author | haftmann |
Fri, 24 Aug 2007 14:14:20 +0200 | |
changeset 24423 | ae9cd0e92423 |
parent 23881 | 851c74f1bb69 |
child 25919 | 8b1c0d434824 |
permissions | -rw-r--r-- |
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(* Title: HOL/Complex/ex/mireif.ML |
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ID: $Id$ |
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Author: Amine Chaieb, TU Muenchen |
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Oracle for Mixed Real-Integer auantifier elimination |
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based on the verified code in HOL/Complex/ex/MIR.thy. |
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*) |
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structure ReflectedMir = |
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struct |
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open Mir; |
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exception MIR; |
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fun num_of_term vs t = |
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case t of |
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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 "1::real"} => C 1 |
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| Term.Bound i => Bound (nat 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$t2 => |
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(case (num_of_term vs t1) of C i => |
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Mul (i,num_of_term vs t2) |
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| _ => error "num_of_term: unsupported Multiplication") |
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| Const("RealDef.real",_)$ (Const (@{const_name "RComplete.floor"},_)$ t') => Floor (num_of_term vs t') |
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| Const("RealDef.real",_)$ (Const (@{const_name "RComplete.ceiling"},_)$ t') => Neg(Floor (Neg (num_of_term vs t'))) |
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| Const("RealDef.real",_) $ Const (@{const_name "Numeral.number_of"},_)$t' => C (HOLogic.dest_numeral t') |
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| Const (@{const_name "Numeral.number_of"},_)$t' => C (HOLogic.dest_numeral t') |
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| _ => error ("num_of_term: unknown term " ^ (Display.raw_string_of_term 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 (@{const_name "MIR.rdvd"},_ )$ (Const("RealDef.real",_) $ (Const(@{const_name "Numeral.number_of"},_)$t1))$t2 => |
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Dvd (HOLogic.dest_numeral t1, num_of_term vs t2) |
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| Const("op =",eqT)$t1$t2 => |
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if (domain_type eqT = @{typ real}) |
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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",_)$t' => Not (fm_of_term vs t') |
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| Const("Ex",_)$Abs(xn,xT,p) => |
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E (fm_of_term (map (fn (v, n) => (v, Suc n)) vs) p) |
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| Const("All",_)$Abs(xn,xT,p) => |
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A (fm_of_term (map (fn(v, n) => (v, Suc n)) vs) p) |
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| _ => error ("fm_of_term : unknown term!" ^ Display.raw_string_of_term t); |
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fun start_vs t = |
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let val fs = term_frees t |
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in fs ~~ map nat (0 upto (length fs - 1)) |
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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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val realC = @{term "real :: int => _"}; |
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val rzero = @{term "0::real"}; |
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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 => valOf (myassoc2 vs n) |
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| Neg (Floor (Neg t')) => realC $ (@{term "ceiling"} $ term_of_num vs t') |
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| Neg t' => @{term "uminus:: real => _"} $ term_of_num vs t' |
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| Add(t1,t2) => @{term "op +:: real => _"} $ term_of_num vs t1 $ term_of_num vs t2 |
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| Sub(t1,t2) => @{term "op -:: real => _"} $ term_of_num vs t1 $ term_of_num vs t2 |
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| Mul(i,t2) => @{term "op -:: real => _"} $ term_of_num vs (C i) $ term_of_num vs t2 |
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| Floor t => realC $ (@{term "floor"} $ term_of_num vs t) |
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| Cn(n,i,t) => term_of_num vs (Add(Mul(i,Bound n),t)) |
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| Cf(c,t,s) => term_of_num vs (Add(Mul(c,Floor t),s)); |
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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 => @{term "op <:: real => _"} $ term_of_num vs t $ rzero |
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| Le t => @{term "op <=:: real => _"} $ term_of_num vs t $ rzero |
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| Gt t => @{term "op <:: real => _"}$ rzero $ term_of_num vs t |
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| Ge t => @{term "op <=:: real => _"} $ rzero $ term_of_num vs t |
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| Eq t => @{term "op = :: real => _"}$ term_of_num vs t $ rzero |
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| NEq t => term_of_fm vs (Not (Eq t)) |
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| NDvd (i,t) => term_of_fm vs (Not (Dvd (i,t))) |
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| Dvd (i,t) => @{term "op rdvd"} $ term_of_num vs (C i) $ term_of_num vs 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.mk_eq (term_of_fm vs t1, 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 mircfr_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 (mircfrqe (fm_of_term vs t)))) |
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end; |
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fun mirlfr_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 (mirlfrqe (fm_of_term vs t)))) |
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end; |
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end; |