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Lax916827.RegularMapLifting

Regular functions are closed under map lifting

concepts/Lax916827/RegularMapLifting.lean · lax-916827

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    Concept map

    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A

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    In the paper

    Theorem

    The map lifting of a regular function is regular (Lemma C.2.10 of Transducers, first item). Map lifting commutes with composition, so it suffices to lift the primes: the map lifting of a rational function is rational, and the map liftings of map reverse and map duplicate are regular.

    Lean source view on GitHub

    1import Lax765601.MapLifting
    2import Lax916827.RegularFunctions
    3
    4/-!
    5---
    6title: Regular functions are closed under map lifting
    7type: theorem
    8---
    9The map lifting of a regular function is regular (Lemma C.2.10 of
    10*Transducers*, first item). Map lifting commutes with composition, so it
    11suffices to lift the primes: the map lifting of a rational function is rational,
    12and the map liftings of map reverse and map duplicate are regular.
    13
    14# Formalization notes
    15
    16Both alphabets are assumed finite, as in the book.
    17-/
    18
    19namespace Lax916827.RegularMapLifting
    20
    21open Lax765601.MapLifting Lax916827.RegularFunctions
    22
    23/-- The map lifting of a regular function is regular. -/
    24axiom isRegularFun_mapLift {A B : Type} [Finite A] [Finite B] {f : List A → List B}
    25 (hf : IsRegularFun f) : IsRegularFun (mapLift f)
    26
    27end Lax916827.RegularMapLifting
    28
    Show Proof

    Formalization notes

    Both alphabets are assumed finite, as in the book.

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