src/HOL/Library/Code_Abstract_Nat.thy
changeset 51113 222fb6cb2c3e
child 55415 05f5fdb8d093
     1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/src/HOL/Library/Code_Abstract_Nat.thy	Thu Feb 14 12:24:56 2013 +0100
     1.3 @@ -0,0 +1,113 @@
     1.4 +(*  Title:      HOL/Library/Code_Abstract_Nat.thy
     1.5 +    Author:     Stefan Berghofer, Florian Haftmann, TU Muenchen
     1.6 +*)
     1.7 +
     1.8 +header {* Avoidance of pattern matching on natural numbers *}
     1.9 +
    1.10 +theory Code_Abstract_Nat
    1.11 +imports Main
    1.12 +begin
    1.13 +
    1.14 +text {*
    1.15 +  When natural numbers are implemented in another than the
    1.16 +  conventional inductive @{term "0::nat"}/@{term Suc} representation,
    1.17 +  it is necessary to avoid all pattern matching on natural numbers
    1.18 +  altogether.  This is accomplished by this theory (up to a certain
    1.19 +  extent).
    1.20 +*}
    1.21 +
    1.22 +subsection {* Case analysis *}
    1.23 +
    1.24 +text {*
    1.25 +  Case analysis on natural numbers is rephrased using a conditional
    1.26 +  expression:
    1.27 +*}
    1.28 +
    1.29 +lemma [code, code_unfold]:
    1.30 +  "nat_case = (\<lambda>f g n. if n = 0 then f else g (n - 1))"
    1.31 +  by (auto simp add: fun_eq_iff dest!: gr0_implies_Suc)
    1.32 +
    1.33 +
    1.34 +subsection {* Preprocessors *}
    1.35 +
    1.36 +text {*
    1.37 +  The term @{term "Suc n"} is no longer a valid pattern.  Therefore,
    1.38 +  all occurrences of this term in a position where a pattern is
    1.39 +  expected (i.e.~on the left-hand side of a code equation) must be
    1.40 +  eliminated.  This can be accomplished – as far as possible – by
    1.41 +  applying the following transformation rule:
    1.42 +*}
    1.43 +
    1.44 +lemma Suc_if_eq: "(\<And>n. f (Suc n) \<equiv> h n) \<Longrightarrow> f 0 \<equiv> g \<Longrightarrow>
    1.45 +  f n \<equiv> if n = 0 then g else h (n - 1)"
    1.46 +  by (rule eq_reflection) (cases n, simp_all)
    1.47 +
    1.48 +text {*
    1.49 +  The rule above is built into a preprocessor that is plugged into
    1.50 +  the code generator.
    1.51 +*}
    1.52 +
    1.53 +setup {*
    1.54 +let
    1.55 +
    1.56 +fun remove_suc thy thms =
    1.57 +  let
    1.58 +    val vname = singleton (Name.variant_list (map fst
    1.59 +      (fold (Term.add_var_names o Thm.full_prop_of) thms []))) "n";
    1.60 +    val cv = cterm_of thy (Var ((vname, 0), HOLogic.natT));
    1.61 +    fun lhs_of th = snd (Thm.dest_comb
    1.62 +      (fst (Thm.dest_comb (cprop_of th))));
    1.63 +    fun rhs_of th = snd (Thm.dest_comb (cprop_of th));
    1.64 +    fun find_vars ct = (case term_of ct of
    1.65 +        (Const (@{const_name Suc}, _) $ Var _) => [(cv, snd (Thm.dest_comb ct))]
    1.66 +      | _ $ _ =>
    1.67 +        let val (ct1, ct2) = Thm.dest_comb ct
    1.68 +        in 
    1.69 +          map (apfst (fn ct => Thm.apply ct ct2)) (find_vars ct1) @
    1.70 +          map (apfst (Thm.apply ct1)) (find_vars ct2)
    1.71 +        end
    1.72 +      | _ => []);
    1.73 +    val eqs = maps
    1.74 +      (fn th => map (pair th) (find_vars (lhs_of th))) thms;
    1.75 +    fun mk_thms (th, (ct, cv')) =
    1.76 +      let
    1.77 +        val th' =
    1.78 +          Thm.implies_elim
    1.79 +           (Conv.fconv_rule (Thm.beta_conversion true)
    1.80 +             (Drule.instantiate'
    1.81 +               [SOME (ctyp_of_term ct)] [SOME (Thm.lambda cv ct),
    1.82 +                 SOME (Thm.lambda cv' (rhs_of th)), NONE, SOME cv']
    1.83 +               @{thm Suc_if_eq})) (Thm.forall_intr cv' th)
    1.84 +      in
    1.85 +        case map_filter (fn th'' =>
    1.86 +            SOME (th'', singleton
    1.87 +              (Variable.trade (K (fn [th'''] => [th''' RS th']))
    1.88 +                (Variable.global_thm_context th'')) th'')
    1.89 +          handle THM _ => NONE) thms of
    1.90 +            [] => NONE
    1.91 +          | thps =>
    1.92 +              let val (ths1, ths2) = split_list thps
    1.93 +              in SOME (subtract Thm.eq_thm (th :: ths1) thms @ ths2) end
    1.94 +      end
    1.95 +  in get_first mk_thms eqs end;
    1.96 +
    1.97 +fun eqn_suc_base_preproc thy thms =
    1.98 +  let
    1.99 +    val dest = fst o Logic.dest_equals o prop_of;
   1.100 +    val contains_suc = exists_Const (fn (c, _) => c = @{const_name Suc});
   1.101 +  in
   1.102 +    if forall (can dest) thms andalso exists (contains_suc o dest) thms
   1.103 +      then thms |> perhaps_loop (remove_suc thy) |> (Option.map o map) Drule.zero_var_indexes
   1.104 +       else NONE
   1.105 +  end;
   1.106 +
   1.107 +val eqn_suc_preproc = Code_Preproc.simple_functrans eqn_suc_base_preproc;
   1.108 +
   1.109 +in
   1.110 +
   1.111 +  Code_Preproc.add_functrans ("eqn_Suc", eqn_suc_preproc)
   1.112 +
   1.113 +end;
   1.114 +*}
   1.115 +
   1.116 +end