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Lax194892.PolyregularOfFor

For-transducers compute polyregular functions

concepts/Lax194892/PolyregularOfFor.lean · lax-194892

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    In the paper

    Theorem

    Every function computed by a for-transducer is polyregular (Theorem D.1.1 of Transducers, the implication from for-transducer to polyregular). The program is put in prenex form (Lemma D.1.3); the tuples of loop variables are enumerated, in the order of the loops, by iterated marked squaring, and the loop-free body is evaluated on each tuple by a rational function.

    Lean source view on GitHub

    1import Lax194892.PolyregularFunctions
    2import Lax194892.ForTransducers
    3
    4/-!
    5---
    6title: For-transducers compute polyregular functions
    7type: theorem
    8---
    9Every function computed by a for-transducer is polyregular (Theorem D.1.1 of
    10*Transducers*, the implication from for-transducer to polyregular). The program
    11is put in prenex form (Lemma D.1.3); the tuples of loop variables are
    12enumerated, in the order of the loops, by iterated marked squaring, and the
    13loop-free body is evaluated on each tuple by a rational function.
    14
    15# Formalization notes
    16
    17Both alphabets are assumed finite, as in the book.
    18-/
    19
    20namespace Lax194892.PolyregularOfFor
    21
    22open Lax194892.PolyregularFunctions Lax194892.ForTransducers
    23
    24/-- A function computed by a for-transducer is polyregular. -/
    25axiom isPolyregular_of_isForTransducer {A B : Type} [Finite A] [Finite B]
    26 {f : List A → List B} (hf : IsForTransducer f) : IsPolyregular f
    27
    28end Lax194892.PolyregularOfFor
    29
    Show Proof

    Formalization notes

    Both alphabets are assumed finite, as in the book.

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