neuper@37906
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1 |
(* WN.020812: theorems in the Reals,
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neuper@37906
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2 |
necessary for special rule sets, in addition to Isabelle2002.
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neuper@37906
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3 |
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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neuper@37906
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!!! THIS IS THE _least_ NUMBER OF ADDITIONAL THEOREMS !!!
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neuper@37906
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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walther@60242
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xxxI contain \<up> instead of ^ in the respective theorem xxx in 2002
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neuper@37906
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changed by: Richard Lang 020912
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neuper@37906
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*)
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neuper@37906
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9 |
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neuper@37950
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theory Poly imports Simplify begin
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neuper@37906
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11 |
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wneuper@59523
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subsection \<open>remark on term-structure of polynomials\<close>
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wneuper@59523
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text \<open>
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wneuper@59523
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WN190319:
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wneuper@59523
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the code below reflects missing coordination between two authors:
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wneuper@59523
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* ML: built the equation solver; simple rule-sets, programs; better predicates for specifications.
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wneuper@59523
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* MG: built simplification of polynomials with AC rewriting by ML code
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wneuper@59523
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wneuper@59523
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WN020919:
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wneuper@59523
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*** there are 5 kinds of expanded normalforms ***
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wneuper@59523
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wneuper@59523
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[1] 'complete polynomial' (Komplettes Polynom), univariate
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wneuper@59523
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a_0 + a_1.x^1 +...+ a_n.x^n not (a_n = 0)
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wneuper@59523
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not (a_n = 0), some a_i may be zero (DON'T disappear),
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wneuper@59523
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variables in monomials lexicographically ordered and complete,
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wneuper@59523
|
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x written as 1*x^1, ...
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wneuper@59523
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[2] 'polynomial' (Polynom), univariate and multivariate
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wneuper@59523
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a_0 + a_1.x +...+ a_n.x^n not (a_n = 0)
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wneuper@59523
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a_0 + a_1.x_1.x_2^n_12...x_m^n_1m +...+ a_n.x_1^n.x_2^n_n2...x_m^n_nm
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wneuper@59523
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not (a_n = 0), some a_i may be zero (ie. monomials disappear),
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wneuper@59523
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exponents and coefficients equal 1 are not (WN060904.TODO in cancel_p_)shown,
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wneuper@59523
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and variables in monomials are lexicographically ordered
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walther@60242
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examples: [1]: "1 + (-10) * x \<up> 1 + 25 * x \<up> 2"
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walther@60242
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[1]: "11 + 0 * x \<up> 1 + 1 * x \<up> 2"
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walther@60242
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[2]: "x + (-50) * x \<up> 3"
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walther@60242
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[2]: "(-1) * x * y \<up> 2 + 7 * x \<up> 3"
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wneuper@59523
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37 |
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wneuper@59523
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[3] 'expanded_term' (Ausmultiplizierter Term):
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wneuper@59523
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pull out unary minus to binary minus,
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wneuper@59523
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as frequently exercised in schools; other conditions for [2] hold however
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walther@60242
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examples: "a \<up> 2 - 2 * a * b + b \<up> 2"
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walther@60242
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"4 * x \<up> 2 - 9 * y \<up> 2"
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wneuper@59523
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[4] 'polynomial_in' (Polynom in):
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wneuper@59523
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polynomial in 1 variable with arbitrary coefficients
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walther@60242
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examples: "2 * x + (-50) * x \<up> 3" (poly in x)
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walther@60242
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"(u + v) + (2 * u \<up> 2) * a + (-u) * a \<up> 2 (poly in a)
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wneuper@59523
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[5] 'expanded_in' (Ausmultiplizierter Termin in):
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wneuper@59523
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analoguous to [3] with binary minus like [3]
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walther@60242
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examples: "2 * x - 50 * x \<up> 3" (expanded in x)
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walther@60242
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"(u + v) + (2 * u \<up> 2) * a - u * a \<up> 2 (expanded in a)
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wneuper@59523
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\<close>
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wneuper@59523
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subsection \<open>consts definition for predicates in specifications\<close>
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neuper@37906
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consts
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neuper@37906
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walther@60278
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is_expanded_in :: "[real, real] => bool" ("_ is'_expanded'_in _")
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walther@60278
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is_poly_in :: "[real, real] => bool" ("_ is'_poly'_in _") (*RL DA *)
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walther@60278
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has_degree_in :: "[real, real] => real" ("_ has'_degree'_in _")(*RL DA *)
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walther@60278
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is_polyrat_in :: "[real, real] => bool" ("_ is'_polyrat'_in _")(*RL030626*)
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neuper@37906
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walther@60278
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is_multUnordered:: "real => bool" ("_ is'_multUnordered")
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walther@60278
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is_addUnordered :: "real => bool" ("_ is'_addUnordered") (*WN030618*)
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walther@60278
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is_polyexp :: "real => bool" ("_ is'_polyexp")
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neuper@37906
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wneuper@59523
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subsection \<open>theorems not yet adopted from Isabelle\<close>
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neuper@52148
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axiomatization where (*.not contained in Isabelle2002,
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neuper@37906
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stated as axioms, TODO: prove as theorems;
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walther@60242
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theorem-IDs 'xxxI' with \<up> instead of ^ in 'xxx' in Isabelle2002.*)
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neuper@37906
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walther@60242
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realpow_pow: "(a \<up> b) \<up> c = a \<up> (b * c)" and
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walther@60242
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realpow_addI: "r \<up> (n + m) = r \<up> n * r \<up> m" and
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walther@60242
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realpow_addI_assoc_l: "r \<up> n * (r \<up> m * s) = r \<up> (n + m) * s" and
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walther@60242
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realpow_addI_assoc_r: "s * r \<up> n * r \<up> m = s * r \<up> (n + m)" and
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neuper@37906
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walther@60242
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realpow_oneI: "r \<up> 1 = r" and
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walther@60242
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realpow_zeroI: "r \<up> 0 = 1" and
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walther@60242
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realpow_eq_oneI: "1 \<up> n = 1" and
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walther@60242
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realpow_multI: "(r * s) \<up> n = r \<up> n * s \<up> n" and
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neuper@37974
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realpow_multI_poly: "[| r is_polyexp; s is_polyexp |] ==>
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walther@60242
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(r * s) \<up> n = r \<up> n * s \<up> n" and
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walther@60242
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realpow_minus_oneI: "(- 1) \<up> (2 * n) = 1" and
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wneuper@59589
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real_diff_0: "0 - x = - (x::real)" and
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neuper@37906
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walther@60242
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realpow_twoI: "r \<up> 2 = r * r" and
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walther@60242
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realpow_twoI_assoc_l: "r * (r * s) = r \<up> 2 * s" and
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walther@60242
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realpow_twoI_assoc_r: "s * r * r = s * r \<up> 2" and
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walther@60242
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realpow_two_atom: "r is_atom ==> r * r = r \<up> 2" and
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walther@60242
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realpow_plus_1: "r * r \<up> n = r \<up> (n + 1)" and
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walther@60242
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realpow_plus_1_assoc_l: "r * (r \<up> m * s) = r \<up> (1 + m) * s" and
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walther@60242
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realpow_plus_1_assoc_l2: "r \<up> m * (r * s) = r \<up> (1 + m) * s" and
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walther@60242
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realpow_plus_1_assoc_r: "s * r * r \<up> m = s * r \<up> (1 + m)" and
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walther@60242
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realpow_plus_1_atom: "r is_atom ==> r * r \<up> n = r \<up> (1 + n)" and
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neuper@37974
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realpow_def_atom: "[| Not (r is_atom); 1 < n |]
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walther@60242
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==> r \<up> n = r * r \<up> (n + -1)" and
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walther@60242
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realpow_addI_atom: "r is_atom ==> r \<up> n * r \<up> m = r \<up> (n + m)" and
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neuper@37906
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neuper@37906
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96 |
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walther@60278
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realpow_minus_even: "n is_even ==> (- r) \<up> n = r \<up> n" and
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walther@60242
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realpow_minus_odd: "Not (n is_even) ==> (- r) \<up> n = -1 * r \<up> n" and
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neuper@37906
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neuper@37906
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neuper@37906
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(* RL 020914 *)
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neuper@52148
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real_pp_binom_times: "(a + b)*(c + d) = a*c + a*d + b*c + b*d" and
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neuper@52148
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real_pm_binom_times: "(a + b)*(c - d) = a*c - a*d + b*c - b*d" and
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neuper@52148
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real_mp_binom_times: "(a - b)*(c + d) = a*c + a*d - b*c - b*d" and
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neuper@52148
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real_mm_binom_times: "(a - b)*(c - d) = a*c - a*d - b*c + b*d" and
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walther@60242
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real_plus_binom_pow3: "(a + b) \<up> 3 = a \<up> 3 + 3*a \<up> 2*b + 3*a*b \<up> 2 + b \<up> 3" and
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neuper@37974
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real_plus_binom_pow3_poly: "[| a is_polyexp; b is_polyexp |] ==>
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walther@60242
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(a + b) \<up> 3 = a \<up> 3 + 3*a \<up> 2*b + 3*a*b \<up> 2 + b \<up> 3" and
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walther@60242
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real_minus_binom_pow3: "(a - b) \<up> 3 = a \<up> 3 - 3*a \<up> 2*b + 3*a*b \<up> 2 - b \<up> 3" and
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walther@60242
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real_minus_binom_pow3_p: "(a + -1 * b) \<up> 3 = a \<up> 3 + -3*a \<up> 2*b + 3*a*b \<up> 2 +
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walther@60242
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-1*b \<up> 3" and
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neuper@37974
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(* real_plus_binom_pow: "[| n is_const; 3 < n |] ==>
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walther@60260
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(a + b) \<up> n = (a + b) * (a + b)\<up>(n - 1)" *)
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walther@60242
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real_plus_binom_pow4: "(a + b) \<up> 4 = (a \<up> 3 + 3*a \<up> 2*b + 3*a*b \<up> 2 + b \<up> 3)
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neuper@52148
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*(a + b)" and
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neuper@37974
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real_plus_binom_pow4_poly: "[| a is_polyexp; b is_polyexp |] ==>
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walther@60242
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(a + b) \<up> 4 = (a \<up> 3 + 3*a \<up> 2*b + 3*a*b \<up> 2 + b \<up> 3)
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neuper@52148
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*(a + b)" and
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walther@60242
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real_plus_binom_pow5: "(a + b) \<up> 5 = (a \<up> 3 + 3*a \<up> 2*b + 3*a*b \<up> 2 + b \<up> 3)
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walther@60242
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*(a \<up> 2 + 2*a*b + b \<up> 2)" and
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neuper@37974
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real_plus_binom_pow5_poly: "[| a is_polyexp; b is_polyexp |] ==>
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walther@60242
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(a + b) \<up> 5 = (a \<up> 3 + 3*a \<up> 2*b + 3*a*b \<up> 2
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walther@60242
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+ b \<up> 3)*(a \<up> 2 + 2*a*b + b \<up> 2)" and
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neuper@52148
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real_diff_plus: "a - b = a + -b" (*17.3.03: do_NOT_use*) and
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neuper@52148
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real_diff_minus: "a - b = a + -1 * b" and
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walther@60242
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real_plus_binom_times: "(a + b)*(a + b) = a \<up> 2 + 2*a*b + b \<up> 2" and
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walther@60242
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real_minus_binom_times: "(a - b)*(a - b) = a \<up> 2 - 2*a*b + b \<up> 2" and
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neuper@37906
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(*WN071229 changed for Schaerding -----vvv*)
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walther@60260
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(*real_plus_binom_pow2: "(a + b) \<up> 2 = a \<up> 2 + 2*a*b + b \<up> 2"*)
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walther@60242
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real_plus_binom_pow2: "(a + b) \<up> 2 = (a + b) * (a + b)" and
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walther@60242
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(*WN071229 changed for Schaerding -----\<up>*)
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neuper@37974
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real_plus_binom_pow2_poly: "[| a is_polyexp; b is_polyexp |] ==>
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walther@60242
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(a + b) \<up> 2 = a \<up> 2 + 2*a*b + b \<up> 2" and
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walther@60242
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134 |
real_minus_binom_pow2: "(a - b) \<up> 2 = a \<up> 2 - 2*a*b + b \<up> 2" and
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walther@60242
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135 |
real_minus_binom_pow2_p: "(a - b) \<up> 2 = a \<up> 2 + -2*a*b + b \<up> 2" and
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walther@60242
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real_plus_minus_binom1: "(a + b)*(a - b) = a \<up> 2 - b \<up> 2" and
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walther@60242
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real_plus_minus_binom1_p: "(a + b)*(a - b) = a \<up> 2 + -1*b \<up> 2" and
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walther@60242
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138 |
real_plus_minus_binom1_p_p: "(a + b)*(a + -1 * b) = a \<up> 2 + -1*b \<up> 2" and
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walther@60242
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real_plus_minus_binom2: "(a - b)*(a + b) = a \<up> 2 - b \<up> 2" and
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walther@60242
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real_plus_minus_binom2_p: "(a - b)*(a + b) = a \<up> 2 + -1*b \<up> 2" and
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walther@60242
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real_plus_minus_binom2_p_p: "(a + -1 * b)*(a + b) = a \<up> 2 + -1*b \<up> 2" and
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walther@60242
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real_plus_binom_times1: "(a + 1*b)*(a + -1*b) = a \<up> 2 + -1*b \<up> 2" and
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walther@60242
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real_plus_binom_times2: "(a + -1*b)*(a + 1*b) = a \<up> 2 + -1*b \<up> 2" and
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neuper@37906
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neuper@37974
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real_num_collect: "[| l is_const; m is_const |] ==>
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neuper@52148
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146 |
l * n + m * n = (l + m) * n" and
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neuper@37906
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147 |
(* FIXME.MG.0401: replace 'real_num_collect_assoc'
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neuper@37906
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148 |
by 'real_num_collect_assoc_l' ... are equal, introduced by MG ! *)
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neuper@37974
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149 |
real_num_collect_assoc: "[| l is_const; m is_const |] ==>
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neuper@52148
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150 |
l * n + (m * n + k) = (l + m) * n + k" and
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neuper@37974
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real_num_collect_assoc_l: "[| l is_const; m is_const |] ==>
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neuper@37950
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152 |
l * n + (m * n + k) = (l + m)
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neuper@52148
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* n + k" and
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neuper@37974
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real_num_collect_assoc_r: "[| l is_const; m is_const |] ==>
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neuper@52148
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155 |
(k + m * n) + l * n = k + (l + m) * n" and
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neuper@52148
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156 |
real_one_collect: "m is_const ==> n + m * n = (1 + m) * n" and
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neuper@37906
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157 |
(* FIXME.MG.0401: replace 'real_one_collect_assoc'
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neuper@37906
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158 |
by 'real_one_collect_assoc_l' ... are equal, introduced by MG ! *)
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neuper@52148
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159 |
real_one_collect_assoc: "m is_const ==> n + (m * n + k) = (1 + m)* n + k" and
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neuper@37906
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160 |
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neuper@52148
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161 |
real_one_collect_assoc_l: "m is_const ==> n + (m * n + k) = (1 + m) * n + k" and
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neuper@52148
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162 |
real_one_collect_assoc_r: "m is_const ==> (k + n) + m * n = k + (1 + m) * n" and
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neuper@37906
|
163 |
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neuper@37906
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164 |
(* FIXME.MG.0401: replace 'real_mult_2_assoc'
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neuper@37906
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165 |
by 'real_mult_2_assoc_l' ... are equal, introduced by MG ! *)
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neuper@52148
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166 |
real_mult_2_assoc: "z1 + (z1 + k) = 2 * z1 + k" and
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neuper@52148
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167 |
real_mult_2_assoc_l: "z1 + (z1 + k) = 2 * z1 + k" and
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neuper@52148
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168 |
real_mult_2_assoc_r: "(k + z1) + z1 = k + 2 * z1" and
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neuper@37906
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169 |
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wneuper@59587
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170 |
real_mult_left_commute: "z1 * (z2 * z3) = z2 * (z1 * z3)" and
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wneuper@59587
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171 |
real_mult_minus1: "-1 * z = - (z::real)" and
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walther@60333
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172 |
(*sym_real_mult_minus1 expands indefinitely without assumptions ...*)
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walther@60343
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173 |
real_mult_minus1_sym: "[| \<not>(matches (- 1 * x) z); \<not>(z is_num) |] ==> - (z::real) = -1 * z" and
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walther@60344
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174 |
real_minus_mult_left: "\<not> ((a::real) is_num) ==> (- a) * b = - (a * b)" and
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wneuper@59587
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175 |
real_mult_2: "2 * z = z + (z::real)" and
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walther@60343
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176 |
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neuper@52148
|
177 |
real_add_mult_distrib_poly: "w is_polyexp ==> (z1 + z2) * w = z1 * w + z2 * w" and
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neuper@37974
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178 |
real_add_mult_distrib2_poly:"w is_polyexp ==> w * (z1 + z2) = w * z1 + w * z2"
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neuper@37950
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179 |
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walther@60278
|
180 |
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wneuper@59523
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181 |
subsection \<open>auxiliary functions\<close>
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wneuper@59530
|
182 |
ML \<open>
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wneuper@59530
|
183 |
val poly_consts =
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wenzelm@60309
|
184 |
[\<^const_name>\<open>plus\<close>, \<^const_name>\<open>minus\<close>,
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wenzelm@60309
|
185 |
\<^const_name>\<open>divide\<close>, \<^const_name>\<open>times\<close>,
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wenzelm@60309
|
186 |
\<^const_name>\<open>powr\<close>];
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walther@60321
|
187 |
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walther@60321
|
188 |
val int_ord_SAVE = int_ord;
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walther@60321
|
189 |
(*for tests on rewrite orders*)
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walther@60321
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190 |
fun int_ord (i1, i2) =
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walther@60321
|
191 |
(@{print} {a = "int_ord (" ^ string_of_int i1 ^ ", " ^ string_of_int i2 ^ ") = ", z = Int.compare (i1, i2)};
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walther@60321
|
192 |
Int.compare (i1, i2));
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walther@60321
|
193 |
(**)val int_ord = int_ord_SAVE; (*..outcomment for tests*)
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wneuper@59530
|
194 |
\<close>
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wneuper@59523
|
195 |
subsubsection \<open>for predicates in specifications (ML)\<close>
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wneuper@59472
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196 |
ML \<open>
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wneuper@59522
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197 |
(*--- auxiliary for is_expanded_in, is_poly_in, has_degree_in ---*)
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walther@60317
|
198 |
(*. a "monomial t in variable v" is a term t with
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wneuper@59522
|
199 |
either (1) v NOT existent in t, or (2) v contained in t,
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wneuper@59522
|
200 |
if (1) then degree 0
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walther@60317
|
201 |
if (2) then v is a factor on the very right, casually with exponent.*)
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wneuper@59522
|
202 |
fun factor_right_deg (*case 2*)
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walther@60335
|
203 |
(Const (\<^const_name>\<open>Groups.times_class.times\<close>, _) $
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walther@60335
|
204 |
t1 $ (Const (\<^const_name>\<open>Transcendental.powr\<close>,_) $ vv $ num)) v =
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walther@60317
|
205 |
if vv = v andalso not (Prog_Expr.occurs_in v t1) then SOME (snd (HOLogic.dest_number num))
|
walther@60317
|
206 |
else NONE
|
walther@60335
|
207 |
| factor_right_deg (Const (\<^const_name>\<open>Transcendental.powr\<close>,_) $ vv $ num) v =
|
walther@60317
|
208 |
if (vv = v) then SOME (snd (HOLogic.dest_number num)) else NONE
|
walther@60331
|
209 |
|
wenzelm@60309
|
210 |
| factor_right_deg (Const (\<^const_name>\<open>times\<close>,_) $ t1 $ vv) v =
|
walther@59603
|
211 |
if vv = v andalso not (Prog_Expr.occurs_in v t1) then SOME 1 else NONE
|
wneuper@59522
|
212 |
| factor_right_deg vv v =
|
wneuper@59522
|
213 |
if (vv = v) then SOME 1 else NONE;
|
wneuper@59522
|
214 |
fun mono_deg_in m v = (*case 1*)
|
walther@59603
|
215 |
if not (Prog_Expr.occurs_in v m) then (*case 1*) SOME 0 else factor_right_deg m v;
|
wneuper@59522
|
216 |
|
wneuper@59522
|
217 |
fun expand_deg_in t v =
|
wneuper@59522
|
218 |
let
|
wenzelm@60309
|
219 |
fun edi ~1 ~1 (Const (\<^const_name>\<open>plus\<close>, _) $ t1 $ t2) =
|
wneuper@59522
|
220 |
(case mono_deg_in t2 v of (* $ is left associative*)
|
wneuper@59522
|
221 |
SOME d' => edi d' d' t1 | NONE => NONE)
|
wenzelm@60309
|
222 |
| edi ~1 ~1 (Const (\<^const_name>\<open>minus\<close>, _) $ t1 $ t2) =
|
wneuper@59522
|
223 |
(case mono_deg_in t2 v of
|
wneuper@59522
|
224 |
SOME d' => edi d' d' t1 | NONE => NONE)
|
wenzelm@60309
|
225 |
| edi d dmax (Const (\<^const_name>\<open>minus\<close>, _) $ t1 $ t2) =
|
wneuper@59522
|
226 |
(case mono_deg_in t2 v of (*(d = 0 andalso d' = 0) handle 3+4-...4 +x*)
|
wneuper@59522
|
227 |
SOME d' => if d > d' orelse (d = 0 andalso d' = 0) then edi d' dmax t1 else NONE
|
wneuper@59522
|
228 |
| NONE => NONE)
|
wenzelm@60309
|
229 |
| edi d dmax (Const (\<^const_name>\<open>plus\<close>,_) $ t1 $ t2) =
|
wneuper@59522
|
230 |
(case mono_deg_in t2 v of
|
wneuper@59522
|
231 |
SOME d' => (*RL (d = 0 andalso d' = 0) need to handle 3+4-...4 +x*)
|
wneuper@59522
|
232 |
if d > d' orelse (d = 0 andalso d' = 0) then edi d' dmax t1 else NONE
|
wneuper@59522
|
233 |
| NONE => NONE)
|
wneuper@59522
|
234 |
| edi ~1 ~1 t =
|
wneuper@59522
|
235 |
(case mono_deg_in t v of d as SOME _ => d | NONE => NONE)
|
wneuper@59522
|
236 |
| edi d dmax t = (*basecase last*)
|
wneuper@59522
|
237 |
(case mono_deg_in t v of
|
wneuper@59522
|
238 |
SOME d' => if d > d' orelse (d = 0 andalso d' = 0) then SOME dmax else NONE
|
wneuper@59522
|
239 |
| NONE => NONE)
|
wneuper@59522
|
240 |
in edi ~1 ~1 t end;
|
wneuper@59522
|
241 |
|
wneuper@59522
|
242 |
fun poly_deg_in t v =
|
wneuper@59522
|
243 |
let
|
wenzelm@60309
|
244 |
fun edi ~1 ~1 (Const (\<^const_name>\<open>plus\<close>,_) $ t1 $ t2) =
|
wneuper@59522
|
245 |
(case mono_deg_in t2 v of (* $ is left associative *)
|
wneuper@59522
|
246 |
SOME d' => edi d' d' t1
|
wneuper@59522
|
247 |
| NONE => NONE)
|
wenzelm@60309
|
248 |
| edi d dmax (Const (\<^const_name>\<open>plus\<close>,_) $ t1 $ t2) =
|
wneuper@59522
|
249 |
(case mono_deg_in t2 v of
|
wneuper@59522
|
250 |
SOME d' => (*RL (d = 0 andalso (d' = 0)) handle 3+4-...4 +x*)
|
wneuper@59522
|
251 |
if d > d' orelse (d = 0 andalso d' = 0) then edi d' dmax t1 else NONE
|
wneuper@59522
|
252 |
| NONE => NONE)
|
wneuper@59522
|
253 |
| edi ~1 ~1 t =
|
wneuper@59522
|
254 |
(case mono_deg_in t v of
|
wneuper@59522
|
255 |
d as SOME _ => d
|
wneuper@59522
|
256 |
| NONE => NONE)
|
wneuper@59522
|
257 |
| edi d dmax t = (* basecase last *)
|
wneuper@59522
|
258 |
(case mono_deg_in t v of
|
wneuper@59522
|
259 |
SOME d' =>
|
wneuper@59522
|
260 |
if d > d' orelse (d = 0 andalso d' = 0) then SOME dmax else NONE
|
wneuper@59522
|
261 |
| NONE => NONE)
|
wneuper@59522
|
262 |
in edi ~1 ~1 t end;
|
wneuper@59523
|
263 |
\<close>
|
neuper@37950
|
264 |
|
wneuper@59523
|
265 |
subsubsection \<open>for hard-coded AC rewriting (MG)\<close>
|
wneuper@59523
|
266 |
ML \<open>
|
wneuper@59523
|
267 |
(**. MG.03: make_polynomial_ ... uses SML-fun for ordering .**)
|
neuper@37950
|
268 |
|
wneuper@59523
|
269 |
(*FIXME.0401: make SML-order local to make_polynomial(_) *)
|
wneuper@59523
|
270 |
(*FIXME.0401: replace 'make_polynomial'(old) by 'make_polynomial_'(MG) *)
|
wneuper@59523
|
271 |
(* Polynom --> List von Monomen *)
|
wenzelm@60309
|
272 |
fun poly2list (Const (\<^const_name>\<open>plus\<close>,_) $ t1 $ t2) =
|
wneuper@59523
|
273 |
(poly2list t1) @ (poly2list t2)
|
wneuper@59523
|
274 |
| poly2list t = [t];
|
neuper@37950
|
275 |
|
wneuper@59523
|
276 |
(* Monom --> Liste von Variablen *)
|
wenzelm@60309
|
277 |
fun monom2list (Const (\<^const_name>\<open>times\<close>,_) $ t1 $ t2) =
|
wneuper@59523
|
278 |
(monom2list t1) @ (monom2list t2)
|
wneuper@59523
|
279 |
| monom2list t = [t];
|
neuper@37950
|
280 |
|
wneuper@59523
|
281 |
(* liefert Variablenname (String) einer Variablen und Basis bei Potenz *)
|
wenzelm@60309
|
282 |
fun get_basStr (Const (\<^const_name>\<open>powr\<close>,_) $ Free (str, _) $ _) = str
|
walther@60335
|
283 |
| get_basStr (Const (\<^const_name>\<open>Transcendental.powr\<close>,_) $ n $ _) = TermC.to_string n
|
wneuper@59523
|
284 |
| get_basStr (Free (str, _)) = str
|
walther@60318
|
285 |
| get_basStr t =
|
walther@60322
|
286 |
if TermC.is_num t then TermC.to_string t
|
walther@60318
|
287 |
else "|||"; (* gross gewichtet; für Brüche ect. *)
|
neuper@37950
|
288 |
|
wneuper@59523
|
289 |
(* liefert Hochzahl (String) einer Variablen bzw Gewichtstring (zum Sortieren) *)
|
walther@60335
|
290 |
fun get_potStr (Const (\<^const_name>\<open>Transcendental.powr\<close>, _) $ Free _ $ Free (str, _)) = str
|
walther@60335
|
291 |
| get_potStr (Const (\<^const_name>\<open>Transcendental.powr\<close>, _) $ Free _ $ t) =
|
walther@60322
|
292 |
if TermC.is_num t then TermC.to_string t else "|||"
|
walther@60321
|
293 |
| get_potStr (Free _) = "---" (* keine Hochzahl --> kleinst gewichtet *)
|
wneuper@59523
|
294 |
| get_potStr _ = "||||||"; (* gross gewichtet; für Brüch ect. *)
|
neuper@37978
|
295 |
|
wneuper@59523
|
296 |
(* Umgekehrte string_ord *)
|
wneuper@59523
|
297 |
val string_ord_rev = rev_order o string_ord;
|
wneuper@59523
|
298 |
|
wneuper@59523
|
299 |
(* Ordnung zum lexikographischen Vergleich zweier Variablen (oder Potenzen)
|
wneuper@59523
|
300 |
innerhalb eines Monomes:
|
wneuper@59523
|
301 |
- zuerst lexikographisch nach Variablenname
|
wneuper@59523
|
302 |
- wenn gleich: nach steigender Potenz *)
|
walther@60321
|
303 |
fun var_ord (a, b) =
|
walther@60321
|
304 |
(@{print} {a = "var_ord ", a_b = "(" ^ UnparseC.term a ^ ", " ^ UnparseC.term b ^ ")",
|
walther@60321
|
305 |
sort_args = "(" ^ get_basStr a ^ ", " ^ get_potStr a ^ "), (" ^ get_basStr b ^ ", " ^ get_potStr b ^ ")"};
|
walther@60321
|
306 |
prod_ord string_ord string_ord
|
walther@60321
|
307 |
((get_basStr a, get_potStr a), (get_basStr b, get_potStr b))
|
walther@60321
|
308 |
);
|
walther@60318
|
309 |
fun var_ord (a,b: term) =
|
walther@60318
|
310 |
prod_ord string_ord string_ord
|
wneuper@59523
|
311 |
((get_basStr a, get_potStr a), (get_basStr b, get_potStr b));
|
neuper@37950
|
312 |
|
wneuper@59523
|
313 |
(* Ordnung zum lexikographischen Vergleich zweier Variablen (oder Potenzen);
|
wneuper@59523
|
314 |
verwendet zum Sortieren von Monomen mittels Gesamtgradordnung:
|
wneuper@59523
|
315 |
- zuerst lexikographisch nach Variablenname
|
wneuper@59523
|
316 |
- wenn gleich: nach sinkender Potenz*)
|
walther@60321
|
317 |
fun var_ord_revPow (a, b: term) =
|
walther@60321
|
318 |
(@{print} {a = "var_ord_revPow ", at_bt = "(" ^ UnparseC.term a ^ ", " ^ UnparseC.term b ^ ")",
|
walther@60321
|
319 |
sort_args = "(" ^ get_basStr a ^ ", " ^ get_potStr a ^ "), (" ^ get_basStr b ^ ", " ^ get_potStr b ^ ")"};
|
walther@60321
|
320 |
prod_ord string_ord string_ord_rev
|
walther@60321
|
321 |
((get_basStr a, get_potStr a), (get_basStr b, get_potStr b))
|
walther@60321
|
322 |
);
|
walther@60318
|
323 |
fun var_ord_revPow (a, b: term) =
|
walther@60318
|
324 |
prod_ord string_ord string_ord_rev
|
wneuper@59523
|
325 |
((get_basStr a, get_potStr a), (get_basStr b, get_potStr b));
|
neuper@37950
|
326 |
|
walther@60278
|
327 |
|
wneuper@59523
|
328 |
(* Ordnet ein Liste von Variablen (und Potenzen) lexikographisch *)
|
walther@60321
|
329 |
fun sort_varList ts =
|
walther@60321
|
330 |
(@{print} {a = "sort_varList", args = UnparseC.terms ts};
|
walther@60321
|
331 |
sort var_ord ts);
|
wneuper@59523
|
332 |
val sort_varList = sort var_ord;
|
wneuper@59523
|
333 |
|
wneuper@59523
|
334 |
(* Entfernet aeussersten Operator (Wurzel) aus einem Term und schreibt
|
wneuper@59523
|
335 |
Argumente in eine Liste *)
|
wneuper@59523
|
336 |
fun args u : term list =
|
walther@60318
|
337 |
let
|
walther@60318
|
338 |
fun stripc (f $ t, ts) = stripc (f, t::ts)
|
walther@60318
|
339 |
| stripc (t as Free _, ts) = (t::ts)
|
walther@60318
|
340 |
| stripc (_, ts) = ts
|
walther@60318
|
341 |
in stripc (u, []) end;
|
wneuper@59523
|
342 |
|
wneuper@59523
|
343 |
(* liefert True, falls der Term (Liste von Termen) nur Zahlen
|
wneuper@59523
|
344 |
(keine Variablen) enthaelt *)
|
walther@60317
|
345 |
fun filter_num ts = fold (curry and_) (map TermC.is_num ts) true
|
wneuper@59523
|
346 |
|
wneuper@59523
|
347 |
(* liefert True, falls der Term nur Zahlen (keine Variablen) enthaelt
|
wneuper@59523
|
348 |
dh. er ist ein numerischer Wert und entspricht einem Koeffizienten *)
|
wneuper@59523
|
349 |
fun is_nums t = filter_num [t];
|
wneuper@59523
|
350 |
|
wneuper@59523
|
351 |
(* Berechnet den Gesamtgrad eines Monoms *)
|
walther@60318
|
352 |
(**)local(**)
|
walther@60317
|
353 |
fun counter (n, []) = n
|
walther@60317
|
354 |
| counter (n, x :: xs) =
|
walther@60317
|
355 |
if (is_nums x) then counter (n, xs)
|
walther@60317
|
356 |
else
|
walther@60317
|
357 |
(case x of
|
walther@60335
|
358 |
(Const (\<^const_name>\<open>Transcendental.powr\<close>, _) $ Free _ $ t) =>
|
walther@60318
|
359 |
if TermC.is_num t
|
walther@60318
|
360 |
then counter (t |> HOLogic.dest_number |> snd |> curry op + n, xs)
|
walther@60318
|
361 |
else counter (n + 1000, xs) (*FIXME.MG?!*)
|
walther@60335
|
362 |
| (Const (\<^const_name>\<open>numeral\<close>, _) $ num) =>
|
walther@60318
|
363 |
counter (n + 1 + HOLogic.dest_numeral num, xs)
|
walther@60318
|
364 |
| _ => counter (n + 1, xs)) (*FIXME.MG?! ... Brüche ect.*)
|
walther@60318
|
365 |
(**)in(**)
|
walther@60317
|
366 |
fun monom_degree l = counter (0, l)
|
walther@60318
|
367 |
(**)end;(*local*)
|
wneuper@59523
|
368 |
|
wneuper@59523
|
369 |
(* wie Ordnung dict_ord (lexicographische Ordnung zweier Listen, mit Vergleich
|
wneuper@59523
|
370 |
der Listen-Elemente mit elem_ord) - Elemente die Bedingung cond erfuellen,
|
wneuper@59523
|
371 |
werden jedoch dabei ignoriert (uebersprungen) *)
|
walther@60321
|
372 |
fun dict_cond_ord _ _ ([], []) = (@{print} {a = "dict_cond_ord ([], [])"}; EQUAL)
|
walther@60321
|
373 |
| dict_cond_ord _ _ ([], _ :: _) = (@{print} {a = "dict_cond_ord ([], _ :: _)"}; LESS)
|
walther@60321
|
374 |
| dict_cond_ord _ _ (_ :: _, []) = (@{print} {a = "dict_cond_ord (_ :: _, [])"}; GREATER)
|
walther@60321
|
375 |
| dict_cond_ord elem_ord cond (x :: xs, y :: ys) =
|
walther@60321
|
376 |
(@{print} {a = "dict_cond_ord", args = "(" ^ UnparseC.terms (x :: xs) ^ ", " ^ UnparseC.terms (y :: ys) ^ ")",
|
walther@60321
|
377 |
is_nums = "(" ^ LibraryC.bool2str (cond x) ^ ", " ^ LibraryC.bool2str (cond y) ^ ")"};
|
walther@60321
|
378 |
case (cond x, cond y) of
|
walther@60321
|
379 |
(false, false) =>
|
walther@60321
|
380 |
(case elem_ord (x, y) of
|
walther@60321
|
381 |
EQUAL => dict_cond_ord elem_ord cond (xs, ys)
|
walther@60321
|
382 |
| ord => ord)
|
walther@60321
|
383 |
| (false, true) => dict_cond_ord elem_ord cond (x :: xs, ys)
|
walther@60321
|
384 |
| (true, false) => dict_cond_ord elem_ord cond (xs, y :: ys)
|
walther@60321
|
385 |
| (true, true) => dict_cond_ord elem_ord cond (xs, ys) );
|
wneuper@59523
|
386 |
fun dict_cond_ord _ _ ([], []) = EQUAL
|
wneuper@59523
|
387 |
| dict_cond_ord _ _ ([], _ :: _) = LESS
|
wneuper@59523
|
388 |
| dict_cond_ord _ _ (_ :: _, []) = GREATER
|
wneuper@59523
|
389 |
| dict_cond_ord elem_ord cond (x :: xs, y :: ys) =
|
wneuper@59523
|
390 |
(case (cond x, cond y) of
|
walther@60318
|
391 |
(false, false) =>
|
walther@60318
|
392 |
(case elem_ord (x, y) of
|
walther@60318
|
393 |
EQUAL => dict_cond_ord elem_ord cond (xs, ys)
|
walther@60318
|
394 |
| ord => ord)
|
walther@60318
|
395 |
| (false, true) => dict_cond_ord elem_ord cond (x :: xs, ys)
|
walther@60318
|
396 |
| (true, false) => dict_cond_ord elem_ord cond (xs, y :: ys)
|
walther@60318
|
397 |
| (true, true) => dict_cond_ord elem_ord cond (xs, ys) );
|
wneuper@59523
|
398 |
|
wneuper@59523
|
399 |
(* Gesamtgradordnung zum Vergleich von Monomen (Liste von Variablen/Potenzen):
|
wneuper@59523
|
400 |
zuerst nach Gesamtgrad, bei gleichem Gesamtgrad lexikographisch ordnen -
|
walther@60260
|
401 |
dabei werden Koeffizienten ignoriert (2*3*a \<up> 2*4*b gilt wie a \<up> 2*b) *)
|
wneuper@59523
|
402 |
fun degree_ord (xs, ys) =
|
walther@60318
|
403 |
prod_ord int_ord (dict_cond_ord var_ord_revPow is_nums)
|
walther@60318
|
404 |
((monom_degree xs, xs), (monom_degree ys, ys));
|
wneuper@59523
|
405 |
|
wneuper@59523
|
406 |
fun hd_str str = substring (str, 0, 1);
|
wneuper@59523
|
407 |
fun tl_str str = substring (str, 1, (size str) - 1);
|
wneuper@59523
|
408 |
|
wneuper@59523
|
409 |
(* liefert nummerischen Koeffizienten eines Monoms oder NONE *)
|
walther@60318
|
410 |
fun get_koeff_of_mon [] = raise ERROR "get_koeff_of_mon: called with l = []"
|
walther@60318
|
411 |
| get_koeff_of_mon (x :: _) = if is_nums x then SOME x else NONE;
|
wneuper@59523
|
412 |
|
wneuper@59523
|
413 |
(* wandelt Koeffizient in (zum sortieren geeigneten) String um *)
|
walther@60318
|
414 |
fun koeff2ordStr (SOME t) =
|
walther@60318
|
415 |
if TermC.is_num t
|
walther@60318
|
416 |
then
|
walther@60318
|
417 |
if (t |> HOLogic.dest_number |> snd) < 0
|
walther@60318
|
418 |
then (t |> HOLogic.dest_number |> snd |> curry op * ~1 |> string_of_int) ^ "0" (* 3 < -3 *)
|
walther@60318
|
419 |
else (t |> HOLogic.dest_number |> snd |> string_of_int)
|
walther@60318
|
420 |
else "aaa" (* "num.Ausdruck" --> gross *)
|
walther@60318
|
421 |
| koeff2ordStr NONE = "---"; (* "kein Koeff" --> kleinste *)
|
wneuper@59523
|
422 |
|
wneuper@59523
|
423 |
(* Order zum Vergleich von Koeffizienten (strings):
|
wneuper@59523
|
424 |
"kein Koeff" < "0" < "1" < "-1" < "2" < "-2" < ... < "num.Ausdruck" *)
|
walther@60318
|
425 |
fun compare_koeff_ord (xs, ys) = string_ord
|
walther@60318
|
426 |
((koeff2ordStr o get_koeff_of_mon) xs,
|
walther@60318
|
427 |
(koeff2ordStr o get_koeff_of_mon) ys);
|
wneuper@59523
|
428 |
|
wneuper@59523
|
429 |
(* Gesamtgradordnung degree_ord + Ordnen nach Koeffizienten falls EQUAL *)
|
wneuper@59523
|
430 |
fun koeff_degree_ord (xs, ys) =
|
wneuper@59523
|
431 |
prod_ord degree_ord compare_koeff_ord ((xs, xs), (ys, ys));
|
wneuper@59523
|
432 |
|
wneuper@59523
|
433 |
(* Ordnet ein Liste von Monomen (Monom = Liste von Variablen) mittels
|
wneuper@59523
|
434 |
Gesamtgradordnung *)
|
wneuper@59523
|
435 |
val sort_monList = sort koeff_degree_ord;
|
wneuper@59523
|
436 |
|
wneuper@59523
|
437 |
(* Alternativ zu degree_ord koennte auch die viel einfachere und
|
wneuper@59523
|
438 |
kuerzere Ordnung simple_ord verwendet werden - ist aber nicht
|
wneuper@59523
|
439 |
fuer unsere Zwecke geeignet!
|
wneuper@59523
|
440 |
|
wneuper@59523
|
441 |
fun simple_ord (al,bl: term list) = dict_ord string_ord
|
wneuper@59523
|
442 |
(map get_basStr al, map get_basStr bl);
|
wneuper@59523
|
443 |
|
wneuper@59523
|
444 |
val sort_monList = sort simple_ord; *)
|
wneuper@59523
|
445 |
|
wneuper@59523
|
446 |
(* aus 2 Variablen wird eine Summe bzw ein Produkt erzeugt
|
wneuper@59523
|
447 |
(mit gewuenschtem Typen T) *)
|
wenzelm@60309
|
448 |
fun plus T = Const (\<^const_name>\<open>plus\<close>, [T,T] ---> T);
|
wenzelm@60309
|
449 |
fun mult T = Const (\<^const_name>\<open>times\<close>, [T,T] ---> T);
|
wneuper@59523
|
450 |
fun binop op_ t1 t2 = op_ $ t1 $ t2;
|
wneuper@59523
|
451 |
fun create_prod T (a,b) = binop (mult T) a b;
|
wneuper@59523
|
452 |
fun create_sum T (a,b) = binop (plus T) a b;
|
wneuper@59523
|
453 |
|
wneuper@59523
|
454 |
(* löscht letztes Element einer Liste *)
|
wneuper@59523
|
455 |
fun drop_last l = take ((length l)-1,l);
|
wneuper@59523
|
456 |
|
wneuper@59523
|
457 |
(* Liste von Variablen --> Monom *)
|
wneuper@59523
|
458 |
fun create_monom T vl = foldr (create_prod T) (drop_last vl, last_elem vl);
|
wneuper@59523
|
459 |
(* Bemerkung:
|
wneuper@59523
|
460 |
foldr bewirkt rechtslastige Klammerung des Monoms - ist notwendig, damit zwei
|
wneuper@59523
|
461 |
gleiche Monome zusammengefasst werden können (collect_numerals)!
|
wneuper@59523
|
462 |
zB: 2*(x*(y*z)) + 3*(x*(y*z)) --> (2+3)*(x*(y*z))*)
|
wneuper@59523
|
463 |
|
wneuper@59523
|
464 |
(* Liste von Monomen --> Polynom *)
|
wneuper@59523
|
465 |
fun create_polynom T ml = foldl (create_sum T) (hd ml, tl ml);
|
wneuper@59523
|
466 |
(* Bemerkung:
|
wneuper@59523
|
467 |
foldl bewirkt linkslastige Klammerung des Polynoms (der Summanten) -
|
wneuper@59523
|
468 |
bessere Darstellung, da keine Klammern sichtbar!
|
wneuper@59523
|
469 |
(und discard_parentheses in make_polynomial hat weniger zu tun) *)
|
wneuper@59523
|
470 |
|
wneuper@59523
|
471 |
(* sorts the variables (faktors) of an expanded polynomial lexicographical *)
|
wneuper@59523
|
472 |
fun sort_variables t =
|
walther@60317
|
473 |
let
|
walther@60317
|
474 |
val ll = map monom2list (poly2list t);
|
walther@60317
|
475 |
val lls = map sort_varList ll;
|
walther@60317
|
476 |
val T = type_of t;
|
walther@60317
|
477 |
val ls = map (create_monom T) lls;
|
walther@60317
|
478 |
in create_polynom T ls end;
|
wneuper@59523
|
479 |
|
wneuper@59523
|
480 |
(* sorts the monoms of an expanded and variable-sorted polynomial
|
wneuper@59523
|
481 |
by total_degree *)
|
wneuper@59523
|
482 |
fun sort_monoms t =
|
walther@60318
|
483 |
let
|
walther@60318
|
484 |
val ll = map monom2list (poly2list t);
|
walther@60318
|
485 |
val lls = sort_monList ll;
|
walther@60318
|
486 |
val T = Term.type_of t;
|
walther@60318
|
487 |
val ls = map (create_monom T) lls;
|
walther@60318
|
488 |
in create_polynom T ls end;
|
wneuper@59523
|
489 |
\<close>
|
wneuper@59523
|
490 |
|
wneuper@59523
|
491 |
subsubsection \<open>rewrite order for hard-coded AC rewriting\<close>
|
wneuper@59523
|
492 |
ML \<open>
|
neuper@37950
|
493 |
local (*. for make_polynomial .*)
|
neuper@37950
|
494 |
|
neuper@37950
|
495 |
open Term; (* for type order = EQUAL | LESS | GREATER *)
|
neuper@37950
|
496 |
|
neuper@37950
|
497 |
fun pr_ord EQUAL = "EQUAL"
|
neuper@37950
|
498 |
| pr_ord LESS = "LESS"
|
neuper@37950
|
499 |
| pr_ord GREATER = "GREATER";
|
neuper@37950
|
500 |
|
neuper@37950
|
501 |
fun dest_hd' (Const (a, T)) = (* ~ term.ML *)
|
neuper@37950
|
502 |
(case a of
|
wenzelm@60309
|
503 |
\<^const_name>\<open>powr\<close> => ((("|||||||||||||", 0), T), 0) (*WN greatest string*)
|
neuper@37950
|
504 |
| _ => (((a, 0), T), 0))
|
walther@60317
|
505 |
| dest_hd' (Free (a, T)) = (((a, 0), T), 1)(*TODOO handle this as numeral, too? see EqSystem.thy*)
|
neuper@37950
|
506 |
| dest_hd' (Var v) = (v, 2)
|
neuper@37950
|
507 |
| dest_hd' (Bound i) = ((("", i), dummyT), 3)
|
wneuper@59523
|
508 |
| dest_hd' (Abs (_, T, _)) = ((("", 0), T), 4)
|
wneuper@59523
|
509 |
| dest_hd' t = raise TERM ("dest_hd'", [t]);
|
neuper@37950
|
510 |
|
neuper@37950
|
511 |
fun size_of_term' (Const(str,_) $ t) =
|
wenzelm@60309
|
512 |
if \<^const_name>\<open>powr\<close>= str then 1000 + size_of_term' t else 1+size_of_term' t(*WN*)
|
neuper@37950
|
513 |
| size_of_term' (Abs (_,_,body)) = 1 + size_of_term' body
|
neuper@37950
|
514 |
| size_of_term' (f$t) = size_of_term' f + size_of_term' t
|
neuper@37950
|
515 |
| size_of_term' _ = 1;
|
neuper@37950
|
516 |
|
neuper@37950
|
517 |
fun term_ord' pr thy (Abs (_, T, t), Abs(_, U, u)) = (* ~ term.ML *)
|
neuper@52070
|
518 |
(case term_ord' pr thy (t, u) of EQUAL => Term_Ord.typ_ord (T, U) | ord => ord)
|
neuper@37950
|
519 |
| term_ord' pr thy (t, u) =
|
neuper@52070
|
520 |
(if pr then
|
neuper@52070
|
521 |
let
|
neuper@52070
|
522 |
val (f, ts) = strip_comb t and (g, us) = strip_comb u;
|
walther@59870
|
523 |
val _ = tracing ("t= f@ts= \"" ^ UnparseC.term_in_thy thy f ^ "\" @ \"[" ^
|
walther@59870
|
524 |
commas (map (UnparseC.term_in_thy thy) ts) ^ "]\"");
|
walther@59870
|
525 |
val _ = tracing("u= g@us= \"" ^ UnparseC.term_in_thy thy g ^ "\" @ \"[" ^
|
walther@59870
|
526 |
commas (map (UnparseC.term_in_thy thy) us) ^ "]\"");
|
neuper@52070
|
527 |
val _ = tracing ("size_of_term(t,u)= (" ^ string_of_int (size_of_term' t) ^ ", " ^
|
neuper@52070
|
528 |
string_of_int (size_of_term' u) ^ ")");
|
neuper@52070
|
529 |
val _ = tracing ("hd_ord(f,g) = " ^ (pr_ord o hd_ord) (f,g));
|
neuper@52070
|
530 |
val _ = tracing ("terms_ord(ts,us) = " ^ (pr_ord o terms_ord str false) (ts, us));
|
neuper@52070
|
531 |
val _ = tracing ("-------");
|
neuper@52070
|
532 |
in () end
|
neuper@37950
|
533 |
else ();
|
neuper@37950
|
534 |
case int_ord (size_of_term' t, size_of_term' u) of
|
neuper@37950
|
535 |
EQUAL =>
|
neuper@37950
|
536 |
let val (f, ts) = strip_comb t and (g, us) = strip_comb u in
|
neuper@37950
|
537 |
(case hd_ord (f, g) of EQUAL => (terms_ord str pr) (ts, us)
|
neuper@37950
|
538 |
| ord => ord)
|
neuper@37950
|
539 |
end
|
neuper@37950
|
540 |
| ord => ord)
|
neuper@37950
|
541 |
and hd_ord (f, g) = (* ~ term.ML *)
|
neuper@37974
|
542 |
prod_ord (prod_ord Term_Ord.indexname_ord Term_Ord.typ_ord) int_ord (dest_hd' f, dest_hd' g)
|
wneuper@59523
|
543 |
and terms_ord _ pr (ts, us) =
|
walther@59881
|
544 |
list_ord (term_ord' pr (ThyC.get_theory "Isac_Knowledge"))(ts, us);
|
neuper@52070
|
545 |
|
neuper@37950
|
546 |
in
|
neuper@37950
|
547 |
|
walther@60324
|
548 |
fun ord_make_polynomial (pr:bool) thy (_: subst) (ts, us) =
|
walther@60324
|
549 |
(term_ord' pr thy(***) (TermC.numerals_to_Free ts, TermC.numerals_to_Free us) = LESS );
|
neuper@37950
|
550 |
|
neuper@37950
|
551 |
end;(*local*)
|
neuper@37950
|
552 |
|
walther@59857
|
553 |
Rewrite_Ord.rew_ord' := overwritel (! Rewrite_Ord.rew_ord', (* TODO: make analogous to KEStore_Elems.add_mets *)
|
wenzelm@60291
|
554 |
[("termlessI", termlessI), ("ord_make_polynomial", ord_make_polynomial false \<^theory>)]);
|
wneuper@59523
|
555 |
\<close>
|
neuper@37950
|
556 |
|
wneuper@59523
|
557 |
subsection \<open>predicates\<close>
|
wneuper@59523
|
558 |
subsubsection \<open>in specifications\<close>
|
wneuper@59523
|
559 |
ML \<open>
|
wneuper@59523
|
560 |
(* is_polyrat_in becomes true, if no bdv is in the denominator of a fraction*)
|
wneuper@59523
|
561 |
fun is_polyrat_in t v =
|
wneuper@59524
|
562 |
let
|
walther@59962
|
563 |
fun finddivide (_ $ _ $ _ $ _) _ = raise ERROR("is_polyrat_in:")
|
wneuper@59523
|
564 |
(* at the moment there is no term like this, but ....*)
|
wenzelm@60309
|
565 |
| finddivide (Const (\<^const_name>\<open>divide\<close>,_) $ _ $ b) v = not (Prog_Expr.occurs_in v b)
|
wneuper@59524
|
566 |
| finddivide (_ $ t1 $ t2) v = finddivide t1 v orelse finddivide t2 v
|
wneuper@59524
|
567 |
| finddivide (_ $ t1) v = finddivide t1 v
|
wneuper@59523
|
568 |
| finddivide _ _ = false;
|
wneuper@59524
|
569 |
in finddivide t v end;
|
wneuper@59523
|
570 |
|
wneuper@59524
|
571 |
fun is_expanded_in t v = case expand_deg_in t v of SOME _ => true | NONE => false;
|
wneuper@59524
|
572 |
fun is_poly_in t v = case poly_deg_in t v of SOME _ => true | NONE => false;
|
wneuper@59524
|
573 |
fun has_degree_in t v = case expand_deg_in t v of SOME d => d | NONE => ~1;
|
neuper@37950
|
574 |
|
wneuper@59523
|
575 |
(*.the expression contains + - * ^ only ?
|
wneuper@59523
|
576 |
this is weaker than 'is_polynomial' !.*)
|
wneuper@59523
|
577 |
fun is_polyexp (Free _) = true
|
wneuper@59529
|
578 |
| is_polyexp (Const _) = true (* potential danger: bdv is not considered *)
|
walther@60335
|
579 |
| is_polyexp (Const (\<^const_name>\<open>plus\<close>,_) $ Free _ $ num) =
|
walther@60318
|
580 |
if TermC.is_num num then true
|
walther@60318
|
581 |
else if TermC.is_variable num then true
|
walther@60318
|
582 |
else is_polyexp num
|
walther@60335
|
583 |
| is_polyexp (Const (\<^const_name>\<open>plus\<close>, _) $ num $ Free _) =
|
walther@60318
|
584 |
if TermC.is_num num then true
|
walther@60318
|
585 |
else if TermC.is_variable num then true
|
walther@60318
|
586 |
else is_polyexp num
|
walther@60335
|
587 |
| is_polyexp (Const (\<^const_name>\<open>minus\<close>, _) $ Free _ $ num) =
|
walther@60318
|
588 |
if TermC.is_num num then true
|
walther@60318
|
589 |
else if TermC.is_variable num then true
|
walther@60318
|
590 |
else is_polyexp num
|
walther@60335
|
591 |
| is_polyexp (Const (\<^const_name>\<open>times\<close>, _) $ num $ Free _) =
|
walther@60318
|
592 |
if TermC.is_num num then true
|
walther@60318
|
593 |
else if TermC.is_variable num then true
|
walther@60318
|
594 |
else is_polyexp num
|
walther@60335
|
595 |
| is_polyexp (Const (\<^const_name>\<open>Transcendental.powr\<close>,_) $ Free _ $ num) =
|
walther@60318
|
596 |
if TermC.is_num num then true
|
walther@60318
|
597 |
else if TermC.is_variable num then true
|
walther@60318
|
598 |
else is_polyexp num
|
walther@60335
|
599 |
| is_polyexp (Const (\<^const_name>\<open>plus_class.plus\<close>,_) $ t1 $ t2) =
|
walther@60318
|
600 |
((is_polyexp t1) andalso (is_polyexp t2))
|
walther@60335
|
601 |
| is_polyexp (Const (\<^const_name>\<open>Groups.minus_class.minus\<close>,_) $ t1 $ t2) =
|
walther@60318
|
602 |
((is_polyexp t1) andalso (is_polyexp t2))
|
walther@60335
|
603 |
| is_polyexp (Const (\<^const_name>\<open>Groups.times_class.times\<close>,_) $ t1 $ t2) =
|
walther@60318
|
604 |
((is_polyexp t1) andalso (is_polyexp t2))
|
walther@60335
|
605 |
| is_polyexp (Const (\<^const_name>\<open>Transcendental.powr\<close>,_) $ t1 $ t2) =
|
walther@60318
|
606 |
((is_polyexp t1) andalso (is_polyexp t2))
|
walther@60317
|
607 |
| is_polyexp num = TermC.is_num num;
|
wneuper@59523
|
608 |
\<close>
|
neuper@37950
|
609 |
|
wneuper@59523
|
610 |
subsubsection \<open>for hard-coded AC rewriting\<close>
|
wneuper@59523
|
611 |
ML \<open>
|
wneuper@59523
|
612 |
(* auch Klammerung muss übereinstimmen;
|
wneuper@59523
|
613 |
sort_variables klammert Produkte rechtslastig*)
|
wneuper@59523
|
614 |
fun is_multUnordered t = ((is_polyexp t) andalso not (t = sort_variables t));
|
wneuper@59523
|
615 |
|
wneuper@59523
|
616 |
fun is_addUnordered t = ((is_polyexp t) andalso not (t = sort_monoms t));
|
wneuper@59523
|
617 |
\<close>
|
wneuper@59523
|
618 |
|
wneuper@59523
|
619 |
subsection \<open>evaluations functions\<close>
|
walther@60278
|
620 |
subsubsection \<open>for predicates\<close>
|
wneuper@59523
|
621 |
ML \<open>
|
walther@60335
|
622 |
fun eval_is_polyrat_in _ _(p as (Const (\<^const_name>\<open>Poly.is_polyrat_in\<close>, _) $ t $ v)) _ =
|
wneuper@59523
|
623 |
if is_polyrat_in t v
|
walther@59868
|
624 |
then SOME ((UnparseC.term p) ^ " = True",
|
wneuper@59523
|
625 |
HOLogic.Trueprop $ (TermC.mk_equality (p, @{term True})))
|
walther@59868
|
626 |
else SOME ((UnparseC.term p) ^ " = True",
|
wneuper@59523
|
627 |
HOLogic.Trueprop $ (TermC.mk_equality (p, @{term False})))
|
wneuper@59523
|
628 |
| eval_is_polyrat_in _ _ _ _ = ((*tracing"### no matches";*) NONE);
|
wneuper@59523
|
629 |
|
walther@60278
|
630 |
(*("is_expanded_in", ("Poly.is_expanded_in", eval_is_expanded_in ""))*)
|
wneuper@59523
|
631 |
fun eval_is_expanded_in _ _
|
walther@60335
|
632 |
(p as (Const (\<^const_name>\<open>Poly.is_expanded_in\<close>, _) $ t $ v)) _ =
|
wneuper@59523
|
633 |
if is_expanded_in t v
|
walther@59868
|
634 |
then SOME ((UnparseC.term p) ^ " = True",
|
wneuper@59523
|
635 |
HOLogic.Trueprop $ (TermC.mk_equality (p, @{term True})))
|
walther@59868
|
636 |
else SOME ((UnparseC.term p) ^ " = True",
|
wneuper@59523
|
637 |
HOLogic.Trueprop $ (TermC.mk_equality (p, @{term False})))
|
wneuper@59523
|
638 |
| eval_is_expanded_in _ _ _ _ = NONE;
|
wneuper@59523
|
639 |
|
walther@60278
|
640 |
(*("is_poly_in", ("Poly.is_poly_in", eval_is_poly_in ""))*)
|
wneuper@59523
|
641 |
fun eval_is_poly_in _ _
|
walther@60335
|
642 |
(p as (Const (\<^const_name>\<open>Poly.is_poly_in\<close>, _) $ t $ v)) _ =
|
wneuper@59523
|
643 |
if is_poly_in t v
|
walther@59868
|
644 |
then SOME ((UnparseC.term p) ^ " = True",
|
wneuper@59523
|
645 |
HOLogic.Trueprop $ (TermC.mk_equality (p, @{term True})))
|
walther@59868
|
646 |
else SOME ((UnparseC.term p) ^ " = True",
|
wneuper@59523
|
647 |
HOLogic.Trueprop $ (TermC.mk_equality (p, @{term False})))
|
wneuper@59523
|
648 |
| eval_is_poly_in _ _ _ _ = NONE;
|
wneuper@59523
|
649 |
|
walther@60278
|
650 |
(*("has_degree_in", ("Poly.has_degree_in", eval_has_degree_in ""))*)
|
wneuper@59523
|
651 |
fun eval_has_degree_in _ _
|
walther@60335
|
652 |
(p as (Const (\<^const_name>\<open>Poly.has_degree_in\<close>, _) $ t $ v)) _ =
|
wneuper@59523
|
653 |
let val d = has_degree_in t v
|
wneuper@59523
|
654 |
val d' = TermC.term_of_num HOLogic.realT d
|
walther@59868
|
655 |
in SOME ((UnparseC.term p) ^ " = " ^ (string_of_int d),
|
wneuper@59523
|
656 |
HOLogic.Trueprop $ (TermC.mk_equality (p, d')))
|
wneuper@59523
|
657 |
end
|
wneuper@59523
|
658 |
| eval_has_degree_in _ _ _ _ = NONE;
|
wneuper@59523
|
659 |
|
walther@60278
|
660 |
(*("is_polyexp", ("Poly.is_polyexp", eval_is_polyexp ""))*)
|
wneuper@59523
|
661 |
fun eval_is_polyexp (thmid:string) _
|
walther@60335
|
662 |
(t as (Const (\<^const_name>\<open>Poly.is_polyexp\<close>, _) $ arg)) thy =
|
wneuper@59523
|
663 |
if is_polyexp arg
|
walther@59870
|
664 |
then SOME (TermC.mk_thmid thmid (UnparseC.term_in_thy thy arg) "",
|
wneuper@59523
|
665 |
HOLogic.Trueprop $ (TermC.mk_equality (t, @{term True})))
|
walther@59870
|
666 |
else SOME (TermC.mk_thmid thmid (UnparseC.term_in_thy thy arg) "",
|
wneuper@59523
|
667 |
HOLogic.Trueprop $ (TermC.mk_equality (t, @{term False})))
|
wneuper@59523
|
668 |
| eval_is_polyexp _ _ _ _ = NONE;
|
wneuper@59523
|
669 |
\<close>
|
wneuper@59523
|
670 |
|
wneuper@59523
|
671 |
subsubsection \<open>for hard-coded AC rewriting\<close>
|
wneuper@59523
|
672 |
ML \<open>
|
wneuper@59523
|
673 |
(*WN.18.6.03 *)
|
walther@60278
|
674 |
(*("is_addUnordered", ("Poly.is_addUnordered", eval_is_addUnordered ""))*)
|
wneuper@59523
|
675 |
fun eval_is_addUnordered (thmid:string) _
|
walther@60335
|
676 |
(t as (Const (\<^const_name>\<open>Poly.is_addUnordered\<close>, _) $ arg)) thy =
|
wneuper@59523
|
677 |
if is_addUnordered arg
|
walther@59870
|
678 |
then SOME (TermC.mk_thmid thmid (UnparseC.term_in_thy thy arg) "",
|
wneuper@59523
|
679 |
HOLogic.Trueprop $ (TermC.mk_equality (t, @{term True})))
|
walther@59870
|
680 |
else SOME (TermC.mk_thmid thmid (UnparseC.term_in_thy thy arg) "",
|
wneuper@59523
|
681 |
HOLogic.Trueprop $ (TermC.mk_equality (t, @{term False})))
|
wneuper@59523
|
682 |
| eval_is_addUnordered _ _ _ _ = NONE;
|
wneuper@59523
|
683 |
|
wneuper@59523
|
684 |
fun eval_is_multUnordered (thmid:string) _
|
walther@60335
|
685 |
(t as (Const (\<^const_name>\<open>Poly.is_multUnordered\<close>, _) $ arg)) thy =
|
wneuper@59523
|
686 |
if is_multUnordered arg
|
walther@59870
|
687 |
then SOME (TermC.mk_thmid thmid (UnparseC.term_in_thy thy arg) "",
|
wneuper@59523
|
688 |
HOLogic.Trueprop $ (TermC.mk_equality (t, @{term True})))
|
walther@59870
|
689 |
else SOME (TermC.mk_thmid thmid (UnparseC.term_in_thy thy arg) "",
|
wneuper@59523
|
690 |
HOLogic.Trueprop $ (TermC.mk_equality (t, @{term False})))
|
wneuper@59523
|
691 |
| eval_is_multUnordered _ _ _ _ = NONE;
|
wneuper@59523
|
692 |
\<close>
|
wenzelm@60313
|
693 |
calculation is_polyrat_in = \<open>eval_is_polyrat_in "#eval_is_polyrat_in"\<close>
|
wenzelm@60313
|
694 |
calculation is_expanded_in = \<open>eval_is_expanded_in ""\<close>
|
wenzelm@60313
|
695 |
calculation is_poly_in = \<open>eval_is_poly_in ""\<close>
|
wenzelm@60313
|
696 |
calculation has_degree_in = \<open>eval_has_degree_in ""\<close>
|
wenzelm@60313
|
697 |
calculation is_polyexp = \<open>eval_is_polyexp ""\<close>
|
wenzelm@60313
|
698 |
calculation is_multUnordered = \<open>eval_is_multUnordered ""\<close>
|
wenzelm@60313
|
699 |
calculation is_addUnordered = \<open>eval_is_addUnordered ""\<close>
|
wneuper@59523
|
700 |
|
wneuper@59523
|
701 |
subsection \<open>rule-sets\<close>
|
wneuper@59523
|
702 |
subsubsection \<open>without specific order\<close>
|
wneuper@59523
|
703 |
ML \<open>
|
wneuper@59523
|
704 |
(* used only for merge *)
|
walther@59852
|
705 |
val calculate_Poly = Rule_Set.append_rules "calculate_PolyFIXXXME.not.impl." Rule_Set.empty [];
|
wneuper@59523
|
706 |
|
wneuper@59523
|
707 |
(*.for evaluation of conditions in rewrite rules.*)
|
walther@59852
|
708 |
val Poly_erls = Rule_Set.append_rules "Poly_erls" Atools_erls
|
wenzelm@60294
|
709 |
[\<^rule_eval>\<open>HOL.eq\<close> (Prog_Expr.eval_equal "#equal_"),
|
wenzelm@60297
|
710 |
\<^rule_thm>\<open>real_unari_minus\<close>,
|
wenzelm@60294
|
711 |
\<^rule_eval>\<open>plus\<close> (eval_binop "#add_"),
|
wenzelm@60294
|
712 |
\<^rule_eval>\<open>minus\<close> (eval_binop "#sub_"),
|
wenzelm@60294
|
713 |
\<^rule_eval>\<open>times\<close> (eval_binop "#mult_"),
|
wenzelm@60294
|
714 |
\<^rule_eval>\<open>powr\<close> (eval_binop "#power_")];
|
wneuper@59523
|
715 |
|
walther@59852
|
716 |
val poly_crls = Rule_Set.append_rules "poly_crls" Atools_crls
|
wenzelm@60294
|
717 |
[\<^rule_eval>\<open>HOL.eq\<close> (Prog_Expr.eval_equal "#equal_"),
|
wenzelm@60297
|
718 |
\<^rule_thm>\<open>real_unari_minus\<close>,
|
wenzelm@60294
|
719 |
\<^rule_eval>\<open>plus\<close> (eval_binop "#add_"),
|
wenzelm@60294
|
720 |
\<^rule_eval>\<open>minus\<close> (eval_binop "#sub_"),
|
wenzelm@60294
|
721 |
\<^rule_eval>\<open>times\<close> (eval_binop "#mult_"),
|
wenzelm@60294
|
722 |
\<^rule_eval>\<open>powr\<close> (eval_binop "#power_")];
|
wneuper@59523
|
723 |
\<close>
|
wneuper@59523
|
724 |
ML \<open>
|
neuper@37950
|
725 |
val expand =
|
walther@59857
|
726 |
Rule_Def.Repeat {id = "expand", preconds = [], rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord),
|
walther@59852
|
727 |
erls = Rule_Set.empty,srls = Rule_Set.Empty, calc = [], errpatts = [],
|
wenzelm@60297
|
728 |
rules = [\<^rule_thm>\<open>distrib_right\<close>,
|
neuper@37950
|
729 |
(*"(z1.0 + z2.0) * w = z1.0 * w + z2.0 * w"*)
|
wenzelm@60297
|
730 |
\<^rule_thm>\<open>distrib_left\<close>
|
neuper@37950
|
731 |
(*"w * (z1.0 + z2.0) = w * z1.0 + w * z2.0"*)
|
walther@59878
|
732 |
], scr = Rule.Empty_Prog};
|
neuper@37950
|
733 |
|
walther@60320
|
734 |
(* erls for calculate_Rational + etc *)
|
walther@60318
|
735 |
val powers_erls =
|
walther@60318
|
736 |
Rule_Def.Repeat {id = "powers_erls", preconds = [], rew_ord = ("dummy_ord",Rewrite_Ord.dummy_ord),
|
walther@60318
|
737 |
erls = Rule_Set.empty, srls = Rule_Set.Empty, calc = [], errpatts = [],
|
walther@60320
|
738 |
rules =
|
walther@60320
|
739 |
[Rule.Eval ("Prog_Expr.matches", Prog_Expr.eval_matches "#matches_"),
|
walther@60320
|
740 |
Rule.Eval ("Prog_Expr.is_atom", Prog_Expr.eval_is_atom "#is_atom_"),
|
walther@60343
|
741 |
Rule.Eval ("Prog_Expr.is_num", Prog_Expr.eval_is_num "#is_num_"),
|
walther@60318
|
742 |
Rule.Eval ("Prog_Expr.is_even", Prog_Expr.eval_is_even "#is_even_"),
|
walther@60318
|
743 |
Rule.Eval ("Orderings.ord_class.less", Prog_Expr.eval_equ "#less_"),
|
walther@60337
|
744 |
Rule.Thm ("not_false", @{thm not_false}),
|
walther@60337
|
745 |
Rule.Thm ("not_true", @{thm not_true}),
|
walther@60318
|
746 |
Rule.Eval ("Groups.plus_class.plus", (**)eval_binop "#add_")
|
walther@60318
|
747 |
],
|
walther@60318
|
748 |
scr = Rule.Empty_Prog
|
walther@60318
|
749 |
};
|
walther@60320
|
750 |
|
walther@60333
|
751 |
\<close> ML \<open>
|
walther@60320
|
752 |
val discard_minus =
|
walther@60320
|
753 |
Rule_Def.Repeat {id = "discard_minus", preconds = [], rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord),
|
walther@60320
|
754 |
erls = powers_erls, srls = Rule_Set.Empty, calc = [], errpatts = [],
|
walther@60341
|
755 |
rules = [
|
walther@60341
|
756 |
\<^rule_thm>\<open>real_diff_minus\<close> (*"a - b = a + -1 * b"*),
|
walther@60341
|
757 |
\<^rule_thm>\<open>real_mult_minus1_sym\<close> (*"\<not>(z is_const) ==> - (z::real) = -1 * z"*)],
|
walther@60341
|
758 |
scr = Rule.Empty_Prog};
|
walther@60320
|
759 |
|
neuper@37950
|
760 |
val expand_poly_ =
|
walther@59851
|
761 |
Rule_Def.Repeat{id = "expand_poly_", preconds = [],
|
walther@59857
|
762 |
rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord),
|
walther@60318
|
763 |
erls = powers_erls, srls = Rule_Set.Empty,
|
neuper@42451
|
764 |
calc = [], errpatts = [],
|
neuper@42407
|
765 |
rules =
|
wenzelm@60297
|
766 |
[\<^rule_thm>\<open>real_plus_binom_pow4\<close>,
|
walther@60260
|
767 |
(*"(a + b) \<up> 4 = ... "*)
|
wenzelm@60297
|
768 |
\<^rule_thm>\<open>real_plus_binom_pow5\<close>,
|
walther@60260
|
769 |
(*"(a + b) \<up> 5 = ... "*)
|
wenzelm@60297
|
770 |
\<^rule_thm>\<open>real_plus_binom_pow3\<close>,
|
walther@60260
|
771 |
(*"(a + b) \<up> 3 = a \<up> 3 + 3*a \<up> 2*b + 3*a*b \<up> 2 + b \<up> 3" *)
|
neuper@42407
|
772 |
(*WN071229 changed/removed for Schaerding -----vvv*)
|
wenzelm@60297
|
773 |
(*\<^rule_thm>\<open>real_plus_binom_pow2\<close>,*)
|
walther@60260
|
774 |
(*"(a + b) \<up> 2 = a \<up> 2 + 2*a*b + b \<up> 2"*)
|
wenzelm@60297
|
775 |
\<^rule_thm>\<open>real_plus_binom_pow2\<close>,
|
walther@60260
|
776 |
(*"(a + b) \<up> 2 = (a + b) * (a + b)"*)
|
wenzelm@60297
|
777 |
(*\<^rule_thm>\<open>real_plus_minus_binom1_p_p\<close>,*)
|
walther@60260
|
778 |
(*"(a + b)*(a + -1 * b) = a \<up> 2 + -1*b \<up> 2"*)
|
wenzelm@60297
|
779 |
(*\<^rule_thm>\<open>real_plus_minus_binom2_p_p\<close>,*)
|
walther@60260
|
780 |
(*"(a + -1 * b)*(a + b) = a \<up> 2 + -1*b \<up> 2"*)
|
walther@60242
|
781 |
(*WN071229 changed/removed for Schaerding -----\<up>*)
|
neuper@37950
|
782 |
|
wenzelm@60297
|
783 |
\<^rule_thm>\<open>distrib_right\<close>,
|
neuper@42407
|
784 |
(*"(z1.0 + z2.0) * w = z1.0 * w + z2.0 * w"*)
|
wenzelm@60297
|
785 |
\<^rule_thm>\<open>distrib_left\<close>,
|
neuper@42407
|
786 |
(*"w * (z1.0 + z2.0) = w * z1.0 + w * z2.0"*)
|
neuper@37950
|
787 |
|
wenzelm@60297
|
788 |
\<^rule_thm>\<open>realpow_multI\<close>,
|
walther@60242
|
789 |
(*"(r * s) \<up> n = r \<up> n * s \<up> n"*)
|
walther@60331
|
790 |
\<^rule_thm>\<open>realpow_pow\<close>,
|
walther@60242
|
791 |
(*"(a \<up> b) \<up> c = a \<up> (b * c)"*)
|
walther@60323
|
792 |
(**)
|
walther@60343
|
793 |
\<^rule_thm>\<open>realpow_minus_even\<close>, (*"n is_even ==> (- r) \<up> n = r \<up> n"*)
|
walther@60343
|
794 |
\<^rule_thm>\<open>realpow_minus_odd\<close> (*"Not (n is_even) ==> (- r) \<up> n = -1 * r \<up> n"*)
|
walther@60323
|
795 |
(**)
|
walther@59878
|
796 |
], scr = Rule.Empty_Prog};
|
neuper@37950
|
797 |
|
neuper@37950
|
798 |
val expand_poly_rat_ =
|
walther@59851
|
799 |
Rule_Def.Repeat{id = "expand_poly_rat_", preconds = [],
|
walther@59857
|
800 |
rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord),
|
walther@60323
|
801 |
erls = Rule_Set.append_rules "Rule_Set.empty-expand_poly_rat_" Rule_Set.empty
|
walther@60323
|
802 |
[Rule.Eval ("Poly.is_polyexp", eval_is_polyexp ""),
|
walther@60323
|
803 |
Rule.Eval ("Prog_Expr.is_even", Prog_Expr.eval_is_even "#is_even_"),
|
walther@60337
|
804 |
Rule.Thm ("not_false", @{thm not_false}),
|
walther@60337
|
805 |
Rule.Thm ("not_true", @{thm not_true})
|
walther@60323
|
806 |
],
|
walther@59851
|
807 |
srls = Rule_Set.Empty,
|
neuper@42451
|
808 |
calc = [], errpatts = [],
|
neuper@37950
|
809 |
rules =
|
wenzelm@60297
|
810 |
[\<^rule_thm>\<open>real_plus_binom_pow4_poly\<close>,
|
walther@60260
|
811 |
(*"[| a is_polyexp; b is_polyexp |] ==> (a + b) \<up> 4 = ... "*)
|
wenzelm@60297
|
812 |
\<^rule_thm>\<open>real_plus_binom_pow5_poly\<close>,
|
walther@60260
|
813 |
(*"[| a is_polyexp; b is_polyexp |] ==> (a + b) \<up> 5 = ... "*)
|
wenzelm@60297
|
814 |
\<^rule_thm>\<open>real_plus_binom_pow2_poly\<close>,
|
neuper@37950
|
815 |
(*"[| a is_polyexp; b is_polyexp |] ==>
|
walther@60260
|
816 |
(a + b) \<up> 2 = a \<up> 2 + 2*a*b + b \<up> 2"*)
|
wenzelm@60297
|
817 |
\<^rule_thm>\<open>real_plus_binom_pow3_poly\<close>,
|
neuper@37950
|
818 |
(*"[| a is_polyexp; b is_polyexp |] ==>
|
walther@60260
|
819 |
(a + b) \<up> 3 = a \<up> 3 + 3*a \<up> 2*b + 3*a*b \<up> 2 + b \<up> 3" *)
|
wenzelm@60297
|
820 |
\<^rule_thm>\<open>real_plus_minus_binom1_p_p\<close>,
|
walther@60260
|
821 |
(*"(a + b)*(a + -1 * b) = a \<up> 2 + -1*b \<up> 2"*)
|
wenzelm@60297
|
822 |
\<^rule_thm>\<open>real_plus_minus_binom2_p_p\<close>,
|
walther@60260
|
823 |
(*"(a + -1 * b)*(a + b) = a \<up> 2 + -1*b \<up> 2"*)
|
neuper@37950
|
824 |
|
wenzelm@60298
|
825 |
\<^rule_thm>\<open>real_add_mult_distrib_poly\<close>,
|
neuper@37950
|
826 |
(*"w is_polyexp ==> (z1.0 + z2.0) * w = z1.0 * w + z2.0 * w"*)
|
wenzelm@60298
|
827 |
\<^rule_thm>\<open>real_add_mult_distrib2_poly\<close>,
|
neuper@37950
|
828 |
(*"w is_polyexp ==> w * (z1.0 + z2.0) = w * z1.0 + w * z2.0"*)
|
neuper@37950
|
829 |
|
wenzelm@60297
|
830 |
\<^rule_thm>\<open>realpow_multI_poly\<close>,
|
neuper@37950
|
831 |
(*"[| r is_polyexp; s is_polyexp |] ==>
|
walther@60242
|
832 |
(r * s) \<up> n = r \<up> n * s \<up> n"*)
|
walther@60337
|
833 |
Rule.Thm ("realpow_pow", @{thm realpow_pow}),
|
walther@60318
|
834 |
(*"(a \<up> b) \<up> c = a \<up> (b * c)"*)
|
walther@60337
|
835 |
Rule.Thm ("realpow_minus_even", @{thm realpow_minus_even}),
|
walther@60318
|
836 |
(*"n is_even ==> (- r) \<up> n = r \<up> n"*)
|
walther@60337
|
837 |
Rule.Thm ("realpow_minus_odd", @{thm realpow_minus_odd})
|
walther@60323
|
838 |
(*"\<not> (n is_even) ==> (- r) \<up> n = -1 * r \<up> n"*)
|
walther@59878
|
839 |
], scr = Rule.Empty_Prog};
|
neuper@37950
|
840 |
|
neuper@37950
|
841 |
val simplify_power_ =
|
walther@59851
|
842 |
Rule_Def.Repeat{id = "simplify_power_", preconds = [],
|
walther@59857
|
843 |
rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord),
|
walther@59852
|
844 |
erls = Rule_Set.empty, srls = Rule_Set.Empty,
|
neuper@42451
|
845 |
calc = [], errpatts = [],
|
wneuper@59416
|
846 |
rules = [(*MG: Reihenfolge der folgenden 2 Rule.Thm muss so bleiben, wegen
|
walther@60260
|
847 |
a*(a*a) --> a*a \<up> 2 und nicht a*(a*a) --> a \<up> 2*a *)
|
wenzelm@60296
|
848 |
\<^rule_thm_sym>\<open>realpow_twoI\<close>,
|
walther@60242
|
849 |
(*"r * r = r \<up> 2"*)
|
wenzelm@60297
|
850 |
\<^rule_thm>\<open>realpow_twoI_assoc_l\<close>,
|
walther@60242
|
851 |
(*"r * (r * s) = r \<up> 2 * s"*)
|
neuper@37950
|
852 |
|
wenzelm@60297
|
853 |
\<^rule_thm>\<open>realpow_plus_1\<close>,
|
walther@60242
|
854 |
(*"r * r \<up> n = r \<up> (n + 1)"*)
|
wenzelm@60298
|
855 |
\<^rule_thm>\<open>realpow_plus_1_assoc_l\<close>,
|
walther@60242
|
856 |
(*"r * (r \<up> m * s) = r \<up> (1 + m) * s"*)
|
walther@60260
|
857 |
(*MG 9.7.03: neues Rule.Thm wegen a*(a*(a*b)) --> a \<up> 2*(a*b) *)
|
wenzelm@60298
|
858 |
\<^rule_thm>\<open>realpow_plus_1_assoc_l2\<close>,
|
walther@60242
|
859 |
(*"r \<up> m * (r * s) = r \<up> (1 + m) * s"*)
|
neuper@37950
|
860 |
|
wenzelm@60296
|
861 |
\<^rule_thm_sym>\<open>realpow_addI\<close>,
|
walther@60242
|
862 |
(*"r \<up> n * r \<up> m = r \<up> (n + m)"*)
|
wenzelm@60297
|
863 |
\<^rule_thm>\<open>realpow_addI_assoc_l\<close>,
|
walther@60242
|
864 |
(*"r \<up> n * (r \<up> m * s) = r \<up> (n + m) * s"*)
|
neuper@37950
|
865 |
|
neuper@37950
|
866 |
(* ist in expand_poly - wird hier aber auch gebraucht, wegen:
|
walther@60260
|
867 |
"r * r = r \<up> 2" wenn r=a \<up> b*)
|
wenzelm@60297
|
868 |
\<^rule_thm>\<open>realpow_pow\<close>
|
walther@60242
|
869 |
(*"(a \<up> b) \<up> c = a \<up> (b * c)"*)
|
walther@59878
|
870 |
], scr = Rule.Empty_Prog};
|
neuper@37950
|
871 |
|
neuper@37950
|
872 |
val calc_add_mult_pow_ =
|
walther@59851
|
873 |
Rule_Def.Repeat{id = "calc_add_mult_pow_", preconds = [],
|
walther@59857
|
874 |
rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord),
|
walther@59851
|
875 |
erls = Atools_erls(*erls3.4.03*),srls = Rule_Set.Empty,
|
wenzelm@60309
|
876 |
calc = [("PLUS" , (\<^const_name>\<open>plus\<close>, eval_binop "#add_")),
|
wenzelm@60309
|
877 |
("TIMES" , (\<^const_name>\<open>times\<close>, eval_binop "#mult_")),
|
wenzelm@60309
|
878 |
("POWER", (\<^const_name>\<open>powr\<close>, eval_binop "#power_"))
|
neuper@37950
|
879 |
],
|
neuper@42451
|
880 |
errpatts = [],
|
wenzelm@60294
|
881 |
rules = [\<^rule_eval>\<open>plus\<close> (eval_binop "#add_"),
|
wenzelm@60294
|
882 |
\<^rule_eval>\<open>times\<close> (eval_binop "#mult_"),
|
wenzelm@60294
|
883 |
\<^rule_eval>\<open>powr\<close> (eval_binop "#power_")
|
walther@59878
|
884 |
], scr = Rule.Empty_Prog};
|
neuper@37950
|
885 |
|
neuper@37950
|
886 |
val reduce_012_mult_ =
|
walther@59851
|
887 |
Rule_Def.Repeat{id = "reduce_012_mult_", preconds = [],
|
walther@59857
|
888 |
rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord),
|
walther@59852
|
889 |
erls = Rule_Set.empty,srls = Rule_Set.Empty,
|
neuper@42451
|
890 |
calc = [], errpatts = [],
|
wneuper@59416
|
891 |
rules = [(* MG: folgende Rule.Thm müssen hier stehen bleiben: *)
|
wenzelm@60297
|
892 |
\<^rule_thm>\<open>mult_1_right\<close>,
|
walther@60260
|
893 |
(*"z * 1 = z"*) (*wegen "a * b * b \<up> (-1) + a"*)
|
wenzelm@60297
|
894 |
\<^rule_thm>\<open>realpow_zeroI\<close>,
|
walther@60260
|
895 |
(*"r \<up> 0 = 1"*) (*wegen "a*a \<up> (-1)*c + b + c"*)
|
wenzelm@60297
|
896 |
\<^rule_thm>\<open>realpow_oneI\<close>,
|
walther@60242
|
897 |
(*"r \<up> 1 = r"*)
|
wenzelm@60297
|
898 |
\<^rule_thm>\<open>realpow_eq_oneI\<close>
|
walther@60242
|
899 |
(*"1 \<up> n = 1"*)
|
walther@59878
|
900 |
], scr = Rule.Empty_Prog};
|
neuper@37950
|
901 |
|
neuper@37950
|
902 |
val collect_numerals_ =
|
walther@59851
|
903 |
Rule_Def.Repeat{id = "collect_numerals_", preconds = [],
|
walther@59857
|
904 |
rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord),
|
walther@59851
|
905 |
erls = Atools_erls, srls = Rule_Set.Empty,
|
wenzelm@60309
|
906 |
calc = [("PLUS" , (\<^const_name>\<open>plus\<close>, eval_binop "#add_"))
|
neuper@42451
|
907 |
], errpatts = [],
|
neuper@37950
|
908 |
rules =
|
wenzelm@60297
|
909 |
[\<^rule_thm>\<open>real_num_collect\<close>,
|
neuper@37950
|
910 |
(*"[| l is_const; m is_const |]==>l * n + m * n = (l + m) * n"*)
|
wenzelm@60297
|
911 |
\<^rule_thm>\<open>real_num_collect_assoc_r\<close>,
|
neuper@37950
|
912 |
(*"[| l is_const; m is_const |] ==> \
|
neuper@37950
|
913 |
\(k + m * n) + l * n = k + (l + m)*n"*)
|
wenzelm@60297
|
914 |
\<^rule_thm>\<open>real_one_collect\<close>,
|
neuper@37950
|
915 |
(*"m is_const ==> n + m * n = (1 + m) * n"*)
|
wenzelm@60297
|
916 |
\<^rule_thm>\<open>real_one_collect_assoc_r\<close>,
|
neuper@37950
|
917 |
(*"m is_const ==> (k + n) + m * n = k + (m + 1) * n"*)
|
neuper@37950
|
918 |
|
wenzelm@60294
|
919 |
\<^rule_eval>\<open>plus\<close> (eval_binop "#add_"),
|
neuper@37950
|
920 |
|
wneuper@59416
|
921 |
(*MG: Reihenfolge der folgenden 2 Rule.Thm muss so bleiben, wegen
|
neuper@37950
|
922 |
(a+a)+a --> a + 2*a --> 3*a and not (a+a)+a --> 2*a + a *)
|
wenzelm@60297
|
923 |
\<^rule_thm>\<open>real_mult_2_assoc_r\<close>,
|
neuper@37950
|
924 |
(*"(k + z1) + z1 = k + 2 * z1"*)
|
wenzelm@60296
|
925 |
\<^rule_thm_sym>\<open>real_mult_2\<close>
|
neuper@37950
|
926 |
(*"z1 + z1 = 2 * z1"*)
|
walther@59878
|
927 |
], scr = Rule.Empty_Prog};
|
neuper@37950
|
928 |
|
neuper@37950
|
929 |
val reduce_012_ =
|
walther@59851
|
930 |
Rule_Def.Repeat{id = "reduce_012_", preconds = [],
|
walther@59857
|
931 |
rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord),
|
walther@59852
|
932 |
erls = Rule_Set.empty,srls = Rule_Set.Empty, calc = [], errpatts = [],
|
wenzelm@60297
|
933 |
rules = [\<^rule_thm>\<open>mult_1_left\<close>,
|
neuper@37950
|
934 |
(*"1 * z = z"*)
|
wenzelm@60297
|
935 |
\<^rule_thm>\<open>mult_zero_left\<close>,
|
neuper@37950
|
936 |
(*"0 * z = 0"*)
|
wenzelm@60297
|
937 |
\<^rule_thm>\<open>mult_zero_right\<close>,
|
neuper@37950
|
938 |
(*"z * 0 = 0"*)
|
wenzelm@60297
|
939 |
\<^rule_thm>\<open>add_0_left\<close>,
|
neuper@37950
|
940 |
(*"0 + z = z"*)
|
wenzelm@60297
|
941 |
\<^rule_thm>\<open>add_0_right\<close>,
|
neuper@37950
|
942 |
(*"z + 0 = z"*) (*wegen a+b-b --> a+(1-1)*b --> a+0 --> a*)
|
neuper@37950
|
943 |
|
wenzelm@60297
|
944 |
(*\<^rule_thm>\<open>realpow_oneI\<close>*)
|
walther@60242
|
945 |
(*"?r \<up> 1 = ?r"*)
|
wenzelm@60297
|
946 |
\<^rule_thm>\<open>division_ring_divide_zero\<close>
|
neuper@37950
|
947 |
(*"0 / ?x = 0"*)
|
walther@59878
|
948 |
], scr = Rule.Empty_Prog};
|
neuper@37950
|
949 |
|
neuper@37979
|
950 |
val discard_parentheses1 =
|
walther@59852
|
951 |
Rule_Set.append_rules "discard_parentheses1" Rule_Set.empty
|
wenzelm@60296
|
952 |
[\<^rule_thm_sym>\<open>mult.assoc\<close>
|
neuper@37950
|
953 |
(*"?z1.1 * (?z2.1 * ?z3.1) = ?z1.1 * ?z2.1 * ?z3.1"*)
|
wenzelm@60296
|
954 |
(*\<^rule_thm_sym>\<open>add.assoc\<close>*)
|
neuper@37950
|
955 |
(*"?z1.1 + (?z2.1 + ?z3.1) = ?z1.1 + ?z2.1 + ?z3.1"*)
|
neuper@37950
|
956 |
];
|
neuper@37950
|
957 |
|
wneuper@59523
|
958 |
val expand_poly =
|
walther@59851
|
959 |
Rule_Def.Repeat{id = "expand_poly", preconds = [],
|
walther@59857
|
960 |
rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord),
|
walther@60320
|
961 |
erls = powers_erls, srls = Rule_Set.Empty, calc = [], errpatts = [],
|
walther@60320
|
962 |
rules =
|
walther@60337
|
963 |
[Rule.Thm ("distrib_right" , @{thm distrib_right}),
|
neuper@37950
|
964 |
(*"(z1.0 + z2.0) * w = z1.0 * w + z2.0 * w"*)
|
wenzelm@60297
|
965 |
\<^rule_thm>\<open>distrib_left\<close>,
|
neuper@37950
|
966 |
(*"w * (z1.0 + z2.0) = w * z1.0 + w * z2.0"*)
|
walther@60337
|
967 |
(*Rule.Thm ("distrib_right1", @{thm distrib_right}1),
|
neuper@37950
|
968 |
....... 18.3.03 undefined???*)
|
neuper@37950
|
969 |
|
wenzelm@60297
|
970 |
\<^rule_thm>\<open>real_plus_binom_pow2\<close>,
|
walther@60260
|
971 |
(*"(a + b) \<up> 2 = a \<up> 2 + 2*a*b + b \<up> 2"*)
|
wenzelm@60297
|
972 |
\<^rule_thm>\<open>real_minus_binom_pow2_p\<close>,
|
walther@60260
|
973 |
(*"(a - b) \<up> 2 = a \<up> 2 + -2*a*b + b \<up> 2"*)
|
wenzelm@60298
|
974 |
\<^rule_thm>\<open>real_plus_minus_binom1_p\<close>,
|
walther@60260
|
975 |
(*"(a + b)*(a - b) = a \<up> 2 + -1*b \<up> 2"*)
|
wenzelm@60298
|
976 |
\<^rule_thm>\<open>real_plus_minus_binom2_p\<close>,
|
walther@60260
|
977 |
(*"(a - b)*(a + b) = a \<up> 2 + -1*b \<up> 2"*)
|
neuper@37950
|
978 |
|
walther@60341
|
979 |
\<^rule_thm>\<open>minus_minus\<close> (*"- (- ?z) = ?z"*),
|
walther@60341
|
980 |
\<^rule_thm>\<open>real_diff_minus\<close> (*"a - b = a + -1 * b"*),
|
walther@60341
|
981 |
\<^rule_thm>\<open>real_mult_minus1_sym\<close> (*"\<not>(z is_const) ==> - (z::real) = -1 * z"*)
|
neuper@37950
|
982 |
|
wenzelm@60298
|
983 |
(*\<^rule_thm>\<open>real_minus_add_distrib\<close>,*)
|
neuper@37950
|
984 |
(*"- (?x + ?y) = - ?x + - ?y"*)
|
wenzelm@60297
|
985 |
(*\<^rule_thm>\<open>real_diff_plus\<close>*)
|
neuper@37950
|
986 |
(*"a - b = a + -b"*)
|
walther@59878
|
987 |
], scr = Rule.Empty_Prog};
|
neuper@37950
|
988 |
|
neuper@37950
|
989 |
val simplify_power =
|
walther@59851
|
990 |
Rule_Def.Repeat{id = "simplify_power", preconds = [],
|
walther@59857
|
991 |
rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord),
|
walther@59852
|
992 |
erls = Rule_Set.empty, srls = Rule_Set.Empty,
|
neuper@42451
|
993 |
calc = [], errpatts = [],
|
wenzelm@60297
|
994 |
rules = [\<^rule_thm>\<open>realpow_multI\<close>,
|
walther@60242
|
995 |
(*"(r * s) \<up> n = r \<up> n * s \<up> n"*)
|
neuper@37950
|
996 |
|
wenzelm@60296
|
997 |
\<^rule_thm_sym>\<open>realpow_twoI\<close>,
|
walther@60242
|
998 |
(*"r1 * r1 = r1 \<up> 2"*)
|
wenzelm@60297
|
999 |
\<^rule_thm>\<open>realpow_plus_1\<close>,
|
walther@60242
|
1000 |
(*"r * r \<up> n = r \<up> (n + 1)"*)
|
wenzelm@60297
|
1001 |
\<^rule_thm>\<open>realpow_pow\<close>,
|
walther@60242
|
1002 |
(*"(a \<up> b) \<up> c = a \<up> (b * c)"*)
|
wenzelm@60296
|
1003 |
\<^rule_thm_sym>\<open>realpow_addI\<close>,
|
walther@60242
|
1004 |
(*"r \<up> n * r \<up> m = r \<up> (n + m)"*)
|
wenzelm@60297
|
1005 |
\<^rule_thm>\<open>realpow_oneI\<close>,
|
walther@60242
|
1006 |
(*"r \<up> 1 = r"*)
|
wenzelm@60297
|
1007 |
\<^rule_thm>\<open>realpow_eq_oneI\<close>
|
walther@60242
|
1008 |
(*"1 \<up> n = 1"*)
|
walther@59878
|
1009 |
], scr = Rule.Empty_Prog};
|
neuper@42451
|
1010 |
|
neuper@37950
|
1011 |
val collect_numerals =
|
walther@59851
|
1012 |
Rule_Def.Repeat{id = "collect_numerals", preconds = [],
|
walther@59857
|
1013 |
rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord),
|
walther@59851
|
1014 |
erls = Atools_erls(*erls3.4.03*),srls = Rule_Set.Empty,
|
wenzelm@60309
|
1015 |
calc = [("PLUS" , (\<^const_name>\<open>plus\<close>, eval_binop "#add_")),
|
wenzelm@60309
|
1016 |
("TIMES" , (\<^const_name>\<open>times\<close>, eval_binop "#mult_")),
|
wenzelm@60309
|
1017 |
("POWER", (\<^const_name>\<open>powr\<close>, eval_binop "#power_"))
|
neuper@42451
|
1018 |
], errpatts = [],
|
wenzelm@60297
|
1019 |
rules = [\<^rule_thm>\<open>real_num_collect\<close>,
|
neuper@37950
|
1020 |
(*"[| l is_const; m is_const |]==>l * n + m * n = (l + m) * n"*)
|
wenzelm@60297
|
1021 |
\<^rule_thm>\<open>real_num_collect_assoc\<close>,
|
neuper@37950
|
1022 |
(*"[| l is_const; m is_const |] ==>
|
neuper@37950
|
1023 |
l * n + (m * n + k) = (l + m) * n + k"*)
|
wenzelm@60297
|
1024 |
\<^rule_thm>\<open>real_one_collect\<close>,
|
neuper@37950
|
1025 |
(*"m is_const ==> n + m * n = (1 + m) * n"*)
|
wenzelm@60297
|
1026 |
\<^rule_thm>\<open>real_one_collect_assoc\<close>,
|
neuper@37950
|
1027 |
(*"m is_const ==> k + (n + m * n) = k + (1 + m) * n"*)
|
wenzelm@60294
|
1028 |
\<^rule_eval>\<open>plus\<close> (eval_binop "#add_"),
|
wenzelm@60294
|
1029 |
\<^rule_eval>\<open>times\<close> (eval_binop "#mult_"),
|
wenzelm@60294
|
1030 |
\<^rule_eval>\<open>powr\<close> (eval_binop "#power_")
|
walther@59878
|
1031 |
], scr = Rule.Empty_Prog};
|
neuper@37950
|
1032 |
val reduce_012 =
|
walther@59851
|
1033 |
Rule_Def.Repeat{id = "reduce_012", preconds = [],
|
walther@59857
|
1034 |
rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord),
|
walther@60344
|
1035 |
erls = Rule_Set.append_rules "erls_in_reduce_012" Rule_Set.empty [
|
walther@60344
|
1036 |
\<^rule_eval>\<open>is_num\<close> (Prog_Expr.eval_is_num "#is_num_"),
|
walther@60344
|
1037 |
\<^rule_thm>\<open>not_false\<close>,
|
walther@60344
|
1038 |
\<^rule_thm>\<open>not_true\<close>],
|
walther@60344
|
1039 |
srls = Rule_Set.Empty, calc = [], errpatts = [],
|
wenzelm@60297
|
1040 |
rules = [\<^rule_thm>\<open>mult_1_left\<close>,
|
neuper@37950
|
1041 |
(*"1 * z = z"*)
|
wenzelm@60297
|
1042 |
(*\<^rule_thm>\<open>real_mult_minus1\<close>,14.3.03*)
|
neuper@37950
|
1043 |
(*"-1 * z = - z"*)
|
walther@60344
|
1044 |
\<^rule_thm>\<open>real_minus_mult_left\<close>, (*"\<not> ((a::real) is_num) ==> (- a) * b = - (a * b)"*)
|
wenzelm@60298
|
1045 |
(*\<^rule_thm>\<open>real_minus_mult_cancel\<close>,
|
neuper@37950
|
1046 |
(*"- ?x * - ?y = ?x * ?y"*)---*)
|
wenzelm@60297
|
1047 |
\<^rule_thm>\<open>mult_zero_left\<close>,
|
neuper@37950
|
1048 |
(*"0 * z = 0"*)
|
walther@60344
|
1049 |
\<^rule_thm>\<open>add_0_left\<close>, (*"0 + z = z"*)
|
walther@60344
|
1050 |
\<^rule_thm>\<open>add_0_right\<close>, (*"a + - a = 0"*)
|
wenzelm@60297
|
1051 |
\<^rule_thm>\<open>right_minus\<close>,
|
neuper@37950
|
1052 |
(*"?z + - ?z = 0"*)
|
wenzelm@60296
|
1053 |
\<^rule_thm_sym>\<open>real_mult_2\<close>,
|
neuper@37950
|
1054 |
(*"z1 + z1 = 2 * z1"*)
|
wenzelm@60297
|
1055 |
\<^rule_thm>\<open>real_mult_2_assoc\<close>
|
neuper@37950
|
1056 |
(*"z1 + (z1 + k) = 2 * z1 + k"*)
|
walther@59878
|
1057 |
], scr = Rule.Empty_Prog};
|
neuper@52139
|
1058 |
|
neuper@37950
|
1059 |
val discard_parentheses =
|
walther@59852
|
1060 |
Rule_Set.append_rules "discard_parentheses" Rule_Set.empty
|
wenzelm@60296
|
1061 |
[\<^rule_thm_sym>\<open>mult.assoc\<close>, \<^rule_thm_sym>\<open>add.assoc\<close>];
|
wneuper@59523
|
1062 |
\<close>
|
neuper@37950
|
1063 |
|
wneuper@59523
|
1064 |
subsubsection \<open>hard-coded AC rewriting\<close>
|
wneuper@59523
|
1065 |
ML \<open>
|
wneuper@59523
|
1066 |
(*MG.0401: termorders for multivariate polys dropped due to principal problems:
|
wneuper@59523
|
1067 |
(total-degree-)ordering of monoms NOT possible with size_of_term GIVEN*)
|
wneuper@59523
|
1068 |
val order_add_mult =
|
walther@59851
|
1069 |
Rule_Def.Repeat{id = "order_add_mult", preconds = [],
|
wenzelm@60291
|
1070 |
rew_ord = ("ord_make_polynomial",ord_make_polynomial false \<^theory>),
|
walther@59852
|
1071 |
erls = Rule_Set.empty,srls = Rule_Set.Empty,
|
neuper@42451
|
1072 |
calc = [], errpatts = [],
|
wenzelm@60297
|
1073 |
rules = [\<^rule_thm>\<open>mult.commute\<close>,
|
wneuper@59523
|
1074 |
(* z * w = w * z *)
|
wenzelm@60297
|
1075 |
\<^rule_thm>\<open>real_mult_left_commute\<close>,
|
wneuper@59523
|
1076 |
(*z1.0 * (z2.0 * z3.0) = z2.0 * (z1.0 * z3.0)*)
|
wenzelm@60297
|
1077 |
\<^rule_thm>\<open>mult.assoc\<close>,
|
wneuper@59523
|
1078 |
(*z1.0 * z2.0 * z3.0 = z1.0 * (z2.0 * z3.0)*)
|
wenzelm@60297
|
1079 |
\<^rule_thm>\<open>add.commute\<close>,
|
wneuper@59523
|
1080 |
(*z + w = w + z*)
|
wenzelm@60297
|
1081 |
\<^rule_thm>\<open>add.left_commute\<close>,
|
wneuper@59523
|
1082 |
(*x + (y + z) = y + (x + z)*)
|
wenzelm@60297
|
1083 |
\<^rule_thm>\<open>add.assoc\<close>
|
wneuper@59523
|
1084 |
(*z1.0 + z2.0 + z3.0 = z1.0 + (z2.0 + z3.0)*)
|
walther@59878
|
1085 |
], scr = Rule.Empty_Prog};
|
wneuper@59523
|
1086 |
(*MG.0401: termorders for multivariate polys dropped due to principal problems:
|
wneuper@59523
|
1087 |
(total-degree-)ordering of monoms NOT possible with size_of_term GIVEN*)
|
wneuper@59523
|
1088 |
val order_mult =
|
walther@59851
|
1089 |
Rule_Def.Repeat{id = "order_mult", preconds = [],
|
wenzelm@60291
|
1090 |
rew_ord = ("ord_make_polynomial",ord_make_polynomial false \<^theory>),
|
walther@59852
|
1091 |
erls = Rule_Set.empty,srls = Rule_Set.Empty,
|
wneuper@59523
|
1092 |
calc = [], errpatts = [],
|
wenzelm@60297
|
1093 |
rules = [\<^rule_thm>\<open>mult.commute\<close>,
|
wneuper@59523
|
1094 |
(* z * w = w * z *)
|
wenzelm@60297
|
1095 |
\<^rule_thm>\<open>real_mult_left_commute\<close>,
|
wneuper@59523
|
1096 |
(*z1.0 * (z2.0 * z3.0) = z2.0 * (z1.0 * z3.0)*)
|
wenzelm@60297
|
1097 |
\<^rule_thm>\<open>mult.assoc\<close>
|
wneuper@59523
|
1098 |
(*z1.0 * z2.0 * z3.0 = z1.0 * (z2.0 * z3.0)*)
|
walther@59878
|
1099 |
], scr = Rule.Empty_Prog};
|
wneuper@59472
|
1100 |
\<close>
|
wneuper@59472
|
1101 |
ML \<open>
|
wneuper@59416
|
1102 |
fun attach_form (_: Rule.rule list list) (_: term) (_: term) = (*still missing*)
|
wneuper@59416
|
1103 |
[]:(Rule.rule * (term * term list)) list;
|
walther@59850
|
1104 |
fun init_state (_: term) = Rule_Set.e_rrlsstate;
|
wneuper@59416
|
1105 |
fun locate_rule (_: Rule.rule list list) (_: term) (_: Rule.rule) =
|
wneuper@59416
|
1106 |
([]:(Rule.rule * (term * term list)) list);
|
wneuper@59416
|
1107 |
fun next_rule (_: Rule.rule list list) (_: term) = (NONE: Rule.rule option);
|
wneuper@59406
|
1108 |
fun normal_form t = SOME (sort_variables t, []: term list);
|
neuper@37950
|
1109 |
|
neuper@37950
|
1110 |
val order_mult_ =
|
walther@59850
|
1111 |
Rule_Set.Rrls {id = "order_mult_",
|
neuper@37950
|
1112 |
prepat =
|
neuper@38036
|
1113 |
(* ?p matched with the current term gives an environment,
|
neuper@38037
|
1114 |
which evaluates (the instantiated) "?p is_multUnordered" to true *)
|
wenzelm@60291
|
1115 |
[([TermC.parse_patt \<^theory> "?p is_multUnordered"],
|
wenzelm@60291
|
1116 |
TermC.parse_patt \<^theory> "?p :: real")],
|
walther@59857
|
1117 |
rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord),
|
walther@59852
|
1118 |
erls = Rule_Set.append_rules "Rule_Set.empty-is_multUnordered" Rule_Set.empty
|
wenzelm@60294
|
1119 |
[\<^rule_eval>\<open>is_multUnordered\<close> (eval_is_multUnordered "")],
|
wenzelm@60309
|
1120 |
calc = [("PLUS" , (\<^const_name>\<open>plus\<close>, eval_binop "#add_")),
|
wenzelm@60309
|
1121 |
("TIMES" , (\<^const_name>\<open>times\<close>, eval_binop "#mult_")),
|
wenzelm@60309
|
1122 |
("DIVIDE", (\<^const_name>\<open>divide\<close>, Prog_Expr.eval_cancel "#divide_e")),
|
wenzelm@60309
|
1123 |
("POWER" , (\<^const_name>\<open>powr\<close>, eval_binop "#power_"))],
|
wneuper@59406
|
1124 |
errpatts = [],
|
wneuper@59416
|
1125 |
scr = Rule.Rfuns {init_state = init_state,
|
neuper@37950
|
1126 |
normal_form = normal_form,
|
neuper@37950
|
1127 |
locate_rule = locate_rule,
|
neuper@37950
|
1128 |
next_rule = next_rule,
|
neuper@37950
|
1129 |
attach_form = attach_form}};
|
neuper@37950
|
1130 |
val order_mult_rls_ =
|
walther@59851
|
1131 |
Rule_Def.Repeat {id = "order_mult_rls_", preconds = [],
|
walther@59857
|
1132 |
rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord),
|
walther@59852
|
1133 |
erls = Rule_Set.empty,srls = Rule_Set.Empty,
|
neuper@42451
|
1134 |
calc = [], errpatts = [],
|
wneuper@59416
|
1135 |
rules = [Rule.Rls_ order_mult_
|
walther@59878
|
1136 |
], scr = Rule.Empty_Prog};
|
neuper@37950
|
1137 |
|
wneuper@59523
|
1138 |
\<close> ML \<open>
|
neuper@37950
|
1139 |
|
wneuper@59416
|
1140 |
fun attach_form (_: Rule.rule list list) (_: term) (_: term) = (*still missing*)
|
wneuper@59416
|
1141 |
[]: (Rule.rule * (term * term list)) list;
|
walther@59850
|
1142 |
fun init_state (_: term) = Rule_Set.e_rrlsstate;
|
wneuper@59416
|
1143 |
fun locate_rule (_: Rule.rule list list) (_: term) (_: Rule.rule) =
|
wneuper@59416
|
1144 |
([]: (Rule.rule * (term * term list)) list);
|
wneuper@59416
|
1145 |
fun next_rule (_: Rule.rule list list) (_: term) = (NONE: Rule.rule option);
|
wneuper@59406
|
1146 |
fun normal_form t = SOME (sort_monoms t,[]: term list);
|
wneuper@59472
|
1147 |
\<close> ML \<open>
|
neuper@37950
|
1148 |
val order_add_ =
|
walther@59850
|
1149 |
Rule_Set.Rrls {id = "order_add_",
|
neuper@37950
|
1150 |
prepat = (*WN.18.6.03 Preconditions und Pattern,
|
walther@59850
|
1151 |
die beide passen muessen, damit das Rule_Set.Rrls angewandt wird*)
|
wneuper@59389
|
1152 |
[([TermC.parse_patt @{theory} "?p is_addUnordered"],
|
wneuper@59389
|
1153 |
TermC.parse_patt @{theory} "?p :: real"
|
neuper@37950
|
1154 |
(*WN.18.6.03 also KEIN pattern, dieses erzeugt nur das Environment
|
neuper@37950
|
1155 |
fuer die Evaluation der Precondition "p is_addUnordered"*))],
|
walther@59857
|
1156 |
rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord),
|
walther@59852
|
1157 |
erls = Rule_Set.append_rules "Rule_Set.empty-is_addUnordered" Rule_Set.empty(*MG: poly_erls*)
|
wenzelm@60294
|
1158 |
[\<^rule_eval>\<open>is_addUnordered\<close> (eval_is_addUnordered "")],
|
wenzelm@60309
|
1159 |
calc = [("PLUS" ,(\<^const_name>\<open>plus\<close>, eval_binop "#add_")),
|
wenzelm@60309
|
1160 |
("TIMES" ,(\<^const_name>\<open>times\<close>, eval_binop "#mult_")),
|
wenzelm@60309
|
1161 |
("DIVIDE",(\<^const_name>\<open>divide\<close>, Prog_Expr.eval_cancel "#divide_e")),
|
wenzelm@60309
|
1162 |
("POWER" ,(\<^const_name>\<open>powr\<close> , eval_binop "#power_"))],
|
neuper@42451
|
1163 |
errpatts = [],
|
wneuper@59416
|
1164 |
scr = Rule.Rfuns {init_state = init_state,
|
neuper@37950
|
1165 |
normal_form = normal_form,
|
neuper@37950
|
1166 |
locate_rule = locate_rule,
|
neuper@37950
|
1167 |
next_rule = next_rule,
|
neuper@37950
|
1168 |
attach_form = attach_form}};
|
neuper@37950
|
1169 |
|
wneuper@59406
|
1170 |
val order_add_rls_ =
|
walther@59851
|
1171 |
Rule_Def.Repeat {id = "order_add_rls_", preconds = [],
|
walther@59857
|
1172 |
rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord),
|
walther@59852
|
1173 |
erls = Rule_Set.empty,srls = Rule_Set.Empty,
|
neuper@42451
|
1174 |
calc = [], errpatts = [],
|
wneuper@59416
|
1175 |
rules = [Rule.Rls_ order_add_
|
walther@59878
|
1176 |
], scr = Rule.Empty_Prog};
|
wneuper@59472
|
1177 |
\<close>
|
neuper@37950
|
1178 |
|
wneuper@59472
|
1179 |
text \<open>rule-set make_polynomial also named norm_Poly:
|
neuper@42398
|
1180 |
Rewrite order has not been implemented properly; the order is better in
|
neuper@42398
|
1181 |
make_polynomial_in (coded in SML).
|
neuper@42398
|
1182 |
Notes on state of development:
|
neuper@42398
|
1183 |
\# surprise 2006: test --- norm_Poly NOT COMPLETE ---
|
neuper@42398
|
1184 |
\# migration Isabelle2002 --> 2011 weakened the rule set, see test
|
walther@59962
|
1185 |
--- Matthias Goldgruber 2003 rewrite orders ---, raise ERROR "ord_make_polynomial_in #16b"
|
wneuper@59472
|
1186 |
\<close>
|
wneuper@59472
|
1187 |
ML \<open>
|
neuper@37950
|
1188 |
(*. see MG-DA.p.52ff .*)
|
neuper@37950
|
1189 |
val make_polynomial(*MG.03, overwrites version from above,
|
neuper@37950
|
1190 |
previously 'make_polynomial_'*) =
|
walther@59878
|
1191 |
Rule_Set.Sequence {id = "make_polynomial", preconds = []:term list,
|
walther@59857
|
1192 |
rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord),
|
walther@59851
|
1193 |
erls = Atools_erls, srls = Rule_Set.Empty,calc = [], errpatts = [],
|
wneuper@59416
|
1194 |
rules = [Rule.Rls_ discard_minus,
|
wneuper@59416
|
1195 |
Rule.Rls_ expand_poly_,
|
wenzelm@60294
|
1196 |
\<^rule_eval>\<open>times\<close> (eval_binop "#mult_"),
|
wneuper@59416
|
1197 |
Rule.Rls_ order_mult_rls_,
|
wneuper@59416
|
1198 |
Rule.Rls_ simplify_power_,
|
wneuper@59416
|
1199 |
Rule.Rls_ calc_add_mult_pow_,
|
wneuper@59416
|
1200 |
Rule.Rls_ reduce_012_mult_,
|
wneuper@59416
|
1201 |
Rule.Rls_ order_add_rls_,
|
wneuper@59416
|
1202 |
Rule.Rls_ collect_numerals_,
|
wneuper@59416
|
1203 |
Rule.Rls_ reduce_012_,
|
wneuper@59416
|
1204 |
Rule.Rls_ discard_parentheses1
|
neuper@37950
|
1205 |
],
|
walther@59878
|
1206 |
scr = Rule.Empty_Prog
|
wneuper@59406
|
1207 |
};
|
wneuper@59472
|
1208 |
\<close>
|
wneuper@59472
|
1209 |
ML \<open>
|
neuper@37950
|
1210 |
val norm_Poly(*=make_polynomial*) =
|
walther@59878
|
1211 |
Rule_Set.Sequence {id = "norm_Poly", preconds = []:term list,
|
walther@59857
|
1212 |
rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord),
|
walther@59851
|
1213 |
erls = Atools_erls, srls = Rule_Set.Empty, calc = [], errpatts = [],
|
wneuper@59416
|
1214 |
rules = [Rule.Rls_ discard_minus,
|
wneuper@59416
|
1215 |
Rule.Rls_ expand_poly_,
|
wenzelm@60294
|
1216 |
\<^rule_eval>\<open>times\<close> (eval_binop "#mult_"),
|
wneuper@59416
|
1217 |
Rule.Rls_ order_mult_rls_,
|
wneuper@59416
|
1218 |
Rule.Rls_ simplify_power_,
|
wneuper@59416
|
1219 |
Rule.Rls_ calc_add_mult_pow_,
|
wneuper@59416
|
1220 |
Rule.Rls_ reduce_012_mult_,
|
wneuper@59416
|
1221 |
Rule.Rls_ order_add_rls_,
|
wneuper@59416
|
1222 |
Rule.Rls_ collect_numerals_,
|
wneuper@59416
|
1223 |
Rule.Rls_ reduce_012_,
|
wneuper@59416
|
1224 |
Rule.Rls_ discard_parentheses1
|
neuper@37950
|
1225 |
],
|
walther@59878
|
1226 |
scr = Rule.Empty_Prog
|
wneuper@59406
|
1227 |
};
|
wneuper@59472
|
1228 |
\<close>
|
wneuper@59472
|
1229 |
ML \<open>
|
wneuper@59416
|
1230 |
(* MG:03 Like make_polynomial_ but without Rule.Rls_ discard_parentheses1
|
neuper@37950
|
1231 |
and expand_poly_rat_ instead of expand_poly_, see MG-DA.p.56ff*)
|
neuper@37950
|
1232 |
(* MG necessary for termination of norm_Rational(*_mg*) in Rational.ML*)
|
neuper@37950
|
1233 |
val make_rat_poly_with_parentheses =
|
walther@59878
|
1234 |
Rule_Set.Sequence{id = "make_rat_poly_with_parentheses", preconds = []:term list,
|
walther@59857
|
1235 |
rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord),
|
walther@59851
|
1236 |
erls = Atools_erls, srls = Rule_Set.Empty, calc = [], errpatts = [],
|
wneuper@59416
|
1237 |
rules = [Rule.Rls_ discard_minus,
|
wneuper@59416
|
1238 |
Rule.Rls_ expand_poly_rat_,(*ignors rationals*)
|
wenzelm@60294
|
1239 |
\<^rule_eval>\<open>times\<close> (eval_binop "#mult_"),
|
wneuper@59416
|
1240 |
Rule.Rls_ order_mult_rls_,
|
wneuper@59416
|
1241 |
Rule.Rls_ simplify_power_,
|
wneuper@59416
|
1242 |
Rule.Rls_ calc_add_mult_pow_,
|
wneuper@59416
|
1243 |
Rule.Rls_ reduce_012_mult_,
|
wneuper@59416
|
1244 |
Rule.Rls_ order_add_rls_,
|
wneuper@59416
|
1245 |
Rule.Rls_ collect_numerals_,
|
wneuper@59416
|
1246 |
Rule.Rls_ reduce_012_
|
wneuper@59416
|
1247 |
(*Rule.Rls_ discard_parentheses1 *)
|
neuper@37950
|
1248 |
],
|
walther@59878
|
1249 |
scr = Rule.Empty_Prog
|
wneuper@59406
|
1250 |
};
|
wneuper@59472
|
1251 |
\<close>
|
wneuper@59472
|
1252 |
ML \<open>
|
neuper@37950
|
1253 |
(*.a minimal ruleset for reverse rewriting of factions [2];
|
neuper@37950
|
1254 |
compare expand_binoms.*)
|
neuper@37950
|
1255 |
val rev_rew_p =
|
walther@59878
|
1256 |
Rule_Set.Sequence{id = "rev_rew_p", preconds = [], rew_ord = ("termlessI",termlessI),
|
walther@59851
|
1257 |
erls = Atools_erls, srls = Rule_Set.Empty,
|
wenzelm@60309
|
1258 |
calc = [(*("PLUS" , (\<^const_name>\<open>plus\<close>, eval_binop "#add_")),
|
wenzelm@60309
|
1259 |
("TIMES" , (\<^const_name>\<open>times\<close>, eval_binop "#mult_")),
|
wenzelm@60309
|
1260 |
("POWER", (\<^const_name>\<open>powr\<close>, eval_binop "#power_"))*)
|
neuper@42451
|
1261 |
], errpatts = [],
|
wenzelm@60297
|
1262 |
rules = [\<^rule_thm>\<open>real_plus_binom_times\<close>,
|
neuper@37950
|
1263 |
(*"(a + b)*(a + b) = a ^ 2 + 2 * a * b + b ^ 2*)
|
wenzelm@60297
|
1264 |
\<^rule_thm>\<open>real_plus_binom_times1\<close>,
|
walther@60260
|
1265 |
(*"(a + 1*b)*(a + -1*b) = a \<up> 2 + -1*b \<up> 2"*)
|
wenzelm@60297
|
1266 |
\<^rule_thm>\<open>real_plus_binom_times2\<close>,
|
walther@60260
|
1267 |
(*"(a + -1*b)*(a + 1*b) = a \<up> 2 + -1*b \<up> 2"*)
|
neuper@37950
|
1268 |
|
wenzelm@60297
|
1269 |
\<^rule_thm>\<open>mult_1_left\<close>,(*"1 * z = z"*)
|
neuper@37950
|
1270 |
|
wenzelm@60297
|
1271 |
\<^rule_thm>\<open>distrib_right\<close>,
|
neuper@37950
|
1272 |
(*"(z1.0 + z2.0) * w = z1.0 * w + z2.0 * w"*)
|
wenzelm@60297
|
1273 |
\<^rule_thm>\<open>distrib_left\<close>,
|
neuper@37950
|
1274 |
(*"w * (z1.0 + z2.0) = w * z1.0 + w * z2.0"*)
|
neuper@37950
|
1275 |
|
wenzelm@60297
|
1276 |
\<^rule_thm>\<open>mult.assoc\<close>,
|
neuper@37950
|
1277 |
(*"?z1.1 * ?z2.1 * ?z3. =1 ?z1.1 * (?z2.1 * ?z3.1)"*)
|
wneuper@59416
|
1278 |
Rule.Rls_ order_mult_rls_,
|
wneuper@59416
|
1279 |
(*Rule.Rls_ order_add_rls_,*)
|
neuper@37950
|
1280 |
|
wenzelm@60294
|
1281 |
\<^rule_eval>\<open>plus\<close> (eval_binop "#add_"),
|
wenzelm@60294
|
1282 |
\<^rule_eval>\<open>times\<close> (eval_binop "#mult_"),
|
wenzelm@60294
|
1283 |
\<^rule_eval>\<open>powr\<close> (eval_binop "#power_"),
|
neuper@37950
|
1284 |
|
wenzelm@60296
|
1285 |
\<^rule_thm_sym>\<open>realpow_twoI\<close>,
|
walther@60242
|
1286 |
(*"r1 * r1 = r1 \<up> 2"*)
|
wenzelm@60296
|
1287 |
\<^rule_thm_sym>\<open>real_mult_2\<close>,
|
neuper@37950
|
1288 |
(*"z1 + z1 = 2 * z1"*)
|
wenzelm@60297
|
1289 |
\<^rule_thm>\<open>real_mult_2_assoc\<close>,
|
neuper@37950
|
1290 |
(*"z1 + (z1 + k) = 2 * z1 + k"*)
|
neuper@37950
|
1291 |
|
wenzelm@60297
|
1292 |
\<^rule_thm>\<open>real_num_collect\<close>,
|
neuper@37950
|
1293 |
(*"[| l is_const; m is_const |]==>l * n + m * n = (l + m) * n"*)
|
wenzelm@60297
|
1294 |
\<^rule_thm>\<open>real_num_collect_assoc\<close>,
|
neuper@37950
|
1295 |
(*"[| l is_const; m is_const |] ==>
|
neuper@37950
|
1296 |
l * n + (m * n + k) = (l + m) * n + k"*)
|
wenzelm@60297
|
1297 |
\<^rule_thm>\<open>real_one_collect\<close>,
|
neuper@37950
|
1298 |
(*"m is_const ==> n + m * n = (1 + m) * n"*)
|
wenzelm@60297
|
1299 |
\<^rule_thm>\<open>real_one_collect_assoc\<close>,
|
neuper@37950
|
1300 |
(*"m is_const ==> k + (n + m * n) = k + (1 + m) * n"*)
|
neuper@37950
|
1301 |
|
wenzelm@60297
|
1302 |
\<^rule_thm>\<open>realpow_multI\<close>,
|
walther@60242
|
1303 |
(*"(r * s) \<up> n = r \<up> n * s \<up> n"*)
|
neuper@37950
|
1304 |
|
wenzelm@60294
|
1305 |
\<^rule_eval>\<open>plus\<close> (eval_binop "#add_"),
|
wenzelm@60294
|
1306 |
\<^rule_eval>\<open>times\<close> (eval_binop "#mult_"),
|
wenzelm@60294
|
1307 |
\<^rule_eval>\<open>powr\<close> (eval_binop "#power_"),
|
neuper@37950
|
1308 |
|
wenzelm@60297
|
1309 |
\<^rule_thm>\<open>mult_1_left\<close>,(*"1 * z = z"*)
|
wenzelm@60297
|
1310 |
\<^rule_thm>\<open>mult_zero_left\<close>,(*"0 * z = 0"*)
|
wenzelm@60297
|
1311 |
\<^rule_thm>\<open>add_0_left\<close>(*0 + z = z*)
|
neuper@37950
|
1312 |
|
wneuper@59416
|
1313 |
(*Rule.Rls_ order_add_rls_*)
|
neuper@37950
|
1314 |
],
|
neuper@37950
|
1315 |
|
walther@59878
|
1316 |
scr = Rule.Empty_Prog};
|
wneuper@59472
|
1317 |
\<close>
|
neuper@52125
|
1318 |
|
wneuper@59523
|
1319 |
subsection \<open>rule-sets with explicit program for intermediate steps\<close>
|
wneuper@59523
|
1320 |
partial_function (tailrec) expand_binoms_2 :: "real \<Rightarrow> real"
|
wneuper@59523
|
1321 |
where
|
walther@59635
|
1322 |
"expand_binoms_2 term = (
|
walther@59635
|
1323 |
Repeat (
|
walther@59637
|
1324 |
(Try (Repeat (Rewrite ''real_plus_binom_pow2''))) #>
|
walther@59637
|
1325 |
(Try (Repeat (Rewrite ''real_plus_binom_times''))) #>
|
walther@59637
|
1326 |
(Try (Repeat (Rewrite ''real_minus_binom_pow2''))) #>
|
walther@59637
|
1327 |
(Try (Repeat (Rewrite ''real_minus_binom_times''))) #>
|
walther@59637
|
1328 |
(Try (Repeat (Rewrite ''real_plus_minus_binom1''))) #>
|
walther@59637
|
1329 |
(Try (Repeat (Rewrite ''real_plus_minus_binom2''))) #>
|
walther@59635
|
1330 |
|
walther@59637
|
1331 |
(Try (Repeat (Rewrite ''mult_1_left''))) #>
|
walther@59637
|
1332 |
(Try (Repeat (Rewrite ''mult_zero_left''))) #>
|
walther@59637
|
1333 |
(Try (Repeat (Rewrite ''add_0_left''))) #>
|
walther@59635
|
1334 |
|
walther@59637
|
1335 |
(Try (Repeat (Calculate ''PLUS''))) #>
|
walther@59637
|
1336 |
(Try (Repeat (Calculate ''TIMES''))) #>
|
walther@59637
|
1337 |
(Try (Repeat (Calculate ''POWER''))) #>
|
walther@59635
|
1338 |
|
walther@59637
|
1339 |
(Try (Repeat (Rewrite ''sym_realpow_twoI''))) #>
|
walther@59637
|
1340 |
(Try (Repeat (Rewrite ''realpow_plus_1''))) #>
|
walther@59637
|
1341 |
(Try (Repeat (Rewrite ''sym_real_mult_2''))) #>
|
walther@59637
|
1342 |
(Try (Repeat (Rewrite ''real_mult_2_assoc''))) #>
|
walther@59635
|
1343 |
|
walther@59637
|
1344 |
(Try (Repeat (Rewrite ''real_num_collect''))) #>
|
walther@59637
|
1345 |
(Try (Repeat (Rewrite ''real_num_collect_assoc''))) #>
|
walther@59635
|
1346 |
|
walther@59637
|
1347 |
(Try (Repeat (Rewrite ''real_one_collect''))) #>
|
walther@59637
|
1348 |
(Try (Repeat (Rewrite ''real_one_collect_assoc''))) #>
|
walther@59635
|
1349 |
|
walther@59637
|
1350 |
(Try (Repeat (Calculate ''PLUS''))) #>
|
walther@59637
|
1351 |
(Try (Repeat (Calculate ''TIMES''))) #>
|
walther@59635
|
1352 |
(Try (Repeat (Calculate ''POWER''))))
|
walther@59635
|
1353 |
term)"
|
wneuper@59523
|
1354 |
ML \<open>
|
wneuper@59523
|
1355 |
val expand_binoms =
|
walther@59851
|
1356 |
Rule_Def.Repeat{id = "expand_binoms", preconds = [], rew_ord = ("termlessI",termlessI),
|
walther@59851
|
1357 |
erls = Atools_erls, srls = Rule_Set.Empty,
|
wenzelm@60309
|
1358 |
calc = [("PLUS" , (\<^const_name>\<open>plus\<close>, eval_binop "#add_")),
|
wenzelm@60309
|
1359 |
("TIMES" , (\<^const_name>\<open>times\<close>, eval_binop "#mult_")),
|
wenzelm@60309
|
1360 |
("POWER", (\<^const_name>\<open>powr\<close>, eval_binop "#power_"))
|
wneuper@59523
|
1361 |
], errpatts = [],
|
wenzelm@60298
|
1362 |
rules = [\<^rule_thm>\<open>real_plus_binom_pow2\<close>,
|
walther@60242
|
1363 |
(*"(a + b) \<up> 2 = a \<up> 2 + 2 * a * b + b \<up> 2"*)
|
wenzelm@60298
|
1364 |
\<^rule_thm>\<open>real_plus_binom_times\<close>,
|
wneuper@59523
|
1365 |
(*"(a + b)*(a + b) = ...*)
|
wenzelm@60298
|
1366 |
\<^rule_thm>\<open>real_minus_binom_pow2\<close>,
|
walther@60242
|
1367 |
(*"(a - b) \<up> 2 = a \<up> 2 - 2 * a * b + b \<up> 2"*)
|
wenzelm@60298
|
1368 |
\<^rule_thm>\<open>real_minus_binom_times\<close>,
|
wneuper@59523
|
1369 |
(*"(a - b)*(a - b) = ...*)
|
wenzelm@60298
|
1370 |
\<^rule_thm>\<open>real_plus_minus_binom1\<close>,
|
walther@60242
|
1371 |
(*"(a + b) * (a - b) = a \<up> 2 - b \<up> 2"*)
|
wenzelm@60298
|
1372 |
\<^rule_thm>\<open>real_plus_minus_binom2\<close>,
|
walther@60242
|
1373 |
(*"(a - b) * (a + b) = a \<up> 2 - b \<up> 2"*)
|
wneuper@59523
|
1374 |
(*RL 020915*)
|
wenzelm@60297
|
1375 |
\<^rule_thm>\<open>real_pp_binom_times\<close>,
|
wneuper@59523
|
1376 |
(*(a + b)*(c + d) = a*c + a*d + b*c + b*d*)
|
wenzelm@60297
|
1377 |
\<^rule_thm>\<open>real_pm_binom_times\<close>,
|
wneuper@59523
|
1378 |
(*(a + b)*(c - d) = a*c - a*d + b*c - b*d*)
|
wenzelm@60297
|
1379 |
\<^rule_thm>\<open>real_mp_binom_times\<close>,
|
wneuper@59523
|
1380 |
(*(a - b)*(c + d) = a*c + a*d - b*c - b*d*)
|
wenzelm@60297
|
1381 |
\<^rule_thm>\<open>real_mm_binom_times\<close>,
|
wneuper@59523
|
1382 |
(*(a - b)*(c - d) = a*c - a*d - b*c + b*d*)
|
wenzelm@60297
|
1383 |
\<^rule_thm>\<open>realpow_multI\<close>,
|
walther@60260
|
1384 |
(*(a*b) \<up> n = a \<up> n * b \<up> n*)
|
wenzelm@60297
|
1385 |
\<^rule_thm>\<open>real_plus_binom_pow3\<close>,
|
walther@60260
|
1386 |
(* (a + b) \<up> 3 = a \<up> 3 + 3*a \<up> 2*b + 3*a*b \<up> 2 + b \<up> 3 *)
|
wenzelm@60298
|
1387 |
\<^rule_thm>\<open>real_minus_binom_pow3\<close>,
|
walther@60260
|
1388 |
(* (a - b) \<up> 3 = a \<up> 3 - 3*a \<up> 2*b + 3*a*b \<up> 2 - b \<up> 3 *)
|
wneuper@59523
|
1389 |
|
wneuper@59523
|
1390 |
|
wenzelm@60297
|
1391 |
(*\<^rule_thm>\<open>distrib_right\<close>,
|
wneuper@59523
|
1392 |
(*"(z1.0 + z2.0) * w = z1.0 * w + z2.0 * w"*)
|
wenzelm@60297
|
1393 |
\<^rule_thm>\<open>distrib_left\<close>,
|
wneuper@59523
|
1394 |
(*"w * (z1.0 + z2.0) = w * z1.0 + w * z2.0"*)
|
wenzelm@60297
|
1395 |
\<^rule_thm>\<open>left_diff_distrib\<close>,
|
wneuper@59523
|
1396 |
(*"(z1.0 - z2.0) * w = z1.0 * w - z2.0 * w"*)
|
wenzelm@60297
|
1397 |
\<^rule_thm>\<open>right_diff_distrib\<close>,
|
wneuper@59523
|
1398 |
(*"w * (z1.0 - z2.0) = w * z1.0 - w * z2.0"*)
|
wneuper@59523
|
1399 |
*)
|
wenzelm@60297
|
1400 |
\<^rule_thm>\<open>mult_1_left\<close>,
|
wneuper@59523
|
1401 |
(*"1 * z = z"*)
|
wenzelm@60297
|
1402 |
\<^rule_thm>\<open>mult_zero_left\<close>,
|
wneuper@59523
|
1403 |
(*"0 * z = 0"*)
|
wenzelm@60297
|
1404 |
\<^rule_thm>\<open>add_0_left\<close>,(*"0 + z = z"*)
|
wneuper@59523
|
1405 |
|
wenzelm@60294
|
1406 |
\<^rule_eval>\<open>plus\<close> (eval_binop "#add_"),
|
wenzelm@60294
|
1407 |
\<^rule_eval>\<open>times\<close> (eval_binop "#mult_"),
|
wenzelm@60294
|
1408 |
\<^rule_eval>\<open>powr\<close> (eval_binop "#power_"),
|
wenzelm@60297
|
1409 |
(*\<^rule_thm>\<open>mult.commute\<close>,
|
wneuper@59523
|
1410 |
(*AC-rewriting*)
|
wenzelm@60298
|
1411 |
\<^rule_thm>\<open>real_mult_left_commute\<close>,
|
wenzelm@60297
|
1412 |
\<^rule_thm>\<open>mult.assoc\<close>,
|
wenzelm@60297
|
1413 |
\<^rule_thm>\<open>add.commute\<close>,
|
wenzelm@60297
|
1414 |
\<^rule_thm>\<open>add.left_commute\<close>,
|
wenzelm@60297
|
1415 |
\<^rule_thm>\<open>add.assoc\<close>,
|
wneuper@59523
|
1416 |
*)
|
wenzelm@60296
|
1417 |
\<^rule_thm_sym>\<open>realpow_twoI\<close>,
|
walther@60242
|
1418 |
(*"r1 * r1 = r1 \<up> 2"*)
|
wenzelm@60297
|
1419 |
\<^rule_thm>\<open>realpow_plus_1\<close>,
|
walther@60242
|
1420 |
(*"r * r \<up> n = r \<up> (n + 1)"*)
|
wenzelm@60296
|
1421 |
(*\<^rule_thm_sym>\<open>real_mult_2\<close>,
|
wneuper@59523
|
1422 |
(*"z1 + z1 = 2 * z1"*)*)
|
wenzelm@60297
|
1423 |
\<^rule_thm>\<open>real_mult_2_assoc\<close>,
|
wneuper@59523
|
1424 |
(*"z1 + (z1 + k) = 2 * z1 + k"*)
|
wneuper@59523
|
1425 |
|
wenzelm@60297
|
1426 |
\<^rule_thm>\<open>real_num_collect\<close>,
|
wneuper@59523
|
1427 |
(*"[| l is_const; m is_const |] ==>l * n + m * n = (l + m) * n"*)
|
wenzelm@60298
|
1428 |
\<^rule_thm>\<open>real_num_collect_assoc\<close>,
|
wneuper@59523
|
1429 |
(*"[| l is_const; m is_const |] ==>
|
wneuper@59523
|
1430 |
l * n + (m * n + k) = (l + m) * n + k"*)
|
wenzelm@60297
|
1431 |
\<^rule_thm>\<open>real_one_collect\<close>,
|
wneuper@59523
|
1432 |
(*"m is_const ==> n + m * n = (1 + m) * n"*)
|
wenzelm@60298
|
1433 |
\<^rule_thm>\<open>real_one_collect_assoc\<close>,
|
wneuper@59523
|
1434 |
(*"m is_const ==> k + (n + m * n) = k + (1 + m) * n"*)
|
wneuper@59523
|
1435 |
|
wenzelm@60294
|
1436 |
\<^rule_eval>\<open>plus\<close> (eval_binop "#add_"),
|
wenzelm@60294
|
1437 |
\<^rule_eval>\<open>times\<close> (eval_binop "#mult_"),
|
wenzelm@60294
|
1438 |
\<^rule_eval>\<open>powr\<close> (eval_binop "#power_")
|
wneuper@59523
|
1439 |
],
|
walther@59618
|
1440 |
scr = Rule.Prog (Program.prep_program @{thm expand_binoms_2.simps})
|
wneuper@59523
|
1441 |
};
|
wneuper@59523
|
1442 |
\<close>
|
wneuper@59523
|
1443 |
|
walther@59887
|
1444 |
subsection \<open>add to Know_Store\<close>
|
wneuper@59523
|
1445 |
subsubsection \<open>rule-sets\<close>
|
walther@59618
|
1446 |
ML \<open>val prep_rls' = Auto_Prog.prep_rls @{theory}\<close>
|
s1210629013@55444
|
1447 |
|
wenzelm@60289
|
1448 |
rule_set_knowledge
|
wenzelm@60286
|
1449 |
norm_Poly = \<open>prep_rls' norm_Poly\<close> and
|
wenzelm@60286
|
1450 |
Poly_erls = \<open>prep_rls' Poly_erls\<close> (*FIXXXME:del with rls.rls'*) and
|
wenzelm@60286
|
1451 |
expand = \<open>prep_rls' expand\<close> and
|
wenzelm@60286
|
1452 |
expand_poly = \<open>prep_rls' expand_poly\<close> and
|
wenzelm@60286
|
1453 |
simplify_power = \<open>prep_rls' simplify_power\<close> and
|
neuper@52125
|
1454 |
|
wenzelm@60286
|
1455 |
order_add_mult = \<open>prep_rls' order_add_mult\<close> and
|
wenzelm@60286
|
1456 |
collect_numerals = \<open>prep_rls' collect_numerals\<close> and
|
wenzelm@60286
|
1457 |
collect_numerals_= \<open>prep_rls' collect_numerals_\<close> and
|
wenzelm@60286
|
1458 |
reduce_012 = \<open>prep_rls' reduce_012\<close> and
|
wenzelm@60286
|
1459 |
discard_parentheses = \<open>prep_rls' discard_parentheses\<close> and
|
neuper@52125
|
1460 |
|
wenzelm@60286
|
1461 |
make_polynomial = \<open>prep_rls' make_polynomial\<close> and
|
wenzelm@60286
|
1462 |
expand_binoms = \<open>prep_rls' expand_binoms\<close> and
|
wenzelm@60286
|
1463 |
rev_rew_p = \<open>prep_rls' rev_rew_p\<close> and
|
wenzelm@60286
|
1464 |
discard_minus = \<open>prep_rls' discard_minus\<close> and
|
wenzelm@60286
|
1465 |
expand_poly_ = \<open>prep_rls' expand_poly_\<close> and
|
neuper@52125
|
1466 |
|
wenzelm@60286
|
1467 |
expand_poly_rat_ = \<open>prep_rls' expand_poly_rat_\<close> and
|
wenzelm@60286
|
1468 |
simplify_power_ = \<open>prep_rls' simplify_power_\<close> and
|
wenzelm@60286
|
1469 |
calc_add_mult_pow_ = \<open>prep_rls' calc_add_mult_pow_\<close> and
|
wenzelm@60286
|
1470 |
reduce_012_mult_ = \<open>prep_rls' reduce_012_mult_\<close> and
|
wenzelm@60286
|
1471 |
reduce_012_ = \<open>prep_rls' reduce_012_\<close> and
|
neuper@52125
|
1472 |
|
wenzelm@60286
|
1473 |
discard_parentheses1 = \<open>prep_rls' discard_parentheses1\<close> and
|
wenzelm@60286
|
1474 |
order_mult_rls_ = \<open>prep_rls' order_mult_rls_\<close> and
|
wenzelm@60286
|
1475 |
order_add_rls_ = \<open>prep_rls' order_add_rls_\<close> and
|
wenzelm@60286
|
1476 |
make_rat_poly_with_parentheses = \<open>prep_rls' make_rat_poly_with_parentheses\<close>
|
wneuper@59523
|
1477 |
|
wneuper@59526
|
1478 |
subsection \<open>problems\<close>
|
wenzelm@60306
|
1479 |
|
wenzelm@60306
|
1480 |
problem pbl_simp_poly : "polynomial/simplification" =
|
wenzelm@60306
|
1481 |
\<open>Rule_Set.append_rules "empty" Rule_Set.empty [(*for preds in where_*)
|
wenzelm@60306
|
1482 |
\<^rule_eval>\<open>is_polyexp\<close> (eval_is_polyexp "")]\<close>
|
wenzelm@60306
|
1483 |
Method: "simplification/for_polynomials"
|
wenzelm@60306
|
1484 |
CAS: "Simplify t_t"
|
wenzelm@60306
|
1485 |
Given: "Term t_t"
|
wenzelm@60306
|
1486 |
Where: "t_t is_polyexp"
|
wenzelm@60306
|
1487 |
Find: "normalform n_n"
|
wneuper@59429
|
1488 |
|
wneuper@59526
|
1489 |
subsection \<open>methods\<close>
|
wneuper@59545
|
1490 |
|
wneuper@59429
|
1491 |
partial_function (tailrec) simplify :: "real \<Rightarrow> real"
|
wneuper@59429
|
1492 |
where
|
walther@59635
|
1493 |
"simplify term = ((Rewrite_Set ''norm_Poly'') term)"
|
wenzelm@60303
|
1494 |
|
wenzelm@60303
|
1495 |
method met_simp_poly : "simplification/for_polynomials" =
|
wenzelm@60303
|
1496 |
\<open>{rew_ord'="tless_true", rls' = Rule_Set.empty, calc = [], srls = Rule_Set.empty,
|
wenzelm@60303
|
1497 |
prls = Rule_Set.append_rules "simplification_for_polynomials_prls" Rule_Set.empty
|
wenzelm@60303
|
1498 |
[(*for preds in where_*) \<^rule_eval>\<open>is_polyexp\<close> (eval_is_polyexp"")],
|
wenzelm@60303
|
1499 |
crls = Rule_Set.empty, errpats = [], nrls = norm_Poly}\<close>
|
wenzelm@60303
|
1500 |
Program: simplify.simps
|
wenzelm@60303
|
1501 |
Given: "Term t_t"
|
wenzelm@60303
|
1502 |
Where: "t_t is_polyexp"
|
wenzelm@60303
|
1503 |
Find: "normalform n_n"
|
wenzelm@60303
|
1504 |
|
wneuper@59472
|
1505 |
ML \<open>
|
wneuper@59472
|
1506 |
\<close> ML \<open>
|
wneuper@59472
|
1507 |
\<close>
|
neuper@37906
|
1508 |
end
|