Structure EncodeVarTheory

signature EncodeVarTheory =
sig
  type thm = Thm.thm

  (*  Definitions  *)
    val fixed_width_def : thm
    val of_length_def : thm

  (*  Theorems  *)
    val fixed_width_bnum : thm
    val fixed_width_bool : thm
    val fixed_width_exists : thm
    val fixed_width_prod : thm
    val fixed_width_sum : thm
    val fixed_width_unit : thm
    val fixed_width_univ : thm
    val of_length_exists_suc : thm
    val of_length_exists_zero : thm
    val of_length_univ_suc : thm
    val of_length_univ_zero : thm

  val EncodeVar_grammars : type_grammar.grammar * term_grammar.grammar
(*
   [Coder] Parent theory of "EncodeVar"

   [fixed_width_def]  Definition

      |- ∀n c.
           fixed_width n c ⇔ ∀x. domain c x ⇒ (LENGTH (encoder c x) = n)

   [of_length_def]  Definition

      |- ∀l n. l ∈ of_length n ⇔ (LENGTH l = n)

   [fixed_width_bnum]  Theorem

      |- ∀m p. fixed_width m (bnum_coder m p)

   [fixed_width_bool]  Theorem

      |- ∀p. fixed_width 1 (bool_coder p)

   [fixed_width_exists]  Theorem

      |- ∀phi c n.
           wf_coder c ∧ fixed_width n c ⇒
           ((∃x. domain c x ∧ phi x) ⇔ ∃w::of_length n. phi (decoder c w))

   [fixed_width_prod]  Theorem

      |- ∀c1 c2 n1 n2.
           fixed_width n1 c1 ∧ fixed_width n2 c2 ⇒
           fixed_width (n1 + n2) (prod_coder c1 c2)

   [fixed_width_sum]  Theorem

      |- ∀c1 c2 n.
           fixed_width n c1 ∧ fixed_width n c2 ⇒
           fixed_width (SUC n) (sum_coder c1 c2)

   [fixed_width_unit]  Theorem

      |- ∀p. fixed_width 0 (unit_coder p)

   [fixed_width_univ]  Theorem

      |- ∀phi c n.
           wf_coder c ∧ fixed_width n c ⇒
           ((∀x. domain c x ⇒ phi x) ⇔ ∀w::of_length n. phi (decoder c w))

   [of_length_exists_suc]  Theorem

      |- ∀phi n.
           (∃w::of_length (SUC n). phi w) ⇔ ∃x (w::of_length n). phi (x::w)

   [of_length_exists_zero]  Theorem

      |- ∀phi. (∃w::of_length 0. phi w) ⇔ phi []

   [of_length_univ_suc]  Theorem

      |- ∀phi n.
           (∀w::of_length (SUC n). phi w) ⇔ ∀x (w::of_length n). phi (x::w)

   [of_length_univ_zero]  Theorem

      |- ∀phi. (∀w::of_length 0. phi w) ⇔ phi []


*)
end

HOL 4, Kananaskis-10