Ziele Untersuchung
mit Columbo Integrität von
Datenbanken Interaktion und
Portierbarkeit Ergonomie der
Schnittstellen

Angebot Produkte Projekt Beratung

Mittel Analytik Modellierung Sprachen Algebra Logik Hardware Denken Kreativität

Zusammenhänge Gesellschaft Wirtschaft Branche Firma


products/Sources/formale Sprachen/Isabelle/HOL/Nitpick_Examples/ (Beweissystem Isabelle Version 2025-1^©) Datei vom 16.11.2025 mit Größe 5 kB

Quelle Special_Nits.thy Sprache: Isabelle

(*  Title:      HOL/Nitpick_Examples/Special_Nits.thy
    Author:     Jasmin Blanchette, TU Muenchen
    Copyright   2009-2011

Examples featuring Nitpick's "specialize" optimization.
*)

section \<open>Examples Featuring Nitpick's \textit{specialize} Optimization\<close>

theory Special_Nits
imports Main
begin

nitpick_params [verbose, card = 4, sat_solver = MiniSat, max_threads = 1,
                timeout = 240]

fun f1 :: "nat \ nat \ nat \ nat \ nat \ nat" where
"f1 a b c d e = a + b + c + d + e"

lemma "f1 0 0 0 0 0 = f1 0 0 0 0 (1 - 1)"
nitpick [expect = none]
nitpick [dont_specialize, expect = none]
sorry

lemma "f1 u v w x y = f1 y x w v u"
nitpick [expect = none]
nitpick [dont_specialize, expect = none]
sorry

fun f2 :: "nat \ nat \ nat \ nat \ nat \ nat" where
"f2 a b c d (Suc e) = a + b + c + d + e"

lemma "f2 0 0 0 0 0 = f2 (1 - 1) 0 0 0 0"
nitpick [expect = none]
nitpick [dont_specialize, expect = none]
sorry

lemma "f2 0 (v - v) 0 (x - x) 0 = f2 (u - u) 0 (w - w) 0 (y - y)"
nitpick [expect = none]
nitpick [dont_specialize, expect = none]
sorry

lemma "f2 1 0 0 0 0 = f2 0 1 0 0 0"
nitpick [expect = genuine]
nitpick [dont_specialize, expect = genuine]
oops

lemma "f2 0 0 0 0 0 = f2 0 0 0 0 0"
nitpick [expect = none]
nitpick [dont_specialize, expect = none]
sorry

fun f3 :: "nat \ nat \ nat \ nat \ nat \ nat" where
"f3 (Suc a) b 0 d (Suc e) = a + b + d + e" |
"f3 0 b 0 d 0 = b + d"

lemma "f3 a b c d e = f3 e d c b a"
nitpick [expect = genuine]
nitpick [dont_specialize, expect = genuine]
oops

lemma "f3 a b c d a = f3 a d c d a"
nitpick [expect = genuine]
nitpick [dont_specialize, expect = genuine]
oops

lemma "\c < 1; a \ e; e \ a\ \ f3 a b c d a = f3 e d c b e"
nitpick [expect = none]
nitpick [dont_specialize, expect = none]
sorry

lemma "(\u. a = u \ f3 a a a a a = f3 u u u u u)
       \<and> (\<forall>u. b = u \<longrightarrow> f3 b b u b b = f3 u u b u u)"
nitpick [expect = none]
nitpick [dont_specialize, expect = none]
sorry

function f4 :: "nat \ nat \ nat" where
"f4 x x = 1" |
"f4 y z = (if y = z then 1 else 0)"
by auto
termination by lexicographic_order

lemma "f4 a b = f4 b a"
nitpick [expect = none]
nitpick [dont_specialize, expect = none]
sorry

lemma "f4 a (Suc a) = f4 a a"
nitpick [expect = genuine]
nitpick [dont_specialize, expect = genuine]
oops

fun f5 :: "(nat \ nat) \ nat \ nat" where
"f5 f (Suc a) = f a"

lemma "\one \ {1}. \two \ {2}.
       f5 (\<lambda>a. if a = one then 1 else if a = two then 2 else a) (Suc x) = x"
nitpick [expect = none]
nitpick [dont_specialize, expect = none]
sorry

lemma "\two \ {2}. \one \ {1}.
       f5 (\<lambda>a. if a = one then 1 else if a = two then 2 else a) (Suc x) = x"
nitpick [expect = none]
nitpick [dont_specialize, expect = none]
sorry

lemma "\one \ {1}. \two \ {2}.
       f5 (\<lambda>a. if a = one then 2 else if a = two then 1 else a) (Suc x) = x"
nitpick [expect = genuine]
oops

lemma "\two \ {2}. \one \ {1}.
       f5 (\<lambda>a. if a = one then 2 else if a = two then 1 else a) (Suc x) = x"
nitpick [expect = genuine]
oops

lemma "\a. g a = a
       \<Longrightarrow> \<exists>one \<in> {1}. \<exists>two \<in> {2}. f5 g x =
                      f5 (\<lambda>a. if a = one then 1 else if a = two then 2 else a) x"
nitpick [expect = none]
nitpick [dont_specialize, expect = none]
sorry

lemma "\a. g a = a
       \<Longrightarrow> \<exists>one \<in> {2}. \<exists>two \<in> {1}. f5 g x =
                      f5 (\<lambda>a. if a = one then 1 else if a = two then 2 else a) x"
nitpick [expect = potential]
nitpick [dont_specialize, expect = potential]
sorry

lemma "\a. g a = a
       \<Longrightarrow> \<exists>b\<^sub>1 b\<^sub>2 b\<^sub>3 b\<^sub>4 b\<^sub>5 b\<^sub>6 b\<^sub>7 b\<^sub>8 b\<^sub>9 b\<^sub>10 (b\<^sub>11::nat).
           b\<^sub>1 < b\<^sub>11 \<and> f5 g x = f5 (\<lambda>a. if b\<^sub>1 < b\<^sub>11 then a else h b\<^sub>2) x"
nitpick [expect = potential]
nitpick [dont_specialize, expect = none]
nitpick [dont_box, expect = none]
nitpick [dont_box, dont_specialize, expect = none]
sorry

lemma "\a. g a = a
       \<Longrightarrow> \<exists>b\<^sub>1 b\<^sub>2 b\<^sub>3 b\<^sub>4 b\<^sub>5 b\<^sub>6 b\<^sub>7 b\<^sub>8 b\<^sub>9 b\<^sub>10 (b\<^sub>11::nat).
           b\<^sub>1 < b\<^sub>11
           \<and> f5 g x = f5 (\<lambda>a. if b\<^sub>1 < b\<^sub>11 then
                                a
                              else
                                h b\<^sub>2 + h b\<^sub>3 + h b\<^sub>4 + h b\<^sub>5 + h b\<^sub>6 + h b\<^sub>7 + h b\<^sub>8
                                + h b\<^sub>9 + h b\<^sub>10) x"
nitpick [card nat = 2, card 'a = 1, expect = none]
nitpick [card nat = 2, card 'a = 1, dont_box, expect = none]
nitpick [card nat = 2, card 'a = 1, dont_specialize, expect = none]
nitpick [card nat = 2, card 'a = 1, dont_box, dont_specialize, expect = none]
sorry

lemma "\a. g a = a
       \<Longrightarrow> \<exists>b\<^sub>1 b\<^sub>2 b\<^sub>3 b\<^sub>4 b\<^sub>5 b\<^sub>6 b\<^sub>7 b\<^sub>8 b\<^sub>9 b\<^sub>10 (b\<^sub>11::nat).
           b\<^sub>1 < b\<^sub>11
           \<and> f5 g x = f5 (\<lambda>a. if b\<^sub>1 \<ge> b\<^sub>11 then
                                a
                              else
                                h b\<^sub>2 + h b\<^sub>3 + h b\<^sub>4 + h b\<^sub>5 + h b\<^sub>6 + h b\<^sub>7 + h b\<^sub>8
                                + h b\<^sub>9 + h b\<^sub>10) x"
nitpick [card nat = 2, card 'a = 1, expect = potential]
nitpick [card nat = 2, card 'a = 1, dont_box, expect = potential]
nitpick [card nat = 2, card 'a = 1, dont_specialize, expect = potential]
nitpick [card nat = 2, card 'a = 1, dont_box, dont_specialize,
         expect = potential]
oops

end

quality99%

¤ Dauer der Verarbeitung: 0.11 Sekunden (vorverarbeitet) ¤

Wurzel

Suchen

Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.