--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Complex/ex/mireif.ML Tue Jun 05 20:44:12 2007 +0200
@@ -0,0 +1,131 @@
+(*
+ The oracle for Mixed Real-Integer auantifier elimination
+ based on the verified Code in ~/work/MIR/MIR.thy
+*)
+
+structure ReflectedMir =
+struct
+
+open Mir;
+
+exception MIR;
+
+(* pseudo reification : term -> intterm *)
+val iT = HOLogic.intT;
+val rT = Type ("RealDef.real",[]);
+val bT = HOLogic.boolT;
+val realC = @{term "real :: int => _"};
+val floorC = @{term "floor"};
+val ceilC = @{term "ceiling"};
+val rzero = @{term "0::real"};
+
+fun num_of_term vs t =
+ case t of
+ Free(xn,xT) => (case AList.lookup (op =) vs t of
+ NONE => error "Variable not found in the list!!"
+ | SOME n => Bound n)
+ | Const("RealDef.real",_)$ @{term "0::int"} => C 0
+ | Const("RealDef.real",_)$ @{term "1::int"} => C 1
+ | @{term "0::real"} => C 0
+ | @{term "1::real"} => C 1
+ | Term.Bound i => Bound (nat (IntInf.fromInt i))
+ | Const(@{const_name "HOL.uminus"},_)$t' => Neg (num_of_term vs t')
+ | Const (@{const_name "HOL.plus"},_)$t1$t2 => Add (num_of_term vs t1,num_of_term vs t2)
+ | Const (@{const_name "HOL.minus"},_)$t1$t2 => Sub (num_of_term vs t1,num_of_term vs t2)
+ | Const (@{const_name "HOL.times"},_)$t1$t2 =>
+ (case (num_of_term vs t1) of C i =>
+ Mul (i,num_of_term vs t2)
+ | _ => error "num_of_term: unsupported Multiplication")
+ | Const("RealDef.real",_)$ (Const (@{const_name "RComplete.floor"},_)$ t') => Floor (num_of_term vs t')
+ | Const("RealDef.real",_)$ (Const (@{const_name "RComplete.ceiling"},_)$ t') => Neg(Floor (Neg (num_of_term vs t')))
+ | Const("RealDef.real",_) $ Const (@{const_name "Numeral.number_of"},_)$t' => C (HOLogic.dest_numeral t')
+ | Const (@{const_name "Numeral.number_of"},_)$t' => C (HOLogic.dest_numeral t')
+ | _ => error ("num_of_term: unknown term " ^ (Display.raw_string_of_term t));
+
+
+(* pseudo reification : term -> fm *)
+fun fm_of_term vs t =
+ case t of
+ Const("True",_) => T
+ | Const("False",_) => F
+ | Const(@{const_name "Orderings.less"},_)$t1$t2 => Lt (Sub (num_of_term vs t1,num_of_term vs t2))
+ | Const(@{const_name "Orderings.less_eq"},_)$t1$t2 => Le (Sub (num_of_term vs t1,num_of_term vs t2))
+ | Const (@{const_name "MIR.op rdvd"},_)$(Const("RealDef.real",_)$(Const(@{const_name "Numeral.number_of"},_)$t1))$t2 =>
+ Dvd(HOLogic.dest_numeral t1,num_of_term vs t2)
+ | Const("op =",eqT)$t1$t2 =>
+ if (domain_type eqT = rT)
+ then Eq (Sub (num_of_term vs t1,num_of_term vs t2))
+ else Iff(fm_of_term vs t1,fm_of_term vs t2)
+ | Const("op &",_)$t1$t2 => And(fm_of_term vs t1,fm_of_term vs t2)
+ | Const("op |",_)$t1$t2 => Or(fm_of_term vs t1,fm_of_term vs t2)
+ | Const("op -->",_)$t1$t2 => Imp(fm_of_term vs t1,fm_of_term vs t2)
+ | Const("Not",_)$t' => NOT(fm_of_term vs t')
+ | Const("Ex",_)$Abs(xn,xT,p) =>
+ E(fm_of_term (map (fn(v,n) => (v,Suc n)) vs) p)
+ | Const("All",_)$Abs(xn,xT,p) =>
+ A(fm_of_term (map (fn(v,n) => (v,Suc n)) vs) p)
+ | _ => error ("fm_of_term : unknown term!" ^ (Display.raw_string_of_term t));
+
+fun zip [] [] = []
+ | zip (x::xs) (y::ys) = (x,y)::(zip xs ys);
+
+
+fun start_vs t =
+ let val fs = term_frees t
+ in zip fs (map (nat o IntInf.fromInt) (0 upto (length fs - 1)))
+ end ;
+
+(* transform num and fm back to terms *)
+
+fun myassoc2 l v =
+ case l of
+ [] => NONE
+ | (x,v')::xs => if v = v' then SOME x
+ else myassoc2 xs v;
+
+fun term_of_num vs t =
+ case t of
+ C i => realC $ (HOLogic.mk_number HOLogic.intT i)
+ | Bound n => valOf (myassoc2 vs n)
+ | Neg (Floor (Neg t')) => realC $ (ceilC $ (term_of_num vs t'))
+ | Neg t' => @{term "uminus:: real => _"} $ term_of_num vs t'
+ | Add(t1,t2) => @{term "op +:: real => _"} $ term_of_num vs t1 $ term_of_num vs t2
+ | Sub(t1,t2) => @{term "op -:: real => _"} $ term_of_num vs t1 $ term_of_num vs t2
+ | Mul(i,t2) => @{term "op -:: real => _"} $ term_of_num vs (C i) $ term_of_num vs t2
+ | Floor t => realC $ (floorC $ (term_of_num vs t))
+ | CN(n,i,t) => term_of_num vs (Add(Mul(i,Bound n),t))
+ | CF(c,t,s) => term_of_num vs (Add(Mul(c,Floor t),s));
+
+fun term_of_fm vs t =
+ case t of
+ T => HOLogic.true_const
+ | F => HOLogic.false_const
+ | Lt t => @{term "op <:: real => _"} $ term_of_num vs t $ rzero
+ | Le t => @{term "op <=:: real => _"} $ term_of_num vs t $ rzero
+ | Gt t => @{term "op <:: real => _"}$ rzero $ term_of_num vs t
+ | Ge t => @{term "op <=:: real => _"} $ rzero $ term_of_num vs t
+ | Eq t => @{term "op = :: real => _"}$ term_of_num vs t $ rzero
+ | NEq t => term_of_fm vs (NOT (Eq t))
+ | NDvd (i,t) => term_of_fm vs (NOT (Dvd (i,t)))
+ | Dvd (i,t) => @{term "op rdvd"} $ term_of_num vs (C i) $ term_of_num vs t
+ | NOT t' => HOLogic.Not$(term_of_fm vs t')
+ | And(t1,t2) => HOLogic.conj $ term_of_fm vs t1 $ term_of_fm vs t2
+ | Or(t1,t2) => HOLogic.disj $ term_of_fm vs t1 $ term_of_fm vs t2
+ | Imp(t1,t2) => HOLogic.imp $ term_of_fm vs t1 $ term_of_fm vs t2
+ | Iff(t1,t2) => HOLogic.eq_const bT $ term_of_fm vs t1 $ term_of_fm vs t2
+ | _ => error "If this is raised, Isabelle/HOL or generate_code is inconsistent!";
+
+(* The oracle *)
+
+fun mircfr_oracle thy t =
+ let
+ val vs = start_vs t
+ in HOLogic.mk_Trueprop (HOLogic.mk_eq(t, term_of_fm vs (mircfrqe (fm_of_term vs t))))
+ end;
+
+fun mirlfr_oracle thy t =
+ let
+ val vs = start_vs t
+ in HOLogic.mk_Trueprop (HOLogic.mk_eq(t, term_of_fm vs (mirlfrqe (fm_of_term vs t))))
+ end;
+end;