1 theory Examples |
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2 imports Spec_Check |
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3 begin |
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4 |
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5 section {* List examples *} |
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6 |
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7 ML_command {* |
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8 check_property "ALL xs. rev xs = xs"; |
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9 *} |
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10 |
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11 ML_command {* |
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12 check_property "ALL xs. rev (rev xs) = xs"; |
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13 *} |
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14 |
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15 |
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16 section {* AList Specification *} |
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17 |
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18 ML_command {* |
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19 (* map_entry applies the function to the element *) |
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20 check_property "ALL k f xs. AList.lookup (op =) (AList.map_entry (op =) k f xs) k = Option.map f (AList.lookup (op =) xs k)"; |
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21 *} |
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22 |
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23 ML_command {* |
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24 (* update always results in an entry *) |
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25 check_property "ALL k v xs. AList.defined (op =) (AList.update (op =) (k, v) xs) k"; |
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26 *} |
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27 |
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28 ML_command {* |
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29 (* update always writes the value *) |
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30 check_property "ALL k v xs. AList.lookup (op =) (AList.update (op =) (k, v) xs) k = SOME v"; |
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31 *} |
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32 |
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33 ML_command {* |
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34 (* default always results in an entry *) |
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35 check_property "ALL k v xs. AList.defined (op =) (AList.default (op =) (k, v) xs) k"; |
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36 *} |
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37 |
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38 ML_command {* |
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39 (* delete always removes the entry *) |
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40 check_property "ALL k xs. not (AList.defined (op =) (AList.delete (op =) k xs) k)"; |
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41 *} |
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42 |
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43 ML_command {* |
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44 (* default writes the entry iff it didn't exist *) |
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45 check_property "ALL k v xs. (AList.lookup (op =) (AList.default (op =) (k, v) xs) k = (if AList.defined (op =) xs k then AList.lookup (op =) xs k else SOME v))"; |
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46 *} |
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47 |
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48 section {* Examples on Types and Terms *} |
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49 |
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50 ML_command {* |
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51 check_property "ALL f g t. map_types (g o f) t = (map_types f o map_types g) t"; |
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52 *} |
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53 |
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54 ML_command {* |
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55 check_property "ALL f g t. map_types (f o g) t = (map_types f o map_types g) t"; |
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56 *} |
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57 |
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58 |
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59 text {* One would think this holds: *} |
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60 |
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61 ML_command {* |
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62 check_property "ALL t ts. strip_comb (list_comb (t, ts)) = (t, ts)" |
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63 *} |
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64 |
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65 text {* But it only holds with this precondition: *} |
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66 |
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67 ML_command {* |
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68 check_property "ALL t ts. case t of _ $ _ => true | _ => strip_comb (list_comb (t, ts)) = (t, ts)" |
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69 *} |
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70 |
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71 section {* Some surprises *} |
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72 |
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73 ML_command {* |
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74 check_property "ALL Ts t. type_of1 (Ts, t) = fastype_of1 (Ts, t)" |
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75 *} |
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76 |
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77 |
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78 ML_command {* |
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79 val thy = @{theory}; |
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80 check_property "ALL t u. if Pattern.matches thy (t, u) then Term.could_unify (t, u) else true" |
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81 *} |
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82 |
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83 end |
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