-based response

FIND<Signal> → ANALYZE<Signal> → EXTRACT<Analysis> → WRITE<Response> → SET<State> → ITERATE<Cycle>

# PHASE 1: Detect Signal
    FIND signal_pattern IN input_stream
    IF NOT signal_detected: ITERATE ON next_input

# PHASE 2: Analyze & Extract
    ANALYZE detected_signal USING processing_operations
    DETERMINE signal_type FROM signal BASED_ON signal_taxonomy
    DETERMINE signal_strength FROM signal.amplitude
    EXTRACT signal_content INTO analysis_output
    SET analysis = { type: signal_type, strength: signal_strength, timestamp: current_time }

# PHASE 3: Respond & Update State
    CREATE system_response FROM analysis USING response_rules
    WRITE system_response INTO context
    SET state USING transformation_mechanism
    IF signal_strength > alert_threshold:
        SET state.alert_level = "elevated"

# PHASE 4: Iterate
    ITERATE Signal-Analysis-Loop ON next_signal

VALIDATION GATE:
    ✅ Signal processed within latency threshold
    ✅ State updated consistently
    ✅ Response generated for significant signals

Integration Protocol & Exampleφ

Four-step process for instantiating algorithms in PAG documents, with a concrete example:

Integration Protocol & Example
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[Algorithm-Integration-Protocol]

FIND<Loop-Pattern> → EXTRACT<Type-Parameters> → SET<Preposition-Slots> → CREATE<Directive-Block>

# STEP 1: Find Loop Pattern
    FIND algorithm_class IN task_requirements BASED_ON classification_table
    Example: Task "analyze codebase for patterns" → Cognitive Loop

# STEP 2: Extract Type Parameters
    EXTRACT domain_objects FROM task_specification INTO type_placeholders
    Example: <Source> = codebase, <Patterns> = code_patterns, <Output> = analysis_report

# STEP 3: Set Preposition Slots
    SET concrete_values TO preposition_operators USING context_mapping
    Example: FROM = "src/**/*.js", IN = parsed_ast, TO = "reports/analysis.json"

# STEP 4: Create Directive Block
    CREATE executable_directive FROM instantiated_algorithm INTO prompt_structure

---

# INTEGRATION EXAMPLE
Task: "Process user requests and route to appropriate handlers"

STEP 1: Task contains "process", "route" → Decision Loop (Option-Selection-Loop)
STEP 2: <Options> = handler_candidates, <Criteria> = request_type_matching
STEP 3: FROM = user_request, BASED_ON = request.type, ON = matched_handler

STEP 4: Final PAG:
AGENT request-router EXECUTES Option-Selection-Loop:

    # PHASE 1: Create Options
        READ user_request FROM input_queue
        CREATE handler_candidates FROM handler_registry

    # PHASE 2: Filter by Type
        FILTER handler_candidates BASED_ON request.type

    # PHASE 3: Find & Execute
        FIND matching_handler IN filtered_candidates
        EXECUTE matched_handler ON user_request
        WRITE response TO output_queue

    VALIDATION GATE:
        ✅ Handler found for request type
        ✅ Response generated

Algorithm Creation Protocolχ

Five-phase process for discovering and creating new algorithms from cross-domain patterns:

Algorithm Creation Protocol
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[Algorithm-Creation-Protocol]

READ<Domains> → LINK<Patterns> → FIND<Isomorphisms> → EXTRACT<Template> → ANALYZE<Uniqueness>

# PHASE 1: Domain Pattern Inspection
    READ cross_domain_sources FOR overlapping_patterns IN domain_literature
    Sources:
    - Natural Language Processing (semantic parsing, discourse analysis)
    - Theory of Mind research (belief modeling, intention recognition)
    - Psychology (cognitive processes, behavioral patterns)
    - Compiler Theory (parsing, optimization passes)

# PHASE 2: Capability Mapping
    LINK identified_patterns TO implementation_capabilities USING feasibility_analysis
    Capabilities:
    - ML/NN architectures (attention mechanisms, recurrent structures)
    - Compiler constructs (AST traversal, code generation)
    - LLM+CLI (tool execution, context management)

# PHASE 3: Common Ground Detection
    FIND structural_equivalences BETWEEN domain_patterns USING pattern_matching
    FIND verb_sequences IN cross_domain_operations
    LINK preposition_relationships TO data_flow_patterns
    EXTRACT control_flow INTO pag_lang_constructs

# PHASE 4: Template Abstraction
    CREATE verb_chain FROM common_operations
    SET type_parameters FOR domain_objects
    WRITE semantic_guarantees FOR each_step
    MARK algorithm INTO algorithm_class

# PHASE 5: Uniqueness Validation
    ANALYZE candidate_algorithm AGAINST existing_algorithms USING redundancy_checks
    ANALYZE verb_chain FOR redundancy IN algorithm_repository
    ANALYZE keywords AGAINST pag_lang_specification

---

# ALGORITHM TEMPLATE FORMAT

[Named-Algorithm] Class: <Loop-Class>

VERB<Type> → VERB<Type> → VERB<Type> → ...

1. **VERB<Type>** – VERB <object> [preposition slots...]
2. **VERB<Type>** – VERB <object> [preposition slots...]
...

Preposition Slotsψ

Semantic meaning of each preposition slot in algorithm definitions:

Verb Semantic Guaranteesω

Each verb carries specific semantic guarantees intended to constrain implementation: