--- a/src/HOL/Complex/ex/linreif.ML Wed Jul 02 07:11:57 2008 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,118 +0,0 @@
-(* ID: $Id$
- Author: Amine Chaieb, TU Muenchen
-
-The oracle for Mixed Real-Integer auantifier elimination
-based on the verified Code in ~/work/MIR/MIR.thy.
-*)
-
-structure ReflectedFerrack =
-struct
-
-open Ferrack;
-
-exception LINR;
-
-(* pseudo reification : term -> intterm *)
-val rT = Type ("RealDef.real",[]);
-val bT = HOLogic.boolT;
-val realC = @{term "RealDef.real :: int => real"};
-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 "0::real"} => C 1
- | Term.Bound i => Bound 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 "Int.number_of"},_)$t' => C (HOLogic.dest_numeral t')
- | Const (@{const_name "Int.number_of"},_)$t' => C (HOLogic.dest_numeral t')
- | _ => error ("num_of_term: unknown term " ^ Syntax.string_of_term_global Pure.thy t);
-
-(* pseudo reification : term -> fm *)
-fun fm_of_term vs t =
- case t of
- Const("True",_) => T
- | Const("False",_) => F
- | Const(@{const_name HOL.less},_)$t1$t2 => Lt (Sub (num_of_term vs t1,num_of_term vs t2))
- | Const(@{const_name HOL.less_eq},_)$t1$t2 => Le (Sub (num_of_term vs 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",_)$t' => Not(fm_of_term vs t')
- | Const("Ex",_)$Term.Abs(xn,xT,p) =>
- E(fm_of_term (map (fn(v,n) => (v,1+ n)) vs) p)
- | Const("All",_)$Term.Abs(xn,xT,p) =>
- A(fm_of_term (map (fn(v,n) => (v,1+ n)) vs) p)
- | _ => error ("fm_of_term : unknown term!" ^ Syntax.string_of_term_global Pure.thy t);
-
-
-fun start_vs t =
- let
- val fs = term_frees t
- in fs ~~ (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 => the (myassoc2 vs n)
- | Neg t' => Const(@{const_name HOL.uminus},rT --> rT)$(term_of_num vs t')
- | Add(t1,t2) => Const(@{const_name HOL.plus},[rT,rT] ---> rT)$
- (term_of_num vs t1)$(term_of_num vs t2)
- | Sub(t1,t2) => Const(@{const_name HOL.minus},[rT,rT] ---> rT)$
- (term_of_num vs t1)$(term_of_num vs t2)
- | Mul(i,t2) => Const(@{const_name HOL.times},[rT,rT] ---> rT)$
- (term_of_num vs (C i))$(term_of_num vs t2)
- | Cn(n,i,t) => term_of_num vs (Add (Mul(i,Bound n),t));
-
-fun term_of_fm vs t =
- case t of
- T => HOLogic.true_const
- | F => HOLogic.false_const
- | Lt t => Const(@{const_name HOL.less},[rT,rT] ---> bT)$
- (term_of_num vs t)$ rzero
- | Le t => Const(@{const_name HOL.less_eq},[rT,rT] ---> bT)$
- (term_of_num vs t)$ rzero
- | Gt t => Const(@{const_name HOL.less},[rT,rT] ---> bT)$
- rzero $(term_of_num vs t)
- | Ge t => Const(@{const_name HOL.less_eq},[rT,rT] ---> bT)$
- rzero $(term_of_num vs t)
- | Eq t => Const("op =",[rT,rT] ---> bT)$
- (term_of_num vs t)$ rzero
- | NEq t => term_of_fm vs (Not (Eq 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 linrqe_oracle thy t =
- let
- val vs = start_vs t
- in HOLogic.mk_Trueprop (HOLogic.mk_eq (t, term_of_fm vs (linrqe (fm_of_term vs t)))) end;
-
-end;