--- a/src/HOL/ex/LSC_Examples.thy Fri Mar 11 15:21:13 2011 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,141 +0,0 @@
-(* Title: HOL/ex/LSC_Examples.thy
- Author: Lukas Bulwahn
- Copyright 2011 TU Muenchen
-*)
-
-header {* Examples for invoking lazysmallcheck (LSC) *}
-
-theory LSC_Examples
-imports "~~/src/HOL/Library/LSC"
-begin
-
-subsection {* Simple list examples *}
-
-lemma "rev xs = xs"
-quickcheck[tester = lazy_exhaustive, finite_types = false, default_type = nat, expect = counterexample]
-oops
-
-text {* Example fails due to some strange thing... *}
-(*
-lemma "rev xs = xs"
-quickcheck[tester = lazy_exhaustive, finite_types = true]
-oops
-*)
-
-subsection {* AVL Trees *}
-
-datatype 'a tree = ET | MKT 'a "'a tree" "'a tree" nat
-
-primrec set_of :: "'a tree \<Rightarrow> 'a set"
-where
-"set_of ET = {}" |
-"set_of (MKT n l r h) = insert n (set_of l \<union> set_of r)"
-
-primrec height :: "'a tree \<Rightarrow> nat"
-where
-"height ET = 0" |
-"height (MKT x l r h) = max (height l) (height r) + 1"
-
-primrec avl :: "'a tree \<Rightarrow> bool"
-where
-"avl ET = True" |
-"avl (MKT x l r h) =
- ((height l = height r \<or> height l = 1+height r \<or> height r = 1+height l) \<and>
- h = max (height l) (height r) + 1 \<and> avl l \<and> avl r)"
-
-primrec is_ord :: "('a::order) tree \<Rightarrow> bool"
-where
-"is_ord ET = True" |
-"is_ord (MKT n l r h) =
- ((\<forall>n' \<in> set_of l. n' < n) \<and> (\<forall>n' \<in> set_of r. n < n') \<and> is_ord l \<and> is_ord r)"
-
-primrec is_in :: "('a::order) \<Rightarrow> 'a tree \<Rightarrow> bool"
-where
- "is_in k ET = False" |
- "is_in k (MKT n l r h) = (if k = n then True else
- if k < n then (is_in k l)
- else (is_in k r))"
-
-primrec ht :: "'a tree \<Rightarrow> nat"
-where
-"ht ET = 0" |
-"ht (MKT x l r h) = h"
-
-definition
- mkt :: "'a \<Rightarrow> 'a tree \<Rightarrow> 'a tree \<Rightarrow> 'a tree" where
-"mkt x l r = MKT x l r (max (ht l) (ht r) + 1)"
-
-(* replaced MKT lrn lrl lrr by MKT lrr lrl *)
-fun l_bal where
-"l_bal(n, MKT ln ll lr h, r) =
- (if ht ll < ht lr
- then case lr of ET \<Rightarrow> ET (* impossible *)
- | MKT lrn lrr lrl lrh \<Rightarrow>
- mkt lrn (mkt ln ll lrl) (mkt n lrr r)
- else mkt ln ll (mkt n lr r))"
-
-fun r_bal where
-"r_bal(n, l, MKT rn rl rr h) =
- (if ht rl > ht rr
- then case rl of ET \<Rightarrow> ET (* impossible *)
- | MKT rln rll rlr h \<Rightarrow> mkt rln (mkt n l rll) (mkt rn rlr rr)
- else mkt rn (mkt n l rl) rr)"
-
-primrec insrt :: "'a::order \<Rightarrow> 'a tree \<Rightarrow> 'a tree"
-where
-"insrt x ET = MKT x ET ET 1" |
-"insrt x (MKT n l r h) =
- (if x=n
- then MKT n l r h
- else if x<n
- then let l' = insrt x l; hl' = ht l'; hr = ht r
- in if hl' = 2+hr then l_bal(n,l',r)
- else MKT n l' r (1 + max hl' hr)
- else let r' = insrt x r; hl = ht l; hr' = ht r'
- in if hr' = 2+hl then r_bal(n,l,r')
- else MKT n l r' (1 + max hl hr'))"
-
-
-subsubsection {* Necessary setup for code generation *}
-
-primrec set_of'
-where
- "set_of' ET = []"
-| "set_of' (MKT n l r h) = n # (set_of' l @ set_of' r)"
-
-lemma set_of':
- "set (set_of' t) = set_of t"
-by (induct t) auto
-
-lemma is_ord_mkt:
- "is_ord (MKT n l r h) = ((ALL n': set (set_of' l). n' < n) & (ALL n': set (set_of' r). n < n') & is_ord l & is_ord r)"
-by (simp add: set_of')
-
-declare is_ord.simps(1)[code] is_ord_mkt[code]
-
-subsection {* Necessary instantiation for quickcheck generator *}
-
-instantiation tree :: (serial) serial
-begin
-
-function series_tree
-where
- "series_tree d = sum (cons ET) (apply (apply (apply (apply (cons MKT) series) series_tree) series_tree) series) d"
-by pat_completeness auto
-
-termination proof (relation "measure nat_of")
-qed (auto simp add: of_int_inverse nat_of_def)
-
-instance ..
-
-end
-
-subsubsection {* Invalid Lemma due to typo in lbal *}
-
-lemma is_ord_l_bal:
- "\<lbrakk> is_ord(MKT (x :: nat) l r h); height l = height r + 2 \<rbrakk> \<Longrightarrow> is_ord(l_bal(x,l,r))"
-quickcheck[tester = lazy_exhaustive, finite_types = false, default_type = nat, size = 1, timeout = 100, expect = counterexample]
-oops
-
-
-end