1 (* $Id$ *) |
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2 |
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3 theory "syntax" |
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4 imports Pure |
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5 begin |
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6 |
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7 chapter {* Syntax primitives *} |
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8 |
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9 text {* |
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10 The rather generic framework of Isabelle/Isar syntax emerges from |
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11 three main syntactic categories: \emph{commands} of the top-level |
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12 Isar engine (covering theory and proof elements), \emph{methods} for |
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13 general goal refinements (analogous to traditional ``tactics''), and |
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14 \emph{attributes} for operations on facts (within a certain |
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15 context). Subsequently we give a reference of basic syntactic |
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16 entities underlying Isabelle/Isar syntax in a bottom-up manner. |
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17 Concrete theory and proof language elements will be introduced later |
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18 on. |
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19 |
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20 \medskip In order to get started with writing well-formed |
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21 Isabelle/Isar documents, the most important aspect to be noted is |
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22 the difference of \emph{inner} versus \emph{outer} syntax. Inner |
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23 syntax is that of Isabelle types and terms of the logic, while outer |
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24 syntax is that of Isabelle/Isar theory sources (specifications and |
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25 proofs). As a general rule, inner syntax entities may occur only as |
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26 \emph{atomic entities} within outer syntax. For example, the string |
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27 @{verbatim "\"x + y\""} and identifier @{verbatim z} are legal term |
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28 specifications within a theory, while @{verbatim "x + y"} without |
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29 quotes is not. |
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30 |
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31 Printed theory documents usually omit quotes to gain readability |
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32 (this is a matter of {\LaTeX} macro setup, say via @{verbatim |
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33 "\\isabellestyle"}, see also \cite{isabelle-sys}). Experienced |
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34 users of Isabelle/Isar may easily reconstruct the lost technical |
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35 information, while mere readers need not care about quotes at all. |
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36 |
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37 \medskip Isabelle/Isar input may contain any number of input |
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38 termination characters ``@{verbatim ";"}'' (semicolon) to separate |
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39 commands explicitly. This is particularly useful in interactive |
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40 shell sessions to make clear where the current command is intended |
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41 to end. Otherwise, the interpreter loop will continue to issue a |
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42 secondary prompt ``@{verbatim "#"}'' until an end-of-command is |
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43 clearly recognized from the input syntax, e.g.\ encounter of the |
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44 next command keyword. |
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45 |
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46 More advanced interfaces such as Proof~General \cite{proofgeneral} |
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47 do not require explicit semicolons, the amount of input text is |
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48 determined automatically by inspecting the present content of the |
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49 Emacs text buffer. In the printed presentation of Isabelle/Isar |
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50 documents semicolons are omitted altogether for readability. |
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51 |
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52 \begin{warn} |
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53 Proof~General requires certain syntax classification tables in |
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54 order to achieve properly synchronized interaction with the |
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55 Isabelle/Isar process. These tables need to be consistent with |
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56 the Isabelle version and particular logic image to be used in a |
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57 running session (common object-logics may well change the outer |
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58 syntax). The standard setup should work correctly with any of the |
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59 ``official'' logic images derived from Isabelle/HOL (including |
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60 HOLCF etc.). Users of alternative logics may need to tell |
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61 Proof~General explicitly, e.g.\ by giving an option @{verbatim "-k ZF"} |
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62 (in conjunction with @{verbatim "-l ZF"}, to specify the default |
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63 logic image). Note that option @{verbatim "-L"} does both |
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64 of this at the same time. |
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65 \end{warn} |
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66 *} |
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67 |
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68 |
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69 section {* Lexical matters \label{sec:lex-syntax} *} |
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70 |
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71 text {* |
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72 The Isabelle/Isar outer syntax provides token classes as presented |
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73 below; most of these coincide with the inner lexical syntax as |
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74 presented in \cite{isabelle-ref}. |
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75 |
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76 \begin{matharray}{rcl} |
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77 @{syntax_def ident} & = & letter\,quasiletter^* \\ |
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78 @{syntax_def longident} & = & ident (\verb,.,ident)^+ \\ |
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79 @{syntax_def symident} & = & sym^+ ~|~ \verb,\,\verb,<,ident\verb,>, \\ |
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80 @{syntax_def nat} & = & digit^+ \\ |
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81 @{syntax_def var} & = & ident ~|~ \verb,?,ident ~|~ \verb,?,ident\verb,.,nat \\ |
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82 @{syntax_def typefree} & = & \verb,',ident \\ |
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83 @{syntax_def typevar} & = & typefree ~|~ \verb,?,typefree ~|~ \verb,?,typefree\verb,.,nat \\ |
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84 @{syntax_def string} & = & \verb,", ~\dots~ \verb,", \\ |
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85 @{syntax_def altstring} & = & \backquote ~\dots~ \backquote \\ |
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86 @{syntax_def verbatim} & = & \verb,{*, ~\dots~ \verb,*,\verb,}, \\[1ex] |
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87 |
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88 letter & = & latin ~|~ \verb,\,\verb,<,latin\verb,>, ~|~ \verb,\,\verb,<,latin\,latin\verb,>, ~|~ greek ~|~ \\ |
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89 & & \verb,\<^isub>, ~|~ \verb,\<^isup>, \\ |
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90 quasiletter & = & letter ~|~ digit ~|~ \verb,_, ~|~ \verb,', \\ |
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91 latin & = & \verb,a, ~|~ \dots ~|~ \verb,z, ~|~ \verb,A, ~|~ \dots ~|~ \verb,Z, \\ |
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92 digit & = & \verb,0, ~|~ \dots ~|~ \verb,9, \\ |
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93 sym & = & \verb,!, ~|~ \verb,#, ~|~ \verb,$, ~|~ \verb,%, ~|~ \verb,&, ~|~ |
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94 \verb,*, ~|~ \verb,+, ~|~ \verb,-, ~|~ \verb,/, ~|~ \\ |
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95 & & \verb,<, ~|~ \verb,=, ~|~ \verb,>, ~|~ \verb,?, ~|~ \texttt{\at} ~|~ |
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96 \verb,^, ~|~ \verb,_, ~|~ \verb,|, ~|~ \verb,~, \\ |
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97 greek & = & \verb,\<alpha>, ~|~ \verb,\<beta>, ~|~ \verb,\<gamma>, ~|~ \verb,\<delta>, ~| \\ |
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98 & & \verb,\<epsilon>, ~|~ \verb,\<zeta>, ~|~ \verb,\<eta>, ~|~ \verb,\<theta>, ~| \\ |
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99 & & \verb,\<iota>, ~|~ \verb,\<kappa>, ~|~ \verb,\<mu>, ~|~ \verb,\<nu>, ~| \\ |
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100 & & \verb,\<xi>, ~|~ \verb,\<pi>, ~|~ \verb,\<rho>, ~|~ \verb,\<sigma>, ~|~ \verb,\<tau>, ~| \\ |
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101 & & \verb,\<upsilon>, ~|~ \verb,\<phi>, ~|~ \verb,\<chi>, ~|~ \verb,\<psi>, ~| \\ |
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102 & & \verb,\<omega>, ~|~ \verb,\<Gamma>, ~|~ \verb,\<Delta>, ~|~ \verb,\<Theta>, ~| \\ |
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103 & & \verb,\<Lambda>, ~|~ \verb,\<Xi>, ~|~ \verb,\<Pi>, ~|~ \verb,\<Sigma>, ~| \\ |
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104 & & \verb,\<Upsilon>, ~|~ \verb,\<Phi>, ~|~ \verb,\<Psi>, ~|~ \verb,\<Omega>, \\ |
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105 \end{matharray} |
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106 |
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107 The syntax of @{syntax string} admits any characters, including |
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108 newlines; ``@{verbatim "\""}'' (double-quote) and ``@{verbatim |
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109 "\\"}'' (backslash) need to be escaped by a backslash; arbitrary |
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110 character codes may be specified as ``@{verbatim "\\"}@{text ddd}'', |
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111 with three decimal digits. Alternative strings according to |
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112 @{syntax altstring} are analogous, using single back-quotes instead. |
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113 The body of @{syntax verbatim} may consist of any text not |
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114 containing ``@{verbatim "*"}@{verbatim "}"}''; this allows |
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115 convenient inclusion of quotes without further escapes. The greek |
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116 letters do \emph{not} include @{verbatim "\<lambda>"}, which is already used |
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117 differently in the meta-logic. |
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118 |
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119 Common mathematical symbols such as @{text \<forall>} are represented in |
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120 Isabelle as @{verbatim \<forall>}. There are infinitely many Isabelle |
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121 symbols like this, although proper presentation is left to front-end |
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122 tools such as {\LaTeX} or Proof~General with the X-Symbol package. |
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123 A list of standard Isabelle symbols that work well with these tools |
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124 is given in \cite[appendix~A]{isabelle-sys}. |
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125 |
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126 Source comments take the form @{verbatim "(*"}~@{text |
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127 "\<dots>"}~@{verbatim "*)"} and may be nested, although user-interface |
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128 tools might prevent this. Note that this form indicates source |
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129 comments only, which are stripped after lexical analysis of the |
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130 input. The Isar document syntax also provides formal comments that |
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131 are considered as part of the text (see \secref{sec:comments}). |
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132 *} |
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133 |
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134 |
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135 section {* Common syntax entities *} |
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136 |
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137 text {* |
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138 We now introduce several basic syntactic entities, such as names, |
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139 terms, and theorem specifications, which are factored out of the |
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140 actual Isar language elements to be described later. |
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141 *} |
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142 |
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143 |
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144 subsection {* Names *} |
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145 |
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146 text {* |
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147 Entity \railqtok{name} usually refers to any name of types, |
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148 constants, theorems etc.\ that are to be \emph{declared} or |
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149 \emph{defined} (so qualified identifiers are excluded here). Quoted |
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150 strings provide an escape for non-identifier names or those ruled |
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151 out by outer syntax keywords (e.g.\ quoted @{verbatim "\"let\""}). |
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152 Already existing objects are usually referenced by |
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153 \railqtok{nameref}. |
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154 |
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155 \indexoutertoken{name}\indexoutertoken{parname}\indexoutertoken{nameref} |
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156 \indexoutertoken{int} |
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157 \begin{rail} |
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158 name: ident | symident | string | nat |
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159 ; |
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160 parname: '(' name ')' |
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161 ; |
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162 nameref: name | longident |
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163 ; |
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164 int: nat | '-' nat |
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165 ; |
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166 \end{rail} |
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167 *} |
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168 |
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169 |
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170 subsection {* Comments \label{sec:comments} *} |
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171 |
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172 text {* |
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173 Large chunks of plain \railqtok{text} are usually given |
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174 \railtok{verbatim}, i.e.\ enclosed in @{verbatim "{"}@{verbatim |
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175 "*"}~@{text "\<dots>"}~@{verbatim "*"}@{verbatim "}"}. For convenience, |
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176 any of the smaller text units conforming to \railqtok{nameref} are |
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177 admitted as well. A marginal \railnonterm{comment} is of the form |
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178 @{verbatim "--"} \railqtok{text}. Any number of these may occur |
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179 within Isabelle/Isar commands. |
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180 |
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181 \indexoutertoken{text}\indexouternonterm{comment} |
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182 \begin{rail} |
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183 text: verbatim | nameref |
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184 ; |
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185 comment: '--' text |
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186 ; |
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187 \end{rail} |
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188 *} |
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189 |
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190 |
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191 subsection {* Type classes, sorts and arities *} |
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192 |
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193 text {* |
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194 Classes are specified by plain names. Sorts have a very simple |
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195 inner syntax, which is either a single class name @{text c} or a |
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196 list @{text "{c\<^sub>1, \<dots>, c\<^sub>n}"} referring to the |
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197 intersection of these classes. The syntax of type arities is given |
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198 directly at the outer level. |
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199 |
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200 \indexouternonterm{sort}\indexouternonterm{arity} |
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201 \indexouternonterm{classdecl} |
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202 \begin{rail} |
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203 classdecl: name (('<' | subseteq) (nameref + ','))? |
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204 ; |
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205 sort: nameref |
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206 ; |
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207 arity: ('(' (sort + ',') ')')? sort |
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208 ; |
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209 \end{rail} |
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210 *} |
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211 |
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212 |
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213 subsection {* Types and terms \label{sec:types-terms} *} |
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214 |
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215 text {* |
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216 The actual inner Isabelle syntax, that of types and terms of the |
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217 logic, is far too sophisticated in order to be modelled explicitly |
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218 at the outer theory level. Basically, any such entity has to be |
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219 quoted to turn it into a single token (the parsing and type-checking |
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220 is performed internally later). For convenience, a slightly more |
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221 liberal convention is adopted: quotes may be omitted for any type or |
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222 term that is already atomic at the outer level. For example, one |
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223 may just write @{verbatim x} instead of quoted @{verbatim "\"x\""}. |
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224 Note that symbolic identifiers (e.g.\ @{verbatim "++"} or @{text |
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225 "\<forall>"} are available as well, provided these have not been superseded |
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226 by commands or other keywords already (such as @{verbatim "="} or |
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227 @{verbatim "+"}). |
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228 |
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229 \indexoutertoken{type}\indexoutertoken{term}\indexoutertoken{prop} |
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230 \begin{rail} |
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231 type: nameref | typefree | typevar |
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232 ; |
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233 term: nameref | var |
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234 ; |
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235 prop: term |
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236 ; |
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237 \end{rail} |
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238 |
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239 Positional instantiations are indicated by giving a sequence of |
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240 terms, or the placeholder ``@{text _}'' (underscore), which means to |
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241 skip a position. |
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242 |
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243 \indexoutertoken{inst}\indexoutertoken{insts} |
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244 \begin{rail} |
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245 inst: underscore | term |
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246 ; |
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247 insts: (inst *) |
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248 ; |
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249 \end{rail} |
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250 |
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251 Type declarations and definitions usually refer to |
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252 \railnonterm{typespec} on the left-hand side. This models basic |
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253 type constructor application at the outer syntax level. Note that |
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254 only plain postfix notation is available here, but no infixes. |
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255 |
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256 \indexouternonterm{typespec} |
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257 \begin{rail} |
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258 typespec: (() | typefree | '(' ( typefree + ',' ) ')') name |
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259 ; |
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260 \end{rail} |
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261 *} |
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262 |
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263 |
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264 subsection {* Mixfix annotations *} |
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265 |
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266 text {* |
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267 Mixfix annotations specify concrete \emph{inner} syntax of Isabelle |
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268 types and terms. Some commands such as @{command "types"} (see |
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269 \secref{sec:types-pure}) admit infixes only, while @{command |
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270 "consts"} (see \secref{sec:consts}) and @{command "syntax"} (see |
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271 \secref{sec:syn-trans}) support the full range of general mixfixes |
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272 and binders. |
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273 |
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274 \indexouternonterm{infix}\indexouternonterm{mixfix}\indexouternonterm{structmixfix} |
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275 \begin{rail} |
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276 infix: '(' ('infix' | 'infixl' | 'infixr') string? nat ')' |
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277 ; |
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278 mixfix: infix | '(' string prios? nat? ')' | '(' 'binder' string prios? nat ')' |
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279 ; |
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280 structmixfix: mixfix | '(' 'structure' ')' |
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281 ; |
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282 |
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283 prios: '[' (nat + ',') ']' |
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284 ; |
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285 \end{rail} |
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286 |
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287 Here the \railtok{string} specifications refer to the actual mixfix |
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288 template (see also \cite{isabelle-ref}), which may include literal |
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289 text, spacing, blocks, and arguments (denoted by ``@{text _}''); the |
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290 special symbol ``@{verbatim "\<index>"}'' (printed as ``@{text "\<index>"}'') |
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291 represents an index argument that specifies an implicit structure |
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292 reference (see also \secref{sec:locale}). Infix and binder |
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293 declarations provide common abbreviations for particular mixfix |
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294 declarations. So in practice, mixfix templates mostly degenerate to |
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295 literal text for concrete syntax, such as ``@{verbatim "++"}'' for |
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296 an infix symbol, or ``@{verbatim "++"}@{text "\<index>"}'' for an infix of |
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297 an implicit structure. |
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298 *} |
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299 |
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300 |
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301 subsection {* Proof methods \label{sec:syn-meth} *} |
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302 |
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303 text {* |
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304 Proof methods are either basic ones, or expressions composed of |
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305 methods via ``@{verbatim ","}'' (sequential composition), |
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306 ``@{verbatim "|"}'' (alternative choices), ``@{verbatim "?"}'' |
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307 (try), ``@{verbatim "+"}'' (repeat at least once), ``@{verbatim |
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308 "["}@{text n}@{verbatim "]"}'' (restriction to first @{text n} |
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309 sub-goals, with default @{text "n = 1"}). In practice, proof |
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310 methods are usually just a comma separated list of |
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311 \railqtok{nameref}~\railnonterm{args} specifications. Note that |
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312 parentheses may be dropped for single method specifications (with no |
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313 arguments). |
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314 |
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315 \indexouternonterm{method} |
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316 \begin{rail} |
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317 method: (nameref | '(' methods ')') (() | '?' | '+' | '[' nat? ']') |
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318 ; |
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319 methods: (nameref args | method) + (',' | '|') |
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320 ; |
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321 \end{rail} |
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322 |
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323 Proper Isar proof methods do \emph{not} admit arbitrary goal |
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324 addressing, but refer either to the first sub-goal or all sub-goals |
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325 uniformly. The goal restriction operator ``@{text "[n]"}'' |
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326 evaluates a method expression within a sandbox consisting of the |
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327 first @{text n} sub-goals (which need to exist). For example, the |
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328 method ``@{text "simp_all[3]"}'' simplifies the first three |
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329 sub-goals, while ``@{text "(rule foo, simp_all)[]"}'' simplifies all |
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330 new goals that emerge from applying rule @{text "foo"} to the |
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331 originally first one. |
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332 |
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333 Improper methods, notably tactic emulations, offer a separate |
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334 low-level goal addressing scheme as explicit argument to the |
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335 individual tactic being involved. Here ``@{text "[!]"}'' refers to |
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336 all goals, and ``@{text "[n-]"}'' to all goals starting from @{text |
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337 "n"}. |
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338 |
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339 \indexouternonterm{goalspec} |
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340 \begin{rail} |
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341 goalspec: '[' (nat '-' nat | nat '-' | nat | '!' ) ']' |
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342 ; |
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343 \end{rail} |
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344 *} |
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345 |
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346 |
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347 subsection {* Attributes and theorems \label{sec:syn-att} *} |
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348 |
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349 text {* |
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350 Attributes (and proof methods, see \secref{sec:syn-meth}) have their |
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351 own ``semi-inner'' syntax, in the sense that input conforming to |
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352 \railnonterm{args} below is parsed by the attribute a second time. |
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353 The attribute argument specifications may be any sequence of atomic |
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354 entities (identifiers, strings etc.), or properly bracketed argument |
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355 lists. Below \railqtok{atom} refers to any atomic entity, including |
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356 any \railtok{keyword} conforming to \railtok{symident}. |
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357 |
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358 \indexoutertoken{atom}\indexouternonterm{args}\indexouternonterm{attributes} |
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359 \begin{rail} |
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360 atom: nameref | typefree | typevar | var | nat | keyword |
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361 ; |
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362 arg: atom | '(' args ')' | '[' args ']' |
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363 ; |
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364 args: arg * |
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365 ; |
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366 attributes: '[' (nameref args * ',') ']' |
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367 ; |
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368 \end{rail} |
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369 |
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370 Theorem specifications come in several flavors: |
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371 \railnonterm{axmdecl} and \railnonterm{thmdecl} usually refer to |
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372 axioms, assumptions or results of goal statements, while |
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373 \railnonterm{thmdef} collects lists of existing theorems. Existing |
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374 theorems are given by \railnonterm{thmref} and |
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375 \railnonterm{thmrefs}, the former requires an actual singleton |
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376 result. |
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377 |
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378 There are three forms of theorem references: |
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379 \begin{enumerate} |
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380 |
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381 \item named facts @{text "a"}, |
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382 |
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383 \item selections from named facts @{text "a(i)"} or @{text "a(j - k)"}, |
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384 |
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385 \item literal fact propositions using @{syntax_ref altstring} syntax |
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386 @{verbatim "`"}@{text "\<phi>"}@{verbatim "`"} (see also method |
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387 @{method_ref fact} in \secref{sec:pure-meth-att}). |
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388 |
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389 \end{enumerate} |
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390 |
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391 Any kind of theorem specification may include lists of attributes |
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392 both on the left and right hand sides; attributes are applied to any |
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393 immediately preceding fact. If names are omitted, the theorems are |
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394 not stored within the theorem database of the theory or proof |
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395 context, but any given attributes are applied nonetheless. |
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396 |
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397 An extra pair of brackets around attributes (like ``@{text |
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398 "[[simproc a]]"}'') abbreviates a theorem reference involving an |
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399 internal dummy fact, which will be ignored later on. So only the |
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400 effect of the attribute on the background context will persist. |
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401 This form of in-place declarations is particularly useful with |
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402 commands like @{command "declare"} and @{command "using"}. |
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403 |
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404 \indexouternonterm{axmdecl}\indexouternonterm{thmdecl} |
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405 \indexouternonterm{thmdef}\indexouternonterm{thmref} |
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406 \indexouternonterm{thmrefs}\indexouternonterm{selection} |
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407 \begin{rail} |
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408 axmdecl: name attributes? ':' |
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409 ; |
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410 thmdecl: thmbind ':' |
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411 ; |
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412 thmdef: thmbind '=' |
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413 ; |
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414 thmref: (nameref selection? | altstring) attributes? | '[' attributes ']' |
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415 ; |
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416 thmrefs: thmref + |
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417 ; |
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418 |
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419 thmbind: name attributes | name | attributes |
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420 ; |
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421 selection: '(' ((nat | nat '-' nat?) + ',') ')' |
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422 ; |
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423 \end{rail} |
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424 *} |
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425 |
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426 |
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427 subsection {* Term patterns and declarations \label{sec:term-decls} *} |
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428 |
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429 text {* |
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430 Wherever explicit propositions (or term fragments) occur in a proof |
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431 text, casual binding of schematic term variables may be given |
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432 specified via patterns of the form ``@{text "(\<IS> p\<^sub>1 \<dots> |
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433 p\<^sub>n)"}''. This works both for \railqtok{term} and \railqtok{prop}. |
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434 |
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435 \indexouternonterm{termpat}\indexouternonterm{proppat} |
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436 \begin{rail} |
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437 termpat: '(' ('is' term +) ')' |
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438 ; |
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439 proppat: '(' ('is' prop +) ')' |
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440 ; |
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441 \end{rail} |
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442 |
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443 \medskip Declarations of local variables @{text "x :: \<tau>"} and |
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444 logical propositions @{text "a : \<phi>"} represent different views on |
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445 the same principle of introducing a local scope. In practice, one |
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446 may usually omit the typing of \railnonterm{vars} (due to |
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447 type-inference), and the naming of propositions (due to implicit |
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448 references of current facts). In any case, Isar proof elements |
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449 usually admit to introduce multiple such items simultaneously. |
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450 |
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451 \indexouternonterm{vars}\indexouternonterm{props} |
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452 \begin{rail} |
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453 vars: (name+) ('::' type)? |
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454 ; |
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455 props: thmdecl? (prop proppat? +) |
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456 ; |
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457 \end{rail} |
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458 |
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459 The treatment of multiple declarations corresponds to the |
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460 complementary focus of \railnonterm{vars} versus |
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461 \railnonterm{props}. In ``@{text "x\<^sub>1 \<dots> x\<^sub>n :: \<tau>"}'' |
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462 the typing refers to all variables, while in @{text "a: \<phi>\<^sub>1 \<dots> |
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463 \<phi>\<^sub>n"} the naming refers to all propositions collectively. |
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464 Isar language elements that refer to \railnonterm{vars} or |
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465 \railnonterm{props} typically admit separate typings or namings via |
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466 another level of iteration, with explicit @{keyword_ref "and"} |
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467 separators; e.g.\ see @{command "fix"} and @{command "assume"} in |
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468 \secref{sec:proof-context}. |
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469 *} |
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470 |
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471 |
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472 subsection {* Antiquotations \label{sec:antiq} *} |
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473 |
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474 text {* |
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475 \begin{matharray}{rcl} |
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476 @{antiquotation_def "theory"} & : & \isarantiq \\ |
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477 @{antiquotation_def "thm"} & : & \isarantiq \\ |
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478 @{antiquotation_def "prop"} & : & \isarantiq \\ |
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479 @{antiquotation_def "term"} & : & \isarantiq \\ |
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480 @{antiquotation_def const} & : & \isarantiq \\ |
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481 @{antiquotation_def abbrev} & : & \isarantiq \\ |
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482 @{antiquotation_def typeof} & : & \isarantiq \\ |
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483 @{antiquotation_def typ} & : & \isarantiq \\ |
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484 @{antiquotation_def thm_style} & : & \isarantiq \\ |
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485 @{antiquotation_def term_style} & : & \isarantiq \\ |
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486 @{antiquotation_def "text"} & : & \isarantiq \\ |
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487 @{antiquotation_def goals} & : & \isarantiq \\ |
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488 @{antiquotation_def subgoals} & : & \isarantiq \\ |
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489 @{antiquotation_def prf} & : & \isarantiq \\ |
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490 @{antiquotation_def full_prf} & : & \isarantiq \\ |
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491 @{antiquotation_def ML} & : & \isarantiq \\ |
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492 @{antiquotation_def ML_type} & : & \isarantiq \\ |
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493 @{antiquotation_def ML_struct} & : & \isarantiq \\ |
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494 \end{matharray} |
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495 |
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496 The text body of formal comments (see also \secref{sec:comments}) |
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497 may contain antiquotations of logical entities, such as theorems, |
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498 terms and types, which are to be presented in the final output |
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499 produced by the Isabelle document preparation system (see also |
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500 \secref{sec:document-prep}). |
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501 |
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502 Thus embedding of ``@{text "@{term [show_types] \"f x = a + x\"}"}'' |
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503 within a text block would cause |
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504 \isa{{\isacharparenleft}f{\isasymColon}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a{\isacharparenright}\ {\isacharparenleft}x{\isasymColon}{\isacharprime}a{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}a{\isasymColon}{\isacharprime}a{\isacharparenright}\ {\isacharplus}\ x} to appear in the final {\LaTeX} document. Also note that theorem |
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505 antiquotations may involve attributes as well. For example, |
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506 @{text "@{thm sym [no_vars]}"} would print the theorem's |
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507 statement where all schematic variables have been replaced by fixed |
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508 ones, which are easier to read. |
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509 |
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510 \begin{rail} |
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511 atsign lbrace antiquotation rbrace |
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512 ; |
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513 |
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514 antiquotation: |
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515 'theory' options name | |
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516 'thm' options thmrefs | |
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517 'prop' options prop | |
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518 'term' options term | |
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519 'const' options term | |
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520 'abbrev' options term | |
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521 'typeof' options term | |
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522 'typ' options type | |
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523 'thm\_style' options name thmref | |
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524 'term\_style' options name term | |
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525 'text' options name | |
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526 'goals' options | |
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527 'subgoals' options | |
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528 'prf' options thmrefs | |
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529 'full\_prf' options thmrefs | |
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530 'ML' options name | |
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531 'ML\_type' options name | |
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532 'ML\_struct' options name |
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533 ; |
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534 options: '[' (option * ',') ']' |
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535 ; |
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536 option: name | name '=' name |
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537 ; |
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538 \end{rail} |
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539 |
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540 Note that the syntax of antiquotations may \emph{not} include source |
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541 comments @{verbatim "(*"}~@{text "\<dots>"}~@{verbatim "*)"} or verbatim |
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542 text @{verbatim "{"}@{verbatim "*"}~@{text "\<dots>"}~@{verbatim |
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543 "*"}@{verbatim "}"}. |
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544 |
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545 \begin{descr} |
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546 |
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547 \item [@{text "@{theory A}"}] prints the name @{text "A"}, which is |
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548 guaranteed to refer to a valid ancestor theory in the current |
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549 context. |
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550 |
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551 \item [@{text "@{thm a\<^sub>1 \<dots> a\<^sub>n}"}] prints theorems |
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552 @{text "a\<^sub>1 \<dots> a\<^sub>n"}. Note that attribute specifications |
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553 may be included as well (see also \secref{sec:syn-att}); the |
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554 @{attribute_ref no_vars} rule (see \secref{sec:misc-meth-att}) would |
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555 be particularly useful to suppress printing of schematic variables. |
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556 |
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557 \item [@{text "@{prop \<phi>}"}] prints a well-typed proposition @{text |
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558 "\<phi>"}. |
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559 |
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560 \item [@{text "@{term t}"}] prints a well-typed term @{text "t"}. |
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561 |
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562 \item [@{text "@{const c}"}] prints a logical or syntactic constant |
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563 @{text "c"}. |
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564 |
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565 \item [@{text "@{abbrev c x\<^sub>1 \<dots> x\<^sub>n}"}] prints a constant |
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566 abbreviation @{text "c x\<^sub>1 \<dots> x\<^sub>n \<equiv> rhs"} as defined in |
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567 the current context. |
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568 |
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569 \item [@{text "@{typeof t}"}] prints the type of a well-typed term |
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570 @{text "t"}. |
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571 |
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572 \item [@{text "@{typ \<tau>}"}] prints a well-formed type @{text "\<tau>"}. |
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573 |
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574 \item [@{text "@{thm_style s a}"}] prints theorem @{text a}, |
|
575 previously applying a style @{text s} to it (see below). |
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576 |
|
577 \item [@{text "@{term_style s t}"}] prints a well-typed term @{text |
|
578 t} after applying a style @{text s} to it (see below). |
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579 |
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580 \item [@{text "@{text s}"}] prints uninterpreted source text @{text |
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581 s}. This is particularly useful to print portions of text according |
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582 to the Isabelle {\LaTeX} output style, without demanding |
|
583 well-formedness (e.g.\ small pieces of terms that should not be |
|
584 parsed or type-checked yet). |
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585 |
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586 \item [@{text "@{goals}"}] prints the current \emph{dynamic} goal |
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587 state. This is mainly for support of tactic-emulation scripts |
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588 within Isar --- presentation of goal states does not conform to |
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589 actual human-readable proof documents. |
|
590 |
|
591 Please do not include goal states into document output unless you |
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592 really know what you are doing! |
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593 |
|
594 \item [@{text "@{subgoals}"}] is similar to @{text "@{goals}"}, but |
|
595 does not print the main goal. |
|
596 |
|
597 \item [@{text "@{prf a\<^sub>1 \<dots> a\<^sub>n}"}] prints the (compact) |
|
598 proof terms corresponding to the theorems @{text "a\<^sub>1 \<dots> |
|
599 a\<^sub>n"}. Note that this requires proof terms to be switched on |
|
600 for the current object logic (see the ``Proof terms'' section of the |
|
601 Isabelle reference manual for information on how to do this). |
|
602 |
|
603 \item [@{text "@{full_prf a\<^sub>1 \<dots> a\<^sub>n}"}] is like @{text |
|
604 "@{prf a\<^sub>1 \<dots> a\<^sub>n}"}, but displays the full proof terms, |
|
605 i.e.\ also displays information omitted in the compact proof term, |
|
606 which is denoted by ``@{text _}'' placeholders there. |
|
607 |
|
608 \item [@{text "@{ML s}"}, @{text "@{ML_type s}"}, and @{text |
|
609 "@{ML_struct s}"}] check text @{text s} as ML value, type, and |
|
610 structure, respectively. The source is displayed verbatim. |
|
611 |
|
612 \end{descr} |
|
613 |
|
614 \medskip The following standard styles for use with @{text |
|
615 thm_style} and @{text term_style} are available: |
|
616 |
|
617 \begin{descr} |
|
618 |
|
619 \item [@{text lhs}] extracts the first argument of any application |
|
620 form with at least two arguments -- typically meta-level or |
|
621 object-level equality, or any other binary relation. |
|
622 |
|
623 \item [@{text rhs}] is like @{text lhs}, but extracts the second |
|
624 argument. |
|
625 |
|
626 \item [@{text "concl"}] extracts the conclusion @{text C} from a rule |
|
627 in Horn-clause normal form @{text "A\<^sub>1 \<Longrightarrow> \<dots> A\<^sub>n \<Longrightarrow> C"}. |
|
628 |
|
629 \item [@{text "prem1"}, \dots, @{text "prem9"}] extract premise |
|
630 number @{text "1, \<dots>, 9"}, respectively, from from a rule in |
|
631 Horn-clause normal form @{text "A\<^sub>1 \<Longrightarrow> \<dots> A\<^sub>n \<Longrightarrow> C"} |
|
632 |
|
633 \end{descr} |
|
634 |
|
635 \medskip |
|
636 The following options are available to tune the output. Note that most of |
|
637 these coincide with ML flags of the same names (see also \cite{isabelle-ref}). |
|
638 |
|
639 \begin{descr} |
|
640 |
|
641 \item[@{text "show_types = bool"} and @{text "show_sorts = bool"}] |
|
642 control printing of explicit type and sort constraints. |
|
643 |
|
644 \item[@{text "show_structs = bool"}] controls printing of implicit |
|
645 structures. |
|
646 |
|
647 \item[@{text "long_names = bool"}] forces names of types and |
|
648 constants etc.\ to be printed in their fully qualified internal |
|
649 form. |
|
650 |
|
651 \item[@{text "short_names = bool"}] forces names of types and |
|
652 constants etc.\ to be printed unqualified. Note that internalizing |
|
653 the output again in the current context may well yield a different |
|
654 result. |
|
655 |
|
656 \item[@{text "unique_names = bool"}] determines whether the printed |
|
657 version of qualified names should be made sufficiently long to avoid |
|
658 overlap with names declared further back. Set to @{text false} for |
|
659 more concise output. |
|
660 |
|
661 \item[@{text "eta_contract = bool"}] prints terms in @{text |
|
662 \<eta>}-contracted form. |
|
663 |
|
664 \item[@{text "display = bool"}] indicates if the text is to be |
|
665 output as multi-line ``display material'', rather than a small piece |
|
666 of text without line breaks (which is the default). |
|
667 |
|
668 \item[@{text "break = bool"}] controls line breaks in non-display |
|
669 material. |
|
670 |
|
671 \item[@{text "quotes = bool"}] indicates if the output should be |
|
672 enclosed in double quotes. |
|
673 |
|
674 \item[@{text "mode = name"}] adds @{text name} to the print mode to |
|
675 be used for presentation (see also \cite{isabelle-ref}). Note that |
|
676 the standard setup for {\LaTeX} output is already present by |
|
677 default, including the modes @{text latex} and @{text xsymbols}. |
|
678 |
|
679 \item[@{text "margin = nat"} and @{text "indent = nat"}] change the |
|
680 margin or indentation for pretty printing of display material. |
|
681 |
|
682 \item[@{text "source = bool"}] prints the source text of the |
|
683 antiquotation arguments, rather than the actual value. Note that |
|
684 this does not affect well-formedness checks of @{antiquotation |
|
685 "thm"}, @{antiquotation "term"}, etc. (only the @{antiquotation |
|
686 "text"} antiquotation admits arbitrary output). |
|
687 |
|
688 \item[@{text "goals_limit = nat"}] determines the maximum number of |
|
689 goals to be printed. |
|
690 |
|
691 \item[@{text "locale = name"}] specifies an alternative locale |
|
692 context used for evaluating and printing the subsequent argument. |
|
693 |
|
694 \end{descr} |
|
695 |
|
696 For boolean flags, ``@{text "name = true"}'' may be abbreviated as |
|
697 ``@{text name}''. All of the above flags are disabled by default, |
|
698 unless changed from ML. |
|
699 |
|
700 \medskip Note that antiquotations do not only spare the author from |
|
701 tedious typing of logical entities, but also achieve some degree of |
|
702 consistency-checking of informal explanations with formal |
|
703 developments: well-formedness of terms and types with respect to the |
|
704 current theory or proof context is ensured here. |
|
705 *} |
|
706 |
|
707 |
|
708 subsection {* Tagged commands \label{sec:tags} *} |
|
709 |
|
710 text {* |
|
711 Each Isabelle/Isar command may be decorated by presentation tags: |
|
712 |
|
713 \indexouternonterm{tags} |
|
714 \begin{rail} |
|
715 tags: ( tag * ) |
|
716 ; |
|
717 tag: '\%' (ident | string) |
|
718 \end{rail} |
|
719 |
|
720 The tags @{text "theory"}, @{text "proof"}, @{text "ML"} are already |
|
721 pre-declared for certain classes of commands: |
|
722 |
|
723 \medskip |
|
724 |
|
725 \begin{tabular}{ll} |
|
726 @{text "theory"} & theory begin/end \\ |
|
727 @{text "proof"} & all proof commands \\ |
|
728 @{text "ML"} & all commands involving ML code \\ |
|
729 \end{tabular} |
|
730 |
|
731 \medskip The Isabelle document preparation system (see also |
|
732 \cite{isabelle-sys}) allows tagged command regions to be presented |
|
733 specifically, e.g.\ to fold proof texts, or drop parts of the text |
|
734 completely. |
|
735 |
|
736 For example ``@{command "by"}~@{text "%invisible auto"}'' would |
|
737 cause that piece of proof to be treated as @{text invisible} instead |
|
738 of @{text "proof"} (the default), which may be either show or hidden |
|
739 depending on the document setup. In contrast, ``@{command |
|
740 "by"}~@{text "%visible auto"}'' would force this text to be shown |
|
741 invariably. |
|
742 |
|
743 Explicit tag specifications within a proof apply to all subsequent |
|
744 commands of the same level of nesting. For example, ``@{command |
|
745 "proof"}~@{text "%visible \<dots>"}~@{command "qed"}'' would force the |
|
746 whole sub-proof to be typeset as @{text visible} (unless some of its |
|
747 parts are tagged differently). |
|
748 *} |
|
749 |
|
750 end |
|