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-13