neuper@37954
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(* some tests are based on specficially simple scripts etc.
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Author: Walther Neuper 2003
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(c) due to copyright terms
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*)
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theory Test imports Atools + Rational + Root + Poly +
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consts
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(*"cancel":: [real, real] => real (infixl "'/'/'/" 70) ...divide 2002*)
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Expand'_binomtest
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:: "['y,
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'y] => 'y"
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("((Script Expand'_binomtest (_ =))//
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(_))" 9)
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Solve'_univar'_err
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:: "[bool,real,bool,
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bool list] => bool list"
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("((Script Solve'_univar'_err (_ _ _ =))//
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(_))" 9)
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Solve'_linear
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:: "[bool,real,
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bool list] => bool list"
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("((Script Solve'_linear (_ _ =))//
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(_))" 9)
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(*17.9.02 aus SqRoot.thy------------------------------vvv---*)
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"is'_root'_free" :: 'a => bool ("is'_root'_free _" 10)
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"contains'_root" :: 'a => bool ("contains'_root _" 10)
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Solve'_root'_equation
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:: "[bool,real,
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bool list] => bool list"
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("((Script Solve'_root'_equation (_ _ =))//
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(_))" 9)
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Solve'_plain'_square
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:: "[bool,real,
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bool list] => bool list"
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("((Script Solve'_plain'_square (_ _ =))//
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(_))" 9)
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Norm'_univar'_equation
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:: "[bool,real,
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bool] => bool"
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("((Script Norm'_univar'_equation (_ _ =))//
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(_))" 9)
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STest'_simplify
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:: "['z,
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'z] => 'z"
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("((Script STest'_simplify (_ =))//
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(_))" 9)
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(*17.9.02 aus SqRoot.thy------------------------------^^^---*)
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axioms (*TODO: prove as theorems*)
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radd_mult_distrib2 "(k::real) * (m + n) = k * m + k * n"
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rdistr_right_assoc "(k::real) + l * n + m * n = k + (l + m) * n"
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rdistr_right_assoc_p "l * n + (m * n + (k::real)) = (l + m) * n + k"
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rdistr_div_right "((k::real) + l) / n = k / n + l / n"
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rcollect_right
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"[| l is_const; m is_const |] ==> (l::real)*n + m*n = (l + m) * n"
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rcollect_one_left
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"m is_const ==> (n::real) + m * n = (1 + m) * n"
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rcollect_one_left_assoc
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"m is_const ==> (k::real) + n + m * n = k + (1 + m) * n"
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rcollect_one_left_assoc_p
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"m is_const ==> n + (m * n + (k::real)) = (1 + m) * n + k"
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rtwo_of_the_same "a + a = 2 * a"
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rtwo_of_the_same_assoc "(x + a) + a = x + 2 * a"
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rtwo_of_the_same_assoc_p"a + (a + x) = 2 * a + x"
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rcancel_den "not(a=0) ==> a * (b / a) = b"
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rcancel_const "[| a is_const; b is_const |] ==> a*(x/b) = a/b*x"
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rshift_nominator "(a::real) * b / c = a / c * b"
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exp_pow "(a ^^^ b) ^^^ c = a ^^^ (b * c)"
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rsqare "(a::real) * a = a ^^^ 2"
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power_1 "(a::real) ^^^ 1 = a"
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rbinom_power_2 "((a::real) + b)^^^ 2 = a^^^ 2 + 2*a*b + b^^^ 2"
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rmult_1 "1 * k = (k::real)"
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rmult_1_right "k * 1 = (k::real)"
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rmult_0 "0 * k = (0::real)"
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rmult_0_right "k * 0 = (0::real)"
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radd_0 "0 + k = (k::real)"
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radd_0_right "k + 0 = (k::real)"
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radd_real_const_eq
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"[| a is_const; c is_const; d is_const |] ==> a/d + c/d = (a+c)/(d::real)"
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radd_real_const
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"[| a is_const; b is_const; c is_const; d is_const |] ==> a/b + c/d = (a*d + b*c)/(b*(d::real))"
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(*for AC-operators*)
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radd_commute "(m::real) + (n::real) = n + m"
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radd_left_commute "(x::real) + (y + z) = y + (x + z)"
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radd_assoc "(m::real) + n + k = m + (n + k)"
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rmult_commute "(m::real) * n = n * m"
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rmult_left_commute "(x::real) * (y * z) = y * (x * z)"
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rmult_assoc "(m::real) * n * k = m * (n * k)"
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(*for equations: 'bdv' is a meta-constant*)
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risolate_bdv_add "((k::real) + bdv = m) = (bdv = m + (-1)*k)"
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risolate_bdv_mult_add "((k::real) + n*bdv = m) = (n*bdv = m + (-1)*k)"
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risolate_bdv_mult "((n::real) * bdv = m) = (bdv = m / n)"
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rnorm_equation_add
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"~(b =!= 0) ==> (a = b) = (a + (-1)*b = 0)"
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(*17.9.02 aus SqRoot.thy------------------------------vvv---*)
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root_ge0 "0 <= a ==> 0 <= sqrt a"
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(*should be dropped with better simplification in eval_rls ...*)
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root_add_ge0
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"[| 0 <= a; 0 <= b |] ==> (0 <= sqrt a + sqrt b) = True"
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root_ge0_1
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"[| 0<=a; 0<=b; 0<=c |] ==> (0 <= a * sqrt b + sqrt c) = True"
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root_ge0_2
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"[| 0<=a; 0<=b; 0<=c |] ==> (0 <= sqrt a + b * sqrt c) = True"
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rroot_square_inv "(sqrt a)^^^ 2 = a"
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rroot_times_root "sqrt a * sqrt b = sqrt(a*b)"
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rroot_times_root_assoc "(a * sqrt b) * sqrt c = a * sqrt(b*c)"
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rroot_times_root_assoc_p "sqrt b * (sqrt c * a)= sqrt(b*c) * a"
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(*for root-equations*)
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square_equation_left
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"[| 0 <= a; 0 <= b |] ==> (((sqrt a)=b)=(a=(b^^^ 2)))"
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square_equation_right
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"[| 0 <= a; 0 <= b |] ==> ((a=(sqrt b))=((a^^^ 2)=b))"
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(*causes frequently non-termination:*)
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square_equation
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"[| 0 <= a; 0 <= b |] ==> ((a=b)=((a^^^ 2)=b^^^ 2))"
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risolate_root_add "(a+ sqrt c = d) = ( sqrt c = d + (-1)*a)"
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risolate_root_mult "(a+b*sqrt c = d) = (b*sqrt c = d + (-1)*a)"
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risolate_root_div "(a * sqrt c = d) = ( sqrt c = d / a)"
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(*for polynomial equations of degree 2; linear case in RatArith*)
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mult_square "(a*bdv^^^2 = b) = (bdv^^^2 = b / a)"
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constant_square "(a + bdv^^^2 = b) = (bdv^^^2 = b + -1*a)"
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constant_mult_square "(a + b*bdv^^^2 = c) = (b*bdv^^^2 = c + -1*a)"
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square_equality
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"0 <= a ==> (x^^^2 = a) = ((x=sqrt a) | (x=-1*sqrt a))"
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square_equality_0
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"(x^^^2 = 0) = (x = 0)"
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(*isolate root on the LEFT hand side of the equation
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otherwise shuffling from left to right would not terminate*)
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rroot_to_lhs
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"is_root_free a ==> (a = sqrt b) = (a + (-1)*sqrt b = 0)"
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rroot_to_lhs_mult
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"is_root_free a ==> (a = c*sqrt b) = (a + (-1)*c*sqrt b = 0)"
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rroot_to_lhs_add_mult
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"is_root_free a ==> (a = d+c*sqrt b) = (a + (-1)*c*sqrt b = d)"
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(*17.9.02 aus SqRoot.thy------------------------------^^^---*)
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ML {*
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(** evaluation of numerals and predicates **)
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(*does a term contain a root ?*)
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fun eval_root_free (thmid:string) _ (t as (Const(op0,t0) $ arg)) thy =
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if strip_thy op0 <> "is'_root'_free"
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then raise error ("eval_root_free: wrong "^op0)
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else if const_in (strip_thy op0) arg
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then SOME (mk_thmid thmid ""
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((Syntax.string_of_term (thy2ctxt thy)) arg) "",
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Trueprop $ (mk_equality (t, false_as_term)))
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else SOME (mk_thmid thmid ""
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((Syntax.string_of_term (thy2ctxt thy)) arg) "",
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Trueprop $ (mk_equality (t, true_as_term)))
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| eval_root_free _ _ _ _ = NONE;
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(*does a term contain a root ?*)
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fun eval_contains_root (thmid:string) _
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(t as (Const("Test.contains'_root",t0) $ arg)) thy =
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if member op = (ids_of arg) "sqrt"
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then SOME (mk_thmid thmid ""
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((Syntax.string_of_term (thy2ctxt thy)) arg) "",
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Trueprop $ (mk_equality (t, true_as_term)))
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else SOME (mk_thmid thmid ""
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((Syntax.string_of_term (thy2ctxt thy)) arg) "",
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Trueprop $ (mk_equality (t, false_as_term)))
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| eval_contains_root _ _ _ _ = NONE;
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calclist':= overwritel (!calclist',
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[("is_root_free", ("Test.is'_root'_free",
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eval_root_free"#is_root_free_")),
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("contains_root", ("Test.contains'_root",
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eval_contains_root"#contains_root_"))
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]);
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(** term order **)
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fun term_order (_:subst) tu = (term_ordI [] tu = LESS);
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(** rule sets **)
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val testerls =
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Rls {id = "testerls", preconds = [], rew_ord = ("termlessI",termlessI),
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erls = e_rls, srls = Erls,
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calc = [],
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rules = [Thm ("refl",num_str refl),
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Thm ("le_refl",num_str le_refl),
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Thm ("radd_left_cancel_le",num_str radd_left_cancel_le),
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Thm ("not_true",num_str not_true),
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Thm ("not_false",num_str not_false),
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Thm ("and_true",and_true),
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Thm ("and_false",and_false),
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Thm ("or_true",or_true),
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Thm ("or_false",or_false),
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Thm ("and_commute",num_str and_commute),
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Thm ("or_commute",num_str or_commute),
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Calc ("Atools.is'_const",eval_const "#is_const_"),
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Calc ("Tools.matches",eval_matches ""),
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Calc ("op +",eval_binop "#add_"),
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Calc ("op *",eval_binop "#mult_"),
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Calc ("Atools.pow" ,eval_binop "#power_"),
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Calc ("op <",eval_equ "#less_"),
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Calc ("op <=",eval_equ "#less_equal_"),
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Calc ("Atools.ident",eval_ident "#ident_")],
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scr = Script ((term_of o the o (parse thy))
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"empty_script")
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}:rls;
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(*.for evaluation of conditions in rewrite rules.*)
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(*FIXXXXXXME 10.8.02: handle like _simplify*)
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val tval_rls =
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Rls{id = "tval_rls", preconds = [],
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rew_ord = ("sqrt_right",sqrt_right false (theory "Pure")),
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erls=testerls,srls = e_rls,
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calc=[],
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rules = [Thm ("refl",num_str refl),
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Thm ("le_refl",num_str le_refl),
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Thm ("radd_left_cancel_le",num_str radd_left_cancel_le),
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Thm ("not_true",num_str not_true),
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Thm ("not_false",num_str not_false),
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Thm ("and_true",and_true),
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Thm ("and_false",and_false),
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Thm ("or_true",or_true),
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Thm ("or_false",or_false),
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Thm ("and_commute",num_str and_commute),
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Thm ("or_commute",num_str or_commute),
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Thm ("real_diff_minus",num_str real_diff_minus),
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Thm ("root_ge0",num_str root_ge0),
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Thm ("root_add_ge0",num_str root_add_ge0),
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Thm ("root_ge0_1",num_str root_ge0_1),
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|
263 |
Thm ("root_ge0_2",num_str root_ge0_2),
|
neuper@37954
|
264 |
|
neuper@37954
|
265 |
Calc ("Atools.is'_const",eval_const "#is_const_"),
|
neuper@37954
|
266 |
Calc ("Test.is'_root'_free",eval_root_free "#is_root_free_"),
|
neuper@37954
|
267 |
Calc ("Tools.matches",eval_matches ""),
|
neuper@37954
|
268 |
Calc ("Test.contains'_root",
|
neuper@37954
|
269 |
eval_contains_root"#contains_root_"),
|
neuper@37954
|
270 |
|
neuper@37954
|
271 |
Calc ("op +",eval_binop "#add_"),
|
neuper@37954
|
272 |
Calc ("op *",eval_binop "#mult_"),
|
neuper@37954
|
273 |
Calc ("Root.sqrt",eval_sqrt "#sqrt_"),
|
neuper@37954
|
274 |
Calc ("Atools.pow" ,eval_binop "#power_"),
|
neuper@37954
|
275 |
|
neuper@37954
|
276 |
Calc ("op <",eval_equ "#less_"),
|
neuper@37954
|
277 |
Calc ("op <=",eval_equ "#less_equal_"),
|
neuper@37954
|
278 |
|
neuper@37954
|
279 |
Calc ("Atools.ident",eval_ident "#ident_")],
|
neuper@37954
|
280 |
scr = Script ((term_of o the o (parse thy))
|
neuper@37954
|
281 |
"empty_script")
|
neuper@37954
|
282 |
}:rls;
|
neuper@37954
|
283 |
|
neuper@37954
|
284 |
|
neuper@37954
|
285 |
ruleset' := overwritelthy thy (!ruleset',
|
neuper@37954
|
286 |
[("testerls", prep_rls testerls)
|
neuper@37954
|
287 |
]);
|
neuper@37954
|
288 |
|
neuper@37954
|
289 |
|
neuper@37954
|
290 |
(*make () dissappear*)
|
neuper@37954
|
291 |
val rearrange_assoc =
|
neuper@37954
|
292 |
Rls{id = "rearrange_assoc", preconds = [],
|
neuper@37954
|
293 |
rew_ord = ("e_rew_ord",e_rew_ord),
|
neuper@37954
|
294 |
erls = e_rls, srls = e_rls, calc = [], (*asm_thm=[],*)
|
neuper@37954
|
295 |
rules =
|
neuper@37954
|
296 |
[Thm ("sym_radd_assoc",num_str (radd_assoc RS sym)),
|
neuper@37954
|
297 |
Thm ("sym_rmult_assoc",num_str (rmult_assoc RS sym))],
|
neuper@37954
|
298 |
scr = Script ((term_of o the o (parse thy))
|
neuper@37954
|
299 |
"empty_script")
|
neuper@37954
|
300 |
}:rls;
|
neuper@37954
|
301 |
|
neuper@37954
|
302 |
val ac_plus_times =
|
neuper@37954
|
303 |
Rls{id = "ac_plus_times", preconds = [], rew_ord = ("term_order",term_order),
|
neuper@37954
|
304 |
erls = e_rls, srls = e_rls, calc = [], (*asm_thm=[],*)
|
neuper@37954
|
305 |
rules =
|
neuper@37954
|
306 |
[Thm ("radd_commute",radd_commute),
|
neuper@37954
|
307 |
Thm ("radd_left_commute",radd_left_commute),
|
neuper@37954
|
308 |
Thm ("radd_assoc",radd_assoc),
|
neuper@37954
|
309 |
Thm ("rmult_commute",rmult_commute),
|
neuper@37954
|
310 |
Thm ("rmult_left_commute",rmult_left_commute),
|
neuper@37954
|
311 |
Thm ("rmult_assoc",rmult_assoc)],
|
neuper@37954
|
312 |
scr = Script ((term_of o the o (parse thy))
|
neuper@37954
|
313 |
"empty_script")
|
neuper@37954
|
314 |
}:rls;
|
neuper@37954
|
315 |
|
neuper@37954
|
316 |
(*todo: replace by Rewrite("rnorm_equation_add",num_str rnorm_equation_add)*)
|
neuper@37954
|
317 |
val norm_equation =
|
neuper@37954
|
318 |
Rls{id = "norm_equation", preconds = [], rew_ord = ("e_rew_ord",e_rew_ord),
|
neuper@37954
|
319 |
erls = tval_rls, srls = e_rls, calc = [], (*asm_thm=[],*)
|
neuper@37954
|
320 |
rules = [Thm ("rnorm_equation_add",num_str rnorm_equation_add)
|
neuper@37954
|
321 |
],
|
neuper@37954
|
322 |
scr = Script ((term_of o the o (parse thy))
|
neuper@37954
|
323 |
"empty_script")
|
neuper@37954
|
324 |
}:rls;
|
neuper@37954
|
325 |
|
neuper@37954
|
326 |
(** rule sets **)
|
neuper@37954
|
327 |
|
neuper@37954
|
328 |
val STest_simplify = (* vv--- not changed to real by parse*)
|
neuper@37954
|
329 |
"Script STest_simplify (t_::'z) = " ^
|
neuper@37954
|
330 |
"(Repeat" ^
|
neuper@37954
|
331 |
" ((Try (Repeat (Rewrite real_diff_minus False))) @@ " ^
|
neuper@37954
|
332 |
" (Try (Repeat (Rewrite radd_mult_distrib2 False))) @@ " ^
|
neuper@37954
|
333 |
" (Try (Repeat (Rewrite rdistr_right_assoc False))) @@ " ^
|
neuper@37954
|
334 |
" (Try (Repeat (Rewrite rdistr_right_assoc_p False))) @@" ^
|
neuper@37954
|
335 |
" (Try (Repeat (Rewrite rdistr_div_right False))) @@ " ^
|
neuper@37954
|
336 |
" (Try (Repeat (Rewrite rbinom_power_2 False))) @@ " ^
|
neuper@37954
|
337 |
|
neuper@37954
|
338 |
" (Try (Repeat (Rewrite radd_commute False))) @@ " ^
|
neuper@37954
|
339 |
" (Try (Repeat (Rewrite radd_left_commute False))) @@ " ^
|
neuper@37954
|
340 |
" (Try (Repeat (Rewrite radd_assoc False))) @@ " ^
|
neuper@37954
|
341 |
" (Try (Repeat (Rewrite rmult_commute False))) @@ " ^
|
neuper@37954
|
342 |
" (Try (Repeat (Rewrite rmult_left_commute False))) @@ " ^
|
neuper@37954
|
343 |
" (Try (Repeat (Rewrite rmult_assoc False))) @@ " ^
|
neuper@37954
|
344 |
|
neuper@37954
|
345 |
" (Try (Repeat (Rewrite radd_real_const_eq False))) @@ " ^
|
neuper@37954
|
346 |
" (Try (Repeat (Rewrite radd_real_const False))) @@ " ^
|
neuper@37954
|
347 |
" (Try (Repeat (Calculate plus))) @@ " ^
|
neuper@37954
|
348 |
" (Try (Repeat (Calculate times))) @@ " ^
|
neuper@37954
|
349 |
" (Try (Repeat (Calculate divide_))) @@" ^
|
neuper@37954
|
350 |
" (Try (Repeat (Calculate power_))) @@ " ^
|
neuper@37954
|
351 |
|
neuper@37954
|
352 |
" (Try (Repeat (Rewrite rcollect_right False))) @@ " ^
|
neuper@37954
|
353 |
" (Try (Repeat (Rewrite rcollect_one_left False))) @@ " ^
|
neuper@37954
|
354 |
" (Try (Repeat (Rewrite rcollect_one_left_assoc False))) @@ " ^
|
neuper@37954
|
355 |
" (Try (Repeat (Rewrite rcollect_one_left_assoc_p False))) @@ " ^
|
neuper@37954
|
356 |
|
neuper@37954
|
357 |
" (Try (Repeat (Rewrite rshift_nominator False))) @@ " ^
|
neuper@37954
|
358 |
" (Try (Repeat (Rewrite rcancel_den False))) @@ " ^
|
neuper@37954
|
359 |
" (Try (Repeat (Rewrite rroot_square_inv False))) @@ " ^
|
neuper@37954
|
360 |
" (Try (Repeat (Rewrite rroot_times_root False))) @@ " ^
|
neuper@37954
|
361 |
" (Try (Repeat (Rewrite rroot_times_root_assoc_p False))) @@ " ^
|
neuper@37954
|
362 |
" (Try (Repeat (Rewrite rsqare False))) @@ " ^
|
neuper@37954
|
363 |
" (Try (Repeat (Rewrite power_1 False))) @@ " ^
|
neuper@37954
|
364 |
" (Try (Repeat (Rewrite rtwo_of_the_same False))) @@ " ^
|
neuper@37954
|
365 |
" (Try (Repeat (Rewrite rtwo_of_the_same_assoc_p False))) @@ " ^
|
neuper@37954
|
366 |
|
neuper@37954
|
367 |
" (Try (Repeat (Rewrite rmult_1 False))) @@ " ^
|
neuper@37954
|
368 |
" (Try (Repeat (Rewrite rmult_1_right False))) @@ " ^
|
neuper@37954
|
369 |
" (Try (Repeat (Rewrite rmult_0 False))) @@ " ^
|
neuper@37954
|
370 |
" (Try (Repeat (Rewrite rmult_0_right False))) @@ " ^
|
neuper@37954
|
371 |
" (Try (Repeat (Rewrite radd_0 False))) @@ " ^
|
neuper@37954
|
372 |
" (Try (Repeat (Rewrite radd_0_right False)))) " ^
|
neuper@37954
|
373 |
" t_)";
|
neuper@37954
|
374 |
|
neuper@37954
|
375 |
|
neuper@37954
|
376 |
(* expects * distributed over + *)
|
neuper@37954
|
377 |
val Test_simplify =
|
neuper@37954
|
378 |
Rls{id = "Test_simplify", preconds = [],
|
neuper@37954
|
379 |
rew_ord = ("sqrt_right",sqrt_right false (theory "Pure")),
|
neuper@37954
|
380 |
erls = tval_rls, srls = e_rls,
|
neuper@37954
|
381 |
calc=[(*since 040209 filled by prep_rls*)],
|
neuper@37954
|
382 |
(*asm_thm = [],*)
|
neuper@37954
|
383 |
rules = [
|
neuper@37954
|
384 |
Thm ("real_diff_minus",num_str real_diff_minus),
|
neuper@37954
|
385 |
Thm ("radd_mult_distrib2",num_str radd_mult_distrib2),
|
neuper@37954
|
386 |
Thm ("rdistr_right_assoc",num_str rdistr_right_assoc),
|
neuper@37954
|
387 |
Thm ("rdistr_right_assoc_p",num_str rdistr_right_assoc_p),
|
neuper@37954
|
388 |
Thm ("rdistr_div_right",num_str rdistr_div_right),
|
neuper@37954
|
389 |
Thm ("rbinom_power_2",num_str rbinom_power_2),
|
neuper@37954
|
390 |
|
neuper@37954
|
391 |
Thm ("radd_commute",num_str radd_commute),
|
neuper@37954
|
392 |
Thm ("radd_left_commute",num_str radd_left_commute),
|
neuper@37954
|
393 |
Thm ("radd_assoc",num_str radd_assoc),
|
neuper@37954
|
394 |
Thm ("rmult_commute",num_str rmult_commute),
|
neuper@37954
|
395 |
Thm ("rmult_left_commute",num_str rmult_left_commute),
|
neuper@37954
|
396 |
Thm ("rmult_assoc",num_str rmult_assoc),
|
neuper@37954
|
397 |
|
neuper@37954
|
398 |
Thm ("radd_real_const_eq",num_str radd_real_const_eq),
|
neuper@37954
|
399 |
Thm ("radd_real_const",num_str radd_real_const),
|
neuper@37954
|
400 |
(* these 2 rules are invers to distr_div_right wrt. termination.
|
neuper@37954
|
401 |
thus they MUST be done IMMEDIATELY before calc *)
|
neuper@37954
|
402 |
Calc ("op +", eval_binop "#add_"),
|
neuper@37954
|
403 |
Calc ("op *", eval_binop "#mult_"),
|
neuper@37954
|
404 |
Calc ("HOL.divide", eval_cancel "#divide_"),
|
neuper@37954
|
405 |
Calc ("Atools.pow", eval_binop "#power_"),
|
neuper@37954
|
406 |
|
neuper@37954
|
407 |
Thm ("rcollect_right",num_str rcollect_right),
|
neuper@37954
|
408 |
Thm ("rcollect_one_left",num_str rcollect_one_left),
|
neuper@37954
|
409 |
Thm ("rcollect_one_left_assoc",num_str rcollect_one_left_assoc),
|
neuper@37954
|
410 |
Thm ("rcollect_one_left_assoc_p",num_str rcollect_one_left_assoc_p),
|
neuper@37954
|
411 |
|
neuper@37954
|
412 |
Thm ("rshift_nominator",num_str rshift_nominator),
|
neuper@37954
|
413 |
Thm ("rcancel_den",num_str rcancel_den),
|
neuper@37954
|
414 |
Thm ("rroot_square_inv",num_str rroot_square_inv),
|
neuper@37954
|
415 |
Thm ("rroot_times_root",num_str rroot_times_root),
|
neuper@37954
|
416 |
Thm ("rroot_times_root_assoc_p",num_str rroot_times_root_assoc_p),
|
neuper@37954
|
417 |
Thm ("rsqare",num_str rsqare),
|
neuper@37954
|
418 |
Thm ("power_1",num_str power_1),
|
neuper@37954
|
419 |
Thm ("rtwo_of_the_same",num_str rtwo_of_the_same),
|
neuper@37954
|
420 |
Thm ("rtwo_of_the_same_assoc_p",num_str rtwo_of_the_same_assoc_p),
|
neuper@37954
|
421 |
|
neuper@37954
|
422 |
Thm ("rmult_1",num_str rmult_1),
|
neuper@37954
|
423 |
Thm ("rmult_1_right",num_str rmult_1_right),
|
neuper@37954
|
424 |
Thm ("rmult_0",num_str rmult_0),
|
neuper@37954
|
425 |
Thm ("rmult_0_right",num_str rmult_0_right),
|
neuper@37954
|
426 |
Thm ("radd_0",num_str radd_0),
|
neuper@37954
|
427 |
Thm ("radd_0_right",num_str radd_0_right)
|
neuper@37954
|
428 |
],
|
neuper@37954
|
429 |
scr = Script ((term_of o the o (parse thy)) "empty_script")
|
neuper@37954
|
430 |
(*since 040209 filled by prep_rls: STest_simplify*)
|
neuper@37954
|
431 |
}:rls;
|
neuper@37954
|
432 |
|
neuper@37954
|
433 |
|
neuper@37954
|
434 |
|
neuper@37954
|
435 |
|
neuper@37954
|
436 |
|
neuper@37954
|
437 |
(** rule sets **)
|
neuper@37954
|
438 |
|
neuper@37954
|
439 |
|
neuper@37954
|
440 |
|
neuper@37954
|
441 |
(*isolate the root in a root-equation*)
|
neuper@37954
|
442 |
val isolate_root =
|
neuper@37954
|
443 |
Rls{id = "isolate_root", preconds = [], rew_ord = ("e_rew_ord",e_rew_ord),
|
neuper@37954
|
444 |
erls=tval_rls,srls = e_rls, calc=[],(*asm_thm = [], *)
|
neuper@37954
|
445 |
rules = [Thm ("rroot_to_lhs",num_str rroot_to_lhs),
|
neuper@37954
|
446 |
Thm ("rroot_to_lhs_mult",num_str rroot_to_lhs_mult),
|
neuper@37954
|
447 |
Thm ("rroot_to_lhs_add_mult",num_str rroot_to_lhs_add_mult),
|
neuper@37954
|
448 |
Thm ("risolate_root_add",num_str risolate_root_add),
|
neuper@37954
|
449 |
Thm ("risolate_root_mult",num_str risolate_root_mult),
|
neuper@37954
|
450 |
Thm ("risolate_root_div",num_str risolate_root_div) ],
|
neuper@37954
|
451 |
scr = Script ((term_of o the o (parse thy))
|
neuper@37954
|
452 |
"empty_script")
|
neuper@37954
|
453 |
}:rls;
|
neuper@37954
|
454 |
|
neuper@37954
|
455 |
(*isolate the bound variable in an equation; 'bdv' is a meta-constant*)
|
neuper@37954
|
456 |
val isolate_bdv =
|
neuper@37954
|
457 |
Rls{id = "isolate_bdv", preconds = [], rew_ord = ("e_rew_ord",e_rew_ord),
|
neuper@37954
|
458 |
erls=tval_rls,srls = e_rls, calc=[],(*asm_thm = [], *)
|
neuper@37954
|
459 |
rules =
|
neuper@37954
|
460 |
[Thm ("risolate_bdv_add",num_str risolate_bdv_add),
|
neuper@37954
|
461 |
Thm ("risolate_bdv_mult_add",num_str risolate_bdv_mult_add),
|
neuper@37954
|
462 |
Thm ("risolate_bdv_mult",num_str risolate_bdv_mult),
|
neuper@37954
|
463 |
Thm ("mult_square",num_str mult_square),
|
neuper@37954
|
464 |
Thm ("constant_square",num_str constant_square),
|
neuper@37954
|
465 |
Thm ("constant_mult_square",num_str constant_mult_square)
|
neuper@37954
|
466 |
],
|
neuper@37954
|
467 |
scr = Script ((term_of o the o (parse thy))
|
neuper@37954
|
468 |
"empty_script")
|
neuper@37954
|
469 |
}:rls;
|
neuper@37954
|
470 |
|
neuper@37954
|
471 |
|
neuper@37954
|
472 |
|
neuper@37954
|
473 |
|
neuper@37954
|
474 |
(* association list for calculate_, calculate
|
neuper@37954
|
475 |
"op +" etc. not usable in scripts *)
|
neuper@37954
|
476 |
val calclist =
|
neuper@37954
|
477 |
[
|
neuper@37954
|
478 |
(*as Tools.ML*)
|
neuper@37954
|
479 |
("Vars" ,("Tools.Vars" ,eval_var "#Vars_")),
|
neuper@37954
|
480 |
("matches",("Tools.matches",eval_matches "#matches_")),
|
neuper@37954
|
481 |
("lhs" ,("Tools.lhs" ,eval_lhs "")),
|
neuper@37954
|
482 |
(*aus Atools.ML*)
|
neuper@37954
|
483 |
("PLUS" ,("op +" ,eval_binop "#add_")),
|
neuper@37954
|
484 |
("TIMES" ,("op *" ,eval_binop "#mult_")),
|
neuper@37954
|
485 |
("DIVIDE" ,("HOL.divide" ,eval_cancel "#divide_")),
|
neuper@37954
|
486 |
("POWER" ,("Atools.pow" ,eval_binop "#power_")),
|
neuper@37954
|
487 |
("is_const",("Atools.is'_const",eval_const "#is_const_")),
|
neuper@37954
|
488 |
("le" ,("op <" ,eval_equ "#less_")),
|
neuper@37954
|
489 |
("leq" ,("op <=" ,eval_equ "#less_equal_")),
|
neuper@37954
|
490 |
("ident" ,("Atools.ident",eval_ident "#ident_")),
|
neuper@37954
|
491 |
(*von hier (ehem.SqRoot*)
|
neuper@37954
|
492 |
("sqrt" ,("Root.sqrt" ,eval_sqrt "#sqrt_")),
|
neuper@37954
|
493 |
("Test.is_root_free",("is'_root'_free", eval_root_free"#is_root_free_")),
|
neuper@37954
|
494 |
("Test.contains_root",("contains'_root",
|
neuper@37954
|
495 |
eval_contains_root"#contains_root_"))
|
neuper@37954
|
496 |
];
|
neuper@37954
|
497 |
|
neuper@37954
|
498 |
ruleset' := overwritelthy thy (!ruleset',
|
neuper@37954
|
499 |
[("Test_simplify", prep_rls Test_simplify),
|
neuper@37954
|
500 |
("tval_rls", prep_rls tval_rls),
|
neuper@37954
|
501 |
("isolate_root", prep_rls isolate_root),
|
neuper@37954
|
502 |
("isolate_bdv", prep_rls isolate_bdv),
|
neuper@37954
|
503 |
("matches",
|
neuper@37954
|
504 |
prep_rls (append_rls "matches" testerls
|
neuper@37954
|
505 |
[Calc ("Tools.matches",eval_matches "#matches_")]))
|
neuper@37954
|
506 |
]);
|
neuper@37954
|
507 |
|
neuper@37954
|
508 |
(** problem types **)
|
neuper@37954
|
509 |
store_pbt
|
neuper@37954
|
510 |
(prep_pbt (theory "Test") "pbl_test" [] e_pblID
|
neuper@37954
|
511 |
(["test"],
|
neuper@37954
|
512 |
[],
|
neuper@37954
|
513 |
e_rls, NONE, []));
|
neuper@37954
|
514 |
store_pbt
|
neuper@37954
|
515 |
(prep_pbt (theory "Test") "pbl_test_equ" [] e_pblID
|
neuper@37954
|
516 |
(["equation","test"],
|
neuper@37954
|
517 |
[("#Given" ,["equality e_","solveFor v_"]),
|
neuper@37954
|
518 |
("#Where" ,["matches (?a = ?b) e_"]),
|
neuper@37954
|
519 |
("#Find" ,["solutions v_i_"])
|
neuper@37954
|
520 |
],
|
neuper@37954
|
521 |
assoc_rls "matches",
|
neuper@37954
|
522 |
SOME "solve (e_::bool, v_)", []));
|
neuper@37954
|
523 |
|
neuper@37954
|
524 |
store_pbt
|
neuper@37954
|
525 |
(prep_pbt (theory "Test") "pbl_test_uni" [] e_pblID
|
neuper@37954
|
526 |
(["univariate","equation","test"],
|
neuper@37954
|
527 |
[("#Given" ,["equality e_","solveFor v_"]),
|
neuper@37954
|
528 |
("#Where" ,["matches (?a = ?b) e_"]),
|
neuper@37954
|
529 |
("#Find" ,["solutions v_i_"])
|
neuper@37954
|
530 |
],
|
neuper@37954
|
531 |
assoc_rls "matches",
|
neuper@37954
|
532 |
SOME "solve (e_::bool, v_)", []));
|
neuper@37954
|
533 |
|
neuper@37954
|
534 |
store_pbt
|
neuper@37954
|
535 |
(prep_pbt (theory "Test") "pbl_test_uni_lin" [] e_pblID
|
neuper@37954
|
536 |
(["linear","univariate","equation","test"],
|
neuper@37954
|
537 |
[("#Given" ,["equality e_","solveFor v_"]),
|
neuper@37954
|
538 |
("#Where" ,["(matches ( v_ = 0) e_) | (matches ( ?b*v_ = 0) e_) |" ^
|
neuper@37954
|
539 |
"(matches (?a+v_ = 0) e_) | (matches (?a+?b*v_ = 0) e_) "]),
|
neuper@37954
|
540 |
("#Find" ,["solutions v_i_"])
|
neuper@37954
|
541 |
],
|
neuper@37954
|
542 |
assoc_rls "matches",
|
neuper@37954
|
543 |
SOME "solve (e_::bool, v_)", [["Test","solve_linear"]]));
|
neuper@37954
|
544 |
|
neuper@37954
|
545 |
(*25.8.01 ------
|
neuper@37954
|
546 |
store_pbt
|
neuper@37954
|
547 |
(prep_pbt (theory "Test")
|
neuper@37954
|
548 |
(["(theory "Test")"],
|
neuper@37954
|
549 |
[("#Given" ,"boolTestGiven g_"),
|
neuper@37954
|
550 |
("#Find" ,"boolTestFind f_")
|
neuper@37954
|
551 |
],
|
neuper@37954
|
552 |
[]));
|
neuper@37954
|
553 |
|
neuper@37954
|
554 |
store_pbt
|
neuper@37954
|
555 |
(prep_pbt (theory "Test")
|
neuper@37954
|
556 |
(["testeq","(theory "Test")"],
|
neuper@37954
|
557 |
[("#Given" ,"boolTestGiven g_"),
|
neuper@37954
|
558 |
("#Find" ,"boolTestFind f_")
|
neuper@37954
|
559 |
],
|
neuper@37954
|
560 |
[]));
|
neuper@37954
|
561 |
|
neuper@37954
|
562 |
|
neuper@37954
|
563 |
val ttt = (term_of o the o (parse (theory "Isac"))) "(matches ( v_ = 0) e_)";
|
neuper@37954
|
564 |
|
neuper@37954
|
565 |
------ 25.8.01*)
|
neuper@37954
|
566 |
|
neuper@37954
|
567 |
|
neuper@37954
|
568 |
(** methods **)
|
neuper@37954
|
569 |
store_met
|
neuper@37954
|
570 |
(prep_met (theory "Diff") "met_test" [] e_metID
|
neuper@37954
|
571 |
(["Test"],
|
neuper@37954
|
572 |
[],
|
neuper@37954
|
573 |
{rew_ord'="tless_true",rls'=Atools_erls,calc = [], srls = e_rls, prls=e_rls,
|
neuper@37954
|
574 |
crls=Atools_erls, nrls=e_rls(*,
|
neuper@37954
|
575 |
asm_rls=[],asm_thm=[]*)}, "empty_script"));
|
neuper@37954
|
576 |
(*
|
neuper@37954
|
577 |
store_met
|
neuper@37954
|
578 |
(prep_met (theory "Script")
|
neuper@37954
|
579 |
(e_metID,(*empty method*)
|
neuper@37954
|
580 |
[],
|
neuper@37954
|
581 |
{rew_ord'="e_rew_ord",rls'=tval_rls,srls=e_rls,prls=e_rls,calc=[],
|
neuper@37954
|
582 |
asm_rls=[],asm_thm=[]},
|
neuper@37954
|
583 |
"Undef"));*)
|
neuper@37954
|
584 |
store_met
|
neuper@37954
|
585 |
(prep_met (theory "Test") "met_test_solvelin" [] e_metID
|
neuper@37954
|
586 |
(["Test","solve_linear"]:metID,
|
neuper@37954
|
587 |
[("#Given" ,["equality e_","solveFor v_"]),
|
neuper@37954
|
588 |
("#Where" ,["matches (?a = ?b) e_"]),
|
neuper@37954
|
589 |
("#Find" ,["solutions v_i_"])
|
neuper@37954
|
590 |
],
|
neuper@37954
|
591 |
{rew_ord'="e_rew_ord",rls'=tval_rls,srls=e_rls,
|
neuper@37954
|
592 |
prls=assoc_rls "matches",
|
neuper@37954
|
593 |
calc=[],
|
neuper@37954
|
594 |
crls=tval_rls, nrls=Test_simplify},
|
neuper@37954
|
595 |
"Script Solve_linear (e_::bool) (v_::real)= " ^
|
neuper@37954
|
596 |
"(let e_ =" ^
|
neuper@37954
|
597 |
" Repeat" ^
|
neuper@37954
|
598 |
" (((Rewrite_Set_Inst [(bdv,v_::real)] isolate_bdv False) @@" ^
|
neuper@37954
|
599 |
" (Rewrite_Set Test_simplify False))) e_" ^
|
neuper@37954
|
600 |
" in [e_::bool])"
|
neuper@37954
|
601 |
)
|
neuper@37954
|
602 |
(*, prep_met (theory "Test") (*test for equations*)
|
neuper@37954
|
603 |
(["Test","testeq"]:metID,
|
neuper@37954
|
604 |
[("#Given" ,["boolTestGiven g_"]),
|
neuper@37954
|
605 |
("#Find" ,["boolTestFind f_"])
|
neuper@37954
|
606 |
],
|
neuper@37954
|
607 |
{rew_ord'="e_rew_ord",rls'="tval_rls",asm_rls=[],
|
neuper@37954
|
608 |
asm_thm=[("square_equation_left","")]},
|
neuper@37954
|
609 |
"Script Testeq (eq_::bool) = " ^
|
neuper@37954
|
610 |
"Repeat " ^
|
neuper@37954
|
611 |
" (let e_ = Try (Repeat (Rewrite rroot_square_inv False eq_)); " ^
|
neuper@37954
|
612 |
" e_ = Try (Repeat (Rewrite square_equation_left True e_)); " ^
|
neuper@37954
|
613 |
" e_ = Try (Repeat (Rewrite rmult_0 False e_)) " ^
|
neuper@37954
|
614 |
" in e_) Until (is_root_free e_)" (*deleted*)
|
neuper@37954
|
615 |
)
|
neuper@37954
|
616 |
, ---------27.4.02*)
|
neuper@37954
|
617 |
);
|
neuper@37954
|
618 |
|
neuper@37954
|
619 |
|
neuper@37954
|
620 |
|
neuper@37954
|
621 |
|
neuper@37954
|
622 |
ruleset' := overwritelthy thy (!ruleset',
|
neuper@37954
|
623 |
[("norm_equation", prep_rls norm_equation),
|
neuper@37954
|
624 |
("ac_plus_times", prep_rls ac_plus_times),
|
neuper@37954
|
625 |
("rearrange_assoc", prep_rls rearrange_assoc)
|
neuper@37954
|
626 |
]);
|
neuper@37954
|
627 |
|
neuper@37954
|
628 |
|
neuper@37954
|
629 |
fun bin_o (Const (op_,(Type ("fun",
|
neuper@37954
|
630 |
[Type (s2,[]),Type ("fun",
|
neuper@37954
|
631 |
[Type (s4,tl4),Type (s5,tl5)])])))) =
|
neuper@37954
|
632 |
if (s2=s4)andalso(s4=s5)then[op_]else[]
|
neuper@37954
|
633 |
| bin_o _ = [];
|
neuper@37954
|
634 |
|
neuper@37954
|
635 |
fun bin_op (t1 $ t2) = union op = (bin_op t1) (bin_op t2)
|
neuper@37954
|
636 |
| bin_op t = bin_o t;
|
neuper@37954
|
637 |
fun is_bin_op t = ((bin_op t)<>[]);
|
neuper@37954
|
638 |
|
neuper@37954
|
639 |
fun bin_op_arg1 ((Const (op_,(Type ("fun",
|
neuper@37954
|
640 |
[Type (s2,[]),Type ("fun",
|
neuper@37954
|
641 |
[Type (s4,tl4),Type (s5,tl5)])]))))$ arg1 $ arg2) =
|
neuper@37954
|
642 |
arg1;
|
neuper@37954
|
643 |
fun bin_op_arg2 ((Const (op_,(Type ("fun",
|
neuper@37954
|
644 |
[Type (s2,[]),Type ("fun",
|
neuper@37954
|
645 |
[Type (s4,tl4),Type (s5,tl5)])]))))$ arg1 $ arg2) =
|
neuper@37954
|
646 |
arg2;
|
neuper@37954
|
647 |
|
neuper@37954
|
648 |
|
neuper@37954
|
649 |
exception NO_EQUATION_TERM;
|
neuper@37954
|
650 |
fun is_equation ((Const ("op =",(Type ("fun",
|
neuper@37954
|
651 |
[Type (_,[]),Type ("fun",
|
neuper@37954
|
652 |
[Type (_,[]),Type ("bool",[])])])))) $ _ $ _)
|
neuper@37954
|
653 |
= true
|
neuper@37954
|
654 |
| is_equation _ = false;
|
neuper@37954
|
655 |
fun equ_lhs ((Const ("op =",(Type ("fun",
|
neuper@37954
|
656 |
[Type (_,[]),Type ("fun",
|
neuper@37954
|
657 |
[Type (_,[]),Type ("bool",[])])])))) $ l $ r)
|
neuper@37954
|
658 |
= l
|
neuper@37954
|
659 |
| equ_lhs _ = raise NO_EQUATION_TERM;
|
neuper@37954
|
660 |
fun equ_rhs ((Const ("op =",(Type ("fun",
|
neuper@37954
|
661 |
[Type (_,[]),Type ("fun",
|
neuper@37954
|
662 |
[Type (_,[]),Type ("bool",[])])])))) $ l $ r)
|
neuper@37954
|
663 |
= r
|
neuper@37954
|
664 |
| equ_rhs _ = raise NO_EQUATION_TERM;
|
neuper@37954
|
665 |
|
neuper@37954
|
666 |
|
neuper@37954
|
667 |
fun atom (Const (_,Type (_,[]))) = true
|
neuper@37954
|
668 |
| atom (Free (_,Type (_,[]))) = true
|
neuper@37954
|
669 |
| atom (Var (_,Type (_,[]))) = true
|
neuper@37954
|
670 |
(*| atom (_ (_,"?DUMMY" )) = true ..ML-error *)
|
neuper@37954
|
671 |
| atom((Const ("Bin.integ_of_bin",_)) $ _) = true
|
neuper@37954
|
672 |
| atom _ = false;
|
neuper@37954
|
673 |
|
neuper@37954
|
674 |
fun varids (Const (s,Type (_,[]))) = [strip_thy s]
|
neuper@37954
|
675 |
| varids (Free (s,Type (_,[]))) = if is_no s then []
|
neuper@37954
|
676 |
else [strip_thy s]
|
neuper@37954
|
677 |
| varids (Var((s,_),Type (_,[]))) = [strip_thy s]
|
neuper@37954
|
678 |
(*| varids (_ (s,"?DUMMY" )) = ..ML-error *)
|
neuper@37954
|
679 |
| varids((Const ("Bin.integ_of_bin",_)) $ _)= [](*8.01: superfluous?*)
|
neuper@37954
|
680 |
| varids (Abs(a,T,t)) = union op = [a] (varids t)
|
neuper@37954
|
681 |
| varids (t1 $ t2) = union op = (varids t1) (varids t2)
|
neuper@37954
|
682 |
| varids _ = [];
|
neuper@37954
|
683 |
(*> val t = term_of (hd (parse Diophant.thy "x"));
|
neuper@37954
|
684 |
val t = Free ("x","?DUMMY") : term
|
neuper@37954
|
685 |
> varids t;
|
neuper@37954
|
686 |
val it = [] : string list [] !!! *)
|
neuper@37954
|
687 |
|
neuper@37954
|
688 |
|
neuper@37954
|
689 |
fun bin_ops_only ((Const op_) $ t1 $ t2) =
|
neuper@37954
|
690 |
if(is_bin_op (Const op_))
|
neuper@37954
|
691 |
then(bin_ops_only t1)andalso(bin_ops_only t2)
|
neuper@37954
|
692 |
else false
|
neuper@37954
|
693 |
| bin_ops_only t =
|
neuper@37954
|
694 |
if atom t then true else bin_ops_only t;
|
neuper@37954
|
695 |
|
neuper@37954
|
696 |
fun polynomial opl t bdVar = (* bdVar TODO *)
|
neuper@37954
|
697 |
subset op = (bin_op t, opl) andalso (bin_ops_only t);
|
neuper@37954
|
698 |
|
neuper@37954
|
699 |
fun poly_equ opl bdVar t = is_equation t (* bdVar TODO *)
|
neuper@37954
|
700 |
andalso polynomial opl (equ_lhs t) bdVar
|
neuper@37954
|
701 |
andalso polynomial opl (equ_rhs t) bdVar
|
neuper@37954
|
702 |
andalso (subset op = (varids bdVar, varids (equ_lhs t)) orelse
|
neuper@37954
|
703 |
subset op = (varids bdVar, varids (equ_lhs t)));
|
neuper@37954
|
704 |
|
neuper@37954
|
705 |
(*fun max is =
|
neuper@37954
|
706 |
let fun max_ m [] = m
|
neuper@37954
|
707 |
| max_ m (i::is) = if m<i then max_ i is else max_ m is;
|
neuper@37954
|
708 |
in max_ (hd is) is end;
|
neuper@37954
|
709 |
> max [1,5,3,7,4,2];
|
neuper@37954
|
710 |
val it = 7 : int *)
|
neuper@37954
|
711 |
|
neuper@37954
|
712 |
fun max (a,b) = if a < b then b else a;
|
neuper@37954
|
713 |
|
neuper@37954
|
714 |
fun degree addl mul bdVar t =
|
neuper@37954
|
715 |
let
|
neuper@37954
|
716 |
fun deg _ _ v (Const (s,Type (_,[]))) = if v=strip_thy s then 1 else 0
|
neuper@37954
|
717 |
| deg _ _ v (Free (s,Type (_,[]))) = if v=strip_thy s then 1 else 0
|
neuper@37954
|
718 |
| deg _ _ v (Var((s,_),Type (_,[]))) = if v=strip_thy s then 1 else 0
|
neuper@37954
|
719 |
(*| deg _ _ v (_ (s,"?DUMMY" )) = ..ML-error *)
|
neuper@37954
|
720 |
| deg _ _ v((Const ("Bin.integ_of_bin",_)) $ _ )= 0
|
neuper@37954
|
721 |
| deg addl mul v (h $ t1 $ t2) =
|
neuper@37954
|
722 |
if subset op = (bin_op h, addl)
|
neuper@37954
|
723 |
then max (deg addl mul v t1 ,deg addl mul v t2)
|
neuper@37954
|
724 |
else (*mul!*)(deg addl mul v t1)+(deg addl mul v t2)
|
neuper@37954
|
725 |
in if polynomial (addl @ [mul]) t bdVar
|
neuper@37954
|
726 |
then SOME (deg addl mul (id_of bdVar) t) else (NONE:int option)
|
neuper@37954
|
727 |
end;
|
neuper@37954
|
728 |
fun degree_ addl mul bdVar t = (* do not export *)
|
neuper@37954
|
729 |
let fun opt (SOME i)= i
|
neuper@37954
|
730 |
| opt NONE = 0
|
neuper@37954
|
731 |
in opt (degree addl mul bdVar t) end;
|
neuper@37954
|
732 |
|
neuper@37954
|
733 |
|
neuper@37954
|
734 |
fun linear addl mul t bdVar = (degree_ addl mul bdVar t)<2;
|
neuper@37954
|
735 |
|
neuper@37954
|
736 |
fun linear_equ addl mul bdVar t =
|
neuper@37954
|
737 |
if is_equation t
|
neuper@37954
|
738 |
then let val degl = degree_ addl mul bdVar (equ_lhs t);
|
neuper@37954
|
739 |
val degr = degree_ addl mul bdVar (equ_rhs t)
|
neuper@37954
|
740 |
in if (degl>0 orelse degr>0)andalso max(degl,degr)<2
|
neuper@37954
|
741 |
then true else false
|
neuper@37954
|
742 |
end
|
neuper@37954
|
743 |
else false;
|
neuper@37954
|
744 |
(* strip_thy op_ before *)
|
neuper@37954
|
745 |
fun is_div_op (dv,(Const (op_,(Type ("fun",
|
neuper@37954
|
746 |
[Type (s2,[]),Type ("fun",
|
neuper@37954
|
747 |
[Type (s4,tl4),Type (s5,tl5)])])))) )= (dv = strip_thy op_)
|
neuper@37954
|
748 |
| is_div_op _ = false;
|
neuper@37954
|
749 |
|
neuper@37954
|
750 |
fun is_denom bdVar div_op t =
|
neuper@37954
|
751 |
let fun is bool[v]dv (Const (s,Type(_,[])))= bool andalso(if v=strip_thy s then true else false)
|
neuper@37954
|
752 |
| is bool[v]dv (Free (s,Type(_,[])))= bool andalso(if v=strip_thy s then true else false)
|
neuper@37954
|
753 |
| is bool[v]dv (Var((s,_),Type(_,[])))= bool andalso(if v=strip_thy s then true else false)
|
neuper@37954
|
754 |
| is bool[v]dv((Const ("Bin.integ_of_bin",_)) $ _) = false
|
neuper@37954
|
755 |
| is bool[v]dv (h$n$d) =
|
neuper@37954
|
756 |
if is_div_op(dv,h)
|
neuper@37954
|
757 |
then (is false[v]dv n)orelse(is true[v]dv d)
|
neuper@37954
|
758 |
else (is bool [v]dv n)orelse(is bool[v]dv d)
|
neuper@37954
|
759 |
in is false (varids bdVar) (strip_thy div_op) t end;
|
neuper@37954
|
760 |
|
neuper@37954
|
761 |
|
neuper@37954
|
762 |
fun rational t div_op bdVar =
|
neuper@37954
|
763 |
is_denom bdVar div_op t andalso bin_ops_only t;
|
neuper@37954
|
764 |
|
neuper@37954
|
765 |
|
neuper@37954
|
766 |
|
neuper@37954
|
767 |
(** problem types **)
|
neuper@37954
|
768 |
|
neuper@37954
|
769 |
store_pbt
|
neuper@37954
|
770 |
(prep_pbt (theory "Test") "pbl_test_uni_plain2" [] e_pblID
|
neuper@37954
|
771 |
(["plain_square","univariate","equation","test"],
|
neuper@37954
|
772 |
[("#Given" ,["equality e_","solveFor v_"]),
|
neuper@37954
|
773 |
("#Where" ,["(matches (?a + ?b*v_ ^^^2 = 0) e_) |" ^
|
neuper@37954
|
774 |
"(matches ( ?b*v_ ^^^2 = 0) e_) |" ^
|
neuper@37954
|
775 |
"(matches (?a + v_ ^^^2 = 0) e_) |" ^
|
neuper@37954
|
776 |
"(matches ( v_ ^^^2 = 0) e_)"]),
|
neuper@37954
|
777 |
("#Find" ,["solutions v_i_"])
|
neuper@37954
|
778 |
],
|
neuper@37954
|
779 |
assoc_rls "matches",
|
neuper@37954
|
780 |
SOME "solve (e_::bool, v_)", [["Test","solve_plain_square"]]));
|
neuper@37954
|
781 |
(*
|
neuper@37954
|
782 |
val e_ = (term_of o the o (parse thy)) "e_::bool";
|
neuper@37954
|
783 |
val ve = (term_of o the o (parse thy)) "4 + 3*x^^^2 = 0";
|
neuper@37954
|
784 |
val env = [(e_,ve)];
|
neuper@37954
|
785 |
|
neuper@37954
|
786 |
val pre = (term_of o the o (parse thy))
|
neuper@37954
|
787 |
"(matches (a + b*v_ ^^^2 = 0, e_::bool)) |" ^
|
neuper@37954
|
788 |
"(matches ( b*v_ ^^^2 = 0, e_::bool)) |" ^
|
neuper@37954
|
789 |
"(matches (a + v_ ^^^2 = 0, e_::bool)) |" ^
|
neuper@37954
|
790 |
"(matches ( v_ ^^^2 = 0, e_::bool))";
|
neuper@37954
|
791 |
val prei = subst_atomic env pre;
|
neuper@37954
|
792 |
val cpre = (cterm_of thy) prei;
|
neuper@37954
|
793 |
|
neuper@37954
|
794 |
val SOME (ct,_) = rewrite_set_ thy false tval_rls cpre;
|
neuper@37954
|
795 |
val ct = "True | False | False | False" : cterm
|
neuper@37954
|
796 |
|
neuper@37954
|
797 |
> val SOME (ct,_) = rewrite_ thy sqrt_right tval_rls false or_false ct;
|
neuper@37954
|
798 |
> val SOME (ct,_) = rewrite_ thy sqrt_right tval_rls false or_false ct;
|
neuper@37954
|
799 |
> val SOME (ct,_) = rewrite_ thy sqrt_right tval_rls false or_false ct;
|
neuper@37954
|
800 |
val ct = "True" : cterm
|
neuper@37954
|
801 |
|
neuper@37954
|
802 |
*)
|
neuper@37954
|
803 |
|
neuper@37954
|
804 |
store_pbt
|
neuper@37954
|
805 |
(prep_pbt (theory "Test") "pbl_test_uni_poly" [] e_pblID
|
neuper@37954
|
806 |
(["polynomial","univariate","equation","test"],
|
neuper@37954
|
807 |
[("#Given" ,["equality (v_ ^^^2 + p_ * v_ + q__ = 0)","solveFor v_"]),
|
neuper@37954
|
808 |
("#Where" ,["False"]),
|
neuper@37954
|
809 |
("#Find" ,["solutions v_i_"])
|
neuper@37954
|
810 |
],
|
neuper@37954
|
811 |
e_rls, SOME "solve (e_::bool, v_)", []));
|
neuper@37954
|
812 |
|
neuper@37954
|
813 |
store_pbt
|
neuper@37954
|
814 |
(prep_pbt (theory "Test") "pbl_test_uni_poly_deg2" [] e_pblID
|
neuper@37954
|
815 |
(["degree_two","polynomial","univariate","equation","test"],
|
neuper@37954
|
816 |
[("#Given" ,["equality (v_ ^^^2 + p_ * v_ + q__ = 0)","solveFor v_"]),
|
neuper@37954
|
817 |
("#Find" ,["solutions v_i_"])
|
neuper@37954
|
818 |
],
|
neuper@37954
|
819 |
e_rls, SOME "solve (v_ ^^^2 + p_ * v_ + q__ = 0, v_)", []));
|
neuper@37954
|
820 |
|
neuper@37954
|
821 |
store_pbt
|
neuper@37954
|
822 |
(prep_pbt (theory "Test") "pbl_test_uni_poly_deg2_pq" [] e_pblID
|
neuper@37954
|
823 |
(["pq_formula","degree_two","polynomial","univariate","equation","test"],
|
neuper@37954
|
824 |
[("#Given" ,["equality (v_ ^^^2 + p_ * v_ + q__ = 0)","solveFor v_"]),
|
neuper@37954
|
825 |
("#Find" ,["solutions v_i_"])
|
neuper@37954
|
826 |
],
|
neuper@37954
|
827 |
e_rls, SOME "solve (v_ ^^^2 + p_ * v_ + q__ = 0, v_)", []));
|
neuper@37954
|
828 |
|
neuper@37954
|
829 |
store_pbt
|
neuper@37954
|
830 |
(prep_pbt (theory "Test") "pbl_test_uni_poly_deg2_abc" [] e_pblID
|
neuper@37954
|
831 |
(["abc_formula","degree_two","polynomial","univariate","equation","test"],
|
neuper@37954
|
832 |
[("#Given" ,["equality (a_ * x ^^^2 + b_ * x + c_ = 0)","solveFor v_"]),
|
neuper@37954
|
833 |
("#Find" ,["solutions v_i_"])
|
neuper@37954
|
834 |
],
|
neuper@37954
|
835 |
e_rls, SOME "solve (a_ * x ^^^2 + b_ * x + c_ = 0, v_)", []));
|
neuper@37954
|
836 |
|
neuper@37954
|
837 |
store_pbt
|
neuper@37954
|
838 |
(prep_pbt (theory "Test") "pbl_test_uni_root" [] e_pblID
|
neuper@37954
|
839 |
(["squareroot","univariate","equation","test"],
|
neuper@37954
|
840 |
[("#Given" ,["equality e_","solveFor v_"]),
|
neuper@37954
|
841 |
("#Where" ,["contains_root (e_::bool)"]),
|
neuper@37954
|
842 |
("#Find" ,["solutions v_i_"])
|
neuper@37954
|
843 |
],
|
neuper@37954
|
844 |
append_rls "contains_root" e_rls [Calc ("Test.contains'_root",
|
neuper@37954
|
845 |
eval_contains_root "#contains_root_")],
|
neuper@37954
|
846 |
SOME "solve (e_::bool, v_)", [["Test","square_equation"]]));
|
neuper@37954
|
847 |
|
neuper@37954
|
848 |
store_pbt
|
neuper@37954
|
849 |
(prep_pbt (theory "Test") "pbl_test_uni_norm" [] e_pblID
|
neuper@37954
|
850 |
(["normalize","univariate","equation","test"],
|
neuper@37954
|
851 |
[("#Given" ,["equality e_","solveFor v_"]),
|
neuper@37954
|
852 |
("#Where" ,[]),
|
neuper@37954
|
853 |
("#Find" ,["solutions v_i_"])
|
neuper@37954
|
854 |
],
|
neuper@37954
|
855 |
e_rls, SOME "solve (e_::bool, v_)", [["Test","norm_univar_equation"]]));
|
neuper@37954
|
856 |
|
neuper@37954
|
857 |
store_pbt
|
neuper@37954
|
858 |
(prep_pbt (theory "Test") "pbl_test_uni_roottest" [] e_pblID
|
neuper@37954
|
859 |
(["sqroot-test","univariate","equation","test"],
|
neuper@37954
|
860 |
[("#Given" ,["equality e_","solveFor v_"]),
|
neuper@37954
|
861 |
(*("#Where" ,["contains_root (e_::bool)"]),*)
|
neuper@37954
|
862 |
("#Find" ,["solutions v_i_"])
|
neuper@37954
|
863 |
],
|
neuper@37954
|
864 |
e_rls, SOME "solve (e_::bool, v_)", []));
|
neuper@37954
|
865 |
|
neuper@37954
|
866 |
(*
|
neuper@37954
|
867 |
(#ppc o get_pbt) ["sqroot-test","univariate","equation"];
|
neuper@37954
|
868 |
*)
|
neuper@37954
|
869 |
|
neuper@37954
|
870 |
|
neuper@37954
|
871 |
store_met
|
neuper@37954
|
872 |
(prep_met (theory "Test") "met_test_sqrt" [] e_metID
|
neuper@37954
|
873 |
(*root-equation, version for tests before 8.01.01*)
|
neuper@37954
|
874 |
(["Test","sqrt-equ-test"]:metID,
|
neuper@37954
|
875 |
[("#Given" ,["equality e_","solveFor v_"]),
|
neuper@37954
|
876 |
("#Where" ,["contains_root (e_::bool)"]),
|
neuper@37954
|
877 |
("#Find" ,["solutions v_i_"])
|
neuper@37954
|
878 |
],
|
neuper@37954
|
879 |
{rew_ord'="e_rew_ord",rls'=tval_rls,
|
neuper@37954
|
880 |
srls =append_rls "srls_contains_root" e_rls
|
neuper@37954
|
881 |
[Calc ("Test.contains'_root",eval_contains_root "")],
|
neuper@37954
|
882 |
prls =append_rls "prls_contains_root" e_rls
|
neuper@37954
|
883 |
[Calc ("Test.contains'_root",eval_contains_root "")],
|
neuper@37954
|
884 |
calc=[],
|
neuper@37954
|
885 |
crls=tval_rls, nrls=e_rls(*,asm_rls=[],
|
neuper@37954
|
886 |
asm_thm=[("square_equation_left",""),
|
neuper@37954
|
887 |
("square_equation_right","")]*)},
|
neuper@37954
|
888 |
"Script Solve_root_equation (e_::bool) (v_::real) = " ^
|
neuper@37954
|
889 |
"(let e_ = " ^
|
neuper@37954
|
890 |
" ((While (contains_root e_) Do" ^
|
neuper@37954
|
891 |
" ((Rewrite square_equation_left True) @@" ^
|
neuper@37954
|
892 |
" (Try (Rewrite_Set Test_simplify False)) @@" ^
|
neuper@37954
|
893 |
" (Try (Rewrite_Set rearrange_assoc False)) @@" ^
|
neuper@37954
|
894 |
" (Try (Rewrite_Set isolate_root False)) @@" ^
|
neuper@37954
|
895 |
" (Try (Rewrite_Set Test_simplify False)))) @@" ^
|
neuper@37954
|
896 |
" (Try (Rewrite_Set norm_equation False)) @@" ^
|
neuper@37954
|
897 |
" (Try (Rewrite_Set Test_simplify False)) @@" ^
|
neuper@37954
|
898 |
" (Rewrite_Set_Inst [(bdv,v_::real)] isolate_bdv False) @@" ^
|
neuper@37954
|
899 |
" (Try (Rewrite_Set Test_simplify False)))" ^
|
neuper@37954
|
900 |
" e_" ^
|
neuper@37954
|
901 |
" in [e_::bool])"
|
neuper@37954
|
902 |
));
|
neuper@37954
|
903 |
|
neuper@37954
|
904 |
store_met
|
neuper@37954
|
905 |
(prep_met (theory "Test") "met_test_sqrt2" [] e_metID
|
neuper@37954
|
906 |
(*root-equation ... for test-*.sml until 8.01*)
|
neuper@37954
|
907 |
(["Test","squ-equ-test2"]:metID,
|
neuper@37954
|
908 |
[("#Given" ,["equality e_","solveFor v_"]),
|
neuper@37954
|
909 |
("#Find" ,["solutions v_i_"])
|
neuper@37954
|
910 |
],
|
neuper@37954
|
911 |
{rew_ord'="e_rew_ord",rls'=tval_rls,
|
neuper@37954
|
912 |
srls = append_rls "srls_contains_root" e_rls
|
neuper@37954
|
913 |
[Calc ("Test.contains'_root",eval_contains_root"")],
|
neuper@37954
|
914 |
prls=e_rls,calc=[],
|
neuper@37954
|
915 |
crls=tval_rls, nrls=e_rls(*,asm_rls=[],
|
neuper@37954
|
916 |
asm_thm=[("square_equation_left",""),
|
neuper@37954
|
917 |
("square_equation_right","")]*)},
|
neuper@37954
|
918 |
"Script Solve_root_equation (e_::bool) (v_::real) = " ^
|
neuper@37954
|
919 |
"(let e_ = " ^
|
neuper@37954
|
920 |
" ((While (contains_root e_) Do" ^
|
neuper@37954
|
921 |
" ((Rewrite square_equation_left True) @@" ^
|
neuper@37954
|
922 |
" (Try (Rewrite_Set Test_simplify False)) @@" ^
|
neuper@37954
|
923 |
" (Try (Rewrite_Set rearrange_assoc False)) @@" ^
|
neuper@37954
|
924 |
" (Try (Rewrite_Set isolate_root False)) @@" ^
|
neuper@37954
|
925 |
" (Try (Rewrite_Set Test_simplify False)))) @@" ^
|
neuper@37954
|
926 |
" (Try (Rewrite_Set norm_equation False)) @@" ^
|
neuper@37954
|
927 |
" (Try (Rewrite_Set Test_simplify False)) @@" ^
|
neuper@37954
|
928 |
" (Rewrite_Set_Inst [(bdv,v_::real)] isolate_bdv False) @@" ^
|
neuper@37954
|
929 |
" (Try (Rewrite_Set Test_simplify False)))" ^
|
neuper@37954
|
930 |
" e_;" ^
|
neuper@37954
|
931 |
" (L_::bool list) = Tac subproblem_equation_dummy; " ^
|
neuper@37954
|
932 |
" L_ = Tac solve_equation_dummy " ^
|
neuper@37954
|
933 |
" in Check_elementwise L_ {(v_::real). Assumptions})"
|
neuper@37954
|
934 |
));
|
neuper@37954
|
935 |
|
neuper@37954
|
936 |
store_met
|
neuper@37954
|
937 |
(prep_met (theory "Test") "met_test_squ_sub" [] e_metID
|
neuper@37954
|
938 |
(*tests subproblem fixed linear*)
|
neuper@37954
|
939 |
(["Test","squ-equ-test-subpbl1"]:metID,
|
neuper@37954
|
940 |
[("#Given" ,["equality e_","solveFor v_"]),
|
neuper@37954
|
941 |
("#Find" ,["solutions v_i_"])
|
neuper@37954
|
942 |
],
|
neuper@37954
|
943 |
{rew_ord'="e_rew_ord",rls'=tval_rls,srls=e_rls,prls=e_rls,calc=[],
|
neuper@37954
|
944 |
crls=tval_rls, nrls=Test_simplify},
|
neuper@37954
|
945 |
"Script Solve_root_equation (e_::bool) (v_::real) = " ^
|
neuper@37954
|
946 |
" (let e_ = ((Try (Rewrite_Set norm_equation False)) @@ " ^
|
neuper@37954
|
947 |
" (Try (Rewrite_Set Test_simplify False))) e_; " ^
|
neuper@37954
|
948 |
"(L_::bool list) = (SubProblem (Test_,[linear,univariate,equation,test]," ^
|
neuper@37954
|
949 |
" [Test,solve_linear]) [bool_ e_, real_ v_])" ^
|
neuper@37954
|
950 |
"in Check_elementwise L_ {(v_::real). Assumptions})"
|
neuper@37954
|
951 |
));
|
neuper@37954
|
952 |
|
neuper@37954
|
953 |
store_met
|
neuper@37954
|
954 |
(prep_met (theory "Test") "met_test_squ_sub2" [] e_metID
|
neuper@37954
|
955 |
(*tests subproblem fixed degree 2*)
|
neuper@37954
|
956 |
(["Test","squ-equ-test-subpbl2"]:metID,
|
neuper@37954
|
957 |
[("#Given" ,["equality e_","solveFor v_"]),
|
neuper@37954
|
958 |
("#Find" ,["solutions v_i_"])
|
neuper@37954
|
959 |
],
|
neuper@37954
|
960 |
{rew_ord'="e_rew_ord",rls'=tval_rls,srls=e_rls,prls=e_rls,calc=[],
|
neuper@37954
|
961 |
crls=tval_rls, nrls=e_rls(*,
|
neuper@37954
|
962 |
asm_rls=[],asm_thm=[("square_equation_left",""),
|
neuper@37954
|
963 |
("square_equation_right","")]*)},
|
neuper@37954
|
964 |
"Script Solve_root_equation (e_::bool) (v_::real) = " ^
|
neuper@37954
|
965 |
" (let e_ = Try (Rewrite_Set norm_equation False) e_; " ^
|
neuper@37954
|
966 |
"(L_::bool list) = (SubProblem (Test_,[linear,univariate,equation,test]," ^
|
neuper@37954
|
967 |
" [Test,solve_by_pq_formula]) [bool_ e_, real_ v_])" ^
|
neuper@37954
|
968 |
"in Check_elementwise L_ {(v_::real). Assumptions})"
|
neuper@37954
|
969 |
));
|
neuper@37954
|
970 |
|
neuper@37954
|
971 |
store_met
|
neuper@37954
|
972 |
(prep_met (theory "Test") "met_test_squ_nonterm" [] e_metID
|
neuper@37954
|
973 |
(*root-equation: see foils..., but notTerminating*)
|
neuper@37954
|
974 |
(["Test","square_equation...notTerminating"]:metID,
|
neuper@37954
|
975 |
[("#Given" ,["equality e_","solveFor v_"]),
|
neuper@37954
|
976 |
("#Find" ,["solutions v_i_"])
|
neuper@37954
|
977 |
],
|
neuper@37954
|
978 |
{rew_ord'="e_rew_ord",rls'=tval_rls,
|
neuper@37954
|
979 |
srls = append_rls "srls_contains_root" e_rls
|
neuper@37954
|
980 |
[Calc ("Test.contains'_root",eval_contains_root"")],
|
neuper@37954
|
981 |
prls=e_rls,calc=[],
|
neuper@37954
|
982 |
crls=tval_rls, nrls=e_rls(*,asm_rls=[],
|
neuper@37954
|
983 |
asm_thm=[("square_equation_left",""),
|
neuper@37954
|
984 |
("square_equation_right","")]*)},
|
neuper@37954
|
985 |
"Script Solve_root_equation (e_::bool) (v_::real) = " ^
|
neuper@37954
|
986 |
"(let e_ = " ^
|
neuper@37954
|
987 |
" ((While (contains_root e_) Do" ^
|
neuper@37954
|
988 |
" ((Rewrite square_equation_left True) @@" ^
|
neuper@37954
|
989 |
" (Try (Rewrite_Set Test_simplify False)) @@" ^
|
neuper@37954
|
990 |
" (Try (Rewrite_Set rearrange_assoc False)) @@" ^
|
neuper@37954
|
991 |
" (Try (Rewrite_Set isolate_root False)) @@" ^
|
neuper@37954
|
992 |
" (Try (Rewrite_Set Test_simplify False)))) @@" ^
|
neuper@37954
|
993 |
" (Try (Rewrite_Set norm_equation False)) @@" ^
|
neuper@37954
|
994 |
" (Try (Rewrite_Set Test_simplify False)))" ^
|
neuper@37954
|
995 |
" e_;" ^
|
neuper@37954
|
996 |
" (L_::bool list) = " ^
|
neuper@37954
|
997 |
" (SubProblem (Test_,[linear,univariate,equation,test]," ^
|
neuper@37954
|
998 |
" [Test,solve_linear]) [bool_ e_, real_ v_])" ^
|
neuper@37954
|
999 |
"in Check_elementwise L_ {(v_::real). Assumptions})"
|
neuper@37954
|
1000 |
));
|
neuper@37954
|
1001 |
|
neuper@37954
|
1002 |
store_met
|
neuper@37954
|
1003 |
(prep_met (theory "Test") "met_test_eq1" [] e_metID
|
neuper@37954
|
1004 |
(*root-equation1:*)
|
neuper@37954
|
1005 |
(["Test","square_equation1"]:metID,
|
neuper@37954
|
1006 |
[("#Given" ,["equality e_","solveFor v_"]),
|
neuper@37954
|
1007 |
("#Find" ,["solutions v_i_"])
|
neuper@37954
|
1008 |
],
|
neuper@37954
|
1009 |
{rew_ord'="e_rew_ord",rls'=tval_rls,
|
neuper@37954
|
1010 |
srls = append_rls "srls_contains_root" e_rls
|
neuper@37954
|
1011 |
[Calc ("Test.contains'_root",eval_contains_root"")],
|
neuper@37954
|
1012 |
prls=e_rls,calc=[],
|
neuper@37954
|
1013 |
crls=tval_rls, nrls=e_rls(*,asm_rls=[],
|
neuper@37954
|
1014 |
asm_thm=[("square_equation_left",""),
|
neuper@37954
|
1015 |
("square_equation_right","")]*)},
|
neuper@37954
|
1016 |
"Script Solve_root_equation (e_::bool) (v_::real) = " ^
|
neuper@37954
|
1017 |
"(let e_ = " ^
|
neuper@37954
|
1018 |
" ((While (contains_root e_) Do" ^
|
neuper@37954
|
1019 |
" ((Rewrite square_equation_left True) @@" ^
|
neuper@37954
|
1020 |
" (Try (Rewrite_Set Test_simplify False)) @@" ^
|
neuper@37954
|
1021 |
" (Try (Rewrite_Set rearrange_assoc False)) @@" ^
|
neuper@37954
|
1022 |
" (Try (Rewrite_Set isolate_root False)) @@" ^
|
neuper@37954
|
1023 |
" (Try (Rewrite_Set Test_simplify False)))) @@" ^
|
neuper@37954
|
1024 |
" (Try (Rewrite_Set norm_equation False)) @@" ^
|
neuper@37954
|
1025 |
" (Try (Rewrite_Set Test_simplify False)))" ^
|
neuper@37954
|
1026 |
" e_;" ^
|
neuper@37954
|
1027 |
" (L_::bool list) = (SubProblem (Test_,[linear,univariate,equation,test]," ^
|
neuper@37954
|
1028 |
" [Test,solve_linear]) [bool_ e_, real_ v_])" ^
|
neuper@37954
|
1029 |
" in Check_elementwise L_ {(v_::real). Assumptions})"
|
neuper@37954
|
1030 |
));
|
neuper@37954
|
1031 |
|
neuper@37954
|
1032 |
store_met
|
neuper@37954
|
1033 |
(prep_met (theory "Test") "met_test_squ2" [] e_metID
|
neuper@37954
|
1034 |
(*root-equation2*)
|
neuper@37954
|
1035 |
(["Test","square_equation2"]:metID,
|
neuper@37954
|
1036 |
[("#Given" ,["equality e_","solveFor v_"]),
|
neuper@37954
|
1037 |
("#Find" ,["solutions v_i_"])
|
neuper@37954
|
1038 |
],
|
neuper@37954
|
1039 |
{rew_ord'="e_rew_ord",rls'=tval_rls,
|
neuper@37954
|
1040 |
srls = append_rls "srls_contains_root" e_rls
|
neuper@37954
|
1041 |
[Calc ("Test.contains'_root",eval_contains_root"")],
|
neuper@37954
|
1042 |
prls=e_rls,calc=[],
|
neuper@37954
|
1043 |
crls=tval_rls, nrls=e_rls(*,asm_rls=[],
|
neuper@37954
|
1044 |
asm_thm=[("square_equation_left",""),
|
neuper@37954
|
1045 |
("square_equation_right","")]*)},
|
neuper@37954
|
1046 |
"Script Solve_root_equation (e_::bool) (v_::real) = " ^
|
neuper@37954
|
1047 |
"(let e_ = " ^
|
neuper@37954
|
1048 |
" ((While (contains_root e_) Do" ^
|
neuper@37954
|
1049 |
" (((Rewrite square_equation_left True) Or " ^
|
neuper@37954
|
1050 |
" (Rewrite square_equation_right True)) @@" ^
|
neuper@37954
|
1051 |
" (Try (Rewrite_Set Test_simplify False)) @@" ^
|
neuper@37954
|
1052 |
" (Try (Rewrite_Set rearrange_assoc False)) @@" ^
|
neuper@37954
|
1053 |
" (Try (Rewrite_Set isolate_root False)) @@" ^
|
neuper@37954
|
1054 |
" (Try (Rewrite_Set Test_simplify False)))) @@" ^
|
neuper@37954
|
1055 |
" (Try (Rewrite_Set norm_equation False)) @@" ^
|
neuper@37954
|
1056 |
" (Try (Rewrite_Set Test_simplify False)))" ^
|
neuper@37954
|
1057 |
" e_;" ^
|
neuper@37954
|
1058 |
" (L_::bool list) = (SubProblem (Test_,[plain_square,univariate,equation,test]," ^
|
neuper@37954
|
1059 |
" [Test,solve_plain_square]) [bool_ e_, real_ v_])" ^
|
neuper@37954
|
1060 |
" in Check_elementwise L_ {(v_::real). Assumptions})"
|
neuper@37954
|
1061 |
));
|
neuper@37954
|
1062 |
|
neuper@37954
|
1063 |
store_met
|
neuper@37954
|
1064 |
(prep_met (theory "Test") "met_test_squeq" [] e_metID
|
neuper@37954
|
1065 |
(*root-equation*)
|
neuper@37954
|
1066 |
(["Test","square_equation"]:metID,
|
neuper@37954
|
1067 |
[("#Given" ,["equality e_","solveFor v_"]),
|
neuper@37954
|
1068 |
("#Find" ,["solutions v_i_"])
|
neuper@37954
|
1069 |
],
|
neuper@37954
|
1070 |
{rew_ord'="e_rew_ord",rls'=tval_rls,
|
neuper@37954
|
1071 |
srls = append_rls "srls_contains_root" e_rls
|
neuper@37954
|
1072 |
[Calc ("Test.contains'_root",eval_contains_root"")],
|
neuper@37954
|
1073 |
prls=e_rls,calc=[],
|
neuper@37954
|
1074 |
crls=tval_rls, nrls=e_rls(*,asm_rls=[],
|
neuper@37954
|
1075 |
asm_thm=[("square_equation_left",""),
|
neuper@37954
|
1076 |
("square_equation_right","")]*)},
|
neuper@37954
|
1077 |
"Script Solve_root_equation (e_::bool) (v_::real) = " ^
|
neuper@37954
|
1078 |
"(let e_ = " ^
|
neuper@37954
|
1079 |
" ((While (contains_root e_) Do" ^
|
neuper@37954
|
1080 |
" (((Rewrite square_equation_left True) Or" ^
|
neuper@37954
|
1081 |
" (Rewrite square_equation_right True)) @@" ^
|
neuper@37954
|
1082 |
" (Try (Rewrite_Set Test_simplify False)) @@" ^
|
neuper@37954
|
1083 |
" (Try (Rewrite_Set rearrange_assoc False)) @@" ^
|
neuper@37954
|
1084 |
" (Try (Rewrite_Set isolate_root False)) @@" ^
|
neuper@37954
|
1085 |
" (Try (Rewrite_Set Test_simplify False)))) @@" ^
|
neuper@37954
|
1086 |
" (Try (Rewrite_Set norm_equation False)) @@" ^
|
neuper@37954
|
1087 |
" (Try (Rewrite_Set Test_simplify False)))" ^
|
neuper@37954
|
1088 |
" e_;" ^
|
neuper@37954
|
1089 |
" (L_::bool list) = (SubProblem (Test_,[univariate,equation,test]," ^
|
neuper@37954
|
1090 |
" [no_met]) [bool_ e_, real_ v_])" ^
|
neuper@37954
|
1091 |
" in Check_elementwise L_ {(v_::real). Assumptions})"
|
neuper@37954
|
1092 |
) ); (*#######*)
|
neuper@37954
|
1093 |
|
neuper@37954
|
1094 |
store_met
|
neuper@37954
|
1095 |
(prep_met (theory "Test") "met_test_eq_plain" [] e_metID
|
neuper@37954
|
1096 |
(*solve_plain_square*)
|
neuper@37954
|
1097 |
(["Test","solve_plain_square"]:metID,
|
neuper@37954
|
1098 |
[("#Given",["equality e_","solveFor v_"]),
|
neuper@37954
|
1099 |
("#Where" ,["(matches (?a + ?b*v_ ^^^2 = 0) e_) |" ^
|
neuper@37954
|
1100 |
"(matches ( ?b*v_ ^^^2 = 0) e_) |" ^
|
neuper@37954
|
1101 |
"(matches (?a + v_ ^^^2 = 0) e_) |" ^
|
neuper@37954
|
1102 |
"(matches ( v_ ^^^2 = 0) e_)"]),
|
neuper@37954
|
1103 |
("#Find" ,["solutions v_i_"])
|
neuper@37954
|
1104 |
],
|
neuper@37954
|
1105 |
{rew_ord'="e_rew_ord",rls'=tval_rls,calc=[],srls=e_rls,
|
neuper@37954
|
1106 |
prls = assoc_rls "matches",
|
neuper@37954
|
1107 |
crls=tval_rls, nrls=e_rls(*,
|
neuper@37954
|
1108 |
asm_rls=[],asm_thm=[]*)},
|
neuper@37954
|
1109 |
"Script Solve_plain_square (e_::bool) (v_::real) = " ^
|
neuper@37954
|
1110 |
" (let e_ = ((Try (Rewrite_Set isolate_bdv False)) @@ " ^
|
neuper@37954
|
1111 |
" (Try (Rewrite_Set Test_simplify False)) @@ " ^
|
neuper@37954
|
1112 |
" ((Rewrite square_equality_0 False) Or " ^
|
neuper@37954
|
1113 |
" (Rewrite square_equality True)) @@ " ^
|
neuper@37954
|
1114 |
" (Try (Rewrite_Set tval_rls False))) e_ " ^
|
neuper@37954
|
1115 |
" in ((Or_to_List e_)::bool list))"
|
neuper@37954
|
1116 |
));
|
neuper@37954
|
1117 |
|
neuper@37954
|
1118 |
store_met
|
neuper@37954
|
1119 |
(prep_met (theory "Test") "met_test_norm_univ" [] e_metID
|
neuper@37954
|
1120 |
(["Test","norm_univar_equation"]:metID,
|
neuper@37954
|
1121 |
[("#Given",["equality e_","solveFor v_"]),
|
neuper@37954
|
1122 |
("#Where" ,[]),
|
neuper@37954
|
1123 |
("#Find" ,["solutions v_i_"])
|
neuper@37954
|
1124 |
],
|
neuper@37954
|
1125 |
{rew_ord'="e_rew_ord",rls'=tval_rls,srls = e_rls,prls=e_rls,
|
neuper@37954
|
1126 |
calc=[],
|
neuper@37954
|
1127 |
crls=tval_rls, nrls=e_rls(*,asm_rls=[],asm_thm=[]*)},
|
neuper@37954
|
1128 |
"Script Norm_univar_equation (e_::bool) (v_::real) = " ^
|
neuper@37954
|
1129 |
" (let e_ = ((Try (Rewrite rnorm_equation_add False)) @@ " ^
|
neuper@37954
|
1130 |
" (Try (Rewrite_Set Test_simplify False))) e_ " ^
|
neuper@37954
|
1131 |
" in (SubProblem (Test_,[univariate,equation,test], " ^
|
neuper@37954
|
1132 |
" [no_met]) [bool_ e_, real_ v_]))"
|
neuper@37954
|
1133 |
));
|
neuper@37954
|
1134 |
|
neuper@37954
|
1135 |
|
neuper@37954
|
1136 |
|
neuper@37954
|
1137 |
(*17.9.02 aus SqRoot.ML------------------------------^^^---*)
|
neuper@37954
|
1138 |
|
neuper@37954
|
1139 |
(*8.4.03 aus Poly.ML--------------------------------vvv---
|
neuper@37954
|
1140 |
make_polynomial ---> make_poly
|
neuper@37954
|
1141 |
^-- for user ^-- for systest _ONLY_*)
|
neuper@37954
|
1142 |
|
neuper@37954
|
1143 |
local (*. for make_polytest .*)
|
neuper@37954
|
1144 |
|
neuper@37954
|
1145 |
open Term; (* for type order = EQUAL | LESS | GREATER *)
|
neuper@37954
|
1146 |
|
neuper@37954
|
1147 |
fun pr_ord EQUAL = "EQUAL"
|
neuper@37954
|
1148 |
| pr_ord LESS = "LESS"
|
neuper@37954
|
1149 |
| pr_ord GREATER = "GREATER";
|
neuper@37954
|
1150 |
|
neuper@37954
|
1151 |
fun dest_hd' (Const (a, T)) = (* ~ term.ML *)
|
neuper@37954
|
1152 |
(case a of
|
neuper@37954
|
1153 |
"Atools.pow" => ((("|||||||||||||", 0), T), 0) (*WN greatest *)
|
neuper@37954
|
1154 |
| _ => (((a, 0), T), 0))
|
neuper@37954
|
1155 |
| dest_hd' (Free (a, T)) = (((a, 0), T), 1)
|
neuper@37954
|
1156 |
| dest_hd' (Var v) = (v, 2)
|
neuper@37954
|
1157 |
| dest_hd' (Bound i) = ((("", i), dummyT), 3)
|
neuper@37954
|
1158 |
| dest_hd' (Abs (_, T, _)) = ((("", 0), T), 4);
|
neuper@37954
|
1159 |
(* RL *)
|
neuper@37954
|
1160 |
fun get_order_pow (t $ (Free(order,_))) =
|
neuper@37954
|
1161 |
(case int_of_str (order) of
|
neuper@37954
|
1162 |
SOME d => d
|
neuper@37954
|
1163 |
| NONE => 0)
|
neuper@37954
|
1164 |
| get_order_pow _ = 0;
|
neuper@37954
|
1165 |
|
neuper@37954
|
1166 |
fun size_of_term' (Const(str,_) $ t) =
|
neuper@37954
|
1167 |
if "Atools.pow"=str then 1000 + size_of_term' t else 1 + size_of_term' t(*WN*)
|
neuper@37954
|
1168 |
| size_of_term' (Abs (_,_,body)) = 1 + size_of_term' body
|
neuper@37954
|
1169 |
| size_of_term' (f$t) = size_of_term' f + size_of_term' t
|
neuper@37954
|
1170 |
| size_of_term' _ = 1;
|
neuper@37954
|
1171 |
|
neuper@37954
|
1172 |
fun term_ord' pr thy (Abs (_, T, t), Abs(_, U, u)) = (* ~ term.ML *)
|
neuper@37954
|
1173 |
(case term_ord' pr thy (t, u) of EQUAL => typ_ord (T, U) | ord => ord)
|
neuper@37954
|
1174 |
| term_ord' pr thy (t, u) =
|
neuper@37954
|
1175 |
(if pr then
|
neuper@37954
|
1176 |
let
|
neuper@37954
|
1177 |
val (f, ts) = strip_comb t and (g, us) = strip_comb u;
|
neuper@37954
|
1178 |
val _=writeln("t= f@ts= " ^ "" ^
|
neuper@37954
|
1179 |
((Syntax.string_of_term (thy2ctxt thy)) f)^ "\" @ " ^ "[" ^
|
neuper@37954
|
1180 |
(commas(map(Syntax.string_of_term (thy2ctxt thy)) ts)) ^ "]""");
|
neuper@37954
|
1181 |
val _=writeln("u= g@us= " ^ "" ^
|
neuper@37954
|
1182 |
((Syntax.string_of_term (thy2ctxt thy)) g) ^ "\" @ " ^ "[" ^
|
neuper@37954
|
1183 |
(commas(map(Syntax.string_of_term (thy2ctxt thy)) us))^"]""");
|
neuper@37954
|
1184 |
val _=writeln("size_of_term(t,u)= ("^
|
neuper@37954
|
1185 |
(string_of_int(size_of_term' t)) ^ ", " ^
|
neuper@37954
|
1186 |
(string_of_int(size_of_term' u)) ^ ")");
|
neuper@37954
|
1187 |
val _=writeln("hd_ord(f,g) = " ^ ((pr_ord o hd_ord)(f,g)));
|
neuper@37954
|
1188 |
val _=writeln("terms_ord(ts,us) = " ^
|
neuper@37954
|
1189 |
((pr_ord o terms_ord str false)(ts,us)));
|
neuper@37954
|
1190 |
val _=writeln("-------");
|
neuper@37954
|
1191 |
in () end
|
neuper@37954
|
1192 |
else ();
|
neuper@37954
|
1193 |
case int_ord (size_of_term' t, size_of_term' u) of
|
neuper@37954
|
1194 |
EQUAL =>
|
neuper@37954
|
1195 |
let val (f, ts) = strip_comb t and (g, us) = strip_comb u in
|
neuper@37954
|
1196 |
(case hd_ord (f, g) of EQUAL => (terms_ord str pr) (ts, us)
|
neuper@37954
|
1197 |
| ord => ord)
|
neuper@37954
|
1198 |
end
|
neuper@37954
|
1199 |
| ord => ord)
|
neuper@37954
|
1200 |
and hd_ord (f, g) = (* ~ term.ML *)
|
neuper@37954
|
1201 |
prod_ord (prod_ord indexname_ord typ_ord) int_ord (dest_hd' f, dest_hd' g)
|
neuper@37954
|
1202 |
and terms_ord str pr (ts, us) =
|
neuper@37954
|
1203 |
list_ord (term_ord' pr (assoc_thy "Isac.thy"))(ts, us);
|
neuper@37954
|
1204 |
in
|
neuper@37954
|
1205 |
|
neuper@37954
|
1206 |
fun ord_make_polytest (pr:bool) thy (_:subst) tu =
|
neuper@37954
|
1207 |
(term_ord' pr thy(***) tu = LESS );
|
neuper@37954
|
1208 |
|
neuper@37954
|
1209 |
end;(*local*)
|
neuper@37954
|
1210 |
|
neuper@37954
|
1211 |
rew_ord' := overwritel (!rew_ord',
|
neuper@37954
|
1212 |
[("termlessI", termlessI),
|
neuper@37954
|
1213 |
("ord_make_polytest", ord_make_polytest false thy)
|
neuper@37954
|
1214 |
]);
|
neuper@37954
|
1215 |
|
neuper@37954
|
1216 |
(*WN060510 this was a preparation for prep_rls ...
|
neuper@37954
|
1217 |
val scr_make_polytest =
|
neuper@37954
|
1218 |
"Script Expand_binomtest t_ =" ^
|
neuper@37954
|
1219 |
"(Repeat " ^
|
neuper@37954
|
1220 |
"((Try (Repeat (Rewrite real_diff_minus False))) @@ " ^
|
neuper@37954
|
1221 |
|
neuper@37954
|
1222 |
" (Try (Repeat (Rewrite real_add_mult_distrib False))) @@ " ^
|
neuper@37954
|
1223 |
" (Try (Repeat (Rewrite real_add_mult_distrib2 False))) @@ " ^
|
neuper@37954
|
1224 |
" (Try (Repeat (Rewrite real_diff_mult_distrib False))) @@ " ^
|
neuper@37954
|
1225 |
" (Try (Repeat (Rewrite real_diff_mult_distrib2 False))) @@ " ^
|
neuper@37954
|
1226 |
|
neuper@37954
|
1227 |
" (Try (Repeat (Rewrite real_mult_1 False))) @@ " ^
|
neuper@37954
|
1228 |
" (Try (Repeat (Rewrite real_mult_0 False))) @@ " ^
|
neuper@37954
|
1229 |
" (Try (Repeat (Rewrite real_add_zero_left False))) @@ " ^
|
neuper@37954
|
1230 |
|
neuper@37954
|
1231 |
" (Try (Repeat (Rewrite real_mult_commute False))) @@ " ^
|
neuper@37954
|
1232 |
" (Try (Repeat (Rewrite real_mult_left_commute False))) @@ " ^
|
neuper@37954
|
1233 |
" (Try (Repeat (Rewrite real_mult_assoc False))) @@ " ^
|
neuper@37954
|
1234 |
" (Try (Repeat (Rewrite real_add_commute False))) @@ " ^
|
neuper@37954
|
1235 |
" (Try (Repeat (Rewrite real_add_left_commute False))) @@ " ^
|
neuper@37954
|
1236 |
" (Try (Repeat (Rewrite real_add_assoc False))) @@ " ^
|
neuper@37954
|
1237 |
|
neuper@37954
|
1238 |
" (Try (Repeat (Rewrite sym_realpow_twoI False))) @@ " ^
|
neuper@37954
|
1239 |
" (Try (Repeat (Rewrite realpow_plus_1 False))) @@ " ^
|
neuper@37954
|
1240 |
" (Try (Repeat (Rewrite sym_real_mult_2 False))) @@ " ^
|
neuper@37954
|
1241 |
" (Try (Repeat (Rewrite real_mult_2_assoc False))) @@ " ^
|
neuper@37954
|
1242 |
|
neuper@37954
|
1243 |
" (Try (Repeat (Rewrite real_num_collect False))) @@ " ^
|
neuper@37954
|
1244 |
" (Try (Repeat (Rewrite real_num_collect_assoc False))) @@ " ^
|
neuper@37954
|
1245 |
|
neuper@37954
|
1246 |
" (Try (Repeat (Rewrite real_one_collect False))) @@ " ^
|
neuper@37954
|
1247 |
" (Try (Repeat (Rewrite real_one_collect_assoc False))) @@ " ^
|
neuper@37954
|
1248 |
|
neuper@37954
|
1249 |
" (Try (Repeat (Calculate plus ))) @@ " ^
|
neuper@37954
|
1250 |
" (Try (Repeat (Calculate times ))) @@ " ^
|
neuper@37954
|
1251 |
" (Try (Repeat (Calculate power_)))) " ^
|
neuper@37954
|
1252 |
" t_)";
|
neuper@37954
|
1253 |
-----------------------------------------------------*)
|
neuper@37954
|
1254 |
|
neuper@37954
|
1255 |
val make_polytest =
|
neuper@37954
|
1256 |
Rls{id = "make_polytest", preconds = []:term list,
|
neuper@37954
|
1257 |
rew_ord = ("ord_make_polytest", ord_make_polytest false (theory "Poly")),
|
neuper@37954
|
1258 |
erls = testerls, srls = Erls,
|
neuper@37954
|
1259 |
calc = [("PLUS" , ("op +", eval_binop "#add_")),
|
neuper@37954
|
1260 |
("TIMES" , ("op *", eval_binop "#mult_")),
|
neuper@37954
|
1261 |
("POWER", ("Atools.pow", eval_binop "#power_"))
|
neuper@37954
|
1262 |
],
|
neuper@37954
|
1263 |
(*asm_thm = [],*)
|
neuper@37954
|
1264 |
rules = [Thm ("real_diff_minus",num_str real_diff_minus),
|
neuper@37954
|
1265 |
(*"a - b = a + (-1) * b"*)
|
neuper@37954
|
1266 |
Thm ("real_add_mult_distrib" ,num_str real_add_mult_distrib),
|
neuper@37954
|
1267 |
(*"(z1.0 + z2.0) * w = z1.0 * w + z2.0 * w"*)
|
neuper@37954
|
1268 |
Thm ("real_add_mult_distrib2",num_str real_add_mult_distrib2),
|
neuper@37954
|
1269 |
(*"w * (z1.0 + z2.0) = w * z1.0 + w * z2.0"*)
|
neuper@37954
|
1270 |
Thm ("real_diff_mult_distrib" ,num_str real_diff_mult_distrib),
|
neuper@37954
|
1271 |
(*"(z1.0 - z2.0) * w = z1.0 * w - z2.0 * w"*)
|
neuper@37954
|
1272 |
Thm ("real_diff_mult_distrib2",num_str real_diff_mult_distrib2),
|
neuper@37954
|
1273 |
(*"w * (z1.0 - z2.0) = w * z1.0 - w * z2.0"*)
|
neuper@37954
|
1274 |
Thm ("real_mult_1",num_str real_mult_1),
|
neuper@37954
|
1275 |
(*"1 * z = z"*)
|
neuper@37954
|
1276 |
Thm ("real_mult_0",num_str real_mult_0),
|
neuper@37954
|
1277 |
(*"0 * z = 0"*)
|
neuper@37954
|
1278 |
Thm ("real_add_zero_left",num_str real_add_zero_left),
|
neuper@37954
|
1279 |
(*"0 + z = z"*)
|
neuper@37954
|
1280 |
|
neuper@37954
|
1281 |
(*AC-rewriting*)
|
neuper@37954
|
1282 |
Thm ("real_mult_commute",num_str real_mult_commute),
|
neuper@37954
|
1283 |
(* z * w = w * z *)
|
neuper@37954
|
1284 |
Thm ("real_mult_left_commute",num_str real_mult_left_commute),
|
neuper@37954
|
1285 |
(*z1.0 * (z2.0 * z3.0) = z2.0 * (z1.0 * z3.0)*)
|
neuper@37954
|
1286 |
Thm ("real_mult_assoc",num_str real_mult_assoc),
|
neuper@37954
|
1287 |
(*z1.0 * z2.0 * z3.0 = z1.0 * (z2.0 * z3.0)*)
|
neuper@37954
|
1288 |
Thm ("real_add_commute",num_str real_add_commute),
|
neuper@37954
|
1289 |
(*z + w = w + z*)
|
neuper@37954
|
1290 |
Thm ("real_add_left_commute",num_str real_add_left_commute),
|
neuper@37954
|
1291 |
(*x + (y + z) = y + (x + z)*)
|
neuper@37954
|
1292 |
Thm ("real_add_assoc",num_str real_add_assoc),
|
neuper@37954
|
1293 |
(*z1.0 + z2.0 + z3.0 = z1.0 + (z2.0 + z3.0)*)
|
neuper@37954
|
1294 |
|
neuper@37954
|
1295 |
Thm ("sym_realpow_twoI",num_str (realpow_twoI RS sym)),
|
neuper@37954
|
1296 |
(*"r1 * r1 = r1 ^^^ 2"*)
|
neuper@37954
|
1297 |
Thm ("realpow_plus_1",num_str realpow_plus_1),
|
neuper@37954
|
1298 |
(*"r * r ^^^ n = r ^^^ (n + 1)"*)
|
neuper@37954
|
1299 |
Thm ("sym_real_mult_2",num_str (real_mult_2 RS sym)),
|
neuper@37954
|
1300 |
(*"z1 + z1 = 2 * z1"*)
|
neuper@37954
|
1301 |
Thm ("real_mult_2_assoc",num_str real_mult_2_assoc),
|
neuper@37954
|
1302 |
(*"z1 + (z1 + k) = 2 * z1 + k"*)
|
neuper@37954
|
1303 |
|
neuper@37954
|
1304 |
Thm ("real_num_collect",num_str real_num_collect),
|
neuper@37954
|
1305 |
(*"[| l is_const; m is_const |]==>l * n + m * n = (l + m) * n"*)
|
neuper@37954
|
1306 |
Thm ("real_num_collect_assoc",num_str real_num_collect_assoc),
|
neuper@37954
|
1307 |
(*"[| l is_const; m is_const |] ==>
|
neuper@37954
|
1308 |
l * n + (m * n + k) = (l + m) * n + k"*)
|
neuper@37954
|
1309 |
Thm ("real_one_collect",num_str real_one_collect),
|
neuper@37954
|
1310 |
(*"m is_const ==> n + m * n = (1 + m) * n"*)
|
neuper@37954
|
1311 |
Thm ("real_one_collect_assoc",num_str real_one_collect_assoc),
|
neuper@37954
|
1312 |
(*"m is_const ==> k + (n + m * n) = k + (1 + m) * n"*)
|
neuper@37954
|
1313 |
|
neuper@37954
|
1314 |
Calc ("op +", eval_binop "#add_"),
|
neuper@37954
|
1315 |
Calc ("op *", eval_binop "#mult_"),
|
neuper@37954
|
1316 |
Calc ("Atools.pow", eval_binop "#power_")
|
neuper@37954
|
1317 |
],
|
neuper@37954
|
1318 |
scr = EmptyScr(*Script ((term_of o the o (parse thy))
|
neuper@37954
|
1319 |
scr_make_polytest)*)
|
neuper@37954
|
1320 |
}:rls;
|
neuper@37954
|
1321 |
(*WN060510 this was done before 'fun prep_rls' ...
|
neuper@37954
|
1322 |
val scr_expand_binomtest =
|
neuper@37954
|
1323 |
"Script Expand_binomtest t_ =" ^
|
neuper@37954
|
1324 |
"(Repeat " ^
|
neuper@37954
|
1325 |
"((Try (Repeat (Rewrite real_plus_binom_pow2 False))) @@ " ^
|
neuper@37954
|
1326 |
" (Try (Repeat (Rewrite real_plus_binom_times False))) @@ " ^
|
neuper@37954
|
1327 |
" (Try (Repeat (Rewrite real_minus_binom_pow2 False))) @@ " ^
|
neuper@37954
|
1328 |
" (Try (Repeat (Rewrite real_minus_binom_times False))) @@ " ^
|
neuper@37954
|
1329 |
" (Try (Repeat (Rewrite real_plus_minus_binom1 False))) @@ " ^
|
neuper@37954
|
1330 |
" (Try (Repeat (Rewrite real_plus_minus_binom2 False))) @@ " ^
|
neuper@37954
|
1331 |
|
neuper@37954
|
1332 |
" (Try (Repeat (Rewrite real_mult_1 False))) @@ " ^
|
neuper@37954
|
1333 |
" (Try (Repeat (Rewrite real_mult_0 False))) @@ " ^
|
neuper@37954
|
1334 |
" (Try (Repeat (Rewrite real_add_zero_left False))) @@ " ^
|
neuper@37954
|
1335 |
|
neuper@37954
|
1336 |
" (Try (Repeat (Calculate plus ))) @@ " ^
|
neuper@37954
|
1337 |
" (Try (Repeat (Calculate times ))) @@ " ^
|
neuper@37954
|
1338 |
" (Try (Repeat (Calculate power_))) @@ " ^
|
neuper@37954
|
1339 |
|
neuper@37954
|
1340 |
" (Try (Repeat (Rewrite sym_realpow_twoI False))) @@ " ^
|
neuper@37954
|
1341 |
" (Try (Repeat (Rewrite realpow_plus_1 False))) @@ " ^
|
neuper@37954
|
1342 |
" (Try (Repeat (Rewrite sym_real_mult_2 False))) @@ " ^
|
neuper@37954
|
1343 |
" (Try (Repeat (Rewrite real_mult_2_assoc False))) @@ " ^
|
neuper@37954
|
1344 |
|
neuper@37954
|
1345 |
" (Try (Repeat (Rewrite real_num_collect False))) @@ " ^
|
neuper@37954
|
1346 |
" (Try (Repeat (Rewrite real_num_collect_assoc False))) @@ " ^
|
neuper@37954
|
1347 |
|
neuper@37954
|
1348 |
" (Try (Repeat (Rewrite real_one_collect False))) @@ " ^
|
neuper@37954
|
1349 |
" (Try (Repeat (Rewrite real_one_collect_assoc False))) @@ " ^
|
neuper@37954
|
1350 |
|
neuper@37954
|
1351 |
" (Try (Repeat (Calculate plus ))) @@ " ^
|
neuper@37954
|
1352 |
" (Try (Repeat (Calculate times ))) @@ " ^
|
neuper@37954
|
1353 |
" (Try (Repeat (Calculate power_)))) " ^
|
neuper@37954
|
1354 |
" t_)";
|
neuper@37954
|
1355 |
------------------------------------------------------*)
|
neuper@37954
|
1356 |
|
neuper@37954
|
1357 |
val expand_binomtest =
|
neuper@37954
|
1358 |
Rls{id = "expand_binomtest", preconds = [],
|
neuper@37954
|
1359 |
rew_ord = ("termlessI",termlessI),
|
neuper@37954
|
1360 |
erls = testerls, srls = Erls,
|
neuper@37954
|
1361 |
calc = [("PLUS" , ("op +", eval_binop "#add_")),
|
neuper@37954
|
1362 |
("TIMES" , ("op *", eval_binop "#mult_")),
|
neuper@37954
|
1363 |
("POWER", ("Atools.pow", eval_binop "#power_"))
|
neuper@37954
|
1364 |
],
|
neuper@37954
|
1365 |
(*asm_thm = [],*)
|
neuper@37954
|
1366 |
rules = [Thm ("real_plus_binom_pow2" ,num_str real_plus_binom_pow2),
|
neuper@37954
|
1367 |
(*"(a + b) ^^^ 2 = a ^^^ 2 + 2 * a * b + b ^^^ 2"*)
|
neuper@37954
|
1368 |
Thm ("real_plus_binom_times" ,num_str real_plus_binom_times),
|
neuper@37954
|
1369 |
(*"(a + b)*(a + b) = ...*)
|
neuper@37954
|
1370 |
Thm ("real_minus_binom_pow2" ,num_str real_minus_binom_pow2),
|
neuper@37954
|
1371 |
(*"(a - b) ^^^ 2 = a ^^^ 2 - 2 * a * b + b ^^^ 2"*)
|
neuper@37954
|
1372 |
Thm ("real_minus_binom_times",num_str real_minus_binom_times),
|
neuper@37954
|
1373 |
(*"(a - b)*(a - b) = ...*)
|
neuper@37954
|
1374 |
Thm ("real_plus_minus_binom1",num_str real_plus_minus_binom1),
|
neuper@37954
|
1375 |
(*"(a + b) * (a - b) = a ^^^ 2 - b ^^^ 2"*)
|
neuper@37954
|
1376 |
Thm ("real_plus_minus_binom2",num_str real_plus_minus_binom2),
|
neuper@37954
|
1377 |
(*"(a - b) * (a + b) = a ^^^ 2 - b ^^^ 2"*)
|
neuper@37954
|
1378 |
(*RL 020915*)
|
neuper@37954
|
1379 |
Thm ("real_pp_binom_times",num_str real_pp_binom_times),
|
neuper@37954
|
1380 |
(*(a + b)*(c + d) = a*c + a*d + b*c + b*d*)
|
neuper@37954
|
1381 |
Thm ("real_pm_binom_times",num_str real_pm_binom_times),
|
neuper@37954
|
1382 |
(*(a + b)*(c - d) = a*c - a*d + b*c - b*d*)
|
neuper@37954
|
1383 |
Thm ("real_mp_binom_times",num_str real_mp_binom_times),
|
neuper@37954
|
1384 |
(*(a - b)*(c p d) = a*c + a*d - b*c - b*d*)
|
neuper@37954
|
1385 |
Thm ("real_mm_binom_times",num_str real_mm_binom_times),
|
neuper@37954
|
1386 |
(*(a - b)*(c p d) = a*c - a*d - b*c + b*d*)
|
neuper@37954
|
1387 |
Thm ("realpow_multI",num_str realpow_multI),
|
neuper@37954
|
1388 |
(*(a*b)^^^n = a^^^n * b^^^n*)
|
neuper@37954
|
1389 |
Thm ("real_plus_binom_pow3",num_str real_plus_binom_pow3),
|
neuper@37954
|
1390 |
(* (a + b)^^^3 = a^^^3 + 3*a^^^2*b + 3*a*b^^^2 + b^^^3 *)
|
neuper@37954
|
1391 |
Thm ("real_minus_binom_pow3",num_str real_minus_binom_pow3),
|
neuper@37954
|
1392 |
(* (a - b)^^^3 = a^^^3 - 3*a^^^2*b + 3*a*b^^^2 - b^^^3 *)
|
neuper@37954
|
1393 |
|
neuper@37954
|
1394 |
|
neuper@37954
|
1395 |
(* Thm ("real_add_mult_distrib" ,num_str real_add_mult_distrib),
|
neuper@37954
|
1396 |
(*"(z1.0 + z2.0) * w = z1.0 * w + z2.0 * w"*)
|
neuper@37954
|
1397 |
Thm ("real_add_mult_distrib2",num_str real_add_mult_distrib2),
|
neuper@37954
|
1398 |
(*"w * (z1.0 + z2.0) = w * z1.0 + w * z2.0"*)
|
neuper@37954
|
1399 |
Thm ("real_diff_mult_distrib" ,num_str real_diff_mult_distrib),
|
neuper@37954
|
1400 |
(*"(z1.0 - z2.0) * w = z1.0 * w - z2.0 * w"*)
|
neuper@37954
|
1401 |
Thm ("real_diff_mult_distrib2",num_str real_diff_mult_distrib2),
|
neuper@37954
|
1402 |
(*"w * (z1.0 - z2.0) = w * z1.0 - w * z2.0"*)
|
neuper@37954
|
1403 |
*)
|
neuper@37954
|
1404 |
|
neuper@37954
|
1405 |
Thm ("real_mult_1",num_str real_mult_1), (*"1 * z = z"*)
|
neuper@37954
|
1406 |
Thm ("real_mult_0",num_str real_mult_0), (*"0 * z = 0"*)
|
neuper@37954
|
1407 |
Thm ("real_add_zero_left",num_str real_add_zero_left),(*"0 + z = z"*)
|
neuper@37954
|
1408 |
|
neuper@37954
|
1409 |
Calc ("op +", eval_binop "#add_"),
|
neuper@37954
|
1410 |
Calc ("op *", eval_binop "#mult_"),
|
neuper@37954
|
1411 |
Calc ("Atools.pow", eval_binop "#power_"),
|
neuper@37954
|
1412 |
(*
|
neuper@37954
|
1413 |
Thm ("real_mult_commute",num_str real_mult_commute), (*AC-rewriting*)
|
neuper@37954
|
1414 |
Thm ("real_mult_left_commute",num_str real_mult_left_commute), (**)
|
neuper@37954
|
1415 |
Thm ("real_mult_assoc",num_str real_mult_assoc), (**)
|
neuper@37954
|
1416 |
Thm ("real_add_commute",num_str real_add_commute), (**)
|
neuper@37954
|
1417 |
Thm ("real_add_left_commute",num_str real_add_left_commute), (**)
|
neuper@37954
|
1418 |
Thm ("real_add_assoc",num_str real_add_assoc), (**)
|
neuper@37954
|
1419 |
*)
|
neuper@37954
|
1420 |
|
neuper@37954
|
1421 |
Thm ("sym_realpow_twoI",num_str (realpow_twoI RS sym)),
|
neuper@37954
|
1422 |
(*"r1 * r1 = r1 ^^^ 2"*)
|
neuper@37954
|
1423 |
Thm ("realpow_plus_1",num_str realpow_plus_1),
|
neuper@37954
|
1424 |
(*"r * r ^^^ n = r ^^^ (n + 1)"*)
|
neuper@37954
|
1425 |
(*Thm ("sym_real_mult_2",num_str (real_mult_2 RS sym)),
|
neuper@37954
|
1426 |
(*"z1 + z1 = 2 * z1"*)*)
|
neuper@37954
|
1427 |
Thm ("real_mult_2_assoc",num_str real_mult_2_assoc),
|
neuper@37954
|
1428 |
(*"z1 + (z1 + k) = 2 * z1 + k"*)
|
neuper@37954
|
1429 |
|
neuper@37954
|
1430 |
Thm ("real_num_collect",num_str real_num_collect),
|
neuper@37954
|
1431 |
(*"[| l is_const; m is_const |] ==> l * n + m * n = (l + m) * n"*)
|
neuper@37954
|
1432 |
Thm ("real_num_collect_assoc",num_str real_num_collect_assoc),
|
neuper@37954
|
1433 |
(*"[| l is_const; m is_const |] ==> l * n + (m * n + k) = (l + m) * n + k"*)
|
neuper@37954
|
1434 |
Thm ("real_one_collect",num_str real_one_collect),
|
neuper@37954
|
1435 |
(*"m is_const ==> n + m * n = (1 + m) * n"*)
|
neuper@37954
|
1436 |
Thm ("real_one_collect_assoc",num_str real_one_collect_assoc),
|
neuper@37954
|
1437 |
(*"m is_const ==> k + (n + m * n) = k + (1 + m) * n"*)
|
neuper@37954
|
1438 |
|
neuper@37954
|
1439 |
Calc ("op +", eval_binop "#add_"),
|
neuper@37954
|
1440 |
Calc ("op *", eval_binop "#mult_"),
|
neuper@37954
|
1441 |
Calc ("Atools.pow", eval_binop "#power_")
|
neuper@37954
|
1442 |
],
|
neuper@37954
|
1443 |
scr = EmptyScr
|
neuper@37954
|
1444 |
(*Script ((term_of o the o (parse thy)) scr_expand_binomtest)*)
|
neuper@37954
|
1445 |
}:rls;
|
neuper@37954
|
1446 |
|
neuper@37954
|
1447 |
|
neuper@37954
|
1448 |
ruleset' := overwritelthy thy (!ruleset',
|
neuper@37954
|
1449 |
[("make_polytest", prep_rls make_polytest),
|
neuper@37954
|
1450 |
("expand_binomtest", prep_rls expand_binomtest)
|
neuper@37954
|
1451 |
]);
|
neuper@37954
|
1452 |
*}
|
neuper@37906
|
1453 |
|
neuper@37906
|
1454 |
end
|