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Lax916827.RegularComposition

Regular functions are closed under composition

concepts/Lax916827/RegularComposition.lean · lax-916827

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    In the paper

    Theorem

    Regular functions are closed under composition (Theorem C.1.1 of Transducers, the composition half): composition is built into the definition of the regular functions as compositions of primes.

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    1import Lax916827.RegularFunctions
    2
    3/-!
    4---
    5title: Regular functions are closed under composition
    6type: theorem
    7---
    8Regular functions are closed under composition (Theorem C.1.1 of
    9*Transducers*, the composition half): composition is built into the definition
    10of the regular functions as compositions of primes.
    11
    12# Formalization notes
    13
    14The intermediate alphabet is assumed finite, as in the composition closure.
    15-/
    16
    17namespace Lax916827.RegularComposition
    18
    19open Lax916827.RegularFunctions
    20
    21/-- The composition of two regular functions is regular. -/
    22axiom isRegularFun_comp {A B C : Type} [Finite B] {f : List A → List B} {g : List B → List C}
    23 (hf : IsRegularFun f) (hg : IsRegularFun g) : IsRegularFun (g ∘ f)
    24
    25end Lax916827.RegularComposition
    26
    Show Proof

    Formalization notes

    The intermediate alphabet is assumed finite, as in the composition closure.

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