author | bulwahn |
Mon, 23 Aug 2010 16:47:55 +0200 | |
changeset 38664 | 7215ae18f44b |
parent 36511 | db2953f5887a |
child 39195 | 5ab54bf226ac |
permissions | -rw-r--r-- |
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1 |
theory Predicate_Compile_Examples |
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imports Predicate_Compile_Alternative_Defs |
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begin |
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subsection {* Basic predicates *} |
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inductive False' :: "bool" |
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code_pred (expected_modes: bool) False' . |
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code_pred [dseq] False' . |
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code_pred [random_dseq] False' . |
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values [expected "{}" pred] "{x. False'}" |
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values [expected "{}" dseq 1] "{x. False'}" |
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values [expected "{}" random_dseq 1, 1, 1] "{x. False'}" |
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value "False'" |
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inductive True' :: "bool" |
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where |
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"True ==> True'" |
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code_pred True' . |
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code_pred [dseq] True' . |
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code_pred [random_dseq] True' . |
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thm True'.equation |
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thm True'.dseq_equation |
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thm True'.random_dseq_equation |
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values [expected "{()}" ]"{x. True'}" |
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values [expected "{}" dseq 0] "{x. True'}" |
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values [expected "{()}" dseq 1] "{x. True'}" |
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values [expected "{()}" dseq 2] "{x. True'}" |
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values [expected "{}" random_dseq 1, 1, 0] "{x. True'}" |
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values [expected "{}" random_dseq 1, 1, 1] "{x. True'}" |
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values [expected "{()}" random_dseq 1, 1, 2] "{x. True'}" |
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values [expected "{()}" random_dseq 1, 1, 3] "{x. True'}" |
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inductive EmptySet :: "'a \<Rightarrow> bool" |
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code_pred (expected_modes: o => bool, i => bool) EmptySet . |
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definition EmptySet' :: "'a \<Rightarrow> bool" |
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where "EmptySet' = {}" |
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code_pred (expected_modes: o => bool, i => bool) [inductify] EmptySet' . |
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inductive EmptyRel :: "'a \<Rightarrow> 'b \<Rightarrow> bool" |
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code_pred (expected_modes: o => o => bool, i => o => bool, o => i => bool, i => i => bool) EmptyRel . |
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inductive EmptyClosure :: "('a \<Rightarrow> 'a \<Rightarrow> bool) \<Rightarrow> 'a \<Rightarrow> 'a \<Rightarrow> bool" |
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for r :: "'a \<Rightarrow> 'a \<Rightarrow> bool" |
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code_pred |
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(expected_modes: (o => o => bool) => o => o => bool, (o => o => bool) => i => o => bool, |
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(o => o => bool) => o => i => bool, (o => o => bool) => i => i => bool, |
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(i => o => bool) => o => o => bool, (i => o => bool) => i => o => bool, |
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(i => o => bool) => o => i => bool, (i => o => bool) => i => i => bool, |
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(o => i => bool) => o => o => bool, (o => i => bool) => i => o => bool, |
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(o => i => bool) => o => i => bool, (o => i => bool) => i => i => bool, |
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(i => i => bool) => o => o => bool, (i => i => bool) => i => o => bool, |
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(i => i => bool) => o => i => bool, (i => i => bool) => i => i => bool) |
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EmptyClosure . |
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thm EmptyClosure.equation |
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(* TODO: inductive package is broken! |
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inductive False'' :: "bool" |
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where |
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"False \<Longrightarrow> False''" |
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code_pred (expected_modes: []) False'' . |
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inductive EmptySet'' :: "'a \<Rightarrow> bool" |
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where |
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"False \<Longrightarrow> EmptySet'' x" |
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code_pred (expected_modes: [1]) EmptySet'' . |
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code_pred (expected_modes: [], [1]) [inductify] EmptySet'' . |
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*) |
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consts a' :: 'a |
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inductive Fact :: "'a \<Rightarrow> 'a \<Rightarrow> bool" |
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where |
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"Fact a' a'" |
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code_pred (expected_modes: o => o => bool, i => o => bool, o => i => bool, i => i => bool) Fact . |
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inductive zerozero :: "nat * nat => bool" |
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where |
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"zerozero (0, 0)" |
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code_pred (expected_modes: i => bool, i * o => bool, o * i => bool, o => bool) zerozero . |
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code_pred [dseq] zerozero . |
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code_pred [random_dseq] zerozero . |
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thm zerozero.equation |
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thm zerozero.dseq_equation |
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thm zerozero.random_dseq_equation |
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text {* We expect the user to expand the tuples in the values command. |
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The following values command is not supported. *} |
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105 |
(*values "{x. zerozero x}" *) |
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text {* Instead, the user must type *} |
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values "{(x, y). zerozero (x, y)}" |
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108 |
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values [expected "{}" dseq 0] "{(x, y). zerozero (x, y)}" |
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values [expected "{(0::nat, 0::nat)}" dseq 1] "{(x, y). zerozero (x, y)}" |
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values [expected "{(0::nat, 0::nat)}" dseq 2] "{(x, y). zerozero (x, y)}" |
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values [expected "{}" random_dseq 1, 1, 2] "{(x, y). zerozero (x, y)}" |
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parents:
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changeset
|
113 |
values [expected "{(0::nat, 0:: nat)}" random_dseq 1, 1, 3] "{(x, y). zerozero (x, y)}" |
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parents:
diff
changeset
|
114 |
|
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parents:
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|
115 |
inductive nested_tuples :: "((int * int) * int * int) => bool" |
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|
116 |
where |
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|
117 |
"nested_tuples ((0, 1), 2, 3)" |
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|
118 |
|
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119 |
code_pred nested_tuples . |
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|
120 |
|
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|
121 |
inductive JamesBond :: "nat => int => code_numeral => bool" |
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122 |
where |
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123 |
"JamesBond 0 0 7" |
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124 |
|
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125 |
code_pred JamesBond . |
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|
126 |
|
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changeset
|
127 |
values [expected "{(0::nat, 0::int , 7::code_numeral)}"] "{(a, b, c). JamesBond a b c}" |
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parents:
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|
128 |
values [expected "{(0::nat, 7::code_numeral, 0:: int)}"] "{(a, c, b). JamesBond a b c}" |
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|
129 |
values [expected "{(0::int, 0::nat, 7::code_numeral)}"] "{(b, a, c). JamesBond a b c}" |
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parents:
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changeset
|
130 |
values [expected "{(0::int, 7::code_numeral, 0::nat)}"] "{(b, c, a). JamesBond a b c}" |
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parents:
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131 |
values [expected "{(7::code_numeral, 0::nat, 0::int)}"] "{(c, a, b). JamesBond a b c}" |
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parents:
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changeset
|
132 |
values [expected "{(7::code_numeral, 0::int, 0::nat)}"] "{(c, b, a). JamesBond a b c}" |
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parents:
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changeset
|
133 |
|
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parents:
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changeset
|
134 |
values [expected "{(7::code_numeral, 0::int)}"] "{(a, b). JamesBond 0 b a}" |
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parents:
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changeset
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135 |
values [expected "{(7::code_numeral, 0::nat)}"] "{(c, a). JamesBond a 0 c}" |
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parents:
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changeset
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136 |
values [expected "{(0::nat, 7::code_numeral)}"] "{(a, c). JamesBond a 0 c}" |
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parents:
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changeset
|
137 |
|
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parents:
diff
changeset
|
138 |
|
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|
139 |
subsection {* Alternative Rules *} |
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140 |
|
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|
141 |
datatype char = C | D | E | F | G | H |
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|
142 |
|
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|
143 |
inductive is_C_or_D |
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144 |
where |
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145 |
"(x = C) \<or> (x = D) ==> is_C_or_D x" |
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parents:
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changeset
|
146 |
|
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parents:
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|
147 |
code_pred (expected_modes: i => bool) is_C_or_D . |
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148 |
thm is_C_or_D.equation |
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changeset
|
149 |
|
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150 |
inductive is_D_or_E |
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|
151 |
where |
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parents:
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|
152 |
"(x = D) \<or> (x = E) ==> is_D_or_E x" |
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parents:
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changeset
|
153 |
|
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parents:
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changeset
|
154 |
lemma [code_pred_intro]: |
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155 |
"is_D_or_E D" |
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156 |
by (auto intro: is_D_or_E.intros) |
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parents:
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changeset
|
157 |
|
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parents:
diff
changeset
|
158 |
lemma [code_pred_intro]: |
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parents:
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|
159 |
"is_D_or_E E" |
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parents:
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changeset
|
160 |
by (auto intro: is_D_or_E.intros) |
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parents:
diff
changeset
|
161 |
|
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parents:
diff
changeset
|
162 |
code_pred (expected_modes: o => bool, i => bool) is_D_or_E |
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parents:
diff
changeset
|
163 |
proof - |
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parents:
diff
changeset
|
164 |
case is_D_or_E |
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parents:
diff
changeset
|
165 |
from this(1) show thesis |
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parents:
diff
changeset
|
166 |
proof |
791ce568d40a
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bulwahn
parents:
diff
changeset
|
167 |
fix xa |
791ce568d40a
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parents:
diff
changeset
|
168 |
assume x: "x = xa" |
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parents:
diff
changeset
|
169 |
assume "xa = D \<or> xa = E" |
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parents:
diff
changeset
|
170 |
from this show thesis |
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parents:
diff
changeset
|
171 |
proof |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
172 |
assume "xa = D" from this x is_D_or_E(2) show thesis by simp |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
173 |
next |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
174 |
assume "xa = E" from this x is_D_or_E(3) show thesis by simp |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
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parents:
diff
changeset
|
175 |
qed |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
176 |
qed |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
177 |
qed |
791ce568d40a
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bulwahn
parents:
diff
changeset
|
178 |
|
791ce568d40a
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parents:
diff
changeset
|
179 |
thm is_D_or_E.equation |
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bulwahn
parents:
diff
changeset
|
180 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
181 |
inductive is_F_or_G |
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parents:
diff
changeset
|
182 |
where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
183 |
"x = F \<or> x = G ==> is_F_or_G x" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
184 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
185 |
lemma [code_pred_intro]: |
791ce568d40a
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parents:
diff
changeset
|
186 |
"is_F_or_G F" |
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parents:
diff
changeset
|
187 |
by (auto intro: is_F_or_G.intros) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
188 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
189 |
lemma [code_pred_intro]: |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
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parents:
diff
changeset
|
190 |
"is_F_or_G G" |
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parents:
diff
changeset
|
191 |
by (auto intro: is_F_or_G.intros) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
192 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
193 |
inductive is_FGH |
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parents:
diff
changeset
|
194 |
where |
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bulwahn
parents:
diff
changeset
|
195 |
"is_F_or_G x ==> is_FGH x" |
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parents:
diff
changeset
|
196 |
| "is_FGH H" |
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parents:
diff
changeset
|
197 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
198 |
text {* Compilation of is_FGH requires elimination rule for is_F_or_G *} |
791ce568d40a
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parents:
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changeset
|
199 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
200 |
code_pred (expected_modes: o => bool, i => bool) is_FGH |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
201 |
proof - |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
202 |
case is_F_or_G |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
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parents:
diff
changeset
|
203 |
from this(1) show thesis |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
204 |
proof |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
205 |
fix xa |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
206 |
assume x: "x = xa" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
207 |
assume "xa = F \<or> xa = G" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
208 |
from this show thesis |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
209 |
proof |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
210 |
assume "xa = F" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
211 |
from this x is_F_or_G(2) show thesis by simp |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
212 |
next |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
213 |
assume "xa = G" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
214 |
from this x is_F_or_G(3) show thesis by simp |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
215 |
qed |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
216 |
qed |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
217 |
qed |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
218 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
219 |
subsection {* Preprocessor Inlining *} |
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changeset
|
220 |
|
791ce568d40a
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parents:
diff
changeset
|
221 |
definition "equals == (op =)" |
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parents:
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changeset
|
222 |
|
791ce568d40a
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parents:
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changeset
|
223 |
inductive zerozero' :: "nat * nat => bool" where |
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parents:
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changeset
|
224 |
"equals (x, y) (0, 0) ==> zerozero' (x, y)" |
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parents:
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changeset
|
225 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
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226 |
code_pred (expected_modes: i => bool) zerozero' . |
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lemma zerozero'_eq: "zerozero' x == zerozero x" |
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proof - |
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have "zerozero' = zerozero" |
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apply (auto simp add: mem_def) |
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apply (cases rule: zerozero'.cases) |
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apply (auto simp add: equals_def intro: zerozero.intros) |
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apply (cases rule: zerozero.cases) |
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apply (auto simp add: equals_def intro: zerozero'.intros) |
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done |
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from this show "zerozero' x == zerozero x" by auto |
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qed |
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|
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declare zerozero'_eq [code_pred_inline] |
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|
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definition "zerozero'' x == zerozero' x" |
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|
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text {* if preprocessing fails, zerozero'' will not have all modes. *} |
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|
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code_pred (expected_modes: i * i => bool, i * o => bool, o * i => bool, o => bool) [inductify] zerozero'' . |
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|
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subsection {* Sets and Numerals *} |
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|
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definition |
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"one_or_two = {Suc 0, (Suc (Suc 0))}" |
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|
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code_pred [inductify] one_or_two . |
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|
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code_pred [dseq] one_or_two . |
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code_pred [random_dseq] one_or_two . |
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thm one_or_two.dseq_equation |
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values [expected "{Suc 0::nat, 2::nat}"] "{x. one_or_two x}" |
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values [random_dseq 0,0,10] 3 "{x. one_or_two x}" |
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|
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inductive one_or_two' :: "nat => bool" |
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where |
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"one_or_two' 1" |
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| "one_or_two' 2" |
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|
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code_pred one_or_two' . |
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thm one_or_two'.equation |
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|
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values "{x. one_or_two' x}" |
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|
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definition one_or_two'': |
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"one_or_two'' == {1, (2::nat)}" |
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|
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code_pred [inductify] one_or_two'' . |
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thm one_or_two''.equation |
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|
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values "{x. one_or_two'' x}" |
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|
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279 |
subsection {* even predicate *} |
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|
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inductive even :: "nat \<Rightarrow> bool" and odd :: "nat \<Rightarrow> bool" where |
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"even 0" |
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| "even n \<Longrightarrow> odd (Suc n)" |
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| "odd n \<Longrightarrow> even (Suc n)" |
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|
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code_pred (expected_modes: i => bool, o => bool) even . |
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code_pred [dseq] even . |
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code_pred [random_dseq] even . |
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|
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thm odd.equation |
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thm even.equation |
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thm odd.dseq_equation |
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thm even.dseq_equation |
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thm odd.random_dseq_equation |
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thm even.random_dseq_equation |
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296 |
|
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297 |
values "{x. even 2}" |
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values "{x. odd 2}" |
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values 10 "{n. even n}" |
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values 10 "{n. odd n}" |
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values [expected "{}" dseq 2] "{x. even 6}" |
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values [expected "{}" dseq 6] "{x. even 6}" |
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values [expected "{()}" dseq 7] "{x. even 6}" |
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values [dseq 2] "{x. odd 7}" |
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values [dseq 6] "{x. odd 7}" |
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values [dseq 7] "{x. odd 7}" |
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values [expected "{()}" dseq 8] "{x. odd 7}" |
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308 |
|
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309 |
values [expected "{}" dseq 0] 8 "{x. even x}" |
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310 |
values [expected "{0::nat}" dseq 1] 8 "{x. even x}" |
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values [expected "{0::nat, 2}" dseq 3] 8 "{x. even x}" |
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values [expected "{0::nat, 2}" dseq 4] 8 "{x. even x}" |
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313 |
values [expected "{0::nat, 2, 4}" dseq 6] 8 "{x. even x}" |
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314 |
|
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315 |
values [random_dseq 1, 1, 0] 8 "{x. even x}" |
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316 |
values [random_dseq 1, 1, 1] 8 "{x. even x}" |
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317 |
values [random_dseq 1, 1, 2] 8 "{x. even x}" |
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318 |
values [random_dseq 1, 1, 3] 8 "{x. even x}" |
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319 |
values [random_dseq 1, 1, 6] 8 "{x. even x}" |
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320 |
|
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321 |
values [expected "{}" random_dseq 1, 1, 7] "{x. odd 7}" |
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322 |
values [random_dseq 1, 1, 8] "{x. odd 7}" |
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323 |
values [random_dseq 1, 1, 9] "{x. odd 7}" |
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324 |
|
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definition odd' where "odd' x == \<not> even x" |
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326 |
|
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327 |
code_pred (expected_modes: i => bool) [inductify] odd' . |
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328 |
code_pred [dseq inductify] odd' . |
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329 |
code_pred [random_dseq inductify] odd' . |
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330 |
|
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331 |
values [expected "{}" dseq 2] "{x. odd' 7}" |
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332 |
values [expected "{()}" dseq 9] "{x. odd' 7}" |
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333 |
values [expected "{}" dseq 2] "{x. odd' 8}" |
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334 |
values [expected "{}" dseq 10] "{x. odd' 8}" |
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335 |
|
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336 |
|
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337 |
inductive is_even :: "nat \<Rightarrow> bool" |
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338 |
where |
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339 |
"n mod 2 = 0 \<Longrightarrow> is_even n" |
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moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
340 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
341 |
code_pred (expected_modes: i => bool) is_even . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
342 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
343 |
subsection {* append predicate *} |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
344 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
345 |
inductive append :: "'a list \<Rightarrow> 'a list \<Rightarrow> 'a list \<Rightarrow> bool" where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
346 |
"append [] xs xs" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
347 |
| "append xs ys zs \<Longrightarrow> append (x # xs) ys (x # zs)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
348 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
349 |
code_pred (modes: i => i => o => bool as "concat", o => o => i => bool as "slice", o => i => i => bool as prefix, |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
350 |
i => o => i => bool as suffix, i => i => i => bool) append . |
38664
7215ae18f44b
added support for xsymbol syntax for mode annotations in code_pred command
bulwahn
parents:
36511
diff
changeset
|
351 |
code_pred (modes: i \<Rightarrow> i \<Rightarrow> o \<Rightarrow> bool as "concat", o \<Rightarrow> o \<Rightarrow> i \<Rightarrow> bool as "slice", o \<Rightarrow> i \<Rightarrow> i \<Rightarrow> bool as prefix, |
7215ae18f44b
added support for xsymbol syntax for mode annotations in code_pred command
bulwahn
parents:
36511
diff
changeset
|
352 |
i \<Rightarrow> o \<Rightarrow> i \<Rightarrow> bool as suffix, i \<Rightarrow> i \<Rightarrow> i \<Rightarrow> bool) append . |
7215ae18f44b
added support for xsymbol syntax for mode annotations in code_pred command
bulwahn
parents:
36511
diff
changeset
|
353 |
|
35950
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
354 |
code_pred [dseq] append . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
355 |
code_pred [random_dseq] append . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
356 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
357 |
thm append.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
358 |
thm append.dseq_equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
359 |
thm append.random_dseq_equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
360 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
361 |
values "{(ys, xs). append xs ys [0, Suc 0, 2]}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
362 |
values "{zs. append [0, Suc 0, 2] [17, 8] zs}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
363 |
values "{ys. append [0, Suc 0, 2] ys [0, Suc 0, 2, 17, 0, 5]}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
364 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
365 |
values [expected "{}" dseq 0] 10 "{(xs, ys). append xs ys [1, 2, 3, 4, (5::nat)]}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
366 |
values [expected "{(([]::nat list), [Suc 0, 2, 3, 4, (5::nat)])}" dseq 1] 10 "{(xs, ys). append xs ys [1, 2, 3, 4, (5::nat)]}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
367 |
values [dseq 4] 10 "{(xs, ys). append xs ys [1, 2, 3, 4, (5::nat)]}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
368 |
values [dseq 6] 10 "{(xs, ys). append xs ys [1, 2, 3, 4, (5::nat)]}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
369 |
values [random_dseq 1, 1, 4] 10 "{(xs, ys). append xs ys [1, 2, 3, 4, (5::nat)]}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
370 |
values [random_dseq 1, 1, 1] 10 "{(xs, ys, zs::int list). append xs ys zs}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
371 |
values [random_dseq 1, 1, 3] 10 "{(xs, ys, zs::int list). append xs ys zs}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
372 |
values [random_dseq 3, 1, 3] 10 "{(xs, ys, zs::int list). append xs ys zs}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
373 |
values [random_dseq 1, 3, 3] 10 "{(xs, ys, zs::int list). append xs ys zs}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
374 |
values [random_dseq 1, 1, 4] 10 "{(xs, ys, zs::int list). append xs ys zs}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
375 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
376 |
value [code] "Predicate.the (concat [0::int, 1, 2] [3, 4, 5])" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
377 |
value [code] "Predicate.the (slice ([]::int list))" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
378 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
379 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
380 |
text {* tricky case with alternative rules *} |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
381 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
382 |
inductive append2 |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
383 |
where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
384 |
"append2 [] xs xs" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
385 |
| "append2 xs ys zs \<Longrightarrow> append2 (x # xs) ys (x # zs)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
386 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
387 |
lemma append2_Nil: "append2 [] (xs::'b list) xs" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
388 |
by (simp add: append2.intros(1)) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
389 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
390 |
lemmas [code_pred_intro] = append2_Nil append2.intros(2) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
391 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
392 |
code_pred (expected_modes: i => i => o => bool, o => o => i => bool, o => i => i => bool, |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
393 |
i => o => i => bool, i => i => i => bool) append2 |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
394 |
proof - |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
395 |
case append2 |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
396 |
from append2(1) show thesis |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
397 |
proof |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
398 |
fix xs |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
399 |
assume "xa = []" "xb = xs" "xc = xs" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
400 |
from this append2(2) show thesis by simp |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
401 |
next |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
402 |
fix xs ys zs x |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
403 |
assume "xa = x # xs" "xb = ys" "xc = x # zs" "append2 xs ys zs" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
404 |
from this append2(3) show thesis by fastsimp |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
405 |
qed |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
406 |
qed |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
407 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
408 |
inductive tupled_append :: "'a list \<times> 'a list \<times> 'a list \<Rightarrow> bool" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
409 |
where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
410 |
"tupled_append ([], xs, xs)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
411 |
| "tupled_append (xs, ys, zs) \<Longrightarrow> tupled_append (x # xs, ys, x # zs)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
412 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
413 |
code_pred (expected_modes: i * i * o => bool, o * o * i => bool, o * i * i => bool, |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
414 |
i * o * i => bool, i * i * i => bool) tupled_append . |
38664
7215ae18f44b
added support for xsymbol syntax for mode annotations in code_pred command
bulwahn
parents:
36511
diff
changeset
|
415 |
|
7215ae18f44b
added support for xsymbol syntax for mode annotations in code_pred command
bulwahn
parents:
36511
diff
changeset
|
416 |
code_pred (expected_modes: i \<times> i \<times> o \<Rightarrow> bool, o \<times> o \<times> i \<Rightarrow> bool, o \<times> i \<times> i \<Rightarrow> bool, |
7215ae18f44b
added support for xsymbol syntax for mode annotations in code_pred command
bulwahn
parents:
36511
diff
changeset
|
417 |
i \<times> o \<times> i \<Rightarrow> bool, i \<times> i \<times> i \<Rightarrow> bool) tupled_append . |
7215ae18f44b
added support for xsymbol syntax for mode annotations in code_pred command
bulwahn
parents:
36511
diff
changeset
|
418 |
|
35950
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
419 |
code_pred [random_dseq] tupled_append . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
420 |
thm tupled_append.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
421 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
422 |
values "{xs. tupled_append ([(1::nat), 2, 3], [4, 5], xs)}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
423 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
424 |
inductive tupled_append' |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
425 |
where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
426 |
"tupled_append' ([], xs, xs)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
427 |
| "[| ys = fst (xa, y); x # zs = snd (xa, y); |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
428 |
tupled_append' (xs, ys, zs) |] ==> tupled_append' (x # xs, xa, y)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
429 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
430 |
code_pred (expected_modes: i * i * o => bool, o * o * i => bool, o * i * i => bool, |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
431 |
i * o * i => bool, i * i * i => bool) tupled_append' . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
432 |
thm tupled_append'.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
433 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
434 |
inductive tupled_append'' :: "'a list \<times> 'a list \<times> 'a list \<Rightarrow> bool" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
435 |
where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
436 |
"tupled_append'' ([], xs, xs)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
437 |
| "ys = fst yszs ==> x # zs = snd yszs ==> tupled_append'' (xs, ys, zs) \<Longrightarrow> tupled_append'' (x # xs, yszs)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
438 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
439 |
code_pred (expected_modes: i * i * o => bool, o * o * i => bool, o * i * i => bool, |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
440 |
i * o * i => bool, i * i * i => bool) tupled_append'' . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
441 |
thm tupled_append''.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
442 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
443 |
inductive tupled_append''' :: "'a list \<times> 'a list \<times> 'a list \<Rightarrow> bool" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
444 |
where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
445 |
"tupled_append''' ([], xs, xs)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
446 |
| "yszs = (ys, zs) ==> tupled_append''' (xs, yszs) \<Longrightarrow> tupled_append''' (x # xs, ys, x # zs)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
447 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
448 |
code_pred (expected_modes: i * i * o => bool, o * o * i => bool, o * i * i => bool, |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
449 |
i * o * i => bool, i * i * i => bool) tupled_append''' . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
450 |
thm tupled_append'''.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
451 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
452 |
subsection {* map_ofP predicate *} |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
453 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
454 |
inductive map_ofP :: "('a \<times> 'b) list \<Rightarrow> 'a \<Rightarrow> 'b \<Rightarrow> bool" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
455 |
where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
456 |
"map_ofP ((a, b)#xs) a b" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
457 |
| "map_ofP xs a b \<Longrightarrow> map_ofP (x#xs) a b" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
458 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
459 |
code_pred (expected_modes: i => o => o => bool, i => i => o => bool, i => o => i => bool, i => i => i => bool) map_ofP . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
460 |
thm map_ofP.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
461 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
462 |
subsection {* filter predicate *} |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
463 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
464 |
inductive filter1 |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
465 |
for P |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
466 |
where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
467 |
"filter1 P [] []" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
468 |
| "P x ==> filter1 P xs ys ==> filter1 P (x#xs) (x#ys)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
469 |
| "\<not> P x ==> filter1 P xs ys ==> filter1 P (x#xs) ys" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
470 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
471 |
code_pred (expected_modes: (i => bool) => i => o => bool, (i => bool) => i => i => bool) filter1 . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
472 |
code_pred [dseq] filter1 . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
473 |
code_pred [random_dseq] filter1 . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
474 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
475 |
thm filter1.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
476 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
477 |
values [expected "{[0::nat, 2, 4]}"] "{xs. filter1 even [0, 1, 2, 3, 4] xs}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
478 |
values [expected "{}" dseq 9] "{xs. filter1 even [0, 1, 2, 3, 4] xs}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
479 |
values [expected "{[0::nat, 2, 4]}" dseq 10] "{xs. filter1 even [0, 1, 2, 3, 4] xs}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
480 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
481 |
inductive filter2 |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
482 |
where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
483 |
"filter2 P [] []" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
484 |
| "P x ==> filter2 P xs ys ==> filter2 P (x#xs) (x#ys)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
485 |
| "\<not> P x ==> filter2 P xs ys ==> filter2 P (x#xs) ys" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
486 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
487 |
code_pred (expected_modes: (i => bool) => i => i => bool, (i => bool) => i => o => bool) filter2 . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
488 |
code_pred [dseq] filter2 . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
489 |
code_pred [random_dseq] filter2 . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
490 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
491 |
thm filter2.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
492 |
thm filter2.random_dseq_equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
493 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
494 |
(* |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
495 |
inductive filter3 |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
496 |
for P |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
497 |
where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
498 |
"List.filter P xs = ys ==> filter3 P xs ys" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
499 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
500 |
code_pred (expected_modes: (o => bool) => i => o => bool, (o => bool) => i => i => bool , (i => bool) => i => o => bool, (i => bool) => i => i => bool) [skip_proof] filter3 . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
501 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
502 |
code_pred [dseq] filter3 . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
503 |
thm filter3.dseq_equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
504 |
*) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
505 |
(* |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
506 |
inductive filter4 |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
507 |
where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
508 |
"List.filter P xs = ys ==> filter4 P xs ys" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
509 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
510 |
code_pred (expected_modes: i => i => o => bool, i => i => i => bool) filter4 . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
511 |
(*code_pred [depth_limited] filter4 .*) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
512 |
(*code_pred [random] filter4 .*) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
513 |
*) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
514 |
subsection {* reverse predicate *} |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
515 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
516 |
inductive rev where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
517 |
"rev [] []" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
518 |
| "rev xs xs' ==> append xs' [x] ys ==> rev (x#xs) ys" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
519 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
520 |
code_pred (expected_modes: i => o => bool, o => i => bool, i => i => bool) rev . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
521 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
522 |
thm rev.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
523 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
524 |
values "{xs. rev [0, 1, 2, 3::nat] xs}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
525 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
526 |
inductive tupled_rev where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
527 |
"tupled_rev ([], [])" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
528 |
| "tupled_rev (xs, xs') \<Longrightarrow> tupled_append (xs', [x], ys) \<Longrightarrow> tupled_rev (x#xs, ys)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
529 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
530 |
code_pred (expected_modes: i * o => bool, o * i => bool, i * i => bool) tupled_rev . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
531 |
thm tupled_rev.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
532 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
533 |
subsection {* partition predicate *} |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
534 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
535 |
inductive partition :: "('a \<Rightarrow> bool) \<Rightarrow> 'a list \<Rightarrow> 'a list \<Rightarrow> 'a list \<Rightarrow> bool" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
536 |
for f where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
537 |
"partition f [] [] []" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
538 |
| "f x \<Longrightarrow> partition f xs ys zs \<Longrightarrow> partition f (x # xs) (x # ys) zs" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
539 |
| "\<not> f x \<Longrightarrow> partition f xs ys zs \<Longrightarrow> partition f (x # xs) ys (x # zs)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
540 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
541 |
code_pred (expected_modes: (i => bool) => i => o => o => bool, (i => bool) => o => i => i => bool, |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
542 |
(i => bool) => i => i => o => bool, (i => bool) => i => o => i => bool, (i => bool) => i => i => i => bool) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
543 |
partition . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
544 |
code_pred [dseq] partition . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
545 |
code_pred [random_dseq] partition . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
546 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
547 |
values 10 "{(ys, zs). partition is_even |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
548 |
[0, Suc 0, 2, 3, 4, 5, 6, 7] ys zs}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
549 |
values 10 "{zs. partition is_even zs [0, 2] [3, 5]}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
550 |
values 10 "{zs. partition is_even zs [0, 7] [3, 5]}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
551 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
552 |
inductive tupled_partition :: "('a \<Rightarrow> bool) \<Rightarrow> ('a list \<times> 'a list \<times> 'a list) \<Rightarrow> bool" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
553 |
for f where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
554 |
"tupled_partition f ([], [], [])" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
555 |
| "f x \<Longrightarrow> tupled_partition f (xs, ys, zs) \<Longrightarrow> tupled_partition f (x # xs, x # ys, zs)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
556 |
| "\<not> f x \<Longrightarrow> tupled_partition f (xs, ys, zs) \<Longrightarrow> tupled_partition f (x # xs, ys, x # zs)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
557 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
558 |
code_pred (expected_modes: (i => bool) => i => bool, (i => bool) => (i * i * o) => bool, (i => bool) => (i * o * i) => bool, |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
559 |
(i => bool) => (o * i * i) => bool, (i => bool) => (i * o * o) => bool) tupled_partition . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
560 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
561 |
thm tupled_partition.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
562 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
563 |
lemma [code_pred_intro]: |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
564 |
"r a b \<Longrightarrow> tranclp r a b" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
565 |
"r a b \<Longrightarrow> tranclp r b c \<Longrightarrow> tranclp r a c" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
566 |
by auto |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
567 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
568 |
subsection {* transitive predicate *} |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
569 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
570 |
text {* Also look at the tabled transitive closure in the Library *} |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
571 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
572 |
code_pred (modes: (i => o => bool) => i => i => bool, (i => o => bool) => i => o => bool as forwards_trancl, |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
573 |
(o => i => bool) => i => i => bool, (o => i => bool) => o => i => bool as backwards_trancl, (o => o => bool) => i => i => bool, (o => o => bool) => i => o => bool, |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
574 |
(o => o => bool) => o => i => bool, (o => o => bool) => o => o => bool) tranclp |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
575 |
proof - |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
576 |
case tranclp |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
577 |
from this converse_tranclpE[OF this(1)] show thesis by metis |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
578 |
qed |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
579 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
580 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
581 |
code_pred [dseq] tranclp . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
582 |
code_pred [random_dseq] tranclp . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
583 |
thm tranclp.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
584 |
thm tranclp.random_dseq_equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
585 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
586 |
inductive rtrancl' :: "'a => 'a => ('a => 'a => bool) => bool" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
587 |
where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
588 |
"rtrancl' x x r" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
589 |
| "r x y ==> rtrancl' y z r ==> rtrancl' x z r" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
590 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
591 |
code_pred [random_dseq] rtrancl' . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
592 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
593 |
thm rtrancl'.random_dseq_equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
594 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
595 |
inductive rtrancl'' :: "('a * 'a * ('a \<Rightarrow> 'a \<Rightarrow> bool)) \<Rightarrow> bool" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
596 |
where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
597 |
"rtrancl'' (x, x, r)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
598 |
| "r x y \<Longrightarrow> rtrancl'' (y, z, r) \<Longrightarrow> rtrancl'' (x, z, r)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
599 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
600 |
code_pred rtrancl'' . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
601 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
602 |
inductive rtrancl''' :: "('a * ('a * 'a) * ('a * 'a => bool)) => bool" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
603 |
where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
604 |
"rtrancl''' (x, (x, x), r)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
605 |
| "r (x, y) ==> rtrancl''' (y, (z, z), r) ==> rtrancl''' (x, (z, z), r)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
606 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
607 |
code_pred rtrancl''' . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
608 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
609 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
610 |
inductive succ :: "nat \<Rightarrow> nat \<Rightarrow> bool" where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
611 |
"succ 0 1" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
612 |
| "succ m n \<Longrightarrow> succ (Suc m) (Suc n)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
613 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
614 |
code_pred (modes: i => i => bool, i => o => bool, o => i => bool, o => o => bool) succ . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
615 |
code_pred [random_dseq] succ . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
616 |
thm succ.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
617 |
thm succ.random_dseq_equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
618 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
619 |
values 10 "{(m, n). succ n m}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
620 |
values "{m. succ 0 m}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
621 |
values "{m. succ m 0}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
622 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
623 |
text {* values command needs mode annotation of the parameter succ |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
624 |
to disambiguate which mode is to be chosen. *} |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
625 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
626 |
values [mode: i => o => bool] 20 "{n. tranclp succ 10 n}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
627 |
values [mode: o => i => bool] 10 "{n. tranclp succ n 10}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
628 |
values 20 "{(n, m). tranclp succ n m}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
629 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
630 |
inductive example_graph :: "int => int => bool" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
631 |
where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
632 |
"example_graph 0 1" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
633 |
| "example_graph 1 2" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
634 |
| "example_graph 1 3" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
635 |
| "example_graph 4 7" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
636 |
| "example_graph 4 5" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
637 |
| "example_graph 5 6" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
638 |
| "example_graph 7 6" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
639 |
| "example_graph 7 8" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
640 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
641 |
inductive not_reachable_in_example_graph :: "int => int => bool" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
642 |
where "\<not> (tranclp example_graph x y) ==> not_reachable_in_example_graph x y" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
643 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
644 |
code_pred (expected_modes: i => i => bool) not_reachable_in_example_graph . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
645 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
646 |
thm not_reachable_in_example_graph.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
647 |
thm tranclp.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
648 |
value "not_reachable_in_example_graph 0 3" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
649 |
value "not_reachable_in_example_graph 4 8" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
650 |
value "not_reachable_in_example_graph 5 6" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
651 |
text {* rtrancl compilation is strange! *} |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
652 |
(* |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
653 |
value "not_reachable_in_example_graph 0 4" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
654 |
value "not_reachable_in_example_graph 1 6" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
655 |
value "not_reachable_in_example_graph 8 4"*) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
656 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
657 |
code_pred [dseq] not_reachable_in_example_graph . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
658 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
659 |
values [dseq 6] "{x. tranclp example_graph 0 3}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
660 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
661 |
values [dseq 0] "{x. not_reachable_in_example_graph 0 3}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
662 |
values [dseq 0] "{x. not_reachable_in_example_graph 0 4}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
663 |
values [dseq 20] "{x. not_reachable_in_example_graph 0 4}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
664 |
values [dseq 6] "{x. not_reachable_in_example_graph 0 3}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
665 |
values [dseq 3] "{x. not_reachable_in_example_graph 4 2}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
666 |
values [dseq 6] "{x. not_reachable_in_example_graph 4 2}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
667 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
668 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
669 |
inductive not_reachable_in_example_graph' :: "int => int => bool" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
670 |
where "\<not> (rtranclp example_graph x y) ==> not_reachable_in_example_graph' x y" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
671 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
672 |
code_pred not_reachable_in_example_graph' . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
673 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
674 |
value "not_reachable_in_example_graph' 0 3" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
675 |
(* value "not_reachable_in_example_graph' 0 5" would not terminate *) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
676 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
677 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
678 |
(*values [depth_limited 0] "{x. not_reachable_in_example_graph' 0 3}"*) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
679 |
(*values [depth_limited 3] "{x. not_reachable_in_example_graph' 0 3}"*) (* fails with undefined *) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
680 |
(*values [depth_limited 5] "{x. not_reachable_in_example_graph' 0 3}"*) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
681 |
(*values [depth_limited 1] "{x. not_reachable_in_example_graph' 0 4}"*) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
682 |
(*values [depth_limit = 4] "{x. not_reachable_in_example_graph' 0 4}"*) (* fails with undefined *) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
683 |
(*values [depth_limit = 20] "{x. not_reachable_in_example_graph' 0 4}"*) (* fails with undefined *) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
684 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
685 |
code_pred [dseq] not_reachable_in_example_graph' . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
686 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
687 |
(*thm not_reachable_in_example_graph'.dseq_equation*) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
688 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
689 |
(*values [dseq 0] "{x. not_reachable_in_example_graph' 0 3}"*) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
690 |
(*values [depth_limited 3] "{x. not_reachable_in_example_graph' 0 3}"*) (* fails with undefined *) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
691 |
(*values [depth_limited 5] "{x. not_reachable_in_example_graph' 0 3}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
692 |
values [depth_limited 1] "{x. not_reachable_in_example_graph' 0 4}"*) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
693 |
(*values [depth_limit = 4] "{x. not_reachable_in_example_graph' 0 4}"*) (* fails with undefined *) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
694 |
(*values [depth_limit = 20] "{x. not_reachable_in_example_graph' 0 4}"*) (* fails with undefined *) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
695 |
|
36511
db2953f5887a
added an example with a free function variable to the Predicate Compile examples
bulwahn
parents:
36260
diff
changeset
|
696 |
subsection {* Free function variable *} |
db2953f5887a
added an example with a free function variable to the Predicate Compile examples
bulwahn
parents:
36260
diff
changeset
|
697 |
|
db2953f5887a
added an example with a free function variable to the Predicate Compile examples
bulwahn
parents:
36260
diff
changeset
|
698 |
inductive FF :: "nat => nat => bool" |
db2953f5887a
added an example with a free function variable to the Predicate Compile examples
bulwahn
parents:
36260
diff
changeset
|
699 |
where |
db2953f5887a
added an example with a free function variable to the Predicate Compile examples
bulwahn
parents:
36260
diff
changeset
|
700 |
"f x = y ==> FF x y" |
db2953f5887a
added an example with a free function variable to the Predicate Compile examples
bulwahn
parents:
36260
diff
changeset
|
701 |
|
db2953f5887a
added an example with a free function variable to the Predicate Compile examples
bulwahn
parents:
36260
diff
changeset
|
702 |
code_pred FF . |
35950
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
703 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
704 |
subsection {* IMP *} |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
705 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
706 |
types |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
707 |
var = nat |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
708 |
state = "int list" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
709 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
710 |
datatype com = |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
711 |
Skip | |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
712 |
Ass var "state => int" | |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
713 |
Seq com com | |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
714 |
IF "state => bool" com com | |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
715 |
While "state => bool" com |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
716 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
717 |
inductive exec :: "com => state => state => bool" where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
718 |
"exec Skip s s" | |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
719 |
"exec (Ass x e) s (s[x := e(s)])" | |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
720 |
"exec c1 s1 s2 ==> exec c2 s2 s3 ==> exec (Seq c1 c2) s1 s3" | |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
721 |
"b s ==> exec c1 s t ==> exec (IF b c1 c2) s t" | |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
722 |
"~b s ==> exec c2 s t ==> exec (IF b c1 c2) s t" | |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
723 |
"~b s ==> exec (While b c) s s" | |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
724 |
"b s1 ==> exec c s1 s2 ==> exec (While b c) s2 s3 ==> exec (While b c) s1 s3" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
725 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
726 |
code_pred exec . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
727 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
728 |
values "{t. exec |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
729 |
(While (%s. s!0 > 0) (Seq (Ass 0 (%s. s!0 - 1)) (Ass 1 (%s. s!1 + 1)))) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
730 |
[3,5] t}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
731 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
732 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
733 |
inductive tupled_exec :: "(com \<times> state \<times> state) \<Rightarrow> bool" where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
734 |
"tupled_exec (Skip, s, s)" | |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
735 |
"tupled_exec (Ass x e, s, s[x := e(s)])" | |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
736 |
"tupled_exec (c1, s1, s2) ==> tupled_exec (c2, s2, s3) ==> tupled_exec (Seq c1 c2, s1, s3)" | |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
737 |
"b s ==> tupled_exec (c1, s, t) ==> tupled_exec (IF b c1 c2, s, t)" | |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
738 |
"~b s ==> tupled_exec (c2, s, t) ==> tupled_exec (IF b c1 c2, s, t)" | |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
739 |
"~b s ==> tupled_exec (While b c, s, s)" | |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
740 |
"b s1 ==> tupled_exec (c, s1, s2) ==> tupled_exec (While b c, s2, s3) ==> tupled_exec (While b c, s1, s3)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
741 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
742 |
code_pred tupled_exec . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
743 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
744 |
values "{s. tupled_exec (While (%s. s!0 > 0) (Seq (Ass 0 (%s. s!0 - 1)) (Ass 1 (%s. s!1 + 1))), [3, 5], s)}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
745 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
746 |
subsection {* CCS *} |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
747 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
748 |
text{* This example formalizes finite CCS processes without communication or |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
749 |
recursion. For simplicity, labels are natural numbers. *} |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
750 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
751 |
datatype proc = nil | pre nat proc | or proc proc | par proc proc |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
752 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
753 |
inductive step :: "proc \<Rightarrow> nat \<Rightarrow> proc \<Rightarrow> bool" where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
754 |
"step (pre n p) n p" | |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
755 |
"step p1 a q \<Longrightarrow> step (or p1 p2) a q" | |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
756 |
"step p2 a q \<Longrightarrow> step (or p1 p2) a q" | |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
757 |
"step p1 a q \<Longrightarrow> step (par p1 p2) a (par q p2)" | |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
758 |
"step p2 a q \<Longrightarrow> step (par p1 p2) a (par p1 q)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
759 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
760 |
code_pred step . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
761 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
762 |
inductive steps where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
763 |
"steps p [] p" | |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
764 |
"step p a q \<Longrightarrow> steps q as r \<Longrightarrow> steps p (a#as) r" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
765 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
766 |
code_pred steps . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
767 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
768 |
values 3 |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
769 |
"{as . steps (par (or (pre 0 nil) (pre 1 nil)) (pre 2 nil)) as (par nil nil)}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
770 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
771 |
values 5 |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
772 |
"{as . steps (par (or (pre 0 nil) (pre 1 nil)) (pre 2 nil)) as (par nil nil)}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
773 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
774 |
values 3 "{(a,q). step (par nil nil) a q}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
775 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
776 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
777 |
inductive tupled_step :: "(proc \<times> nat \<times> proc) \<Rightarrow> bool" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
778 |
where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
779 |
"tupled_step (pre n p, n, p)" | |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
780 |
"tupled_step (p1, a, q) \<Longrightarrow> tupled_step (or p1 p2, a, q)" | |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
781 |
"tupled_step (p2, a, q) \<Longrightarrow> tupled_step (or p1 p2, a, q)" | |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
782 |
"tupled_step (p1, a, q) \<Longrightarrow> tupled_step (par p1 p2, a, par q p2)" | |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
783 |
"tupled_step (p2, a, q) \<Longrightarrow> tupled_step (par p1 p2, a, par p1 q)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
784 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
785 |
code_pred tupled_step . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
786 |
thm tupled_step.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
787 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
788 |
subsection {* divmod *} |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
789 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
790 |
inductive divmod_rel :: "nat \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow> bool" where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
791 |
"k < l \<Longrightarrow> divmod_rel k l 0 k" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
792 |
| "k \<ge> l \<Longrightarrow> divmod_rel (k - l) l q r \<Longrightarrow> divmod_rel k l (Suc q) r" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
793 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
794 |
code_pred divmod_rel .. |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
795 |
thm divmod_rel.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
796 |
value [code] "Predicate.the (divmod_rel_i_i_o_o 1705 42)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
797 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
798 |
subsection {* Transforming predicate logic into logic programs *} |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
799 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
800 |
subsection {* Transforming functions into logic programs *} |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
801 |
definition |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
802 |
"case_f xs ys = (case (xs @ ys) of [] => [] | (x # xs) => xs)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
803 |
|
36040
fcd7bea01a93
adding skip_proof in the examples because proof procedure cannot handle alternative compilations yet
bulwahn
parents:
35954
diff
changeset
|
804 |
code_pred [inductify, skip_proof] case_f . |
35950
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
805 |
thm case_fP.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
806 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
807 |
fun fold_map_idx where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
808 |
"fold_map_idx f i y [] = (y, [])" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
809 |
| "fold_map_idx f i y (x # xs) = |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
810 |
(let (y', x') = f i y x; (y'', xs') = fold_map_idx f (Suc i) y' xs |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
811 |
in (y'', x' # xs'))" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
812 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
813 |
text {* mode analysis explores thousand modes - this is infeasible at the moment... *} |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
814 |
(*code_pred [inductify, show_steps] fold_map_idx .*) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
815 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
816 |
subsection {* Minimum *} |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
817 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
818 |
definition Min |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
819 |
where "Min s r x \<equiv> s x \<and> (\<forall>y. r x y \<longrightarrow> x = y)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
820 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
821 |
code_pred [inductify] Min . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
822 |
thm Min.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
823 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
824 |
subsection {* Lexicographic order *} |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
825 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
826 |
declare lexord_def[code_pred_def] |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
827 |
code_pred [inductify] lexord . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
828 |
code_pred [random_dseq inductify] lexord . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
829 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
830 |
thm lexord.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
831 |
thm lexord.random_dseq_equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
832 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
833 |
inductive less_than_nat :: "nat * nat => bool" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
834 |
where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
835 |
"less_than_nat (0, x)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
836 |
| "less_than_nat (x, y) ==> less_than_nat (Suc x, Suc y)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
837 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
838 |
code_pred less_than_nat . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
839 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
840 |
code_pred [dseq] less_than_nat . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
841 |
code_pred [random_dseq] less_than_nat . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
842 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
843 |
inductive test_lexord :: "nat list * nat list => bool" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
844 |
where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
845 |
"lexord less_than_nat (xs, ys) ==> test_lexord (xs, ys)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
846 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
847 |
code_pred test_lexord . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
848 |
code_pred [dseq] test_lexord . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
849 |
code_pred [random_dseq] test_lexord . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
850 |
thm test_lexord.dseq_equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
851 |
thm test_lexord.random_dseq_equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
852 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
853 |
values "{x. test_lexord ([1, 2, 3], [1, 2, 5])}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
854 |
(*values [depth_limited 5] "{x. test_lexord ([1, 2, 3], [1, 2, 5])}"*) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
855 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
856 |
lemmas [code_pred_def] = lexn_conv lex_conv lenlex_conv |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
857 |
(* |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
858 |
code_pred [inductify] lexn . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
859 |
thm lexn.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
860 |
*) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
861 |
(* |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
862 |
code_pred [random_dseq inductify] lexn . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
863 |
thm lexn.random_dseq_equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
864 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
865 |
values [random_dseq 4, 4, 6] 100 "{(n, xs, ys::int list). lexn (%(x, y). x <= y) n (xs, ys)}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
866 |
*) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
867 |
inductive has_length |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
868 |
where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
869 |
"has_length [] 0" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
870 |
| "has_length xs i ==> has_length (x # xs) (Suc i)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
871 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
872 |
lemma has_length: |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
873 |
"has_length xs n = (length xs = n)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
874 |
proof (rule iffI) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
875 |
assume "has_length xs n" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
876 |
from this show "length xs = n" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
877 |
by (rule has_length.induct) auto |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
878 |
next |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
879 |
assume "length xs = n" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
880 |
from this show "has_length xs n" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
881 |
by (induct xs arbitrary: n) (auto intro: has_length.intros) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
882 |
qed |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
883 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
884 |
lemma lexn_intros [code_pred_intro]: |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
885 |
"has_length xs i ==> has_length ys i ==> r (x, y) ==> lexn r (Suc i) (x # xs, y # ys)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
886 |
"lexn r i (xs, ys) ==> lexn r (Suc i) (x # xs, x # ys)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
887 |
proof - |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
888 |
assume "has_length xs i" "has_length ys i" "r (x, y)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
889 |
from this has_length show "lexn r (Suc i) (x # xs, y # ys)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
890 |
unfolding lexn_conv Collect_def mem_def |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
891 |
by fastsimp |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
892 |
next |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
893 |
assume "lexn r i (xs, ys)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
894 |
thm lexn_conv |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
895 |
from this show "lexn r (Suc i) (x#xs, x#ys)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
896 |
unfolding Collect_def mem_def lexn_conv |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
897 |
apply auto |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
898 |
apply (rule_tac x="x # xys" in exI) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
899 |
by auto |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
900 |
qed |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
901 |
|
36055
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
902 |
code_pred [random_dseq] lexn |
35950
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
903 |
proof - |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
904 |
fix r n xs ys |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
905 |
assume 1: "lexn r n (xs, ys)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
906 |
assume 2: "\<And>r' i x xs' y ys'. r = r' ==> n = Suc i ==> (xs, ys) = (x # xs', y # ys') ==> has_length xs' i ==> has_length ys' i ==> r' (x, y) ==> thesis" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
907 |
assume 3: "\<And>r' i x xs' ys'. r = r' ==> n = Suc i ==> (xs, ys) = (x # xs', x # ys') ==> lexn r' i (xs', ys') ==> thesis" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
908 |
from 1 2 3 show thesis |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
909 |
unfolding lexn_conv Collect_def mem_def |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
910 |
apply (auto simp add: has_length) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
911 |
apply (case_tac xys) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
912 |
apply auto |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
913 |
apply fastsimp |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
914 |
apply fastsimp done |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
915 |
qed |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
916 |
|
36055
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
917 |
values [random_dseq 1, 2, 5] 10 "{(n, xs, ys::int list). lexn (%(x, y). x <= y) n (xs, ys)}" |
35950
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
918 |
|
36040
fcd7bea01a93
adding skip_proof in the examples because proof procedure cannot handle alternative compilations yet
bulwahn
parents:
35954
diff
changeset
|
919 |
code_pred [inductify, skip_proof] lex . |
35950
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
920 |
thm lex.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
921 |
thm lex_def |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
922 |
declare lenlex_conv[code_pred_def] |
36040
fcd7bea01a93
adding skip_proof in the examples because proof procedure cannot handle alternative compilations yet
bulwahn
parents:
35954
diff
changeset
|
923 |
code_pred [inductify, skip_proof] lenlex . |
35950
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
924 |
thm lenlex.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
925 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
926 |
code_pred [random_dseq inductify] lenlex . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
927 |
thm lenlex.random_dseq_equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
928 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
929 |
values [random_dseq 4, 2, 4] 100 "{(xs, ys::int list). lenlex (%(x, y). x <= y) (xs, ys)}" |
36055
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
930 |
|
35950
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
931 |
thm lists.intros |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
932 |
code_pred [inductify] lists . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
933 |
thm lists.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
934 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
935 |
subsection {* AVL Tree *} |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
936 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
937 |
datatype 'a tree = ET | MKT 'a "'a tree" "'a tree" nat |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
938 |
fun height :: "'a tree => nat" where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
939 |
"height ET = 0" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
940 |
| "height (MKT x l r h) = max (height l) (height r) + 1" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
941 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
942 |
consts avl :: "'a tree => bool" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
943 |
primrec |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
944 |
"avl ET = True" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
945 |
"avl (MKT x l r h) = ((height l = height r \<or> height l = 1 + height r \<or> height r = 1+height l) \<and> |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
946 |
h = max (height l) (height r) + 1 \<and> avl l \<and> avl r)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
947 |
(* |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
948 |
code_pred [inductify] avl . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
949 |
thm avl.equation*) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
950 |
|
36257
3f3e9f18f302
adopting examples to changes in the predicate compiler
bulwahn
parents:
36253
diff
changeset
|
951 |
code_pred [new_random_dseq inductify] avl . |
3f3e9f18f302
adopting examples to changes in the predicate compiler
bulwahn
parents:
36253
diff
changeset
|
952 |
thm avl.new_random_dseq_equation |
35950
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
953 |
|
36257
3f3e9f18f302
adopting examples to changes in the predicate compiler
bulwahn
parents:
36253
diff
changeset
|
954 |
values [new_random_dseq 2, 1, 7] 5 "{t:: int tree. avl t}" |
35950
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
955 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
956 |
fun set_of |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
957 |
where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
958 |
"set_of ET = {}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
959 |
| "set_of (MKT n l r h) = insert n (set_of l \<union> set_of r)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
960 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
961 |
fun is_ord :: "nat tree => bool" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
962 |
where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
963 |
"is_ord ET = True" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
964 |
| "is_ord (MKT n l r h) = |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
965 |
((\<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)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
966 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
967 |
code_pred (expected_modes: i => o => bool, i => i => bool) [inductify] set_of . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
968 |
thm set_of.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
969 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
970 |
code_pred (expected_modes: i => bool) [inductify] is_ord . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
971 |
thm is_ord_aux.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
972 |
thm is_ord.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
973 |
|
36055
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
974 |
subsection {* Definitions about Relations *} |
35950
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
975 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
976 |
term "converse" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
977 |
code_pred (modes: |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
978 |
(i * i => bool) => i * i => bool, |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
979 |
(i * o => bool) => o * i => bool, |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
980 |
(i * o => bool) => i * i => bool, |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
981 |
(o * i => bool) => i * o => bool, |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
982 |
(o * i => bool) => i * i => bool, |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
983 |
(o * o => bool) => o * o => bool, |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
984 |
(o * o => bool) => i * o => bool, |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
985 |
(o * o => bool) => o * i => bool, |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
986 |
(o * o => bool) => i * i => bool) [inductify] converse . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
987 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
988 |
thm converse.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
989 |
code_pred [inductify] rel_comp . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
990 |
thm rel_comp.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
991 |
code_pred [inductify] Image . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
992 |
thm Image.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
993 |
declare singleton_iff[code_pred_inline] |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
994 |
declare Id_on_def[unfolded Bex_def UNION_def singleton_iff, code_pred_def] |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
995 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
996 |
code_pred (expected_modes: |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
997 |
(o => bool) => o => bool, |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
998 |
(o => bool) => i * o => bool, |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
999 |
(o => bool) => o * i => bool, |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1000 |
(o => bool) => i => bool, |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1001 |
(i => bool) => i * o => bool, |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1002 |
(i => bool) => o * i => bool, |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1003 |
(i => bool) => i => bool) [inductify] Id_on . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1004 |
thm Id_on.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1005 |
thm Domain_def |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1006 |
code_pred (modes: |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1007 |
(o * o => bool) => o => bool, |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1008 |
(o * o => bool) => i => bool, |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1009 |
(i * o => bool) => i => bool) [inductify] Domain . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1010 |
thm Domain.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1011 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1012 |
thm Range_def |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1013 |
code_pred (modes: |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1014 |
(o * o => bool) => o => bool, |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1015 |
(o * o => bool) => i => bool, |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1016 |
(o * i => bool) => i => bool) [inductify] Range . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1017 |
thm Range.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1018 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1019 |
code_pred [inductify] Field . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1020 |
thm Field.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1021 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1022 |
thm refl_on_def |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1023 |
code_pred [inductify] refl_on . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1024 |
thm refl_on.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1025 |
code_pred [inductify] total_on . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1026 |
thm total_on.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1027 |
code_pred [inductify] antisym . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1028 |
thm antisym.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1029 |
code_pred [inductify] trans . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1030 |
thm trans.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1031 |
code_pred [inductify] single_valued . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1032 |
thm single_valued.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1033 |
thm inv_image_def |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1034 |
code_pred [inductify] inv_image . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1035 |
thm inv_image.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1036 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1037 |
subsection {* Inverting list functions *} |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1038 |
|
36055
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1039 |
code_pred [inductify] size_list . |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1040 |
code_pred [new_random_dseq inductify] size_list . |
35950
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1041 |
thm size_listP.equation |
36055
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1042 |
thm size_listP.new_random_dseq_equation |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1043 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1044 |
values [new_random_dseq 2,3,10] 3 "{xs. size_listP (xs::nat list) (5::nat)}" |
35950
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1045 |
|
36040
fcd7bea01a93
adding skip_proof in the examples because proof procedure cannot handle alternative compilations yet
bulwahn
parents:
35954
diff
changeset
|
1046 |
code_pred (expected_modes: i => o => bool, o => i => bool, i => i => bool) [inductify, skip_proof] List.concat . |
35950
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1047 |
thm concatP.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1048 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1049 |
values "{ys. concatP [[1, 2], [3, (4::int)]] ys}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1050 |
values "{ys. concatP [[1, 2], [3]] [1, 2, (3::nat)]}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1051 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1052 |
code_pred [dseq inductify] List.concat . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1053 |
thm concatP.dseq_equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1054 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1055 |
values [dseq 3] 3 |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1056 |
"{xs. concatP xs ([0] :: nat list)}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1057 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1058 |
values [dseq 5] 3 |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1059 |
"{xs. concatP xs ([1] :: int list)}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1060 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1061 |
values [dseq 5] 3 |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1062 |
"{xs. concatP xs ([1] :: nat list)}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1063 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1064 |
values [dseq 5] 3 |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1065 |
"{xs. concatP xs [(1::int), 2]}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1066 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1067 |
code_pred (expected_modes: i => o => bool, i => i => bool) [inductify] hd . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1068 |
thm hdP.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1069 |
values "{x. hdP [1, 2, (3::int)] x}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1070 |
values "{(xs, x). hdP [1, 2, (3::int)] 1}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1071 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1072 |
code_pred (expected_modes: i => o => bool, i => i => bool) [inductify] tl . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1073 |
thm tlP.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1074 |
values "{x. tlP [1, 2, (3::nat)] x}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1075 |
values "{x. tlP [1, 2, (3::int)] [3]}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1076 |
|
36040
fcd7bea01a93
adding skip_proof in the examples because proof procedure cannot handle alternative compilations yet
bulwahn
parents:
35954
diff
changeset
|
1077 |
code_pred [inductify, skip_proof] last . |
35950
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1078 |
thm lastP.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1079 |
|
36040
fcd7bea01a93
adding skip_proof in the examples because proof procedure cannot handle alternative compilations yet
bulwahn
parents:
35954
diff
changeset
|
1080 |
code_pred [inductify, skip_proof] butlast . |
35950
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1081 |
thm butlastP.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1082 |
|
36040
fcd7bea01a93
adding skip_proof in the examples because proof procedure cannot handle alternative compilations yet
bulwahn
parents:
35954
diff
changeset
|
1083 |
code_pred [inductify, skip_proof] take . |
35950
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1084 |
thm takeP.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1085 |
|
36040
fcd7bea01a93
adding skip_proof in the examples because proof procedure cannot handle alternative compilations yet
bulwahn
parents:
35954
diff
changeset
|
1086 |
code_pred [inductify, skip_proof] drop . |
35950
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1087 |
thm dropP.equation |
36040
fcd7bea01a93
adding skip_proof in the examples because proof procedure cannot handle alternative compilations yet
bulwahn
parents:
35954
diff
changeset
|
1088 |
code_pred [inductify, skip_proof] zip . |
35950
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1089 |
thm zipP.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1090 |
|
36040
fcd7bea01a93
adding skip_proof in the examples because proof procedure cannot handle alternative compilations yet
bulwahn
parents:
35954
diff
changeset
|
1091 |
code_pred [inductify, skip_proof] upt . |
fcd7bea01a93
adding skip_proof in the examples because proof procedure cannot handle alternative compilations yet
bulwahn
parents:
35954
diff
changeset
|
1092 |
code_pred [inductify, skip_proof] remdups . |
35950
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1093 |
thm remdupsP.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1094 |
code_pred [dseq inductify] remdups . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1095 |
values [dseq 4] 5 "{xs. remdupsP xs [1, (2::int)]}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1096 |
|
36040
fcd7bea01a93
adding skip_proof in the examples because proof procedure cannot handle alternative compilations yet
bulwahn
parents:
35954
diff
changeset
|
1097 |
code_pred [inductify, skip_proof] remove1 . |
35950
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1098 |
thm remove1P.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1099 |
values "{xs. remove1P 1 xs [2, (3::int)]}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1100 |
|
36040
fcd7bea01a93
adding skip_proof in the examples because proof procedure cannot handle alternative compilations yet
bulwahn
parents:
35954
diff
changeset
|
1101 |
code_pred [inductify, skip_proof] removeAll . |
35950
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1102 |
thm removeAllP.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1103 |
code_pred [dseq inductify] removeAll . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1104 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1105 |
values [dseq 4] 10 "{xs. removeAllP 1 xs [(2::nat)]}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1106 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1107 |
code_pred [inductify] distinct . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1108 |
thm distinct.equation |
36040
fcd7bea01a93
adding skip_proof in the examples because proof procedure cannot handle alternative compilations yet
bulwahn
parents:
35954
diff
changeset
|
1109 |
code_pred [inductify, skip_proof] replicate . |
35950
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1110 |
thm replicateP.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1111 |
values 5 "{(n, xs). replicateP n (0::int) xs}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1112 |
|
36040
fcd7bea01a93
adding skip_proof in the examples because proof procedure cannot handle alternative compilations yet
bulwahn
parents:
35954
diff
changeset
|
1113 |
code_pred [inductify, skip_proof] splice . |
35950
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1114 |
thm splice.simps |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1115 |
thm spliceP.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1116 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1117 |
values "{xs. spliceP xs [1, 2, 3] [1, 1, 1, 2, 1, (3::nat)]}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1118 |
|
36040
fcd7bea01a93
adding skip_proof in the examples because proof procedure cannot handle alternative compilations yet
bulwahn
parents:
35954
diff
changeset
|
1119 |
code_pred [inductify, skip_proof] List.rev . |
35950
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1120 |
code_pred [inductify] map . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1121 |
code_pred [inductify] foldr . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1122 |
code_pred [inductify] foldl . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1123 |
code_pred [inductify] filter . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1124 |
code_pred [random_dseq inductify] filter . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1125 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1126 |
subsection {* Context Free Grammar *} |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1127 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1128 |
datatype alphabet = a | b |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1129 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1130 |
inductive_set S\<^isub>1 and A\<^isub>1 and B\<^isub>1 where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1131 |
"[] \<in> S\<^isub>1" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1132 |
| "w \<in> A\<^isub>1 \<Longrightarrow> b # w \<in> S\<^isub>1" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1133 |
| "w \<in> B\<^isub>1 \<Longrightarrow> a # w \<in> S\<^isub>1" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1134 |
| "w \<in> S\<^isub>1 \<Longrightarrow> a # w \<in> A\<^isub>1" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1135 |
| "w \<in> S\<^isub>1 \<Longrightarrow> b # w \<in> S\<^isub>1" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1136 |
| "\<lbrakk>v \<in> B\<^isub>1; v \<in> B\<^isub>1\<rbrakk> \<Longrightarrow> a # v @ w \<in> B\<^isub>1" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1137 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1138 |
code_pred [inductify] S\<^isub>1p . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1139 |
code_pred [random_dseq inductify] S\<^isub>1p . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1140 |
thm S\<^isub>1p.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1141 |
thm S\<^isub>1p.random_dseq_equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1142 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1143 |
values [random_dseq 5, 5, 5] 5 "{x. S\<^isub>1p x}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1144 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1145 |
inductive_set S\<^isub>2 and A\<^isub>2 and B\<^isub>2 where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1146 |
"[] \<in> S\<^isub>2" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1147 |
| "w \<in> A\<^isub>2 \<Longrightarrow> b # w \<in> S\<^isub>2" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1148 |
| "w \<in> B\<^isub>2 \<Longrightarrow> a # w \<in> S\<^isub>2" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1149 |
| "w \<in> S\<^isub>2 \<Longrightarrow> a # w \<in> A\<^isub>2" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1150 |
| "w \<in> S\<^isub>2 \<Longrightarrow> b # w \<in> B\<^isub>2" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1151 |
| "\<lbrakk>v \<in> B\<^isub>2; v \<in> B\<^isub>2\<rbrakk> \<Longrightarrow> a # v @ w \<in> B\<^isub>2" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1152 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1153 |
code_pred [random_dseq inductify] S\<^isub>2p . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1154 |
thm S\<^isub>2p.random_dseq_equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1155 |
thm A\<^isub>2p.random_dseq_equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1156 |
thm B\<^isub>2p.random_dseq_equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1157 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1158 |
values [random_dseq 5, 5, 5] 10 "{x. S\<^isub>2p x}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1159 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1160 |
inductive_set S\<^isub>3 and A\<^isub>3 and B\<^isub>3 where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1161 |
"[] \<in> S\<^isub>3" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1162 |
| "w \<in> A\<^isub>3 \<Longrightarrow> b # w \<in> S\<^isub>3" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1163 |
| "w \<in> B\<^isub>3 \<Longrightarrow> a # w \<in> S\<^isub>3" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1164 |
| "w \<in> S\<^isub>3 \<Longrightarrow> a # w \<in> A\<^isub>3" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1165 |
| "w \<in> S\<^isub>3 \<Longrightarrow> b # w \<in> B\<^isub>3" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1166 |
| "\<lbrakk>v \<in> B\<^isub>3; w \<in> B\<^isub>3\<rbrakk> \<Longrightarrow> a # v @ w \<in> B\<^isub>3" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1167 |
|
36040
fcd7bea01a93
adding skip_proof in the examples because proof procedure cannot handle alternative compilations yet
bulwahn
parents:
35954
diff
changeset
|
1168 |
code_pred [inductify, skip_proof] S\<^isub>3p . |
35950
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1169 |
thm S\<^isub>3p.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1170 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1171 |
values 10 "{x. S\<^isub>3p x}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1172 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1173 |
inductive_set S\<^isub>4 and A\<^isub>4 and B\<^isub>4 where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1174 |
"[] \<in> S\<^isub>4" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1175 |
| "w \<in> A\<^isub>4 \<Longrightarrow> b # w \<in> S\<^isub>4" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1176 |
| "w \<in> B\<^isub>4 \<Longrightarrow> a # w \<in> S\<^isub>4" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1177 |
| "w \<in> S\<^isub>4 \<Longrightarrow> a # w \<in> A\<^isub>4" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1178 |
| "\<lbrakk>v \<in> A\<^isub>4; w \<in> A\<^isub>4\<rbrakk> \<Longrightarrow> b # v @ w \<in> A\<^isub>4" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1179 |
| "w \<in> S\<^isub>4 \<Longrightarrow> b # w \<in> B\<^isub>4" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1180 |
| "\<lbrakk>v \<in> B\<^isub>4; w \<in> B\<^isub>4\<rbrakk> \<Longrightarrow> a # v @ w \<in> B\<^isub>4" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1181 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1182 |
code_pred (expected_modes: o => bool, i => bool) S\<^isub>4p . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1183 |
|
36176
3fe7e97ccca8
replaced generic 'hide' command by more conventional 'hide_class', 'hide_type', 'hide_const', 'hide_fact' -- frees some popular keywords;
wenzelm
parents:
36055
diff
changeset
|
1184 |
hide_const a b |
36055
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1185 |
|
35950
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1186 |
subsection {* Lambda *} |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1187 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1188 |
datatype type = |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1189 |
Atom nat |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1190 |
| Fun type type (infixr "\<Rightarrow>" 200) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1191 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1192 |
datatype dB = |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1193 |
Var nat |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1194 |
| App dB dB (infixl "\<degree>" 200) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1195 |
| Abs type dB |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1196 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1197 |
primrec |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1198 |
nth_el :: "'a list \<Rightarrow> nat \<Rightarrow> 'a option" ("_\<langle>_\<rangle>" [90, 0] 91) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1199 |
where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1200 |
"[]\<langle>i\<rangle> = None" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1201 |
| "(x # xs)\<langle>i\<rangle> = (case i of 0 \<Rightarrow> Some x | Suc j \<Rightarrow> xs \<langle>j\<rangle>)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1202 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1203 |
inductive nth_el' :: "'a list \<Rightarrow> nat \<Rightarrow> 'a \<Rightarrow> bool" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1204 |
where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1205 |
"nth_el' (x # xs) 0 x" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1206 |
| "nth_el' xs i y \<Longrightarrow> nth_el' (x # xs) (Suc i) y" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1207 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1208 |
inductive typing :: "type list \<Rightarrow> dB \<Rightarrow> type \<Rightarrow> bool" ("_ \<turnstile> _ : _" [50, 50, 50] 50) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1209 |
where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1210 |
Var [intro!]: "nth_el' env x T \<Longrightarrow> env \<turnstile> Var x : T" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1211 |
| Abs [intro!]: "T # env \<turnstile> t : U \<Longrightarrow> env \<turnstile> Abs T t : (T \<Rightarrow> U)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1212 |
| App [intro!]: "env \<turnstile> s : T \<Rightarrow> U \<Longrightarrow> env \<turnstile> t : T \<Longrightarrow> env \<turnstile> (s \<degree> t) : U" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1213 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1214 |
primrec |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1215 |
lift :: "[dB, nat] => dB" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1216 |
where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1217 |
"lift (Var i) k = (if i < k then Var i else Var (i + 1))" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1218 |
| "lift (s \<degree> t) k = lift s k \<degree> lift t k" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1219 |
| "lift (Abs T s) k = Abs T (lift s (k + 1))" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1220 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1221 |
primrec |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1222 |
subst :: "[dB, dB, nat] => dB" ("_[_'/_]" [300, 0, 0] 300) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1223 |
where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1224 |
subst_Var: "(Var i)[s/k] = |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1225 |
(if k < i then Var (i - 1) else if i = k then s else Var i)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1226 |
| subst_App: "(t \<degree> u)[s/k] = t[s/k] \<degree> u[s/k]" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1227 |
| subst_Abs: "(Abs T t)[s/k] = Abs T (t[lift s 0 / k+1])" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1228 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1229 |
inductive beta :: "[dB, dB] => bool" (infixl "\<rightarrow>\<^sub>\<beta>" 50) |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1230 |
where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1231 |
beta [simp, intro!]: "Abs T s \<degree> t \<rightarrow>\<^sub>\<beta> s[t/0]" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1232 |
| appL [simp, intro!]: "s \<rightarrow>\<^sub>\<beta> t ==> s \<degree> u \<rightarrow>\<^sub>\<beta> t \<degree> u" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1233 |
| appR [simp, intro!]: "s \<rightarrow>\<^sub>\<beta> t ==> u \<degree> s \<rightarrow>\<^sub>\<beta> u \<degree> t" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1234 |
| abs [simp, intro!]: "s \<rightarrow>\<^sub>\<beta> t ==> Abs T s \<rightarrow>\<^sub>\<beta> Abs T t" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1235 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1236 |
code_pred (expected_modes: i => i => o => bool, i => i => i => bool) typing . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1237 |
thm typing.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1238 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1239 |
code_pred (modes: i => i => bool, i => o => bool as reduce') beta . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1240 |
thm beta.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1241 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1242 |
values "{x. App (Abs (Atom 0) (Var 0)) (Var 1) \<rightarrow>\<^sub>\<beta> x}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1243 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1244 |
definition "reduce t = Predicate.the (reduce' t)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1245 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1246 |
value "reduce (App (Abs (Atom 0) (Var 0)) (Var 1))" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1247 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1248 |
code_pred [dseq] typing . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1249 |
code_pred [random_dseq] typing . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1250 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1251 |
values [random_dseq 1,1,5] 10 "{(\<Gamma>, t, T). \<Gamma> \<turnstile> t : T}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1252 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1253 |
subsection {* A minimal example of yet another semantics *} |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1254 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1255 |
text {* thanks to Elke Salecker *} |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1256 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1257 |
types |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1258 |
vname = nat |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1259 |
vvalue = int |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1260 |
var_assign = "vname \<Rightarrow> vvalue" --"variable assignment" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1261 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1262 |
datatype ir_expr = |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1263 |
IrConst vvalue |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1264 |
| ObjAddr vname |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1265 |
| Add ir_expr ir_expr |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1266 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1267 |
datatype val = |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1268 |
IntVal vvalue |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1269 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1270 |
record configuration = |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1271 |
Env :: var_assign |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1272 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1273 |
inductive eval_var :: |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1274 |
"ir_expr \<Rightarrow> configuration \<Rightarrow> val \<Rightarrow> bool" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1275 |
where |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1276 |
irconst: "eval_var (IrConst i) conf (IntVal i)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1277 |
| objaddr: "\<lbrakk> Env conf n = i \<rbrakk> \<Longrightarrow> eval_var (ObjAddr n) conf (IntVal i)" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1278 |
| plus: "\<lbrakk> eval_var l conf (IntVal vl); eval_var r conf (IntVal vr) \<rbrakk> \<Longrightarrow> eval_var (Add l r) conf (IntVal (vl+vr))" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1279 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1280 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1281 |
code_pred eval_var . |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1282 |
thm eval_var.equation |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1283 |
|
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1284 |
values "{val. eval_var (Add (IrConst 1) (IrConst 2)) (| Env = (\<lambda>x. 0)|) val}" |
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1285 |
|
36055
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1286 |
section {* Function predicate replacement *} |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1287 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1288 |
text {* |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1289 |
If the mode analysis uses the functional mode, we |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1290 |
replace predicates that resulted from functions again by their functions. |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1291 |
*} |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1292 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1293 |
inductive test_append |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1294 |
where |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1295 |
"List.append xs ys = zs ==> test_append xs ys zs" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1296 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1297 |
code_pred [inductify, skip_proof] test_append . |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1298 |
thm test_append.equation |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1299 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1300 |
text {* If append is not turned into a predicate, then the mode |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1301 |
o => o => i => bool could not be inferred. *} |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1302 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1303 |
values 4 "{(xs::int list, ys). test_append xs ys [1, 2, 3, 4]}" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1304 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1305 |
text {* If appendP is not reverted back to a function, then mode i => i => o => bool |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1306 |
fails after deleting the predicate equation. *} |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1307 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1308 |
declare appendP.equation[code del] |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1309 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1310 |
values "{xs::int list. test_append [1,2] [3,4] xs}" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1311 |
values "{xs::int list. test_append (replicate 1000 1) (replicate 1000 2) xs}" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1312 |
values "{xs::int list. test_append (replicate 2000 1) (replicate 2000 2) xs}" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1313 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1314 |
subsection {* Function with tuples *} |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1315 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1316 |
fun append' |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1317 |
where |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1318 |
"append' ([], ys) = ys" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1319 |
| "append' (x # xs, ys) = x # append' (xs, ys)" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1320 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1321 |
inductive test_append' |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1322 |
where |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1323 |
"append' (xs, ys) = zs ==> test_append' xs ys zs" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1324 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1325 |
code_pred [inductify, skip_proof] test_append' . |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1326 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1327 |
thm test_append'.equation |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1328 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1329 |
values "{(xs::int list, ys). test_append' xs ys [1, 2, 3, 4]}" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1330 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1331 |
declare append'P.equation[code del] |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1332 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1333 |
values "{zs :: int list. test_append' [1,2,3] [4,5] zs}" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1334 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1335 |
section {* Arithmetic examples *} |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1336 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1337 |
subsection {* Examples on nat *} |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1338 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1339 |
inductive plus_nat_test :: "nat => nat => nat => bool" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1340 |
where |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1341 |
"x + y = z ==> plus_nat_test x y z" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1342 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1343 |
code_pred [inductify, skip_proof] plus_nat_test . |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1344 |
code_pred [new_random_dseq inductify] plus_nat_test . |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1345 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1346 |
thm plus_nat_test.equation |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1347 |
thm plus_nat_test.new_random_dseq_equation |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1348 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1349 |
values [expected "{9::nat}"] "{z. plus_nat_test 4 5 z}" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1350 |
values [expected "{9::nat}"] "{z. plus_nat_test 7 2 z}" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1351 |
values [expected "{4::nat}"] "{y. plus_nat_test 5 y 9}" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1352 |
values [expected "{}"] "{y. plus_nat_test 9 y 8}" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1353 |
values [expected "{6::nat}"] "{y. plus_nat_test 1 y 7}" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1354 |
values [expected "{2::nat}"] "{x. plus_nat_test x 7 9}" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1355 |
values [expected "{}"] "{x. plus_nat_test x 9 7}" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1356 |
values [expected "{(0::nat,0::nat)}"] "{(x, y). plus_nat_test x y 0}" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1357 |
values [expected "{(0, Suc 0), (Suc 0, 0)}"] "{(x, y). plus_nat_test x y 1}" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1358 |
values [expected "{(0, 5), (4, Suc 0), (3, 2), (2, 3), (Suc 0, 4), (5, 0)}"] |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1359 |
"{(x, y). plus_nat_test x y 5}" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1360 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1361 |
inductive minus_nat_test :: "nat => nat => nat => bool" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1362 |
where |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1363 |
"x - y = z ==> minus_nat_test x y z" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1364 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1365 |
code_pred [inductify, skip_proof] minus_nat_test . |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1366 |
code_pred [new_random_dseq inductify] minus_nat_test . |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1367 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1368 |
thm minus_nat_test.equation |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1369 |
thm minus_nat_test.new_random_dseq_equation |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1370 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1371 |
values [expected "{0::nat}"] "{z. minus_nat_test 4 5 z}" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1372 |
values [expected "{5::nat}"] "{z. minus_nat_test 7 2 z}" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1373 |
values [expected "{16::nat}"] "{x. minus_nat_test x 7 9}" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1374 |
values [expected "{16::nat}"] "{x. minus_nat_test x 9 7}" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1375 |
values [expected "{0, Suc 0, 2, 3}"] "{x. minus_nat_test x 3 0}" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1376 |
values [expected "{0::nat}"] "{x. minus_nat_test x 0 0}" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1377 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1378 |
subsection {* Examples on int *} |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1379 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1380 |
inductive plus_int_test :: "int => int => int => bool" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1381 |
where |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1382 |
"a + b = c ==> plus_int_test a b c" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1383 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1384 |
code_pred [inductify, skip_proof] plus_int_test . |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1385 |
code_pred [new_random_dseq inductify] plus_int_test . |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1386 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1387 |
thm plus_int_test.equation |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1388 |
thm plus_int_test.new_random_dseq_equation |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1389 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1390 |
values [expected "{1::int}"] "{a. plus_int_test a 6 7}" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1391 |
values [expected "{1::int}"] "{b. plus_int_test 6 b 7}" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1392 |
values [expected "{11::int}"] "{c. plus_int_test 5 6 c}" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1393 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1394 |
inductive minus_int_test :: "int => int => int => bool" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1395 |
where |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1396 |
"a - b = c ==> minus_int_test a b c" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1397 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1398 |
code_pred [inductify, skip_proof] minus_int_test . |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1399 |
code_pred [new_random_dseq inductify] minus_int_test . |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1400 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1401 |
thm minus_int_test.equation |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1402 |
thm minus_int_test.new_random_dseq_equation |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1403 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1404 |
values [expected "{4::int}"] "{c. minus_int_test 9 5 c}" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1405 |
values [expected "{9::int}"] "{a. minus_int_test a 4 5}" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1406 |
values [expected "{- 1::int}"] "{b. minus_int_test 4 b 5}" |
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1407 |
|
36253
6e969ce3dfcc
added further inlining of boolean constants to the predicate compiler
bulwahn
parents:
36176
diff
changeset
|
1408 |
subsection {* minus on bool *} |
6e969ce3dfcc
added further inlining of boolean constants to the predicate compiler
bulwahn
parents:
36176
diff
changeset
|
1409 |
|
6e969ce3dfcc
added further inlining of boolean constants to the predicate compiler
bulwahn
parents:
36176
diff
changeset
|
1410 |
inductive All :: "nat => bool" |
6e969ce3dfcc
added further inlining of boolean constants to the predicate compiler
bulwahn
parents:
36176
diff
changeset
|
1411 |
where |
6e969ce3dfcc
added further inlining of boolean constants to the predicate compiler
bulwahn
parents:
36176
diff
changeset
|
1412 |
"All x" |
6e969ce3dfcc
added further inlining of boolean constants to the predicate compiler
bulwahn
parents:
36176
diff
changeset
|
1413 |
|
6e969ce3dfcc
added further inlining of boolean constants to the predicate compiler
bulwahn
parents:
36176
diff
changeset
|
1414 |
inductive None :: "nat => bool" |
6e969ce3dfcc
added further inlining of boolean constants to the predicate compiler
bulwahn
parents:
36176
diff
changeset
|
1415 |
|
6e969ce3dfcc
added further inlining of boolean constants to the predicate compiler
bulwahn
parents:
36176
diff
changeset
|
1416 |
definition "test_minus_bool x = (None x - All x)" |
6e969ce3dfcc
added further inlining of boolean constants to the predicate compiler
bulwahn
parents:
36176
diff
changeset
|
1417 |
|
6e969ce3dfcc
added further inlining of boolean constants to the predicate compiler
bulwahn
parents:
36176
diff
changeset
|
1418 |
code_pred [inductify] test_minus_bool . |
6e969ce3dfcc
added further inlining of boolean constants to the predicate compiler
bulwahn
parents:
36176
diff
changeset
|
1419 |
thm test_minus_bool.equation |
6e969ce3dfcc
added further inlining of boolean constants to the predicate compiler
bulwahn
parents:
36176
diff
changeset
|
1420 |
|
6e969ce3dfcc
added further inlining of boolean constants to the predicate compiler
bulwahn
parents:
36176
diff
changeset
|
1421 |
values "{x. test_minus_bool x}" |
36055
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1422 |
|
36260 | 1423 |
subsection {* Examples for detecting switches *} |
1424 |
||
1425 |
inductive detect_switches1 where |
|
1426 |
"detect_switches1 [] []" |
|
1427 |
| "detect_switches1 (x # xs) (y # ys)" |
|
1428 |
||
1429 |
code_pred [detect_switches, skip_proof] detect_switches1 . |
|
1430 |
||
1431 |
thm detect_switches1.equation |
|
1432 |
||
1433 |
inductive detect_switches2 :: "('a => bool) => bool" |
|
1434 |
where |
|
1435 |
"detect_switches2 P" |
|
1436 |
||
1437 |
code_pred [detect_switches, skip_proof] detect_switches2 . |
|
1438 |
thm detect_switches2.equation |
|
1439 |
||
1440 |
inductive detect_switches3 :: "('a => bool) => 'a list => bool" |
|
1441 |
where |
|
1442 |
"detect_switches3 P []" |
|
1443 |
| "detect_switches3 P (x # xs)" |
|
1444 |
||
1445 |
code_pred [detect_switches, skip_proof] detect_switches3 . |
|
1446 |
||
1447 |
thm detect_switches3.equation |
|
1448 |
||
1449 |
inductive detect_switches4 :: "('a => bool) => 'a list => 'a list => bool" |
|
1450 |
where |
|
1451 |
"detect_switches4 P [] []" |
|
1452 |
| "detect_switches4 P (x # xs) (y # ys)" |
|
1453 |
||
1454 |
code_pred [detect_switches, skip_proof] detect_switches4 . |
|
1455 |
thm detect_switches4.equation |
|
1456 |
||
1457 |
inductive detect_switches5 :: "('a => 'a => bool) => 'a list => 'a list => bool" |
|
1458 |
where |
|
1459 |
"detect_switches5 P [] []" |
|
1460 |
| "detect_switches5 P xs ys ==> P x y ==> detect_switches5 P (x # xs) (y # ys)" |
|
1461 |
||
1462 |
code_pred [detect_switches, skip_proof] detect_switches5 . |
|
1463 |
||
1464 |
thm detect_switches5.equation |
|
1465 |
||
1466 |
inductive detect_switches6 :: "(('a => 'b => bool) * 'a list * 'b list) => bool" |
|
1467 |
where |
|
1468 |
"detect_switches6 (P, [], [])" |
|
1469 |
| "detect_switches6 (P, xs, ys) ==> P x y ==> detect_switches6 (P, x # xs, y # ys)" |
|
1470 |
||
1471 |
code_pred [detect_switches, skip_proof] detect_switches6 . |
|
1472 |
||
1473 |
inductive detect_switches7 :: "('a => bool) => ('b => bool) => ('a * 'b list) => bool" |
|
1474 |
where |
|
1475 |
"detect_switches7 P Q (a, [])" |
|
1476 |
| "P a ==> Q x ==> detect_switches7 P Q (a, x#xs)" |
|
1477 |
||
1478 |
code_pred [skip_proof] detect_switches7 . |
|
1479 |
||
1480 |
thm detect_switches7.equation |
|
1481 |
||
1482 |
inductive detect_switches8 :: "nat => bool" |
|
1483 |
where |
|
1484 |
"detect_switches8 0" |
|
1485 |
| "x mod 2 = 0 ==> detect_switches8 (Suc x)" |
|
1486 |
||
1487 |
code_pred [detect_switches, skip_proof] detect_switches8 . |
|
1488 |
||
1489 |
thm detect_switches8.equation |
|
1490 |
||
1491 |
inductive detect_switches9 :: "nat => nat => bool" |
|
1492 |
where |
|
1493 |
"detect_switches9 0 0" |
|
1494 |
| "detect_switches9 0 (Suc x)" |
|
1495 |
| "detect_switches9 (Suc x) 0" |
|
1496 |
| "x = y ==> detect_switches9 (Suc x) (Suc y)" |
|
1497 |
| "c1 = c2 ==> detect_switches9 c1 c2" |
|
1498 |
||
1499 |
code_pred [detect_switches, skip_proof] detect_switches9 . |
|
1500 |
||
1501 |
thm detect_switches9.equation |
|
1502 |
||
36055
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1503 |
|
537876d0fa62
adding examples of function predicate replacement and arithmetic examples for the predicate compiler; tuned
bulwahn
parents:
36040
diff
changeset
|
1504 |
|
35950
791ce568d40a
moved examples for the predicate compiler into its own session Predicate_Compile_Examples to slenderise the HOL-ex session
bulwahn
parents:
diff
changeset
|
1505 |
end |