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1 theory Quick_Reference |
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2 imports Base Main |
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3 begin |
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4 |
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5 chapter {* Isabelle/Isar quick reference \label{ap:refcard} *} |
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6 |
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7 section {* Proof commands *} |
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8 |
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9 subsection {* Primitives and basic syntax *} |
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10 |
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11 text {* |
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12 \begin{tabular}{ll} |
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13 @{command "fix"}~@{text x} & augment context by @{text "\<And>x. \<box>"} \\ |
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14 @{command "assume"}~@{text "a: \<phi>"} & augment context by @{text "\<phi> \<Longrightarrow> \<box>"} \\ |
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15 @{command "then"} & indicate forward chaining of facts \\ |
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16 @{command "have"}~@{text "a: \<phi>"} & prove local result \\ |
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17 @{command "show"}~@{text "a: \<phi>"} & prove local result, refining some goal \\ |
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18 @{command "using"}~@{text a} & indicate use of additional facts \\ |
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19 @{command "unfolding"}~@{text a} & unfold definitional equations \\ |
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20 @{command "proof"}~@{text "m\<^sub>1"}~\dots~@{command "qed"}~@{text "m\<^sub>2"} & indicate proof structure and refinements \\ |
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21 @{command "{"}~@{text "\<dots>"}~@{command "}"} & indicate explicit blocks \\ |
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22 @{command "next"} & switch blocks \\ |
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23 @{command "note"}~@{text "a = b"} & reconsider facts \\ |
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24 @{command "let"}~@{text "p = t"} & abbreviate terms by higher-order matching \\ |
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25 @{command "write"}~@{text "c (mx)"} & declare local mixfix syntax \\ |
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26 \end{tabular} |
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27 |
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28 \medskip |
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29 |
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30 \begin{tabular}{rcl} |
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31 @{text "proof"} & = & @{text "prfx\<^sup>*"}~@{command "proof"}~@{text "method\<^sup>? stmt\<^sup>*"}~@{command "qed"}~@{text "method\<^sup>?"} \\ |
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32 & @{text "|"} & @{text "prfx\<^sup>*"}~@{command "done"} \\ |
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33 @{text prfx} & = & @{command "apply"}~@{text method} \\ |
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34 & @{text "|"} & @{command "using"}~@{text "facts"} \\ |
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35 & @{text "|"} & @{command "unfolding"}~@{text "facts"} \\ |
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36 @{text stmt} & = & @{command "{"}~@{text "stmt\<^sup>*"}~@{command "}"} \\ |
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37 & @{text "|"} & @{command "next"} \\ |
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38 & @{text "|"} & @{command "note"}~@{text "name = facts"} \\ |
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39 & @{text "|"} & @{command "let"}~@{text "term = term"} \\ |
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40 & @{text "|"} & @{command "write"}~@{text "name (mixfix)"} \\ |
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41 & @{text "|"} & @{command "fix"}~@{text "var\<^sup>+"} \\ |
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42 & @{text "|"} & @{command "assume"}~@{text "name: props"} \\ |
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43 & @{text "|"} & @{command "then"}@{text "\<^sup>?"}~@{text goal} \\ |
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44 @{text goal} & = & @{command "have"}~@{text "name: props proof"} \\ |
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45 & @{text "|"} & @{command "show"}~@{text "name: props proof"} \\ |
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46 \end{tabular} |
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47 *} |
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48 |
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49 |
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50 subsection {* Abbreviations and synonyms *} |
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51 |
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52 text {* |
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53 \begin{tabular}{rcl} |
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54 @{command "by"}~@{text "m\<^sub>1 m\<^sub>2"} & @{text "\<equiv>"} & |
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55 @{command "proof"}~@{text "m\<^sub>1"}~@{command "qed"}~@{text "m\<^sub>2"} \\ |
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56 @{command ".."} & @{text "\<equiv>"} & @{command "by"}~@{text rule} \\ |
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57 @{command "."} & @{text "\<equiv>"} & @{command "by"}~@{text this} \\ |
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58 @{command "hence"} & @{text "\<equiv>"} & @{command "then"}~@{command "have"} \\ |
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59 @{command "thus"} & @{text "\<equiv>"} & @{command "then"}~@{command "show"} \\ |
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60 @{command "from"}~@{text a} & @{text "\<equiv>"} & @{command "note"}~@{text a}~@{command "then"} \\ |
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61 @{command "with"}~@{text a} & @{text "\<equiv>"} & @{command "from"}~@{text "a \<AND> this"} \\ |
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62 @{command "from"}~@{text this} & @{text "\<equiv>"} & @{command "then"} \\ |
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63 @{command "from"}~@{text this}~@{command "have"} & @{text "\<equiv>"} & @{command "hence"} \\ |
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64 @{command "from"}~@{text this}~@{command "show"} & @{text "\<equiv>"} & @{command "thus"} \\ |
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65 \end{tabular} |
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66 *} |
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67 |
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68 |
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69 subsection {* Derived elements *} |
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70 |
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71 text {* |
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72 \begin{tabular}{rcl} |
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73 @{command "also"}@{text "\<^sub>0"} & @{text "\<approx>"} & |
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74 @{command "note"}~@{text "calculation = this"} \\ |
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75 @{command "also"}@{text "\<^sub>n\<^sub>+\<^sub>1"} & @{text "\<approx>"} & |
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76 @{command "note"}~@{text "calculation = trans [OF calculation this]"} \\ |
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77 @{command "finally"} & @{text "\<approx>"} & |
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78 @{command "also"}~@{command "from"}~@{text calculation} \\[0.5ex] |
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79 @{command "moreover"} & @{text "\<approx>"} & |
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80 @{command "note"}~@{text "calculation = calculation this"} \\ |
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81 @{command "ultimately"} & @{text "\<approx>"} & |
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82 @{command "moreover"}~@{command "from"}~@{text calculation} \\[0.5ex] |
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83 @{command "presume"}~@{text "a: \<phi>"} & @{text "\<approx>"} & |
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84 @{command "assume"}~@{text "a: \<phi>"} \\ |
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85 @{command "def"}~@{text "a: x \<equiv> t"} & @{text "\<approx>"} & |
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86 @{command "fix"}~@{text x}~@{command "assume"}~@{text "a: x \<equiv> t"} \\ |
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87 @{command "obtain"}~@{text "x \<WHERE> a: \<phi>"} & @{text "\<approx>"} & |
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88 @{text "\<dots>"}~@{command "fix"}~@{text x}~@{command "assume"}~@{text "a: \<phi>"} \\ |
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89 @{command "case"}~@{text c} & @{text "\<approx>"} & |
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90 @{command "fix"}~@{text x}~@{command "assume"}~@{text "c: \<phi>"} \\ |
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91 @{command "sorry"} & @{text "\<approx>"} & |
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92 @{command "by"}~@{text cheating} \\ |
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93 \end{tabular} |
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94 *} |
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95 |
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96 |
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97 subsection {* Diagnostic commands *} |
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98 |
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99 text {* |
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100 \begin{tabular}{ll} |
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101 @{command "pr"} & print current state \\ |
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102 @{command "thm"}~@{text a} & print fact \\ |
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103 @{command "prop"}~@{text \<phi>} & print proposition \\ |
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104 @{command "term"}~@{text t} & print term \\ |
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105 @{command "typ"}~@{text \<tau>} & print type \\ |
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106 \end{tabular} |
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107 *} |
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108 |
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109 |
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110 section {* Proof methods *} |
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111 |
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112 text {* |
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113 \begin{tabular}{ll} |
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114 \multicolumn{2}{l}{\textbf{Single steps (forward-chaining facts)}} \\[0.5ex] |
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115 @{method assumption} & apply some assumption \\ |
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116 @{method this} & apply current facts \\ |
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117 @{method rule}~@{text a} & apply some rule \\ |
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118 @{method rule} & apply standard rule (default for @{command "proof"}) \\ |
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119 @{method contradiction} & apply @{text "\<not>"} elimination rule (any order) \\ |
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120 @{method cases}~@{text t} & case analysis (provides cases) \\ |
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121 @{method induct}~@{text x} & proof by induction (provides cases) \\[2ex] |
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122 |
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123 \multicolumn{2}{l}{\textbf{Repeated steps (inserting facts)}} \\[0.5ex] |
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124 @{method "-"} & no rules \\ |
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125 @{method intro}~@{text a} & introduction rules \\ |
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126 @{method intro_classes} & class introduction rules \\ |
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127 @{method elim}~@{text a} & elimination rules \\ |
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128 @{method unfold}~@{text a} & definitional rewrite rules \\[2ex] |
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129 |
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130 \multicolumn{2}{l}{\textbf{Automated proof tools (inserting facts)}} \\[0.5ex] |
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131 @{method iprover} & intuitionistic proof search \\ |
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132 @{method blast}, @{method fast} & Classical Reasoner \\ |
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133 @{method simp}, @{method simp_all} & Simplifier (+ Splitter) \\ |
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134 @{method auto}, @{method force} & Simplifier + Classical Reasoner \\ |
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135 @{method arith} & Arithmetic procedures \\ |
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136 \end{tabular} |
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137 *} |
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138 |
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139 |
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140 section {* Attributes *} |
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141 |
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142 text {* |
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143 \begin{tabular}{ll} |
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144 \multicolumn{2}{l}{\textbf{Rules}} \\[0.5ex] |
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145 @{attribute OF}~@{text a} & rule resolved with facts (skipping ``@{text _}'') \\ |
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146 @{attribute of}~@{text t} & rule instantiated with terms (skipping ``@{text _}'') \\ |
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147 @{attribute "where"}~@{text "x = t"} & rule instantiated with terms, by variable name \\ |
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148 @{attribute symmetric} & resolution with symmetry rule \\ |
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149 @{attribute THEN}~@{text b} & resolution with another rule \\ |
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150 @{attribute rule_format} & result put into standard rule format \\ |
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151 @{attribute elim_format} & destruct rule turned into elimination rule format \\[1ex] |
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152 |
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153 \multicolumn{2}{l}{\textbf{Declarations}} \\[0.5ex] |
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154 @{attribute simp} & Simplifier rule \\ |
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155 @{attribute intro}, @{attribute elim}, @{attribute dest} & Pure or Classical Reasoner rule \\ |
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156 @{attribute iff} & Simplifier + Classical Reasoner rule \\ |
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157 @{attribute split} & case split rule \\ |
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158 @{attribute trans} & transitivity rule \\ |
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159 @{attribute sym} & symmetry rule \\ |
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160 \end{tabular} |
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161 *} |
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162 |
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163 |
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164 section {* Rule declarations and methods *} |
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165 |
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166 text {* |
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167 \begin{tabular}{l|lllll} |
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168 & @{method rule} & @{method iprover} & @{method blast} & @{method simp} & @{method auto} \\ |
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169 & & & @{method fast} & @{method simp_all} & @{method force} \\ |
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170 \hline |
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171 @{attribute Pure.elim}@{text "!"} @{attribute Pure.intro}@{text "!"} |
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172 & @{text "\<times>"} & @{text "\<times>"} \\ |
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173 @{attribute Pure.elim} @{attribute Pure.intro} |
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174 & @{text "\<times>"} & @{text "\<times>"} \\ |
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175 @{attribute elim}@{text "!"} @{attribute intro}@{text "!"} |
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176 & @{text "\<times>"} & & @{text "\<times>"} & & @{text "\<times>"} \\ |
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177 @{attribute elim} @{attribute intro} |
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178 & @{text "\<times>"} & & @{text "\<times>"} & & @{text "\<times>"} \\ |
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179 @{attribute iff} |
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180 & @{text "\<times>"} & & @{text "\<times>"} & @{text "\<times>"} & @{text "\<times>"} \\ |
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181 @{attribute iff}@{text "?"} |
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182 & @{text "\<times>"} \\ |
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183 @{attribute elim}@{text "?"} @{attribute intro}@{text "?"} |
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184 & @{text "\<times>"} \\ |
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185 @{attribute simp} |
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186 & & & & @{text "\<times>"} & @{text "\<times>"} \\ |
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187 @{attribute cong} |
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188 & & & & @{text "\<times>"} & @{text "\<times>"} \\ |
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189 @{attribute split} |
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190 & & & & @{text "\<times>"} & @{text "\<times>"} \\ |
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191 \end{tabular} |
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192 *} |
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193 |
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194 |
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195 section {* Emulating tactic scripts *} |
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196 |
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197 subsection {* Commands *} |
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198 |
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199 text {* |
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200 \begin{tabular}{ll} |
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201 @{command "apply"}~@{text m} & apply proof method at initial position \\ |
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202 @{command "apply_end"}~@{text m} & apply proof method near terminal position \\ |
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203 @{command "done"} & complete proof \\ |
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204 @{command "defer"}~@{text n} & move subgoal to end \\ |
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205 @{command "prefer"}~@{text n} & move subgoal to beginning \\ |
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206 @{command "back"} & backtrack last command \\ |
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207 \end{tabular} |
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208 *} |
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209 |
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210 |
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211 subsection {* Methods *} |
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212 |
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213 text {* |
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214 \begin{tabular}{ll} |
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215 @{method rule_tac}~@{text insts} & resolution (with instantiation) \\ |
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216 @{method erule_tac}~@{text insts} & elim-resolution (with instantiation) \\ |
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217 @{method drule_tac}~@{text insts} & destruct-resolution (with instantiation) \\ |
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218 @{method frule_tac}~@{text insts} & forward-resolution (with instantiation) \\ |
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219 @{method cut_tac}~@{text insts} & insert facts (with instantiation) \\ |
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220 @{method thin_tac}~@{text \<phi>} & delete assumptions \\ |
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221 @{method subgoal_tac}~@{text \<phi>} & new claims \\ |
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222 @{method rename_tac}~@{text x} & rename innermost goal parameters \\ |
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223 @{method rotate_tac}~@{text n} & rotate assumptions of goal \\ |
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224 @{method tactic}~@{text "text"} & arbitrary ML tactic \\ |
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225 @{method case_tac}~@{text t} & exhaustion (datatypes) \\ |
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226 @{method induct_tac}~@{text x} & induction (datatypes) \\ |
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227 @{method ind_cases}~@{text t} & exhaustion + simplification (inductive predicates) \\ |
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228 \end{tabular} |
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229 *} |
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230 |
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231 end |