author | bulwahn |
Fri, 11 Mar 2011 10:37:38 +0100 | |
changeset 41909 | 383bbdad1650 |
parent 41908 | 3bd9a21366d2 |
child 41910 | 709c04e7b703 |
permissions | -rw-r--r-- |
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(* Author: Lukas Bulwahn, TU Muenchen *) |
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header {* Counterexample generator based on LazySmallCheck *} |
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theory LSC |
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imports Main "~~/src/HOL/Library/Code_Char" |
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uses ("~~/src/HOL/Tools/LSC/lazysmallcheck.ML") |
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begin |
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subsection {* Counterexample generator *} |
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subsubsection {* Code generation setup *} |
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code_type typerep |
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("Haskell" "Typerep") |
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code_const Typerep.Typerep |
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("Haskell" "Typerep") |
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code_reserved Haskell Typerep |
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subsubsection {* Type code_int for Haskell's Int type *} |
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typedef (open) code_int = "UNIV \<Colon> int set" |
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morphisms int_of of_int by rule |
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lemma int_of_inject [simp]: |
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"int_of k = int_of l \<longleftrightarrow> k = l" |
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by (rule int_of_inject) |
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instantiation code_int :: "{zero, one, minus, linorder}" |
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begin |
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definition [simp, code del]: |
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"0 = of_int 0" |
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definition [simp, code del]: |
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"1 = of_int 1" |
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definition [simp, code del]: |
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"n - m = of_int (int_of n - int_of m)" |
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definition [simp, code del]: |
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"n \<le> m \<longleftrightarrow> int_of n \<le> int_of m" |
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definition [simp, code del]: |
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"n < m \<longleftrightarrow> int_of n < int_of m" |
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instance proof qed (auto) |
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end |
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(* |
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lemma zero_code_int_code [code, code_unfold]: |
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"(0\<Colon>code_int) = Numeral0" |
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by (simp add: number_of_code_numeral_def Pls_def) |
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lemma [code_post]: "Numeral0 = (0\<Colon>code_numeral)" |
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using zero_code_numeral_code .. |
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lemma one_code_numeral_code [code, code_unfold]: |
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"(1\<Colon>code_int) = Numeral1" |
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by (simp add: number_of_code_numeral_def Pls_def Bit1_def) |
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lemma [code_post]: "Numeral1 = (1\<Colon>code_int)" |
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using one_code_numeral_code .. |
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*) |
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code_const "0 \<Colon> code_int" |
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(Haskell "0") |
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code_const "1 \<Colon> code_int" |
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(Haskell "1") |
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code_const "minus \<Colon> code_int \<Rightarrow> code_int \<Rightarrow> code_int" |
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(Haskell "(_/ -/ _)") |
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code_const "op \<le> \<Colon> code_int \<Rightarrow> code_int \<Rightarrow> bool" |
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(Haskell infix 4 "<=") |
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code_const "op < \<Colon> code_int \<Rightarrow> code_int \<Rightarrow> bool" |
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(Haskell infix 4 "<") |
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code_type code_int |
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(Haskell "Int") |
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subsubsection {* LSC's deep representation of types of terms *} |
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datatype type = SumOfProd "type list list" |
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datatype "term" = Var "code_int list" type | Ctr code_int "term list" |
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datatype 'a cons = C type "(term list => 'a) list" |
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subsubsection {* auxilary functions for LSC *} |
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consts nth :: "'a list => code_int => 'a" |
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code_const nth ("Haskell" infixl 9 "!!") |
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consts error :: "char list => 'a" |
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code_const error ("Haskell" "error") |
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consts toEnum :: "code_int => char" |
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code_const toEnum ("Haskell" "toEnum") |
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consts map_index :: "(code_int * 'a => 'b) => 'a list => 'b list" |
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consts split_At :: "code_int => 'a list => 'a list * 'a list" |
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subsubsection {* LSC's basic operations *} |
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type_synonym 'a series = "code_int => 'a cons" |
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definition empty :: "'a series" |
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where |
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"empty d = C (SumOfProd []) []" |
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definition cons :: "'a => 'a series" |
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where |
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"cons a d = (C (SumOfProd [[]]) [(%_. a)])" |
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fun conv :: "(term list => 'a) list => term => 'a" |
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where |
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"conv cs (Var p _) = error (Char Nibble0 Nibble0 # map toEnum p)" |
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| "conv cs (Ctr i xs) = (nth cs i) xs" |
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fun nonEmpty :: "type => bool" |
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where |
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"nonEmpty (SumOfProd ps) = (\<not> (List.null ps))" |
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definition "apply" :: "('a => 'b) series => 'a series => 'b series" |
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where |
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"apply f a d = |
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(case f d of C (SumOfProd ps) cfs => |
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case a (d - 1) of C ta cas => |
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let |
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shallow = (d > 0 \<and> nonEmpty ta); |
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cs = [(%xs'. (case xs' of [] => undefined | x # xs => cf xs (conv cas x))). shallow, cf <- cfs] |
|
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in C (SumOfProd [ta # p. shallow, p <- ps]) cs)" |
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142 |
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definition sum :: "'a series => 'a series => 'a series" |
|
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where |
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"sum a b d = |
|
146 |
(case a d of C (SumOfProd ssa) ca => |
|
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case b d of C (SumOfProd ssb) cb => |
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C (SumOfProd (ssa @ ssb)) (ca @ cb))" |
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149 |
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definition cons0 :: "'a => 'a series" |
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where |
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"cons0 f = cons f" |
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type_synonym pos = "code_int list" |
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155 |
|
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subsubsection {* Term refinement *} |
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157 |
|
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definition new :: "pos => type list list => term list" |
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where |
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"new p ps = map_index (%(c, ts). Ctr c (map_index (%(i, t). Var (p @ [i]) t) ts)) ps" |
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161 |
|
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fun refine :: "term => pos => term list" and refineList :: "term list => pos => (term list) list" |
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where |
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"refine (Var p (SumOfProd ss)) [] = new p ss" |
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| "refine (Ctr c xs) p = map (Ctr c) (refineList xs p)" |
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166 |
| "refineList xs (i # is) = (let (ls, xrs) = split_At i xs in (case xrs of x#rs => [ls @ y # rs. y <- refine x is]))" |
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167 |
|
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text {* Find total instantiations of a partial value *} |
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169 |
|
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function total :: "term => term list" |
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171 |
where |
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"total (Ctr c xs) = [Ctr c ys. ys <- map total xs]" |
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173 |
| "total (Var p (SumOfProd ss)) = [y. x <- new p ss, y <- total x]" |
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by pat_completeness auto |
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175 |
|
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termination sorry |
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|
178 |
subsubsection {* LSC's type class for enumeration *} |
|
179 |
||
180 |
class serial = |
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fixes series :: "code_int => 'a cons" |
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|
183 |
definition cons1 :: "('a::serial => 'b) => 'b series" |
|
184 |
where |
|
185 |
"cons1 f = apply (cons f) series" |
|
186 |
||
187 |
definition cons2 :: "('a :: serial => 'b :: serial => 'c) => 'c series" |
|
188 |
where |
|
189 |
"cons2 f = apply (apply (cons f) series) series" |
|
190 |
||
191 |
instantiation unit :: serial |
|
192 |
begin |
|
193 |
||
194 |
definition |
|
195 |
"series = cons0 ()" |
|
196 |
||
197 |
instance .. |
|
198 |
||
199 |
end |
|
200 |
||
201 |
instantiation bool :: serial |
|
202 |
begin |
|
203 |
||
204 |
definition |
|
205 |
"series = sum (cons0 True) (cons0 False)" |
|
206 |
||
207 |
instance .. |
|
208 |
||
209 |
end |
|
210 |
||
211 |
instantiation option :: (serial) serial |
|
212 |
begin |
|
213 |
||
214 |
definition |
|
215 |
"series = sum (cons0 None) (cons1 Some)" |
|
216 |
||
217 |
instance .. |
|
218 |
||
219 |
end |
|
220 |
||
221 |
instantiation sum :: (serial, serial) serial |
|
222 |
begin |
|
223 |
||
224 |
definition |
|
225 |
"series = sum (cons1 Inl) (cons1 Inr)" |
|
226 |
||
227 |
instance .. |
|
228 |
||
229 |
end |
|
230 |
||
231 |
instantiation list :: (serial) serial |
|
232 |
begin |
|
233 |
||
234 |
function series_list :: "'a list series" |
|
235 |
where |
|
236 |
"series_list d = sum (cons []) (apply (apply (cons Cons) series) series_list) d" |
|
237 |
by pat_completeness auto |
|
238 |
||
239 |
termination sorry |
|
240 |
||
241 |
instance .. |
|
242 |
||
243 |
end |
|
244 |
||
245 |
instantiation nat :: serial |
|
246 |
begin |
|
247 |
||
248 |
function series_nat :: "nat series" |
|
249 |
where |
|
250 |
"series_nat d = sum (cons 0) (apply (cons Suc) series_nat) d" |
|
251 |
by pat_completeness auto |
|
252 |
||
253 |
termination sorry |
|
254 |
||
255 |
instance .. |
|
256 |
||
257 |
end |
|
258 |
||
259 |
instantiation Enum.finite_1 :: serial |
|
260 |
begin |
|
261 |
||
262 |
definition series_finite_1 :: "Enum.finite_1 series" |
|
263 |
where |
|
264 |
"series_finite_1 = cons (Enum.finite_1.a\<^isub>1 :: Enum.finite_1)" |
|
265 |
||
266 |
instance .. |
|
267 |
||
268 |
end |
|
269 |
||
270 |
instantiation Enum.finite_2 :: serial |
|
271 |
begin |
|
272 |
||
273 |
definition series_finite_2 :: "Enum.finite_2 series" |
|
274 |
where |
|
275 |
"series_finite_2 = sum (cons (Enum.finite_2.a\<^isub>1 :: Enum.finite_2)) (cons (Enum.finite_2.a\<^isub>2 :: Enum.finite_2))" |
|
276 |
||
277 |
instance .. |
|
278 |
||
279 |
end |
|
280 |
||
281 |
instantiation Enum.finite_3 :: serial |
|
282 |
begin |
|
283 |
||
284 |
definition series_finite_3 :: "Enum.finite_3 series" |
|
285 |
where |
|
286 |
"series_finite_3 = sum (cons (Enum.finite_3.a\<^isub>1 :: Enum.finite_3)) (sum (cons (Enum.finite_3.a\<^isub>2 :: Enum.finite_3)) (cons (Enum.finite_3.a\<^isub>3 :: Enum.finite_3)))" |
|
287 |
||
288 |
instance .. |
|
289 |
||
290 |
end |
|
291 |
||
292 |
subsubsection {* class is_testable *} |
|
293 |
||
294 |
text {* The class is_testable ensures that all necessary type instances are generated. *} |
|
295 |
||
296 |
class is_testable |
|
297 |
||
298 |
instance bool :: is_testable .. |
|
299 |
||
300 |
instance "fun" :: ("{term_of, serial}", is_testable) is_testable .. |
|
301 |
||
302 |
definition ensure_testable :: "'a :: is_testable => 'a :: is_testable" |
|
303 |
where |
|
304 |
"ensure_testable f = f" |
|
305 |
||
306 |
subsubsection {* Setting up the counterexample generator *} |
|
307 |
||
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use "~~/src/HOL/Tools/LSC/lazysmallcheck.ML" |
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|
310 |
setup {* Lazysmallcheck.setup *} |
|
311 |
||
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hide_const (open) empty |
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313 |
|
41905 | 314 |
end |