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Lax194892.PolyregularContinuity

Polyregular functions are continuous

concepts/Lax194892/PolyregularContinuity.lean · lax-194892

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    In the paper

    Theorem

    Polyregular functions are continuous (Theorem D.0.2 of Transducers): regular functions are, continuity is preserved by composition, and marked squaring is continuous — an automaton for the target language is run on the marked square from right to left, remembering the state transformation of the underlined suffix and how the state transformation of the prefix transforms the contribution of the suffix.

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    1import Lax765601.Continuity
    2import Lax194892.PolyregularFunctions
    3
    4/-!
    5---
    6title: Polyregular functions are continuous
    7type: theorem
    8---
    9Polyregular functions are continuous (Theorem D.0.2 of *Transducers*):
    10regular functions are, continuity is preserved by composition, and marked
    11squaring is continuous — an automaton for the target language is run on the
    12marked square from right to left, remembering the state transformation of the
    13underlined suffix and how the state transformation of the prefix transforms the
    14contribution of the suffix.
    15
    16# Formalization notes
    17
    18Both alphabets are assumed finite, as in the book.
    19-/
    20
    21namespace Lax194892.PolyregularContinuity
    22
    23open Lax765601.Continuity Lax194892.PolyregularFunctions
    24
    25/-- A polyregular function is continuous. -/
    26axiom continuous_of_isPolyregular {A B : Type} [Finite A] [Finite B] {f : List A → List B}
    27 (hf : IsPolyregular f) : Continuous f
    28
    29end Lax194892.PolyregularContinuity
    30
    Show Proof

    Formalization notes

    Both alphabets are assumed finite, as in the book.

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