(* Title: HOL/IMP/Hoare.thy
ID: $Id$
Author: Tobias Nipkow
Copyright 1995 TUM
Semantic embedding of Hoare logic
*)
Hoare = Denotation +
consts
spec :: "[state=>bool,com,state=>bool] => bool"
(* syntax "@spec" :: "[bool,com,bool] => bool" *)
("{{(1_)}}/ (_)/ {{(1_)}}" 10)
defs
spec_def "spec P c Q == !s t. <s,t> : C(c) --> P s --> Q t"
end
(* Pretty-printing of assertions.
Not very helpful as long as programs are not pretty-printed.
ML
local open Syntax
fun is_loc a = let val ch = hd(explode a)
in ord "A" <= ord ch andalso ord ch <= ord "Z" end;
fun tr(s$t,i) = tr(s,i)$tr(t,i)
| tr(Abs(x,T,u),i) = Abs(x,T,tr(u,i+1))
| tr(t as Free(a,T),i) = if is_loc a then Bound(i) $ free(a) else t
| tr(t,_) = t;
fun cond_tr(p) = Abs("",dummyT,tr(p,0))
fun spec_tr[p,c,q] = const"spec" $ cond_tr p $ c $ cond_tr q;
fun tr'(t as (Bound j $ (u as Free(a,_))),i) = if i=j then u else t
| tr'(s$t,i) = tr'(s,i)$tr'(t,i)
| tr'(Abs(x,T,u),i) = Abs(x,T,tr'(u,i+1))
| tr'(t,_) = t;
fun spec_tr'[Abs(_,_,p),c,Abs(_,_,q)] =
const"@spec" $ tr'(p,0) $ c $ tr'(q,0);
in
val parse_translation = [("@spec", spec_tr)];
val print_translation = [("spec", spec_tr')];
end
*)