(* Title: HOL/Hoare/hoare_syntax.ML
Author: Leonor Prensa Nieto & Tobias Nipkow
Syntax translations for Hoare logic.
*)
signature HOARE_SYNTAX =
sig
val hoare_vars_tr: term list -> term
val spec_tr': string -> term list -> term
end;
structure Hoare_Syntax: HOARE_SYNTAX =
struct
(** parse translation **)
local
fun idt_name (Free (x, _)) = SOME x
| idt_name (Const (\<^syntax_const>\<open>_constrain\<close>, _) $ t $ _) = idt_name t
| idt_name _ = NONE;
fun eq_idt tu =
(case apply2 idt_name tu of
(SOME x, SOME y) => x = y
| _ => false);
fun mk_abstuple [x] body = Syntax_Trans.abs_tr [x, body]
| mk_abstuple (x :: xs) body =
Syntax.const \<^const_syntax>\<open>case_prod\<close> $ Syntax_Trans.abs_tr [x, mk_abstuple xs body];
fun mk_fbody x e [y] = if eq_idt (x, y) then e else y
| mk_fbody x e (y :: xs) =
Syntax.const \<^const_syntax>\<open>Pair\<close> $
(if eq_idt (x, y) then e else y) $ mk_fbody x e xs;
fun mk_fexp x e xs = mk_abstuple xs (mk_fbody x e xs);
(* bexp_tr & assn_tr *)
(*all meta-variables for bexp except for TRUE are translated as if they
were boolean expressions*)
fun bexp_tr (Const ("TRUE", _)) _ = Syntax.const "TRUE" (* FIXME !? *)
| bexp_tr b xs = Syntax.const \<^const_syntax>\<open>Collect\<close> $ mk_abstuple xs b;
fun assn_tr r xs = Syntax.const \<^const_syntax>\<open>Collect\<close> $ mk_abstuple xs r;
(* com_tr *)
fun com_tr (Const (\<^syntax_const>\<open>_assign\<close>, _) $ x $ e) xs =
Syntax.const \<^const_syntax>\<open>Basic\<close> $ mk_fexp x e xs
| com_tr (Const (\<^const_syntax>\<open>Basic\<close>,_) $ f) _ = Syntax.const \<^const_syntax>\<open>Basic\<close> $ f
| com_tr (Const (\<^const_syntax>\<open>Seq\<close>,_) $ c1 $ c2) xs =
Syntax.const \<^const_syntax>\<open>Seq\<close> $ com_tr c1 xs $ com_tr c2 xs
| com_tr (Const (\<^const_syntax>\<open>Cond\<close>,_) $ b $ c1 $ c2) xs =
Syntax.const \<^const_syntax>\<open>Cond\<close> $ bexp_tr b xs $ com_tr c1 xs $ com_tr c2 xs
| com_tr (Const (\<^const_syntax>\<open>While\<close>,_) $ b $ I $ c) xs =
Syntax.const \<^const_syntax>\<open>While\<close> $ bexp_tr b xs $ assn_tr I xs $ com_tr c xs
| com_tr t _ = t;
fun vars_tr (Const (\<^syntax_const>\<open>_idts\<close>, _) $ idt $ vars) = idt :: vars_tr vars
| vars_tr t = [t];
in
fun hoare_vars_tr [vars, pre, prg, post] =
let val xs = vars_tr vars
in Syntax.const \<^const_syntax>\<open>Valid\<close> $
assn_tr pre xs $ com_tr prg xs $ assn_tr post xs
end
| hoare_vars_tr ts = raise TERM ("hoare_vars_tr", ts);
end;
(** print translation **)
local
fun dest_abstuple
(Const (\<^const_syntax>\<open>case_prod\<close>, _) $ Abs (v, _, body)) =
subst_bound (Syntax.free v, dest_abstuple body)
| dest_abstuple (Abs (v,_, body)) = subst_bound (Syntax.free v, body)
| dest_abstuple tm = tm;
fun abs2list (Const (\<^const_syntax>\<open>case_prod\<close>, _) $ Abs (x, T, t)) = Free (x, T) :: abs2list t
| abs2list (Abs (x, T, _)) = [Free (x, T)]
| abs2list _ = [];
fun mk_ts (Const (\<^const_syntax>\<open>case_prod\<close>, _) $ Abs (_, _, t)) = mk_ts t
| mk_ts (Abs (_, _, t)) = mk_ts t
| mk_ts (Const (\<^const_syntax>\<open>Pair\<close>, _) $ a $ b) = a :: mk_ts b
| mk_ts t = [t];
fun mk_vts (Const (\<^const_syntax>\<open>case_prod\<close>,_) $ Abs (x, _, t)) =
(Syntax.free x :: abs2list t, mk_ts t)
| mk_vts (Abs (x, _, t)) = ([Syntax.free x], [t])
| mk_vts _ = raise Match;
fun find_ch [] _ _ = (false, (Syntax.free "not_ch", Syntax.free "not_ch")) (* FIXME no_ch!? *)
| find_ch ((v, t) :: vts) i xs =
if t = Bound i then find_ch vts (i - 1) xs
else (true, (v, subst_bounds (xs, t)));
fun is_f (Const (\<^const_syntax>\<open>case_prod\<close>, _) $ Abs _) = true
| is_f (Abs _) = true
| is_f _ = false;
(* assn_tr' & bexp_tr'*)
fun assn_tr' (Const (\<^const_syntax>\<open>Collect\<close>, _) $ T) = dest_abstuple T
| assn_tr' (Const (\<^const_syntax>\<open>inter\<close>, _) $
(Const (\<^const_syntax>\<open>Collect\<close>, _) $ T1) $ (Const (\<^const_syntax>\<open>Collect\<close>, _) $ T2)) =
Syntax.const \<^const_syntax>\<open>inter\<close> $ dest_abstuple T1 $ dest_abstuple T2
| assn_tr' t = t;
fun bexp_tr' (Const (\<^const_syntax>\<open>Collect\<close>, _) $ T) = dest_abstuple T
| bexp_tr' t = t;
(* com_tr' *)
fun mk_assign f =
let
val (vs, ts) = mk_vts f;
val (ch, which) = find_ch (vs ~~ ts) (length vs - 1) (rev vs);
in
if ch
then Syntax.const \<^syntax_const>\<open>_assign\<close> $ fst which $ snd which
else Syntax.const \<^const_syntax>\<open>annskip\<close>
end;
fun com_tr' (Const (\<^const_syntax>\<open>Basic\<close>, _) $ f) =
if is_f f then mk_assign f
else Syntax.const \<^const_syntax>\<open>Basic\<close> $ f
| com_tr' (Const (\<^const_syntax>\<open>Seq\<close>,_) $ c1 $ c2) =
Syntax.const \<^const_syntax>\<open>Seq\<close> $ com_tr' c1 $ com_tr' c2
| com_tr' (Const (\<^const_syntax>\<open>Cond\<close>, _) $ b $ c1 $ c2) =
Syntax.const \<^const_syntax>\<open>Cond\<close> $ bexp_tr' b $ com_tr' c1 $ com_tr' c2
| com_tr' (Const (\<^const_syntax>\<open>While\<close>, _) $ b $ I $ c) =
Syntax.const \<^const_syntax>\<open>While\<close> $ bexp_tr' b $ assn_tr' I $ com_tr' c
| com_tr' t = t;
in
fun spec_tr' syn [p, c, q] = Syntax.const syn $ assn_tr' p $ com_tr' c $ assn_tr' q;
end;
end;