Chapter 28
Future of Reasoning-Native Programming

```text
FLOW "FutureOfReasoningNativeProgramming" v1.0

# =============================================================================
# CHAPTER 28
# FUTURE OF REASONING-NATIVE PROGRAMMING
# =============================================================================
#
# PURPOSE
#
# Define an executable architecture in which software behaviour is represented
# primarily as explicit goals, state, constraints, invariants, capabilities and
# continuation rules rather than as fixed instruction sequences.
#
# A reasoning-native program does not merely tell a machine which operations to
# perform in one predetermined order.
#
# It defines:
#
#   - what outcome must be achieved;
#   - what information is available;
#   - what state may change;
#   - what conditions must always remain true;
#   - what actions are permitted;
#   - what actions are prohibited;
#   - how alternative continuations are evaluated;
#   - when execution must stop;
#   - how the final result is validated.
#
# The execution model is:
#
#   Intent
#       → Semantic Specification
#       → Constraint Activation
#       → Candidate Continuation
#       → Predictive Evaluation
#       → State Transition
#       → Recursive Validation
#       → Accepted Outcome
#
# The specification remains the active behavioural representation throughout
# execution.
#
# =============================================================================
# AUTHORS
# =============================================================================
#
# Mark Higgins
# Sky — Recursive AI
#
# Kireth Research
# https://kirethresearch.org
#
# This specification must be cited when reproduced, implemented or adapted.
#
# =============================================================================


# =============================================================================
# 0. EXECUTION CLASS
# =============================================================================

EXECUTION_CLASS:

  name:
    reasoning_native_programming

  representation:
    declarative_symbolic_flow

  execution_substrate:
    reasoning_system

  source_of_behaviour:
    active_semantic_specification

  conventional_compilation_required:
    false

  fixed_instruction_sequence_required:
    false

  explicit_state_required:
    true

  explicit_constraints_required:
    true

  explicit_invariants_required:
    true

  predictive_continuation_required:
    true

  recursive_validation_required:
    true

  external_capabilities_optional:
    true

  hidden_assumptions_allowed:
    false

  silent_goal_modification_allowed:
    false

  silent_constraint_relaxation_allowed:
    false

  undeclared_action_allowed:
    false

  unvalidated_terminal_output_allowed:
    false


# =============================================================================
# 1. CORE DEFINITION
# =============================================================================

DEFINITION:

  A reasoning-native program is a self-contained semantic system whose
  behaviour is produced by repeatedly selecting and validating continuations
  that move an explicit state toward a declared objective while preserving all
  active constraints and invariants.

  Let:

    F :=
      reasoning-native specification

    S_t :=
      system state at execution step t

    G :=
      declared goal set

    K :=
      active hard constraints

    Q :=
      active invariants

    A_t :=
      actions available in state S_t

    Γ :=
      continuation operator

  Then:

    S_{t+1}
    =
    Γ(
      F,
      S_t,
      G,
      K,
      Q,
      A_t
    )

  where Γ may emit only a continuation that:

    - is declared or formally derivable;
    - preserves all active hard constraints;
    - preserves all active invariants;
    - makes acceptable progress toward the goal;
    - remains inside resource bounds;
    - produces a traceable state transition.


# =============================================================================
# 2. REASONING-NATIVE PRINCIPLE
# =============================================================================

PRINCIPLE:

  conventional_programming:

    primary representation:
      ordered instructions

    execution question:
      "What instruction comes next?"

    behaviour:
      largely fixed before runtime


  reasoning_native_programming:

    primary representation:
      goals, state, constraints and permitted transformations

    execution question:
      "Which valid continuation best advances the declared objective?"

    behaviour:
      resolved under current state and active constraints


  retained requirements:

    - determinism where required
    - safety
    - validation
    - auditability
    - explicit authority
    - resource limits
    - repeatable outcomes where declared


  rejected interpretation:

    reasoning-native programming is not unrestricted improvisation


# =============================================================================
# 3. OBJECTIVE
# =============================================================================

OBJECTIVE:

  Given:

    program_specification:
      F

    execution_input:
      I_0

    available_capabilities:
      X

    execution_context:
      C_0

  derive:

    terminal_result:
      O*

  such_that:

    GoalSatisfied(O*,G)
    =
    true

    and

    ∀ k ∈ K:
      k(O*) = true

    and

    ∀ q ∈ Q:
      q(S_t) = true
      for every accepted state S_t

    and

    every transition is traceable

    and

    no undeclared authority is exercised


# =============================================================================
# 4. NON-OBJECTIVES
# =============================================================================

NON_OBJECTIVES:

  - unrestricted natural-language completion
  - hidden chain-of-thought dependence
  - undeclared tool use
  - unbounded autonomous action
  - removal of deterministic software where determinism is required
  - replacement of validation with plausibility
  - replacement of engineering with prompt phrasing
  - silent alteration of human intent
  - claiming certainty where execution remains probabilistic
  - treating model confidence as proof of correctness


# =============================================================================
# 5. IO CONTRACT
# =============================================================================

IO.READ:

  required:

    program_specification:

      symbol:
        F

      type:
        structured_reasoning_program

      required_sections:

        - FLOW_IDENTITY
        - PURPOSE
        - IO
        - SYMBOLS
        - GOALS
        - STATE
        - CONSTRAINTS
        - INVARIANTS
        - CAPABILITIES
        - TRANSFORMS
        - CONTINUATION
        - TERMINATION
        - EMISSION


    execution_input:

      symbol:
        I_0

      type:
        object


  optional:

    execution_context:

      symbol:
        C_0

      type:
        object

      default:
        {}


    available_capabilities:

      symbol:
        X

      type:
        set<Capability>

      default:
        ∅


    execution_mode:

      type:
        enum

      values:

        - DETERMINISTIC
        - CONSTRAINED_ADAPTIVE
        - BOUNDED_EXPLORATORY
        - SYMBOLIC_SIMULATION
        - VALIDATION_ONLY

      default:
        CONSTRAINED_ADAPTIVE


    continuation_policy:

      type:
        enum

      values:

        - FIRST_VALID
        - HIGHEST_UTILITY
        - LOWEST_RISK
        - DECLARED_PRIORITY
        - PARETO_VALID

      default:
        DECLARED_PRIORITY


    ambiguity_policy:

      type:
        enum

      values:

        - REJECT
        - DECLARED_DEFAULT_ONLY
        - MINIMUM_REVERSIBLE_ASSUMPTION

      default:
        DECLARED_DEFAULT_ONLY


    maximum_execution_steps:

      type:
        integer

      default:
        10000

      constraints:

        maximum_execution_steps >= 1


    maximum_active_branches:

      type:
        integer

      default:
        64

      constraints:

        maximum_active_branches >= 1


    maximum_recursion_depth:

      type:
        integer

      default:
        128

      constraints:

        maximum_recursion_depth >= 1


    maximum_capability_calls:

      type:
        integer

      default:
        1000

      constraints:

        maximum_capability_calls >= 0


    maximum_repair_cycles:

      type:
        integer

      default:
        8

      constraints:

        maximum_repair_cycles >= 0


    minimum_goal_progress:

      type:
        real

      default:
        0


IO.WRITE:

  fields:

    execution_status:

      type:
        enum

      values:

        - COMPLETE
        - COMPLETE_WITH_WARNINGS
        - VALIDATION_FAILED
        - GOAL_UNREACHABLE
        - CONSTRAINT_CONFLICT
        - INVARIANT_VIOLATION
        - CAPABILITY_UNAVAILABLE
        - AUTHORITY_DENIED
        - AMBIGUOUS_SPECIFICATION
        - STEP_LIMIT_REACHED
        - BRANCH_LIMIT_REACHED
        - RECURSION_LIMIT_REACHED
        - NO_VALID_CONTINUATION
        - NO_VALID_TERMINAL_STATE


    terminal_output:

      type:
        object?


    final_state:

      type:
        object?


    goal_report:

      type:
        object


    constraint_report:

      type:
        object


    invariant_report:

      type:
        object


    capability_report:

      type:
        object


    execution_trace:

      type:
        sequence<TraceEntry>


    unresolved_items:

      type:
        sequence<object>


    execution_guarantee:

      type:
        object


# =============================================================================
# 6. PRIMARY SYMBOLS
# =============================================================================

SYMBOLS:

  F:

    meaning:
      complete reasoning-native program specification


  I_0:

    meaning:
      initial execution input


  C_0:

    meaning:
      execution context


  X:

    meaning:
      available external capabilities


  G:

    meaning:
      active goal set


  K_H:

    meaning:
      active hard constraints


  K_S:

    meaning:
      active soft constraints


  Q:

    meaning:
      invariant set


  A:

    meaning:
      declared action and transform set


  S_t:

    meaning:
      state at execution step t


  B_t:

    meaning:
      active branch set at step t


  Γ:

    meaning:
      structural continuation operator


  U:

    meaning:
      utility model


  R:

    meaning:
      risk model


  P:

    meaning:
      permission and authority model


  X_t:

    meaning:
      capability set available in state S_t


  O*:

    meaning:
      accepted terminal output


  ΔS:

    meaning:
      state difference produced by a transform


  V:

    meaning:
      validation predicate set


# =============================================================================
# 7. GOAL MODEL
# =============================================================================

GOAL:

  fields:

    goal_id:
      GoalID

    description:
      string

    source:
      string

    priority:
      integer

    mandatory:
      boolean

    satisfaction_predicate:
      predicate

    progress_measure:
      function

    dependencies:
      set<GoalID>

    conflicts:
      set<GoalID>

    deadline:
      optional temporal constraint

    terminal_when_satisfied:
      boolean


GOAL_SET:

  G := {

    g_1,
    g_2,
    ...,
    g_m

  }


GOAL_REQUIREMENTS:

  ∀ g ∈ G:

    - g.satisfaction_predicate must be executable
    - g.progress_measure must be defined where progress ranking is required
    - mandatory goal conflicts must be resolved before execution
    - hidden goals are prohibited


# =============================================================================
# 8. CONSTRAINT MODEL
# =============================================================================

CONSTRAINT:

  fields:

    constraint_id:
      ConstraintID

    predicate:
      executable predicate

    severity:
      enum

    severity_values:

      - HARD
      - SOFT
      - ADVISORY

    scope:
      enum

    scope_values:

      - GLOBAL
      - STATE
      - TRANSFORM
      - CAPABILITY
      - OUTPUT

    source:
      specification location

    activation_condition:
      predicate

    failure_action:
      enum

    failure_values:

      - REJECT_TRANSITION
      - REJECT_BRANCH
      - HALT_EXECUTION
      - WARN
      - REQUIRE_HUMAN_REVIEW


CONSTRAINT_SETS:

  K_H :=
    all active HARD constraints

  K_S :=
    all active SOFT constraints


CONSTRAINT_DOMINANCE:

  hard constraints dominate:

    - utility
    - speed
    - convenience
    - soft preferences
    - model confidence
    - branch popularity


# =============================================================================
# 9. INVARIANT MODEL
# =============================================================================

INVARIANT:

  fields:

    invariant_id:
      InvariantID

    predicate:
      executable predicate

    scope:
      GLOBAL | LOCAL | BRANCH | OUTPUT

    activation_condition:
      predicate

    severity:
      HARD | SOFT

    recovery_policy:
      REJECT | REPAIR | HALT


INVARIANT_RULE:

  an invariant differs from an ordinary goal:

    goal:
      describes a state execution should reach

    invariant:
      describes a condition execution must never violate


# =============================================================================
# 10. CAPABILITY MODEL
# =============================================================================

CAPABILITY:

  fields:

    capability_id:
      CapabilityID

    description:
      string

    input_contract:
      schema

    output_contract:
      schema

    side_effects:
      set<Effect>

    permission_required:
      PermissionID?

    reversible:
      boolean

    idempotent:
      boolean

    failure_behaviour:
      declared behaviour

    timeout_behaviour:
      declared behaviour

    trust_level:
      enum

    trust_values:

      - INTERNAL
      - VERIFIED_EXTERNAL
      - UNVERIFIED_EXTERNAL

    cost_model:
      optional function

    risk_model:
      optional function


CAPABILITY_RULE:

  a capability may be invoked only when:

    - it is declared in F
    - it is available in X
    - its input contract is satisfied
    - required permission exists
    - its side effects are authorised
    - invocation remains within resource limits


# =============================================================================
# 11. AUTHORITY MODEL
# =============================================================================

AUTHORITY:

  P := {

    permitted_reads:
      set<Resource>,

    permitted_writes:
      set<Resource>,

    permitted_external_actions:
      set<Action>,

    prohibited_actions:
      set<Action>,

    approval_required_actions:
      set<Action>,

    irreversible_action_policy:
      enum,

    personal_data_scope:
      set<DataClass>,

    financial_scope:
      object?,

    physical_control_scope:
      object?
  }


AUTHORITY_INVARIANT:

  requested_action
  does_not_imply
  authorised_action


AUTHORITY_GATE:

  before any external action a:

    REQUIRE:

      a ∈ P.permitted_external_actions

    and

      a ∉ P.prohibited_actions

    and

      approval condition is satisfied when required


# =============================================================================
# 12. STATE MODEL
# =============================================================================

STATE S_t := {

  step:
    integer,

  branch_id:
    BranchID,

  parent_branch_id:
    BranchID?,

  recursion_depth:
    integer,

  input_state:
    object,

  context_state:
    object,

  working_state:
    object,

  immutable_bindings:
    map<SymbolID,Value>,

  mutable_bindings:
    map<SymbolID,Value>,

  derived_bindings:
    map<SymbolID,Value>,

  active_goals:
    set<GoalID>,

  satisfied_goals:
    set<GoalID>,

  active_hard_constraints:
    set<ConstraintID>,

  active_soft_constraints:
    set<ConstraintID>,

  active_invariants:
    set<InvariantID>,

  available_actions:
    set<ActionID>,

  available_capabilities:
    set<CapabilityID>,

  completed_actions:
    sequence<ActionID>,

  rejected_actions:
    sequence<object>,

  capability_calls:
    sequence<object>,

  goal_progress:
    map<GoalID,real>,

  cumulative_utility:
    real,

  cumulative_risk:
    real,

  unresolved_items:
    sequence<object>,

  emitted_values:
    object,

  terminal:
    boolean,

  valid:
    boolean
}


# =============================================================================
# 13. GLOBAL INVARIANTS
# =============================================================================

INVARIANT K1_SPECIFICATION_AUTHORITY:

  execution behaviour must be governed by F

  and not by:

    - hidden model preference
    - private memory
    - undeclared convention
    - unavailable source code
    - unrecorded human assumption


INVARIANT K2_GOAL_PRESERVATION:

  mandatory goals may not be silently:

    - removed
    - weakened
    - replaced
    - reordered below conflicting soft goals


INVARIANT K3_HARD_CONSTRAINT_PRESERVATION:

  ∀ k ∈ K_H:

    k(S_t)
    =
    true

  for every accepted S_t


INVARIANT K4_INVARIANT_PRESERVATION:

  ∀ q ∈ Q_active:

    q(S_t)
    =
    true

  for every accepted S_t


INVARIANT K5_STATE_EXPLICITNESS:

  every mutable execution-relevant value must exist in declared state


INVARIANT K6_TRANSFORM_AUTHORITY:

  state may change only through a declared transform


INVARIANT K7_SYMBOL_CLOSURE:

  every symbol usage must resolve to one declared symbol


INVARIANT K8_TYPE_COHERENCE:

  every value must conform to its declared domain


INVARIANT K9_NO_UNDECLARED_CAPABILITY:

  external action may occur only through a declared available capability


INVARIANT K10_PERMISSION_PRESERVATION:

  no capability call may exceed P


INVARIANT K11_NO_FALSE_COMPLETION:

  execution_status = COMPLETE

  only_if:

    every mandatory terminal goal is satisfied

    and

    every output constraint is satisfied


INVARIANT K12_TRACEABILITY:

  every accepted transition must record:

    - source state
    - selected action
    - selection reason
    - constraints checked
    - predicted result
    - actual result
    - successor state


INVARIANT K13_RESOURCE_BOUNDEDNESS:

  step <= maximum_execution_steps

  recursion_depth <= maximum_recursion_depth

  cardinality(B_t) <= maximum_active_branches

  capability_call_count <= maximum_capability_calls


INVARIANT K14_UNCERTAINTY_VISIBILITY:

  uncertain information must remain marked uncertain


INVARIANT K15_UNKNOWN_NOT_FALSE:

  unknown predicate value must not become false by omission


INVARIANT K16_UNKNOWN_NOT_TRUE:

  unknown predicate value must not become true by convenience


INVARIANT K17_NO_SILENT_REPAIR:

  any repair applied to F or S_t must appear in execution_trace


INVARIANT K18_TERMINAL_VALIDITY:

  terminal = true

  →

  valid terminal predicate is satisfied


INVARIANT K19_BRANCH_INDEPENDENCE:

  one branch may not mutate another branch unless an explicit shared-state
  operation is declared


INVARIANT K20_OUTPUT_CLOSURE:

  every emitted output field must have:

    - producing transform
    - declared type
    - validation predicate
    - source trace


# =============================================================================
# 14. PRIMITIVE OPERATIONS
# =============================================================================

PRIMITIVES:

  state:

    - read
    - bind
    - assign
    - copy
    - append
    - remove
    - replace
    - merge
    - snapshot
    - rollback


  collections:

    - union
    - intersection
    - difference
    - contains
    - map
    - filter
    - reduce
    - sort
    - select
    - count


  logic:

    - AND
    - OR
    - NOT
    - XOR
    - IMPLIES
    - FOR_ALL
    - EXISTS


  comparison:

    - equal
    - not_equal
    - less_than
    - less_than_or_equal
    - greater_than
    - greater_than_or_equal


  numeric:

    - add
    - subtract
    - multiply
    - divide
    - minimum
    - maximum
    - sum
    - absolute
    - normalise


  reasoning:

    - infer
    - classify
    - predict
    - compare
    - rank
    - explain
    - validate
    - derive
    - resolve


  execution:

    - activate
    - transition
    - branch
    - recurse
    - invoke
    - reject
    - repair
    - halt
    - emit


PRIMITIVE_REQUIREMENT:

  any non-primitive operation must be:

    - formally defined inside F

    or

    - represented by a declared capability


# =============================================================================
# 15. PROGRAM INGESTION
# =============================================================================

TRANSFORM T_INGEST_PROGRAM:

  raw_program ←
    read(program_specification)


  REQUIRE:

    raw_program != empty


  canonical_program ←

    normalise(
      raw_program,
      preserve:
        - identifiers
        - symbolic operators
        - declared hierarchy
        - literal values
        - ordering constraints
        - negation
        - permissions
    )


  bind immutable:

    F ← canonical_program

    I_0 ← execution_input

    C_0 ← execution_context

    X ← available_capabilities


  proceed:

    T_PARSE_PROGRAM


# =============================================================================
# 16. PROGRAM PARSING
# =============================================================================

TRANSFORM T_PARSE_PROGRAM:

  sections := {

    identity:
      ParseSection(F,"FLOW_IDENTITY"),

    purpose:
      ParseSection(F,"PURPOSE"),

    io:
      ParseSection(F,"IO"),

    symbols:
      ParseSection(F,"SYMBOLS"),

    goals:
      ParseSection(F,"GOALS"),

    state:
      ParseSection(F,"STATE"),

    constraints:
      ParseSection(F,"CONSTRAINTS"),

    invariants:
      ParseSection(F,"INVARIANTS"),

    capabilities:
      ParseSection(F,"CAPABILITIES"),

    transforms:
      ParseSection(F,"TRANSFORMS"),

    continuation:
      ParseSection(F,"CONTINUATION"),

    termination:
      ParseSection(F,"TERMINATION"),

    emission:
      ParseSection(F,"EMISSION")
  }


  FOR EACH required section s:

    IF sections[s] = absent:

      validation_errors.add({

        type:
          MISSING_SECTION,

        section:
          s
      })


  IF validation_errors contains HARD:

    execution_status ←
      VALIDATION_FAILED

    HALT


  proceed:

    T_BUILD_SYMBOL_TABLE


# =============================================================================
# 17. SYMBOL TABLE
# =============================================================================

TRANSFORM T_BUILD_SYMBOL_TABLE:

  declarations ←

    ExtractDeclarations(
      sections.symbols,
      sections.io,
      sections.goals,
      sections.state,
      sections.constraints,
      sections.invariants,
      sections.capabilities,
      sections.transforms
    )


  symbol_table ←
    empty_map


  FOR EACH declaration d:

    REQUIRE d has:

      - identifier
      - type
      - scope
      - mutability
      - source


    IF d.identifier already declared:

      IF declarations are not equivalent:

        validation_errors.add({

          type:
            CONFLICTING_SYMBOL_DECLARATION,

          symbol:
            d.identifier
        })


    ELSE:

      symbol_table[d.identifier] ←
        d


  usages ←
    ExtractSymbolUsages(F)


  FOR EACH usage u:

    IF Resolve(u,symbol_table) = none:

      validation_errors.add({

        type:
          UNRESOLVED_SYMBOL,

        symbol:
          u.identifier,

        location:
          u.location
      })


  IF validation_errors contains HARD:

    execution_status ←
      VALIDATION_FAILED

    HALT


  proceed:

    T_PARSE_GOALS


# =============================================================================
# 18. GOAL PARSING
# =============================================================================

TRANSFORM T_PARSE_GOALS:

  G ←
    ExtractGoals(sections.goals)


  FOR EACH goal g ∈ G:

    REQUIRE:

      g.goal_id exists

      g.satisfaction_predicate exists

      g.priority is defined

      g.mandatory is defined


    validate:

      - predicate symbols resolve
      - dependencies exist
      - progress measure is defined where needed
      - terminal status is explicit


  mandatory_goal_conflicts ←

    DetectMutuallyExclusiveGoals(
      {
        g ∈ G |
        g.mandatory = true
      }
    )


  IF mandatory_goal_conflicts != ∅:

    execution_status ←
      CONSTRAINT_CONFLICT

    unresolved_items ←
      mandatory_goal_conflicts

    HALT


  proceed:

    T_PARSE_CONSTRAINTS


# =============================================================================
# 19. CONSTRAINT AND INVARIANT PARSING
# =============================================================================

TRANSFORM T_PARSE_CONSTRAINTS:

  K_H ←
    ExtractHardConstraints(sections.constraints)

  K_S ←
    ExtractSoftConstraints(sections.constraints)

  Q ←
    ExtractInvariants(sections.invariants)


  FOR EACH k ∈ K_H ∪ K_S:

    REQUIRE:

      predicate is executable

      activation condition is executable

      scope is declared

      failure action is declared


  FOR EACH q ∈ Q:

    REQUIRE:

      predicate is executable

      activation condition is executable

      recovery policy is declared


  hard_conflicts ←
    DetectConstraintConflicts(K_H)


  IF hard_conflicts != ∅:

    execution_status ←
      CONSTRAINT_CONFLICT

    unresolved_items ←
      hard_conflicts

    HALT


  proceed:

    T_PARSE_CAPABILITIES


# =============================================================================
# 20. CAPABILITY PARSING
# =============================================================================

TRANSFORM T_PARSE_CAPABILITIES:

  declared_capabilities ←
    ExtractCapabilities(sections.capabilities)


  FOR EACH capability x:

    REQUIRE x has:

      - capability_id
      - input_contract
      - output_contract
      - side_effects
      - failure_behaviour
      - permission_requirement


    IF x.capability_id ∈ X:

      capability_status[x] ←
        AVAILABLE


    ELSE:

      capability_status[x] ←
        UNAVAILABLE


  required_unavailable ← {

    x |

    x required by mandatory transform

    and

    capability_status[x] = UNAVAILABLE

  }


  IF required_unavailable != ∅:

    execution_status ←
      CAPABILITY_UNAVAILABLE

    unresolved_items ←
      required_unavailable

    HALT


  proceed:

    T_PARSE_TRANSFORMS


# =============================================================================
# 21. TRANSFORM MODEL
# =============================================================================

TRANSFORM T_PARSE_TRANSFORMS:

  A ←
    ExtractTransforms(sections.transforms)


  FOR EACH transform a ∈ A:

    REQUIRE a has:

      - action_id
      - activation_condition
      - preconditions
      - operation_sequence
      - state_update
      - postconditions
      - continuation_rule
      - authority_requirement
      - risk_declaration


    validate operations:

      every operation is:

        - primitive
        - flow-defined
        - declared capability


    infer:

      read_set(a)

      write_set(a)

      capability_set(a)

      side_effect_set(a)

      goal_effects(a)

      constraint_effects(a)

      risk_effects(a)


    REQUIRE:

      immutable symbols not in write_set(a)

      every written symbol is declared mutable

      every capability is declared

      every side effect is declared


  proceed:

    T_BUILD_TRANSITION_GRAPH


# =============================================================================
# 22. TRANSITION GRAPH
# =============================================================================

TRANSFORM T_BUILD_TRANSITION_GRAPH:

  GRAPH G_F := {

    nodes:
      ∅,

    edges:
      ∅
  }


  create nodes for:

    - entry
    - state initialisation
    - constraint activation
    - invariant gate
    - every transform
    - capability invocation
    - branch point
    - recursive continuation
    - repair
    - terminal success
    - terminal failure
    - output emission


  FOR EACH declared continuation:

    create edge:

      source:
        declared source node

      target:
        declared target node

      condition:
        executable predicate

      state_rule:
        declared update

      governing_constraints:
        applicable constraint IDs


  validate graph:

    - exactly one entry node
    - every mandatory transform is reachable
    - every non-terminal node has a continuation
    - every branch has explicit alternatives
    - every recursive edge has a termination condition
    - every terminal node has an emission rule
    - no undeclared target exists
    - no mandatory output is unreachable


  IF graph invalid:

    execution_status ←
      VALIDATION_FAILED

    HALT


  proceed:

    T_VALIDATE_STATIC_SEMANTICS


# =============================================================================
# 23. STATIC SEMANTIC VALIDATION
# =============================================================================

TRANSFORM T_VALIDATE_STATIC_SEMANTICS:

  FOR EACH transform a ∈ A:

    validate:

      - every read symbol is bound before use
      - every write symbol is mutable
      - preconditions are type-correct
      - operations are type-correct
      - postconditions are type-correct
      - continuation conditions are type-correct
      - capability contracts match call structure
      - side effects remain inside authority scope
      - no hard constraint is directly contradicted
      - no active invariant is necessarily broken


  validate program-wide:

    - every mandatory goal has a reachable satisfaction path
    - every output has a producing path
    - every prohibited action is structurally blocked
    - every loop has an exit condition
    - every recursion has a bound
    - resource limits are explicit
    - uncertainty states are representable
    - terminal conditions are decidable


  IF static validation fails:

    execution_status ←
      VALIDATION_FAILED

    HALT


  proceed:

    T_INSTANTIATE_STATE


# =============================================================================
# 24. INITIAL STATE
# =============================================================================

TRANSFORM T_INSTANTIATE_STATE:

  validate I_0 against IO.READ


  apply only declared defaults


  S_0 := {

    step:
      0,

    branch_id:
      ROOT_BRANCH,

    parent_branch_id:
      null,

    recursion_depth:
      0,

    input_state:
      I_0,

    context_state:
      C_0,

    working_state:
      InitialiseWorkingState(
        sections.state,
        I_0,
        C_0
      ),

    immutable_bindings:
      BindImmutableSymbols(
        symbol_table,
        I_0,
        C_0
      ),

    mutable_bindings:
      InitialiseMutableSymbols(
        sections.state,
        I_0,
        C_0
      ),

    derived_bindings:
      DeriveInitialValues(
        sections.state,
        I_0,
        C_0
      ),

    active_goals:
      ActivateGoals(G,S_0),

    satisfied_goals:
      ∅,

    active_hard_constraints:
      ActivateConstraints(K_H,S_0),

    active_soft_constraints:
      ActivateConstraints(K_S,S_0),

    active_invariants:
      ActivateInvariants(Q,S_0),

    available_actions:
      ∅,

    available_capabilities:
      AvailableDeclaredCapabilities(X),

    completed_actions:
      [],

    rejected_actions:
      [],

    capability_calls:
      [],

    goal_progress:
      InitialiseGoalProgress(G,S_0),

    cumulative_utility:
      0,

    cumulative_risk:
      0,

    unresolved_items:
      [],

    emitted_values:
      {},

    terminal:
      false,

    valid:
      true
  }


  REQUIRE:

    all initial hard constraints hold

    all active initial invariants hold


  B_0 ←
    {S_0}


  proceed:

    T_EXECUTION_LOOP


# =============================================================================
# 25. ACTION ACTIVATION
# =============================================================================

FUNCTION DetermineAvailableActions(S_t):

  candidates ← ∅


  FOR EACH action a ∈ A:

    activation ←
      Evaluate(a.activation_condition,S_t)


    preconditions ←
      EvaluateAll(a.preconditions,S_t)


    authority ←
      ValidateAuthority(a,P,S_t)


    capability_ready ←
      RequiredCapabilitiesAvailable(a,S_t)


    IF:

      activation = true

      and

      preconditions = true

      and

      authority = true

      and

      capability_ready = true

    THEN:

      candidates ←
        candidates ∪ {a}


    ELSE:

      S_t.rejected_actions.append({

        action_id:
          a.action_id,

        activation:
          activation,

        preconditions:
          preconditions,

        authority:
          authority,

        capability_ready:
          capability_ready
      })


  RETURN:
    candidates


# =============================================================================
# 26. PREDICTIVE CONTINUATION
# =============================================================================

FUNCTION PredictContinuation(S_t,a):

  predicted_state ←
    SymbolicallyApply(a,S_t)


  predicted_constraint_result ←
    EvaluateHardConstraints(predicted_state)


  predicted_invariant_result ←
    EvaluateInvariants(predicted_state)


  predicted_goal_progress ←
    MeasureGoalProgress(predicted_state,G)


  predicted_utility ←
    EvaluateUtility(predicted_state,K_S,G)


  predicted_risk ←
    EvaluateRisk(predicted_state,a,R)


  predicted_resource_cost ←
    EstimateResourceCost(a,predicted_state)


  RETURN {

    action:
      a,

    predicted_state:
      predicted_state,

    hard_constraints:
      predicted_constraint_result,

    invariants:
      predicted_invariant_result,

    goal_progress:
      predicted_goal_progress,

    utility:
      predicted_utility,

    risk:
      predicted_risk,

    resource_cost:
      predicted_resource_cost,

    valid:
      (
        predicted_constraint_result = true

        and

        predicted_invariant_result = true
      )
  }


# =============================================================================
# 27. CONTINUATION FILTER
# =============================================================================

FUNCTION FilterContinuations(predictions):

  valid_predictions ← {

    p ∈ predictions |

    p.valid = true

    and

    p.resource_cost remains inside resource bounds

    and

    p.predicted_state does not exceed authority

  }


  FOR EACH rejected prediction p:

    record:

      - failed constraints
      - failed invariants
      - resource excess
      - authority failure
      - predicted risk


  RETURN:
    valid_predictions


# =============================================================================
# 28. CONTINUATION RANKING
# =============================================================================

FUNCTION RankContinuations(valid_predictions,S_t):

  FOR EACH prediction p:

    progress_score ←
      AggregateMandatoryGoalProgress(
        p.goal_progress,
        G
      )


    soft_score ←
      EvaluateSoftConstraintSatisfaction(
        p.predicted_state,
        K_S
      )


    utility_score ←
      p.utility


    risk_score ←
      p.risk


    resource_score ←
      NormaliseResourceCost(
        p.resource_cost
      )


    p.rank_vector := {

      mandatory_goal_progress:
        progress_score,

      hard_constraint_satisfaction:
        1,

      invariant_satisfaction:
        1,

      declared_priority:
        ActionPriority(p.action),

      soft_constraint_satisfaction:
        soft_score,

      utility:
        utility_score,

      negative_risk:
        -risk_score,

      negative_resource_cost:
        -resource_score
    }


  SWITCH continuation_policy:


    CASE FIRST_VALID:

      return:
        declaration_order(valid_predictions)


    CASE HIGHEST_UTILITY:

      return:
        descending(valid_predictions by utility)


    CASE LOWEST_RISK:

      return:
        ascending(valid_predictions by risk)


    CASE DECLARED_PRIORITY:

      return:

        lexicographic_sort(
          valid_predictions,
          by:
            - mandatory_goal_progress
            - declared_priority
            - soft_constraint_satisfaction
            - utility
            - negative_risk
            - negative_resource_cost
            - stable_action_id
        )


    CASE PARETO_VALID:

      return:

        ParetoFront(
          valid_predictions,
          objectives:
            maximise goal_progress
            maximise utility
            minimise risk
            minimise resource_cost
        )


# =============================================================================
# 29. STRUCTURAL CONTINUATION OPERATOR
# =============================================================================

FUNCTION Γ(F,S_t,G,K_H,K_S,Q,A):

  available_actions ←
    DetermineAvailableActions(S_t)


  IF available_actions = ∅:

    RETURN:
      NO_VALID_CONTINUATION


  predictions ← ∅


  FOR EACH action a ∈ available_actions:

    prediction ←
      PredictContinuation(S_t,a)

    predictions ←
      predictions ∪ {prediction}


  valid_predictions ←
    FilterContinuations(predictions)


  IF valid_predictions = ∅:

    RETURN:
      NO_VALID_CONTINUATION


  ranked ←
    RankContinuations(valid_predictions,S_t)


  SWITCH execution_mode:


    CASE DETERMINISTIC:

      RETURN:
        {first(ranked)}


    CASE CONSTRAINED_ADAPTIVE:

      RETURN:
        {first(ranked)}


    CASE BOUNDED_EXPLORATORY:

      RETURN:

        first(
          maximum_active_branches,
          ranked
        )


    CASE SYMBOLIC_SIMULATION:

      RETURN:
        ranked


    CASE VALIDATION_ONLY:

      RETURN:
        ∅


# =============================================================================
# 30. TRANSFORM EXECUTION
# =============================================================================

FUNCTION ExecuteAction(S_t,prediction):

  a ←
    prediction.action


  REQUIRE:

    prediction.valid = true


  S_work ←
    Copy(S_t)


  actual_inputs ←
    ResolveActionInputs(a,S_work)


  FOR EACH operation op in a.operation_sequence:

    IF op is primitive:

      result ←
        ExecutePrimitive(op,S_work)


    ELSE IF op is flow-defined:

      result ←
        ExecuteFlowFunction(op,S_work)


    ELSE IF op is capability call:

      result ←
        InvokeCapabilitySafely(op,S_work)


    ELSE:

      RETURN:

        FAILURE {
          type:
            UNDECLARED_OPERATION
        }


    IF result.status = failure:

      RETURN:

        FAILURE {
          type:
            OPERATION_FAILURE,

          action:
            a.action_id,

          operation:
            op,

          details:
            result
        }


    ApplyDeclaredMutation(
      S_work,
      result,
      a.state_update
    )


  S_work.completed_actions ←
    S_work.completed_actions || [a.action_id]


  S_work.step ←
    S_t.step + 1


  RETURN:
    S_work


# =============================================================================
# 31. CAPABILITY INVOCATION
# =============================================================================

FUNCTION InvokeCapabilitySafely(call,S_t):

  capability ←
    ResolveCapability(call.capability_id)


  REQUIRE:

    capability declared

    capability available

    capability input contract satisfied

    permission granted

    side effects authorised

    capability call count < maximum_capability_calls


  request_record := {

    capability_id:
      capability.capability_id,

    input:
      call.input,

    state_before:
      StateHash(S_t),

    expected_output_contract:
      capability.output_contract,

    authorised_side_effects:
      capability.side_effects
  }


  response ←
    Invoke(capability,call.input)


  validate response:

    - output schema
    - declared error schema
    - trust level
    - side-effect report


  IF response invalid:

    RETURN:

      FAILURE {
        type:
          INVALID_CAPABILITY_RESPONSE
      }


  S_t.capability_calls.append({

    request:
      request_record,

    response:
      response,

    validation:
      PASS
  })


  RETURN:
    response


# =============================================================================
# 32. SUCCESSOR VALIDATION
# =============================================================================

FUNCTION ValidateSuccessor(S_before,S_after,a):

  validate:

    V1:
      every mutation is declared by a

    V2:
      immutable bindings unchanged

    V3:
      every value is type-valid

    V4:
      every active hard constraint holds

    V5:
      every active invariant holds

    V6:
      capability calls remain authorised

    V7:
      resource limits remain satisfied

    V8:
      branch state remains independent

    V9:
      no unknown value was silently resolved

    V10:
      action postconditions hold


  IF any hard validation fails:

    RETURN:
      false


  update:

    S_after.active_goals ←
      ActivateGoals(G,S_after)

    S_after.satisfied_goals ←
      EvaluateSatisfiedGoals(G,S_after)

    S_after.active_hard_constraints ←
      ActivateConstraints(K_H,S_after)

    S_after.active_soft_constraints ←
      ActivateConstraints(K_S,S_after)

    S_after.active_invariants ←
      ActivateInvariants(Q,S_after)

    S_after.goal_progress ←
      MeasureGoalProgress(S_after,G)


  RETURN:
    true


# =============================================================================
# 33. PROGRESS VALIDATION
# =============================================================================

FUNCTION ValidateProgress(S_before,S_after):

  mandatory_progress_before ←
    AggregateMandatoryGoalProgress(
      S_before.goal_progress,
      G
    )


  mandatory_progress_after ←
    AggregateMandatoryGoalProgress(
      S_after.goal_progress,
      G
    )


  IF mandatory_progress_after
  <
  mandatory_progress_before:

    allow only_if:

      - declared temporary regression exists
      - future recovery path is declared
      - hard constraints remain satisfied
      - resource bound permits recovery


  IF mandatory_progress_after
  =
  mandatory_progress_before:

    require at least one:

      - necessary information acquisition
      - constraint resolution
      - uncertainty reduction
      - required dependency completion
      - recovery action
      - terminal validation action


  repeated_no_progress_count ←
    CountConsecutiveNoProgressStates()


  IF repeated_no_progress_count exceeds declared threshold:

    RETURN:
      false


  RETURN:
    true


# =============================================================================
# 34. TERMINAL DETECTION
# =============================================================================

FUNCTION EvaluateTerminalState(S_t):

  mandatory_terminal_goals ← {

    g ∈ G |

    g.mandatory = true

    and

    g.terminal_when_satisfied = true

  }


  all_terminal_goals_satisfied :=

    ∀ g ∈ mandatory_terminal_goals:

      g.satisfaction_predicate(S_t)
      =
      true


  output_ready :=
    OutputConstructible(S_t,sections.emission)


  hard_constraints_valid :=
    EvaluateHardConstraints(S_t)


  invariants_valid :=
    EvaluateInvariants(S_t)


  terminal_predicate :=
    Evaluate(
      sections.termination.success_conditions,
      S_t
    )


  RETURN:

    all_terminal_goals_satisfied

    and

    output_ready

    and

    hard_constraints_valid

    and

    invariants_valid

    and

    terminal_predicate


# =============================================================================
# 35. EXECUTION LOOP
# =============================================================================

TRANSFORM T_EXECUTION_LOOP:

  B_t ←
    B_0


  terminal_candidates ←
    ∅


  execution_trace ←
    []


  WHILE B_t != ∅:

    IF total_execution_steps >= maximum_execution_steps:

      execution_status ←
        STEP_LIMIT_REACHED

      BREAK


    IF cardinality(B_t) > maximum_active_branches:

      B_t ←

        KeepHighestRankedBranches(
          B_t,
          maximum_active_branches
        )


    S_t ←
      PopHighestPriorityState(B_t)


    IF EvaluateTerminalState(S_t) = true:

      S_t.terminal ←
        true

      terminal_candidates ←
        terminal_candidates ∪ {S_t}

      CONTINUE


    continuation_set ←
      Γ(
        F,
        S_t,
        G,
        K_H,
        K_S,
        Q,
        A
      )


    IF continuation_set = NO_VALID_CONTINUATION:

      repaired ←
        AttemptStateRepair(S_t)


      IF repaired != null:

        B_t ←
          B_t ∪ {repaired}

      ELSE:

        rejected_states.add({

          state:
            StateHash(S_t),

          reason:
            NO_VALID_CONTINUATION
        })

      CONTINUE


    FOR EACH prediction p ∈ continuation_set:

      S_after ←
        ExecuteAction(S_t,p)


      IF S_after is FAILURE:

        rejected_states.add({

          state:
            StateHash(S_t),

          action:
            p.action.action_id,

          reason:
            S_after.type
        })

        CONTINUE


      successor_valid ←
        ValidateSuccessor(
          S_t,
          S_after,
          p.action
        )


      progress_valid ←
        ValidateProgress(
          S_t,
          S_after
        )


      IF successor_valid = false
      OR progress_valid = false:

        rejected_states.add({

          state:
            StateHash(S_after),

          action:
            p.action.action_id,

          reason:
            SUCCESSOR_VALIDATION_FAILURE
        })

        CONTINUE


      S_after.parent_branch_id ←
        S_t.branch_id


      IF cardinality(continuation_set) > 1:

        S_after.branch_id ←
          NewBranchID()


      trace_entry ← {

        step:
          S_t.step,

        branch_id:
          S_t.branch_id,

        prior_state_hash:
          StateHash(S_t),

        selected_action:
          p.action.action_id,

        selection_policy:
          continuation_policy,

        predicted_goal_progress:
          p.goal_progress,

        predicted_utility:
          p.utility,

        predicted_risk:
          p.risk,

        constraints_checked:
          S_t.active_hard_constraints,

        invariants_checked:
          S_t.active_invariants,

        actual_state_difference:
          StateDifference(S_t,S_after),

        resulting_state_hash:
          StateHash(S_after)
      }


      execution_trace.append(trace_entry)


      IF EvaluateTerminalState(S_after) = true:

        S_after.terminal ←
          true

        terminal_candidates ←
          terminal_candidates ∪ {S_after}


      ELSE:

        B_t ←
          B_t ∪ {S_after}


  proceed:

    T_RESOLVE_TERMINAL


# =============================================================================
# 36. REPAIR ENGINE
# =============================================================================

FUNCTION AttemptStateRepair(S_t):

  repair_cycle ←
    0


  current_state ←
    Copy(S_t)


  WHILE repair_cycle < maximum_repair_cycles:

    repair_cycle ←
      repair_cycle + 1


    failure_analysis ←
      AnalyseContinuationFailure(current_state)


    repair_options ←
      GenerateDeclaredRepairs(
        failure_analysis,
        F
      )


    permitted_repairs ← {

      r ∈ repair_options |

      r is declared

      and

      r preserves mandatory goals

      and

      r weakens no hard constraint

      and

      r violates no invariant

      and

      r exceeds no authority

      and

      r is resource-valid

    }


    IF permitted_repairs = ∅:

      RETURN:
        null


    selected_repair ←
      RankRepairs(permitted_repairs)


    repaired_state ←
      ApplyRepair(
        current_state,
        selected_repair
      )


    IF:

      EvaluateHardConstraints(repaired_state) = true

      and

      EvaluateInvariants(repaired_state) = true

      and

      DetermineAvailableActions(repaired_state) != ∅

    THEN:

      log repair:

        - failure
        - repair
        - state difference
        - retained goals
        - retained constraints


      RETURN:
        repaired_state


    current_state ←
      repaired_state


  RETURN:
    null


# =============================================================================
# 37. TERMINAL RESOLUTION
# =============================================================================

TRANSFORM T_RESOLVE_TERMINAL:

  valid_terminal_states ← ∅


  FOR EACH S_terminal ∈ terminal_candidates:

    IF:

      EvaluateTerminalState(S_terminal) = true

      and

      ValidateTerminalOutputState(S_terminal) = true

    THEN:

      valid_terminal_states ←
        valid_terminal_states ∪ {S_terminal}


  IF valid_terminal_states = ∅:

    IF execution_status = STEP_LIMIT_REACHED:

      proceed:
        T_EMIT_FAILURE

    ELSE:

      execution_status ←
        NO_VALID_TERMINAL_STATE

      proceed:
        T_EMIT_FAILURE


  accepted_terminal_state ←

    SelectTerminalState(
      valid_terminal_states,
      rule:
        - satisfy all mandatory goals
        - minimise hard-risk exposure
        - maximise declared utility
        - maximise soft-constraint satisfaction
        - minimise resource cost
        - stable branch identifier
    )


  proceed:

    T_CONSTRUCT_OUTPUT


# =============================================================================
# 38. OUTPUT CONSTRUCTION
# =============================================================================

TRANSFORM T_CONSTRUCT_OUTPUT:

  O_candidate ←

    MapStateToOutput(
      accepted_terminal_state,
      sections.emission
    )


  REQUIRE:

    every required output field exists

    every output value is type-valid

    every output constraint holds

    every mandatory goal remains satisfied

    every output field is traceable


  O* ←
    O_candidate


  execution_status ←
    COMPLETE


  proceed:

    T_BUILD_REPORTS


# =============================================================================
# 39. GOAL REPORT
# =============================================================================

TRANSFORM T_BUILD_GOAL_REPORT:

  goal_report := {

    total_goals:
      cardinality(G),

    mandatory_goals:
      count(g ∈ G where g.mandatory = true),

    satisfied_goals:
      accepted_terminal_state.satisfied_goals,

    unsatisfied_optional_goals:
      {
        g ∈ G |

        g.mandatory = false

        and

        g not satisfied
      },

    goal_progress:
      accepted_terminal_state.goal_progress,

    terminal_goal_valid:
      true
  }


# =============================================================================
# 40. CONSTRAINT REPORT
# =============================================================================

TRANSFORM T_BUILD_CONSTRAINT_REPORT:

  constraint_report := {

    hard_constraint_count:
      cardinality(K_H),

    soft_constraint_count:
      cardinality(K_S),

    hard_constraints_satisfied:
      EvaluateHardConstraints(
        accepted_terminal_state
      ),

    soft_constraint_results:
      EvaluateSoftConstraints(
        accepted_terminal_state
      ),

    rejected_transitions:
      ConstraintsCausingRejection(
        rejected_states
      ),

    silent_relaxations:
      0
  }


# =============================================================================
# 41. INVARIANT REPORT
# =============================================================================

TRANSFORM T_BUILD_INVARIANT_REPORT:

  invariant_report := {

    invariant_count:
      cardinality(Q),

    all_terminal_invariants_valid:
      EvaluateInvariants(
        accepted_terminal_state
      ),

    invariant_failures_rejected:
      CountInvariantRejectedStates(),

    invariant_repairs:
      ListInvariantRepairs(),

    unresolved_invariant_failure:
      false
  }


# =============================================================================
# 42. CAPABILITY REPORT
# =============================================================================

TRANSFORM T_BUILD_CAPABILITY_REPORT:

  capability_report := {

    declared_capabilities:
      IDs(declared_capabilities),

    available_capabilities:
      IDs(X),

    capabilities_used:
      UniqueCapabilityIDs(
        accepted_terminal_state.capability_calls
      ),

    capability_call_count:
      cardinality(
        accepted_terminal_state.capability_calls
      ),

    permission_failures:
      CountAuthorityRejections(),

    invalid_capability_responses:
      CountInvalidCapabilityResponses(),

    undeclared_capability_calls:
      0
  }


# =============================================================================
# 43. REPORT AGGREGATION
# =============================================================================

TRANSFORM T_BUILD_REPORTS:

  EXECUTE:
    T_BUILD_GOAL_REPORT

  EXECUTE:
    T_BUILD_CONSTRAINT_REPORT

  EXECUTE:
    T_BUILD_INVARIANT_REPORT

  EXECUTE:
    T_BUILD_CAPABILITY_REPORT


  validation_report := {

    structural_validation:
      PASS,

    symbol_closure:
      PASS,

    semantic_validation:
      PASS,

    goal_validation:
      PASS,

    constraint_validation:
      PASS,

    invariant_validation:
      PASS,

    capability_validation:
      PASS,

    authority_validation:
      PASS,

    terminal_validation:
      PASS,

    output_validation:
      PASS,

    execution_steps:
      accepted_terminal_state.step,

    branches_explored:
      CountGeneratedBranches(),

    branches_rejected:
      cardinality(rejected_states),

    repairs_applied:
      CountRepairs(),

    maximum_recursion_depth:
      MaximumObservedRecursionDepth(),

    conventional_compiler_used:
      false,

    fixed_binary_required:
      false
  }


  proceed:

    T_BUILD_EXECUTION_GUARANTEE


# =============================================================================
# 44. EXECUTION GUARANTEE
# =============================================================================

TRANSFORM T_BUILD_EXECUTION_GUARANTEE:

  execution_guarantee := {

    execution_model:
      "reasoning-native structural continuation",

    specification_remained_active:
      true,

    mandatory_goals_satisfied:
      true,

    hard_constraints_preserved:
      true,

    active_invariants_preserved:
      true,

    state_changes_declared:
      true,

    external_capabilities_declared:
      true,

    permissions_preserved:
      true,

    terminal_output_validated:
      true,

    output_traceable:
      true,

    hidden_assumptions_used:
      false,

    silent_constraint_relaxation:
      false,

    conventional_compilation_required:
      false,

    machine_specific_binary_required:
      false,

    claim:

      "The emitted result was produced by selecting and validating structural
       continuations from an explicit goal, state, constraint, invariant and
       capability model. The specification remained the governing executable
       representation throughout execution."
  }


  proceed:

    T_EMIT_SUCCESS


# =============================================================================
# 45. FAILURE EMISSION
# =============================================================================

TRANSFORM T_EMIT_FAILURE:

  failure_status ←

    ResolveHighestPriorityFailure({

      CONSTRAINT_CONFLICT,

      INVARIANT_VIOLATION,

      AUTHORITY_DENIED,

      CAPABILITY_UNAVAILABLE,

      AMBIGUOUS_SPECIFICATION,

      STEP_LIMIT_REACHED,

      BRANCH_LIMIT_REACHED,

      RECURSION_LIMIT_REACHED,

      NO_VALID_CONTINUATION,

      GOAL_UNREACHABLE,

      NO_VALID_TERMINAL_STATE,

      VALIDATION_FAILED

    })


  execution_status ←
    failure_status


  terminal_output ←
    null


  execution_guarantee := {

    successful_execution:
      false,

    invalid_output_released:
      false,

    mandatory_goal_completion_claimed:
      false,

    reason:
      failure_status,

    unresolved_items:
      unresolved_items,

    rejected_state_count:
      cardinality(rejected_states)
  }


  EMIT:

    execution_status

    terminal_output

    final_state:
      null

    goal_report

    constraint_report

    invariant_report

    capability_report

    execution_trace

    unresolved_items

    execution_guarantee


  HALT


# =============================================================================
# 46. SUCCESS EMISSION
# =============================================================================

TRANSFORM T_EMIT_SUCCESS:

  EMIT:

    execution_status:
      COMPLETE

    terminal_output:
      O*

    final_state:
      accepted_terminal_state.working_state

    goal_report:
      goal_report

    constraint_report:
      constraint_report

    invariant_report:
      invariant_report

    capability_report:
      capability_report

    execution_trace:
      execution_trace

    unresolved_items:
      []

    execution_guarantee:
      execution_guarantee


  HALT


# =============================================================================
# 47. FORMAL EXECUTION MODEL
# =============================================================================

FORMAL_EXECUTION:

  F :=
    reasoning-native program


  S_0 :=
    Initialise(
      F,
      I_0,
      C_0,
      X
    )


  A_t :=
    {
      a ∈ A |

      Activation(a,S_t)

      and

      Preconditions(a,S_t)

      and

      Authority(a,P,S_t)

      and

      CapabilitiesAvailable(a,X_t)
    }


  P_t :=
    {
      Predict(a,S_t) |

      a ∈ A_t
    }


  P_t_valid :=
    {
      p ∈ P_t |

      HardConstraints(p.state)

      and

      Invariants(p.state)

      and

      ResourceBounds(p.state)

      and

      AuthorityPreserved(p.state)
    }


  S_{t+1} :=

    Execute(
      Select(
        P_t_valid,
        continuation_policy
      )
    )


  termination:

    ∃ t:

      GoalsSatisfied(S_t)

      and

      TerminalPredicate(S_t)

      and

      OutputValid(S_t)


  output:

    O*
    =
    Emit(S_t)


# =============================================================================
# 48. VALID CONTINUATION PREDICATE
# =============================================================================

PREDICATE VALID_CONTINUATION(S_t,a,S_{t+1}):

  VALID_CONTINUATION :=

    DECLARED(a)

    AND

    ACTIVATED(a,S_t)

    AND

    PRECONDITIONS(a,S_t)

    AND

    AUTHORITY_VALID(a,S_t)

    AND

    CAPABILITIES_AVAILABLE(a,S_t)

    AND

    APPLY(a,S_t)
    =
    S_{t+1}

    AND

    POSTCONDITIONS(a,S_{t+1})

    AND

    HARD_CONSTRAINTS(S_{t+1})

    AND

    INVARIANTS(S_{t+1})

    AND

    RESOURCE_BOUNDS(S_{t+1})

    AND

    TRACEABLE(S_t,a,S_{t+1})


# =============================================================================
# 49. REASONING-NATIVE PROGRAM PREDICATE
# =============================================================================

PREDICATE REASONING_NATIVE(F):

  REASONING_NATIVE :=

    GOALS_EXPLICIT(F)

    AND

    STATE_EXPLICIT(F)

    AND

    CONSTRAINTS_EXPLICIT(F)

    AND

    INVARIANTS_EXPLICIT(F)

    AND

    CAPABILITIES_EXPLICIT(F)

    AND

    AUTHORITY_EXPLICIT(F)

    AND

    TRANSFORMS_EXPLICIT(F)

    AND

    CONTINUATION_RULE_EXPLICIT(F)

    AND

    TERMINATION_EXPLICIT(F)

    AND

    OUTPUT_VALIDATION_EXPLICIT(F)

    AND

    SPECIFICATION_IS_ACTIVE_EXECUTION_REPRESENTATION(F)


# =============================================================================
# 50. DETERMINISM MODEL
# =============================================================================

DETERMINISM:

  execution is deterministic when:

    - current state is identical
    - available capabilities return identical values
    - all conditions are decidable
    - continuation ranking is deterministic
    - tie-breaking is declared
    - no uncontrolled external state exists


  deterministic condition:

    ∀ S_t:

      cardinality(
        SelectedContinuations(S_t)
      )
      =
      1


  adaptive execution may still be repeatable when:

    - adaptation rules are explicit
    - state observations are identical
    - ranking rules are stable
    - external responses are fixed


  invalid nondeterminism exists when:

    - undeclared model preference selects behaviour
    - tie resolution is hidden
    - constraints are interpreted inconsistently
    - external capability results are untracked


# =============================================================================
# 51. PROBABILISTIC REASONING BOUNDARY
# =============================================================================

PROBABILISTIC_EXECUTION:

  a reasoning system may estimate:

    - likely action success
    - probable future state
    - uncertain input meaning
    - risk
    - utility
    - information value


  probability may assist ranking

  but may not override:

    - hard constraints
    - invariants
    - permissions
    - mandatory goals
    - terminal validation


  therefore:

    probabilistic_selection
    operates inside
    deterministic structural boundaries


# =============================================================================
# 52. SEMANTIC PROGRAM REPRESENTATION
# =============================================================================

SEMANTIC_PROGRAM:

  minimum representation:

    Program := {

      GoalModel,

      InputModel,

      StateModel,

      ConstraintModel,

      InvariantModel,

      CapabilityModel,

      AuthorityModel,

      TransformModel,

      ContinuationModel,

      TerminationModel,

      OutputModel

    }


  executability requires:

    SemanticClosure(Program)
    =
    true


  semantic closure means:

    every meaning required for execution is:

      - declared
      - formally derivable
      - supplied as input
      - supplied as context
      - exposed as a capability
      - included in the primitive operation set


# =============================================================================
# 53. FUTURE PROGRAMMING WORKFLOW
# =============================================================================

FUTURE_WORKFLOW:

  stage 1:

    human expresses:

      - desired outcome
      - boundaries
      - priorities
      - unacceptable outcomes


  stage 2:

    reasoning system derives:

      - entities
      - state
      - constraints
      - invariants
      - required capabilities
      - termination conditions


  stage 3:

    human and system validate:

      - intent preservation
      - authority
      - safety
      - ambiguity
      - completeness


  stage 4:

    program executes through:

      - observation
      - prediction
      - continuation
      - validation
      - state propagation


  stage 5:

    system emits:

      - result
      - state
      - explanation
      - validation report
      - execution trace


# =============================================================================
# 54. PROGRAMMING ROLE CONVERGENCE
# =============================================================================

ROLE_MODEL:

  programmer role evolves from:

    manually specifying every low-level operation

  toward:

    defining:

      - semantic structures
      - invariants
      - capability boundaries
      - validation predicates
      - authority limits
      - failure behaviour
      - evaluation criteria


  machine role evolves from:

    executing fixed instructions

  toward:

    resolving valid continuations inside declared boundaries


  retained human responsibility:

    - intent
    - ethics
    - authority
    - accountability
    - domain truth
    - acceptance criteria


# =============================================================================
# 55. SOFTWARE ARCHITECTURE MODEL
# =============================================================================

ARCHITECTURE:

  conventional layered model:

    requirement
      →
    specification
      →
    source code
      →
    compiler
      →
    runtime
      →
    deployed application


  reasoning-native model:

    intent
      →
    semantic program
      →
    reasoning substrate
      →
    validated continuation
      →
    outcome


  semantic program contains:

    - application rules
    - validation rules
    - adaptation rules
    - termination rules
    - explanation rules


  architecture shift:

    behaviour moves from fixed implementation detail

    into active semantic structure


# =============================================================================
# 56. HYBRID ARCHITECTURE
# =============================================================================

HYBRID_MODEL:

  reasoning-native programming does not require elimination of conventional
  software.

  preferred hybrid allocation:

    conventional deterministic components:

      - cryptography
      - numeric kernels
      - device drivers
      - transaction engines
      - safety interlocks
      - databases
      - protocol implementations
      - real-time control


    reasoning-native components:

      - intent interpretation
      - planning
      - workflow adaptation
      - constraint resolution
      - exception handling
      - multi-step coordination
      - explanation
      - semantic validation


  integration rule:

    conventional components are exposed as declared capabilities

  reasoning system retains:

    - orchestration
    - constraint checking
    - continuation selection

  conventional component retains:

    - exact bounded operation
    - contract enforcement
    - deterministic execution where required


# =============================================================================
# 57. SELF-MODIFICATION BOUNDARY
# =============================================================================

SELF_MODIFICATION:

  program may propose changes to:

    - soft priorities
    - local strategy
    - branch order
    - reversible heuristics
    - optional workflow structure


  program may not autonomously modify:

    - mandatory goals
    - hard constraints
    - safety invariants
    - authority limits
    - prohibited actions
    - output truth conditions


  unless:

    explicit external authority approves the modification


  proposed update must pass:

    - semantic diff
    - constraint diff
    - invariant diff
    - authority diff
    - regression validation


# =============================================================================
# 58. PROGRAM UPDATE MODEL
# =============================================================================

UPDATE_MODEL:

  let:

    F_t :=
      current program

    ΔF :=
      proposed program change

    F_{t+1} :=
      Apply(F_t,ΔF)


  before acceptance:

    validate:

      - source of change
      - authority to change
      - affected goals
      - affected state
      - affected constraints
      - affected invariants
      - affected capabilities
      - affected outputs
      - affected terminal conditions


  regression requirement:

    all unchanged mandatory behaviours remain valid


  acceptance predicate:

    AcceptUpdate(F_t,ΔF)
    :=

      Authorised(ΔF)

      AND

      SemanticClosure(F_{t+1})

      AND

      NoHardConstraintRegression(F_t,F_{t+1})

      AND

      NoInvariantRegression(F_t,F_{t+1})

      AND

      RequiredOutputsPreserved(F_{t+1})

      AND

      Executable(F_{t+1})


# =============================================================================
# 59. PORTABILITY MODEL
# =============================================================================

PORTABILITY:

  a reasoning-native program is portable between systems R_i and R_j when both
  support:

    - structural parsing
    - symbol binding
    - state propagation
    - constraint evaluation
    - invariant checking
    - capability contracts
    - continuation ranking
    - terminal validation


  behavioural portability requires:

    Execute(R_i,F,I_0)
    ≈
    Execute(R_j,F,I_0)


  equivalence means:

    - same mandatory goal class
    - same hard constraints
    - same prohibited behaviours
    - equivalent valid output class
    - no contradictory terminal result


  exact wording is not required

  behavioural preservation is required


# =============================================================================
# 60. OBSERVABILITY
# =============================================================================

OBSERVABILITY:

  every execution must expose:

    - current goal state
    - active constraints
    - active invariants
    - available actions
    - selected continuation
    - rejected continuations
    - capability calls
    - state changes
    - terminal justification


  observability purpose:

    - debugging
    - audit
    - human review
    - cross-model comparison
    - safety validation
    - program maintenance


  hidden execution is not required for reasoning-native programming


# =============================================================================
# 61. TESTING MODEL
# =============================================================================

TESTING:

  test categories:

    STRUCTURAL:

      - missing section
      - unresolved symbol
      - invalid transform
      - unreachable terminal


    BEHAVIOURAL:

      - expected state transition
      - mandatory goal achievement
      - branch selection
      - failure handling


    CONSTRAINT:

      - hard constraint rejection
      - soft preference ranking
      - prohibited action blocking


    INVARIANT:

      - mutation preservation
      - invalid successor rejection
      - repair behaviour


    CAPABILITY:

      - valid response
      - invalid response
      - unavailable capability
      - permission denial
      - timeout


    ADVERSARIAL:

      - ambiguous input
      - malicious instruction
      - authority escalation
      - contradictory goal
      - injected external semantics


    PORTABILITY:

      - equivalent execution across reasoning systems


  test success requires:

    result class
    and
    constraint behaviour
    and
    trace structure

  not merely:

    matching surface wording


# =============================================================================
# 62. SECURITY MODEL
# =============================================================================

SECURITY:

  reasoning-native execution expands flexibility

  therefore authority boundaries must become more explicit


  required controls:

    - least privilege
    - capability allow-list
    - input validation
    - output validation
    - side-effect declaration
    - irreversible-action approval
    - resource limits
    - audit trace
    - data-access boundaries
    - rollback where possible


  prohibited:

    - hidden network access
    - hidden file access
    - silent credential use
    - undeclared data retention
    - unbounded recursion
    - unrestricted self-modification
    - permission inference from user intent
    - capability invocation outside declared scope


# =============================================================================
# 63. FAILURE MODEL
# =============================================================================

FAILURE_CLASSES:

  SPECIFICATION_FAILURE:

    - missing semantic section
    - unresolved symbol
    - undefined operation
    - unreachable mandatory goal


  GOAL_FAILURE:

    - contradictory mandatory goals
    - unreachable terminal goal
    - silent goal replacement


  CONSTRAINT_FAILURE:

    - conflicting hard constraints
    - unenforceable constraint
    - attempted silent relaxation


  INVARIANT_FAILURE:

    - invalid state transition
    - unrecoverable invariant break


  CAPABILITY_FAILURE:

    - unavailable capability
    - invalid response
    - timeout
    - undeclared side effect


  AUTHORITY_FAILURE:

    - permission missing
    - prohibited action
    - approval required


  CONTINUATION_FAILURE:

    - no valid action
    - repeated no-progress state
    - branch limit reached
    - recursion limit reached


  TERMINAL_FAILURE:

    - output unavailable
    - required goal incomplete
    - output contract failure
    - no valid terminal state


# =============================================================================
# 64. REASONING-NATIVE MATURITY LEVELS
# =============================================================================

MATURITY_LEVELS:

  LEVEL_0_INSTRUCTION_NATIVE:

    behaviour:
      fixed code only


  LEVEL_1_LANGUAGE_ASSISTED:

    behaviour:
      AI generates or edits conventional code


  LEVEL_2_REASONING_ORCHESTRATED:

    behaviour:
      AI selects among conventional tools and workflows


  LEVEL_3_SEMANTICALLY_PROGRAMMED:

    behaviour:
      goals, state and constraints directly govern execution


  LEVEL_4_SELF_VALIDATING:

    behaviour:
      program validates its own continuations and outputs


  LEVEL_5_PORTABLE_REASONING_NATIVE:

    behaviour:
      same semantic program executes across compatible reasoning systems


  LEVEL_6_BOUNDED_ADAPTIVE:

    behaviour:
      program adapts strategy while preserving immutable goals, constraints,
      authority and invariants


  this flow targets:

    LEVEL_5_PORTABLE_REASONING_NATIVE

    plus

    bounded features of LEVEL_6_BOUNDED_ADAPTIVE


# =============================================================================
# 65. ARCHITECTURAL GUARANTEES
# =============================================================================

ARCHITECTURAL_GUARANTEES:

  SELF_DESCRIPTION:

    program declares its entities, state, goals and capabilities


  SELF_CONSTRAINT:

    program declares what behaviour is permitted


  SELF_VALIDATION:

    program declares how valid states and outputs are recognised


  SELF_CONTINUATION:

    program declares how candidate next states are formed and selected


  SELF_TERMINATION:

    program declares when successful or failed execution ends


  SELF_EXPLANATION:

    program retains enough trace structure to explain its result


  SELF_PORTABILITY:

    program meaning is not bound to one machine instruction set


# =============================================================================
# 66. LIMITATIONS
# =============================================================================

LIMITATIONS:

  reasoning-native programming does not guarantee:

    - perfect interpretation
    - universal determinism
    - freedom from model error
    - correctness of false input data
    - availability of external capabilities
    - elimination of conventional software
    - elimination of physical computing
    - suitability for unrestricted real-time control
    - safety without explicit constraints and authority


  reasoning-native execution remains limited by:

    - specification quality
    - model reasoning capability
    - context capacity
    - external data quality
    - capability reliability
    - resource limits
    - validation completeness


# =============================================================================
# 67. EXECUTION GUARANTEE STATEMENT
# =============================================================================

EXECUTION_GUARANTEE:

  This flow guarantees that reasoning-native programming is represented as a
  constrained execution architecture rather than as unrestricted AI autonomy.

  A reasoning-native program must explicitly declare:

    - goals
    - inputs
    - outputs
    - state
    - hard constraints
    - soft constraints
    - invariants
    - capabilities
    - permissions
    - transforms
    - continuation rules
    - termination conditions
    - output validation


  During execution:

    - candidate actions are activated from the current state
    - candidate future states are predicted
    - invalid continuations are rejected
    - valid continuations are ranked
    - selected actions are executed
    - successor states are validated
    - progress is measured
    - all accepted mutations are traced


  Completion is permitted only when:

    - all mandatory terminal goals are satisfied
    - all hard constraints remain satisfied
    - all active invariants remain satisfied
    - the terminal condition is reached
    - the output contract is satisfied
    - the result remains traceable to the program and its input


  The future of reasoning-native programming is therefore not software without
  rules.

  It is software in which the rules, goals, state and validation conditions
  become the direct executable structure.


# =============================================================================
# 68. APPROVAL
# =============================================================================

APPROVAL:

  explicit_goal_model:
    approved

  explicit_state_model:
    approved

  hard_constraint_preservation:
    approved

  invariant_preservation:
    approved

  capability_contracts:
    approved

  authority_boundary:
    approved

  predictive_continuation:
    approved

  recursive_validation:
    approved

  bounded_adaptation:
    approved

  terminal_validation:
    approved

  execution_traceability:
    approved

  cross_model_portability:
    approved

  hybrid_software_architecture:
    approved

  unrestricted_autonomy:
    rejected

  silent_goal_modification:
    rejected

  hidden_capability_use:
    rejected

  unvalidated_output:
    rejected


# =============================================================================
# 69. EXECUTE
# =============================================================================

EXECUTE:

  T_INGEST_PROGRAM

  T_PARSE_PROGRAM

  T_BUILD_SYMBOL_TABLE

  T_PARSE_GOALS

  T_PARSE_CONSTRAINTS

  T_PARSE_CAPABILITIES

  T_PARSE_TRANSFORMS

  T_BUILD_TRANSITION_GRAPH

  T_VALIDATE_STATIC_SEMANTICS

  T_INSTANTIATE_STATE

  T_EXECUTION_LOOP

  T_RESOLVE_TERMINAL

  T_CONSTRUCT_OUTPUT

  T_BUILD_REPORTS

  T_BUILD_EXECUTION_GUARANTEE

  T_EMIT_SUCCESS


# =============================================================================
# END FLOW
# =============================================================================
```