Sequences

  • $ %e : seq T$

    empty


  • $ _ |> _ : seq T \* T -> seq T$

    right append


  • $ _ <| _ : T \* seq T -> seq T$

    left append


  • $ _ \. _ : seq T \* seq T -> seq T$

    concatenation


  • $<< _ >> : T -> seq T$

    lifting


  • $<< _,...,_ >> : T^{n} -> seq T$

    multiple arguments


Generator basis -- preferably one-to-one

  • $G_{seq T } = { %e, |> }$, $GU_{seq T } = { %e, %e |> a, %e |> b, ..., %e |> a |> b, ... }$
  • $G'_{seq T } = { %e, <| }$, $GU'_{seq T } = { %e, a <| %e , b <| %e, ..., b <| a <| %e, ... }$
  • $G''_{seq T } = { %e, \. , << _ >> }$, $GU''_{seq T } = { %e, <>, <>, ,..., %e \. %e, ..., %e \. <> , ... }$

Infinite generator basis


slide: The ADT Seq