author | wenzelm |
Thu, 27 Mar 2008 14:41:07 +0100 | |
changeset 26423 | 8408edac8f6b |
parent 25938 | 2c1c0e989615 |
child 26939 | 1035c89b4c02 |
permissions | -rw-r--r-- |
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(* ID: $Id$ |
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Author: Amine Chaieb, TU Muenchen |
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The oracle for Mixed Real-Integer auantifier elimination |
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based on the verified Code in ~/work/MIR/MIR.thy. |
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*) |
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structure ReflectedFerrack = |
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struct |
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open Ferrack; |
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exception LINR; |
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(* pseudo reification : term -> intterm *) |
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val rT = Type ("RealDef.real",[]); |
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val bT = HOLogic.boolT; |
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val realC = @{term "RealDef.real :: int => real"}; |
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val rzero = @{term "0 :: real"}; |
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fun num_of_term vs t = case t |
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of Free(xn,xT) => (case AList.lookup (op =) vs t of |
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NONE => error "Variable not found in the list!" |
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| SOME n => Bound n) |
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| Const("RealDef.real",_)$ @{term "0::int"} => C 0 |
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| Const("RealDef.real",_)$ @{term "1::int"} => C 1 |
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| @{term "0::real"} => C 0 |
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| @{term "0::real"} => C 1 |
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| Term.Bound i => Bound i |
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| Const (@{const_name "HOL.uminus"},_)$t' => Neg (num_of_term vs t') |
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| Const (@{const_name "HOL.plus"},_)$t1$t2 => Add (num_of_term vs t1,num_of_term vs t2) |
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| Const (@{const_name "HOL.minus"},_)$t1$t2 => Sub (num_of_term vs t1,num_of_term vs t2) |
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| Const (@{const_name "HOL.times"},_)$t1$t2 => (case (num_of_term vs t1) of C i => |
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Mul (i,num_of_term vs t2) |
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| _ => error "num_of_term: unsupported Multiplication") |
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| Const("RealDef.real",_) $ Const (@{const_name "Int.number_of"},_)$t' => C (HOLogic.dest_numeral t') |
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| Const (@{const_name "Int.number_of"},_)$t' => C (HOLogic.dest_numeral t') |
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| _ => error ("num_of_term: unknown term " ^ Sign.string_of_term CPure.thy t); |
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(* pseudo reification : term -> fm *) |
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fun fm_of_term vs t = |
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case t of |
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Const("True",_) => T |
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| Const("False",_) => F |
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| Const(@{const_name HOL.less},_)$t1$t2 => Lt (Sub (num_of_term vs t1,num_of_term vs t2)) |
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| Const(@{const_name HOL.less_eq},_)$t1$t2 => Le (Sub (num_of_term vs t1,num_of_term vs t2)) |
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| Const("op =",eqT)$t1$t2 => |
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if (domain_type eqT = rT) |
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then Eq (Sub (num_of_term vs t1,num_of_term vs t2)) |
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else Iff(fm_of_term vs t1,fm_of_term vs t2) |
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| Const("op &",_)$t1$t2 => And(fm_of_term vs t1,fm_of_term vs t2) |
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| Const("op |",_)$t1$t2 => Or(fm_of_term vs t1,fm_of_term vs t2) |
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| Const("op -->",_)$t1$t2 => Imp(fm_of_term vs t1,fm_of_term vs t2) |
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| Const("Not",_)$t' => Not(fm_of_term vs t') |
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| Const("Ex",_)$Term.Abs(xn,xT,p) => |
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E(fm_of_term (map (fn(v,n) => (v,1+ n)) vs) p) |
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| Const("All",_)$Term.Abs(xn,xT,p) => |
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A(fm_of_term (map (fn(v,n) => (v,1+ n)) vs) p) |
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| _ => error ("fm_of_term : unknown term!" ^ Sign.string_of_term CPure.thy t); |
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fun start_vs t = |
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let |
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val fs = term_frees t |
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in fs ~~ (0 upto (length fs - 1)) end; |
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(* transform num and fm back to terms *) |
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fun myassoc2 l v = |
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case l of |
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[] => NONE |
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| (x,v')::xs => if v = v' then SOME x |
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else myassoc2 xs v; |
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fun term_of_num vs t = |
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case t of |
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C i => realC $ (HOLogic.mk_number HOLogic.intT i) |
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| Bound n => the (myassoc2 vs n) |
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| Neg t' => Const(@{const_name HOL.uminus},rT --> rT)$(term_of_num vs t') |
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| Add(t1,t2) => Const(@{const_name HOL.plus},[rT,rT] ---> rT)$ |
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(term_of_num vs t1)$(term_of_num vs t2) |
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| Sub(t1,t2) => Const(@{const_name HOL.minus},[rT,rT] ---> rT)$ |
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(term_of_num vs t1)$(term_of_num vs t2) |
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| Mul(i,t2) => Const(@{const_name HOL.times},[rT,rT] ---> rT)$ |
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(term_of_num vs (C i))$(term_of_num vs t2) |
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| Cn(n,i,t) => term_of_num vs (Add (Mul(i,Bound n),t)); |
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fun term_of_fm vs t = |
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case t of |
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T => HOLogic.true_const |
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| F => HOLogic.false_const |
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| Lt t => Const(@{const_name HOL.less},[rT,rT] ---> bT)$ |
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(term_of_num vs t)$ rzero |
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| Le t => Const(@{const_name HOL.less_eq},[rT,rT] ---> bT)$ |
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(term_of_num vs t)$ rzero |
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| Gt t => Const(@{const_name HOL.less},[rT,rT] ---> bT)$ |
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rzero $(term_of_num vs t) |
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| Ge t => Const(@{const_name HOL.less_eq},[rT,rT] ---> bT)$ |
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rzero $(term_of_num vs t) |
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| Eq t => Const("op =",[rT,rT] ---> bT)$ |
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(term_of_num vs t)$ rzero |
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| NEq t => term_of_fm vs (Not (Eq t)) |
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| Not t' => HOLogic.Not$(term_of_fm vs t') |
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| And(t1,t2) => HOLogic.conj$(term_of_fm vs t1)$(term_of_fm vs t2) |
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| Or(t1,t2) => HOLogic.disj$(term_of_fm vs t1)$(term_of_fm vs t2) |
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| Imp(t1,t2) => HOLogic.imp$(term_of_fm vs t1)$(term_of_fm vs t2) |
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| Iff(t1,t2) => (HOLogic.eq_const bT)$(term_of_fm vs t1)$ |
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(term_of_fm vs t2) |
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| _ => error "If this is raised, Isabelle/HOL or generate_code is inconsistent!"; |
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(* The oracle *) |
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fun linrqe_oracle thy t = |
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let |
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val vs = start_vs t |
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in HOLogic.mk_Trueprop (HOLogic.mk_eq (t, term_of_fm vs (linrqe (fm_of_term vs t)))) end; |
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end; |