Lax Lean Archive

Bounded machine configurations

Lax733996.BoundedConfigurations · concepts/Lax733996/BoundedConfigurations.lean · lax-733996

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    Definition

    A configuration using at most ss work cells consists of a control state, an input-head position, a work-head position, and ss work symbols. Cells beyond this prefix are blank.

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    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A

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    • page 1 of this submission's paper

    Lean source view on GitHub

    1import Lax434930.SpaceMachines
    2import Mathlib.Data.Fintype.Pi
    3
    4set_option backward.isDefEq.respectTransparency false
    5
    6/-!
    7---
    8title: Bounded machine configurations
    9type: definition
    10---
    11A configuration using at most ss work cells consists of a control state,
    12an input-head position, a work-head position, and ss work symbols.
    13Cells beyond this prefix are blank.
    14-/
    15
    16namespace Lax733996.BoundedConfigurations
    17
    18open Lax434930.SpaceMachines
    19
    20structure Config (M : Machine) (n s : ℕ) where
    21 state : M.Q
    22 inputHead : Fin (n + 2)
    23 workHead : Fin s
    24 tape : Fin s → M.Γ
    25 deriving Fintype
    26
    27def expand {M : Machine} {n s : ℕ} (c : Config M n s) : M.Config :=
    28 ⟨c.state, c.inputHead.val, c.workHead.val,
    29 fun i => if h : i < s then c.tape ⟨i, h⟩ else M.blank⟩
    30
    31end Lax733996.BoundedConfigurations
    32
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    From Mathlib

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