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Conditional compiler theorem

FPRD-T102

A stationary frontier allocator is the exact compiler interface

Exact statement

Every partial deterministic visible machine equipped with one stationary fixed-slot frontier allocator compiles to an exact Loff–Moreira–Reis scaffolding automaton for its forgotten call, return, and local-action projection. The allocator is letter-synchronous and source-selecting, and the compiled scaffold recognizes exactly the successful hidden-action runs after the same prefix, including epsilon.

StatusMechanically checked and internally audited
External reviewNo documented external or specialist review of this FPRD result is recorded.

Context

This theorem isolates the remaining recognition obligation after persistent root sharing: a single stationary transition must keep the exact successful frontier in finitely many named slots.

Definitions

  • The semantic frontier is extensional membership in the successful call, return, and local successors; list order and duplicate multiplicity are irrelevant.
  • A fixed-slot allocator supplies initial validity, step validity, initial exactness, step exactness, and exact accepting-control readout.

Proof or evidence

Lean proves the frontier append law, equivalence with successful tagged runs, allocator validity and exactness for every prefix, Boolean readout, and composition with the source-selecting stack compiler. A two-slot fork calibration exercises push and keep from one old root in the same round.

Exact allocator interface →

Verification notes

The public statement was rederived from the partial-machine semantics and the five allocator laws. The formal endpoints, same-prefix timing, epsilon case, inactive-slot convention, and proof-hole scan were checked against the pinned source and adversarial specification.

Limitations

  • The theorem assumes a lawful stationary allocator; bounded frontier cardinality alone does not supply one.
  • It does not assume that finite control can compare arbitrary unbounded stacks for equality.
  • Carrier finiteness, positive scaffold degree, reversal, and the final LMR-to-PEG specialization remain external obligations.

Open work

Seek external review of the allocator laws and their correspondence with forgotten-action visibly pushdown semantics.

Notes

Lean 4.30.0 checks partial tagged command semantics, the exact successful-run frontier recurrence, existential same-round hidden-action equivalence, allocator validity, initial and step exactness, all-prefix frontier equality, final-control readout, and composition with FPRD-T101. The two-slot calibration splits one old empty root into a pushed [7] branch and a kept empty branch and proves for all words that the compiled machine accepts exactly [true]. The theorem does not construct a stationary allocator from bounded frontier cardinality or assume finite-control equality testing of unbounded stacks. Carrier finiteness, positive degree, reversal, and LMR's PEG correspondence stay outside Lean. This opens no M34 and does not edit the paused EPAL publication.