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Lax194892.ForIffPolyregular

For-transducers compute exactly the polyregular functions

concepts/Lax194892/ForIffPolyregular.lean · lax-194892

proven

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    In the paper

    Theorem

    A string-to-string function is polyregular if and only if it is computed by a for-transducer (Theorem D.1.1 of Transducers). The two implications are the separate statements ForOfPolyregularForOfPolyregular and PolyregularOfForPolyregularOfFor; this statement is their conjunction.

    Lean source view on GitHub

    1import Lax194892.PolyregularFunctions
    2import Lax194892.ForTransducers
    3
    4/-!
    5---
    6title: For-transducers compute exactly the polyregular functions
    7type: theorem
    8---
    9A string-to-string function is polyregular if and only if it is computed by a
    10for-transducer (Theorem D.1.1 of *Transducers*). The two implications are the
    11separate statements `ForOfPolyregular` and `PolyregularOfFor`; this statement
    12is their conjunction.
    13
    14# Formalization notes
    15
    16Both alphabets are assumed finite.
    17-/
    18
    19namespace Lax194892.ForIffPolyregular
    20
    21open Lax194892.PolyregularFunctions Lax194892.ForTransducers
    22
    23/-- A function is polyregular if and only if a for-transducer computes it. -/
    24axiom isPolyregular_iff_isForTransducer {A B : Type} [Finite A] [Finite B]
    25 (f : List A → List B) : IsPolyregular f ↔ IsForTransducer f
    26
    27end Lax194892.ForIffPolyregular
    28
    Show Proof

    Formalization notes

    Both alphabets are assumed finite.

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