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refactor(MultiTapeTM): Rename TransitionOut to Action and its fields after the tapes #827

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refactor(MultiTapeTM): Rename TransitionOut to Action and its fields after the tapes #827

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24 changes: 12 additions & 12 deletions Cslib/Computability/Machines/Turing/MultiTape/Deterministic.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -102,15 +102,15 @@ namespace Turing
variable {k : ℕ} {State Symbol : Type*}

/-- The output of the transition function. -/
structure TransitionOut (k : ℕ) (Symbol State : Type*) where
structure Action (k : ℕ) (Symbol State : Type*) where
/-- The movement (attempt) of the input head. -/
inputMove : SignType
inputTape : SignType
/-- Actions on the work tapes: optionally a symbol to write and the head movement. -/
workActions : Fin k → (Option (Option Symbol)) × SignType
workTapes : Fin k → (Option (Option Symbol)) × SignType
/-- An optional symbol to output. -/
outS : Option Symbol
output : Option Symbol
/-- The successor state or none to halt. -/
q' : Option State
state : Option State

/--
A multi-tape Turing machine with `k` work tapes over the alphabet of `Option Symbol` (where `none`
Expand All @@ -125,7 +125,7 @@ structure MultiTapeTM (k : ℕ) (Symbol State : Type*) where
symbols to a movement for the input head, actions on the work tape, optionally a symbol to output
and the successor state -/
tr (q : State) (input : Option Symbol) (work : Fin k → Option Symbol) :
TransitionOut k Symbol State
Action k Symbol State

namespace MultiTapeTM

Expand Down Expand Up @@ -230,21 +230,21 @@ def step (cfg : Cfg k Symbol State input) : Cfg k Symbol State input :=
-- in the halting state, we stay at the configuration
| none => cfg
| some q =>
let {inputMove, workActions, q', ..} := tm.tr q cfg.inputSymbol cfg.workTapeSymbols
let action := tm.tr q cfg.inputSymbol cfg.workTapeSymbols
{
state := q',
inputPos := moveInputPos cfg.inputPos inputMove,
workTapes i := match (workActions i).1 with
state := action.state,
inputPos := moveInputPos cfg.inputPos action.inputTape,
workTapes i := match (action.workTapes i).1 with
| none => cfg.workTapes i
| some s => Function.update (cfg.workTapes i) (cfg.workTapePos i) s
workTapePos i := (cfg.workTapePos i) + (workActions i).2
workTapePos i := (cfg.workTapePos i) + (action.workTapes i).2
}

/-- The symbol (optionally) output when executing one step starting from configuration `cfg`. -/
def outputSymbol (cfg : Cfg k Symbol State input) : Option Symbol :=
match cfg.state with
| none => none
| some q => (tm.tr q cfg.inputSymbol cfg.workTapeSymbols).outS
| some q => (tm.tr q cfg.inputSymbol cfg.workTapeSymbols).output

/-- The initial configuration corresponding to an input string. -/
@[simp]
Expand Down
2 changes: 1 addition & 1 deletion Cslib/Computability/Machines/Turing/MultiTape/TapeLemmas.lean
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Expand Up @@ -39,7 +39,7 @@ lemma step_workTapes_eq_of_ne
cases hst : cfg.state with
| none => simp_all
| some q =>
rcases hw : ((tm.tr q cfg.inputSymbol cfg.workTapeSymbols).workActions j).1 <;> simp_all
rcases hw : ((tm.tr q cfg.inputSymbol cfg.workTapeSymbols).workTapes j).1 <;> simp_all

lemma mem_visitedByTapeHead {t : ℕ} {i : Fin k} {z : ℤ} :
z ∈ tm.visitedByTapeHead cfg t i ↔ ∃ t' < t + 1, (tm.configs cfg t').workTapePos i = z := by
Expand Down
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