Theory Old_Show_Generator

Copyright 2009-2014 Christian Sternagel, René Thiemann

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section ‹Generating Show-Functions for Data Types›

theory Old_Show_Generator

subsection ‹Introduction›

text ‹
  The show-generator registers itself at the derive-manager for the class @{class show}. To be more
  precise, it automatically generates the functions @{const shows_prec} and @{const shows_list} for
  some data type dtyp› and proves the following instantiation.
  \item instantiation dtyp :: (show, ..., show) show›
  All the non-recursive types that are used in the data type must have a similar instantiation. For
  recursive type-dependencies this is automatically generated.

  For example, for the data type datatype tree = Leaf nat | Node (tree list)› we require
  that nat› is already in @{class show}, whereas for type @{typ "'a list"} nothing is
  required, since it is used recursively.

  However, if we define datatype tree = Leaf (nat list) | Node tree tree› then also
  @{typ "'a list"} must provide a @{class show} instance.

subsection ‹Implementation Notes›

text ‹
  The generator uses the recursors from the data type package to define the show function.
  Constructors are displayed by their short names and arguments are separated by blanks and
  surrounded by parenthesis.

  The associativity is proven using the induction theorem from the data type package.

subsection ‹Features and Limitations›

text ‹
  The show-generator has been developed mainly for data types without explicit mutual recursion. For
  mutual recursive data types -- like datatype a = C b and b = D a a› -- only for the first
  mentioned data type -- here a› -- instantiations of the @{class show} are derived.

  Indirect recursion like in datatype tree = Leaf nat | Node (tree list)› should work
  without problems.

subsection ‹Installing the Generator›

definition shows_sep_paren :: "shows  shows"
  "shows_sep_paren s = ('' ('' +#+ s +@+ shows '')'')"

text ‹
  The four crucial properties which are used to ensure associativity.
lemma append_assoc_trans:
  assumes "r s. b r @ s = b (r @ s)"
  shows "((@) a +@+ b) r @ s = ((@) a +@+ b) (r @ s)"
  using assms by simp

lemma shows_sep_paren:
  assumes "r s. a r @ s = a (r @ s)"
    and "r s. b r @ s = b (r @ s)"
  shows "(shows_sep_paren a +@+ b) r @ s = (shows_sep_paren a +@+ b) (r @ s)"
  unfolding shows_sep_paren_def by (simp add: assms)

lemma shows_sep_paren_final:
  assumes "r s. a r @ s = a (r @ s)"
  shows "(shows_sep_paren a) r @ s = (shows_sep_paren a) (r @ s)"
  unfolding shows_sep_paren_def by (simp add: assms)

ML_file ‹old_show_generator.ML›