author | wenzelm |
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permissions | -rw-r--r-- |
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(* Title: HOL/ex/SML_Quickcheck_Examples.thy |
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Author: Stefan Berghofer, Lukas Bulwahn |
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Copyright 2011 TU Muenchen |
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*) |
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theory SML_Quickcheck_Examples |
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imports "~~/src/HOL/Library/SML_Quickcheck" |
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begin |
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text {* |
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This is a regression test for the 'quickcheck' counterexample generator based on the |
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SML code generator. |
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The counterexample generator has been superseded by counterexample generators based on |
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the generic code generator. |
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*} |
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declare [[quickcheck_finite_types = false]] |
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declare [[quickcheck_timeout = 600.0]] |
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subsection {* Lists *} |
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theorem "map g (map f xs) = map (g o f) xs" |
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quickcheck[SML, expect = no_counterexample] |
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oops |
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theorem "map g (map f xs) = map (f o g) xs" |
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quickcheck[SML, expect = counterexample] |
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oops |
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theorem "rev (xs @ ys) = rev ys @ rev xs" |
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quickcheck[SML, expect = no_counterexample] |
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oops |
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theorem "rev (xs @ ys) = rev xs @ rev ys" |
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quickcheck[SML, expect = counterexample] |
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oops |
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theorem "rev (rev xs) = xs" |
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quickcheck[SML, expect = no_counterexample] |
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oops |
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theorem "rev xs = xs" |
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quickcheck[tester = SML, expect = counterexample] |
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oops |
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text {* An example involving functions inside other data structures *} |
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primrec app :: "('a \<Rightarrow> 'a) list \<Rightarrow> 'a \<Rightarrow> 'a" where |
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"app [] x = x" |
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| "app (f # fs) x = app fs (f x)" |
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lemma "app (fs @ gs) x = app gs (app fs x)" |
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quickcheck[SML, expect = no_counterexample] |
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by (induct fs arbitrary: x) simp_all |
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lemma "app (fs @ gs) x = app fs (app gs x)" |
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quickcheck[SML, expect = counterexample] |
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oops |
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primrec occurs :: "'a \<Rightarrow> 'a list \<Rightarrow> nat" where |
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"occurs a [] = 0" |
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| "occurs a (x#xs) = (if (x=a) then Suc(occurs a xs) else occurs a xs)" |
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primrec del1 :: "'a \<Rightarrow> 'a list \<Rightarrow> 'a list" where |
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"del1 a [] = []" |
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| "del1 a (x#xs) = (if (x=a) then xs else (x#del1 a xs))" |
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text {* A lemma, you'd think to be true from our experience with delAll *} |
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lemma "Suc (occurs a (del1 a xs)) = occurs a xs" |
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-- {* Wrong. Precondition needed.*} |
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quickcheck[SML, expect = counterexample] |
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oops |
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lemma "xs ~= [] \<longrightarrow> Suc (occurs a (del1 a xs)) = occurs a xs" |
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quickcheck[SML, expect = counterexample] |
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-- {* Also wrong.*} |
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oops |
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lemma "0 < occurs a xs \<longrightarrow> Suc (occurs a (del1 a xs)) = occurs a xs" |
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quickcheck[SML, expect = no_counterexample] |
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by (induct xs) auto |
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primrec replace :: "'a \<Rightarrow> 'a \<Rightarrow> 'a list \<Rightarrow> 'a list" where |
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"replace a b [] = []" |
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| "replace a b (x#xs) = (if (x=a) then (b#(replace a b xs)) |
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else (x#(replace a b xs)))" |
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lemma "occurs a xs = occurs b (replace a b xs)" |
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quickcheck[SML, expect = counterexample] |
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-- {* Wrong. Precondition needed.*} |
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oops |
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lemma "occurs b xs = 0 \<or> a=b \<longrightarrow> occurs a xs = occurs b (replace a b xs)" |
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quickcheck[SML, expect = no_counterexample] |
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by (induct xs) simp_all |
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subsection {* Trees *} |
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datatype 'a tree = Twig | Leaf 'a | Branch "'a tree" "'a tree" |
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primrec leaves :: "'a tree \<Rightarrow> 'a list" where |
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"leaves Twig = []" |
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| "leaves (Leaf a) = [a]" |
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| "leaves (Branch l r) = (leaves l) @ (leaves r)" |
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primrec plant :: "'a list \<Rightarrow> 'a tree" where |
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"plant [] = Twig " |
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| "plant (x#xs) = Branch (Leaf x) (plant xs)" |
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primrec mirror :: "'a tree \<Rightarrow> 'a tree" where |
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"mirror (Twig) = Twig " |
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| "mirror (Leaf a) = Leaf a " |
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| "mirror (Branch l r) = Branch (mirror r) (mirror l)" |
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theorem "plant (rev (leaves xt)) = mirror xt" |
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quickcheck[SML, expect = counterexample] |
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--{* Wrong! *} |
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121 |
oops |
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122 |
|
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123 |
theorem "plant((leaves xt) @ (leaves yt)) = Branch xt yt" |
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124 |
quickcheck[SML, expect = counterexample] |
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125 |
--{* Wrong! *} |
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126 |
oops |
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127 |
|
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128 |
datatype 'a ntree = Tip "'a" | Node "'a" "'a ntree" "'a ntree" |
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129 |
|
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130 |
primrec inOrder :: "'a ntree \<Rightarrow> 'a list" where |
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131 |
"inOrder (Tip a)= [a]" |
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132 |
| "inOrder (Node f x y) = (inOrder x)@[f]@(inOrder y)" |
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133 |
|
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134 |
primrec root :: "'a ntree \<Rightarrow> 'a" where |
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135 |
"root (Tip a) = a" |
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136 |
| "root (Node f x y) = f" |
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137 |
|
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138 |
theorem "hd (inOrder xt) = root xt" |
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139 |
quickcheck[SML, expect = counterexample] |
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140 |
--{* Wrong! *} |
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141 |
oops |
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142 |
|
43686
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tuning options to avoid spurious isabelle test failures
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143 |
end |