(* Title: HOL/SVC_Oracle.ML
ID: $Id$
Author: Lawrence C Paulson
Copyright 1999 University of Cambridge
Installing the oracle for SVC (Stanford Validity Checker)
The following code merely CALLS the oracle;
the soundness-critical functions are at HOL/Tools/svc_funcs.ML
Based upon the work of Søren T. Heilmann
*)
(*Generalize an Isabelle formula, replacing by Vars
all subterms not intelligible to SVC.*)
fun svc_abstract t =
let
(*The oracle's result is given to the subgoal using compose_tac because
its premises are matched against the assumptions rather than used
to make subgoals. Therefore , abstraction must copy the parameters
precisely and make them available to all generated Vars.*)
val params = Term.strip_all_vars t
and body = Term.strip_all_body t
val Us = map #2 params
val nPar = length params
val vname = ref "V_a"
val pairs = ref ([] : (term*term) list)
fun insert t =
let val T = fastype_of t
val v = Logic.combound (Var ((!vname,0), Us--->T), 0, nPar)
in vname := Symbol.bump_string (!vname);
pairs := (t, v) :: !pairs;
v
end;
fun replace t =
case t of
Free _ => t (*but not existing Vars, lest the names clash*)
| Bound _ => t
| _ => (case AList.lookup Pattern.aeconv (!pairs) t of
SOME v => v
| NONE => insert t)
(*abstraction of a numeric literal*)
fun lit (t as Const("0", _)) = t
| lit (t as Const("1", _)) = t
| lit (t as Const("Numeral.number_of", _) $ w) = t
| lit t = replace t
(*abstraction of a real/rational expression*)
fun rat ((c as Const("HOL.plus", _)) $ x $ y) = c $ (rat x) $ (rat y)
| rat ((c as Const("HOL.minus", _)) $ x $ y) = c $ (rat x) $ (rat y)
| rat ((c as Const("HOL.divide", _)) $ x $ y) = c $ (rat x) $ (rat y)
| rat ((c as Const("HOL.times", _)) $ x $ y) = c $ (rat x) $ (rat y)
| rat ((c as Const("HOL.uminus", _)) $ x) = c $ (rat x)
| rat t = lit t
(*abstraction of an integer expression: no div, mod*)
fun int ((c as Const("HOL.plus", _)) $ x $ y) = c $ (int x) $ (int y)
| int ((c as Const("HOL.minus", _)) $ x $ y) = c $ (int x) $ (int y)
| int ((c as Const("HOL.times", _)) $ x $ y) = c $ (int x) $ (int y)
| int ((c as Const("HOL.uminus", _)) $ x) = c $ (int x)
| int t = lit t
(*abstraction of a natural number expression: no minus*)
fun nat ((c as Const("HOL.plus", _)) $ x $ y) = c $ (nat x) $ (nat y)
| nat ((c as Const("HOL.times", _)) $ x $ y) = c $ (nat x) $ (nat y)
| nat ((c as Const("Suc", _)) $ x) = c $ (nat x)
| nat t = lit t
(*abstraction of a relation: =, <, <=*)
fun rel (T, c $ x $ y) =
if T = HOLogic.realT then c $ (rat x) $ (rat y)
else if T = HOLogic.intT then c $ (int x) $ (int y)
else if T = HOLogic.natT then c $ (nat x) $ (nat y)
else if T = HOLogic.boolT then c $ (fm x) $ (fm y)
else replace (c $ x $ y) (*non-numeric comparison*)
(*abstraction of a formula*)
and fm ((c as Const("op &", _)) $ p $ q) = c $ (fm p) $ (fm q)
| fm ((c as Const("op |", _)) $ p $ q) = c $ (fm p) $ (fm q)
| fm ((c as Const("op -->", _)) $ p $ q) = c $ (fm p) $ (fm q)
| fm ((c as Const("Not", _)) $ p) = c $ (fm p)
| fm ((c as Const("True", _))) = c
| fm ((c as Const("False", _))) = c
| fm (t as Const("op =", Type ("fun", [T,_])) $ _ $ _) = rel (T, t)
| fm (t as Const("Orderings.less", Type ("fun", [T,_])) $ _ $ _) = rel (T, t)
| fm (t as Const("Orderings.less_eq", Type ("fun", [T,_])) $ _ $ _) = rel (T, t)
| fm t = replace t
(*entry point, and abstraction of a meta-formula*)
fun mt ((c as Const("Trueprop", _)) $ p) = c $ (fm p)
| mt ((c as Const("==>", _)) $ p $ q) = c $ (mt p) $ (mt q)
| mt t = fm t (*it might be a formula*)
in (list_all (params, mt body), !pairs) end;
(*Present the entire subgoal to the oracle, assumptions and all, but possibly
abstracted. Use via compose_tac, which performs no lifting but will
instantiate variables.*)
fun svc_tac i st =
let
val (abs_goal, _) = svc_abstract (Logic.get_goal (Thm.prop_of st) i)
val th = svc_oracle (Thm.theory_of_thm st) abs_goal
in compose_tac (false, th, 0) i st end
handle TERM _ => no_tac st;
(*check if user has SVC installed*)
fun svc_enabled () = getenv "SVC_HOME" <> "";
fun if_svc_enabled f x = if svc_enabled () then f x else ();