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Lax916827.ReversalContinuous

String reversal is continuous

concepts/Lax916827/ReversalContinuous.lean · lax-916827

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    In the paper

    Theorem

    String reversal w↦reverse(w)w \mapsto \mathrm{reverse}(w) is continuous (Lemma C.1.2 of Transducers, first half): the inverse image of a regular language under reversal is recognised by the automaton with all transitions reversed and initial and accepting states swapped.

    Lean source view on GitHub

    1import Lax765601.Continuity
    2
    3/-!
    4---
    5title: String reversal is continuous
    6type: theorem
    7---
    8String reversal w↦reverse(w)w \mapsto \mathrm{reverse}(w) is continuous (Lemma C.1.2 of
    9*Transducers*, first half): the inverse image of a regular language under
    10reversal is recognised by the automaton with all transitions reversed and
    11initial and accepting states swapped.
    12
    13# Formalization notes
    14
    15The alphabet is assumed finite, as in the book.
    16-/
    17
    18namespace Lax916827.ReversalContinuous
    19
    20open Lax765601.Continuity
    21
    22/-- String reversal is continuous. -/
    23axiom continuous_reverse {A : Type} [Finite A] : Continuous (List.reverse : List A → List A)
    24
    25end Lax916827.ReversalContinuous
    26
    Show Proof

    Formalization notes

    The alphabet is assumed finite, as in the book.

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