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refactor(MultiTape): build seq and repeatUntilBlank by wiring machines - #46
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seq and repeatUntilBlank by wiring adapted machinesseq and repeatUntilBlank by wiring machines
Adds `wire`, which runs two machines on the same tapes in one, in the states `State₀ ⊕ State₁`, and takes two wires, `next₀` and `next₁`, saying where the steps of each machine lead: within the same machine, to the other one, or to halting. Each half follows its machine through the adapter relabeling its next states (`Wire.follows_left`, `Wire.follows_right`), and the adapted transition `adaptedTr` is shared with `adapt`, whose `follows_adapt` becomes `Adapt.follows`. Defines `seq` as the wiring of its two machines, and `repeatUntilBlank` as the wiring of `tm` with `blankTest`, a one-state machine that halts on a blank cell and otherwise hands back to `tm`. The loop's first phase is that of `seq`: `Sequential.leftState` and `leftCfg` now take the state handed over to, so the loop reuses them in place of its own `runState`. The loop's states become `State ⊕ Unit`, replacing `RepeatUntilBlankState`, and the hand-written `Follows` proofs of both combinators are removed, as is `Action.mapState`, now used only to define `Adapter.mapState`. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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Adds
wire, which runs two machines on the same tapes in one, in the statesState₀ ⊕ State₁, and takes two wires,next₀andnext₁, saying where the steps of each machine lead: within the same machine, to the other one, or to halting. Each half follows its machine through the adapter relabeling its next states (Wire.follows_left,Wire.follows_right), and the adapted transitionadaptedTris shared withadapt, whosefollows_adaptbecomesAdapt.follows.Defines
seqas the wiring of its two machines, andrepeatUntilBlankas the wiring oftmwithblankTest, a one-state machine that halts on a blank cell and otherwise hands back totm. The loop's first phase is that ofseq:Sequential.leftStateandleftCfgnow take the state handed over to, so the loop reuses them in place of its ownrunState. The loop's states becomeState ⊕ Unit, replacingRepeatUntilBlankState, and the hand-writtenFollowsproofs of both combinators are removed, as isAction.mapState, now used only to defineAdapter.mapState.Depends on #32.
Composed with Claude Code.