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1 (* Title: HOLCF/ex/Pattern_Match.thy |
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2 Author: Brian Huffman |
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3 *) |
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4 |
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5 header {* An experimental pattern-matching notation *} |
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6 |
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7 theory Pattern_Match |
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8 imports HOLCF |
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9 begin |
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10 |
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11 default_sort pcpo |
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12 |
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13 text {* FIXME: Find a proper way to un-hide constants. *} |
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14 |
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15 abbreviation fail :: "'a match" |
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16 where "fail \<equiv> Fixrec.fail" |
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17 |
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18 abbreviation succeed :: "'a \<rightarrow> 'a match" |
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19 where "succeed \<equiv> Fixrec.succeed" |
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20 |
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21 abbreviation run :: "'a match \<rightarrow> 'a" |
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22 where "run \<equiv> Fixrec.run" |
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23 |
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24 subsection {* Fatbar combinator *} |
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25 |
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26 definition |
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27 fatbar :: "('a \<rightarrow> 'b match) \<rightarrow> ('a \<rightarrow> 'b match) \<rightarrow> ('a \<rightarrow> 'b match)" where |
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28 "fatbar = (\<Lambda> a b x. a\<cdot>x +++ b\<cdot>x)" |
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29 |
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30 abbreviation |
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31 fatbar_syn :: "['a \<rightarrow> 'b match, 'a \<rightarrow> 'b match] \<Rightarrow> 'a \<rightarrow> 'b match" (infixr "\<parallel>" 60) where |
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32 "m1 \<parallel> m2 == fatbar\<cdot>m1\<cdot>m2" |
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33 |
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34 lemma fatbar1: "m\<cdot>x = \<bottom> \<Longrightarrow> (m \<parallel> ms)\<cdot>x = \<bottom>" |
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35 by (simp add: fatbar_def) |
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36 |
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37 lemma fatbar2: "m\<cdot>x = fail \<Longrightarrow> (m \<parallel> ms)\<cdot>x = ms\<cdot>x" |
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38 by (simp add: fatbar_def) |
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39 |
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40 lemma fatbar3: "m\<cdot>x = succeed\<cdot>y \<Longrightarrow> (m \<parallel> ms)\<cdot>x = succeed\<cdot>y" |
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41 by (simp add: fatbar_def) |
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42 |
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43 lemmas fatbar_simps = fatbar1 fatbar2 fatbar3 |
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44 |
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45 lemma run_fatbar1: "m\<cdot>x = \<bottom> \<Longrightarrow> run\<cdot>((m \<parallel> ms)\<cdot>x) = \<bottom>" |
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46 by (simp add: fatbar_def) |
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47 |
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48 lemma run_fatbar2: "m\<cdot>x = fail \<Longrightarrow> run\<cdot>((m \<parallel> ms)\<cdot>x) = run\<cdot>(ms\<cdot>x)" |
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49 by (simp add: fatbar_def) |
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50 |
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51 lemma run_fatbar3: "m\<cdot>x = succeed\<cdot>y \<Longrightarrow> run\<cdot>((m \<parallel> ms)\<cdot>x) = y" |
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52 by (simp add: fatbar_def) |
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53 |
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54 lemmas run_fatbar_simps [simp] = run_fatbar1 run_fatbar2 run_fatbar3 |
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55 |
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56 subsection {* Bind operator for match monad *} |
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57 |
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58 definition match_bind :: "'a match \<rightarrow> ('a \<rightarrow> 'b match) \<rightarrow> 'b match" where |
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59 "match_bind = (\<Lambda> m k. sscase\<cdot>(\<Lambda> _. fail)\<cdot>(fup\<cdot>k)\<cdot>(Rep_match m))" |
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60 |
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61 lemma match_bind_simps [simp]: |
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62 "match_bind\<cdot>\<bottom>\<cdot>k = \<bottom>" |
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63 "match_bind\<cdot>fail\<cdot>k = fail" |
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64 "match_bind\<cdot>(succeed\<cdot>x)\<cdot>k = k\<cdot>x" |
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65 unfolding match_bind_def fail_def succeed_def |
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66 by (simp_all add: cont2cont_Rep_match cont_Abs_match |
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67 Rep_match_strict Abs_match_inverse) |
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68 |
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69 subsection {* Case branch combinator *} |
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70 |
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71 definition |
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72 branch :: "('a \<rightarrow> 'b match) \<Rightarrow> ('b \<rightarrow> 'c) \<rightarrow> ('a \<rightarrow> 'c match)" where |
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73 "branch p \<equiv> \<Lambda> r x. match_bind\<cdot>(p\<cdot>x)\<cdot>(\<Lambda> y. succeed\<cdot>(r\<cdot>y))" |
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74 |
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75 lemma branch_simps: |
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76 "p\<cdot>x = \<bottom> \<Longrightarrow> branch p\<cdot>r\<cdot>x = \<bottom>" |
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77 "p\<cdot>x = fail \<Longrightarrow> branch p\<cdot>r\<cdot>x = fail" |
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78 "p\<cdot>x = succeed\<cdot>y \<Longrightarrow> branch p\<cdot>r\<cdot>x = succeed\<cdot>(r\<cdot>y)" |
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79 by (simp_all add: branch_def) |
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80 |
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81 lemma branch_succeed [simp]: "branch succeed\<cdot>r\<cdot>x = succeed\<cdot>(r\<cdot>x)" |
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82 by (simp add: branch_def) |
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83 |
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84 subsection {* Cases operator *} |
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85 |
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86 definition |
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87 cases :: "'a match \<rightarrow> 'a::pcpo" where |
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88 "cases = Fixrec.run" |
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89 |
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90 text {* rewrite rules for cases *} |
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91 |
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92 lemma cases_strict [simp]: "cases\<cdot>\<bottom> = \<bottom>" |
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93 by (simp add: cases_def) |
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94 |
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95 lemma cases_fail [simp]: "cases\<cdot>fail = \<bottom>" |
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96 by (simp add: cases_def) |
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97 |
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98 lemma cases_succeed [simp]: "cases\<cdot>(succeed\<cdot>x) = x" |
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99 by (simp add: cases_def) |
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100 |
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101 subsection {* Case syntax *} |
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102 |
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103 nonterminals |
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104 Case_syn Cases_syn |
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105 |
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106 syntax |
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107 "_Case_syntax":: "['a, Cases_syn] => 'b" ("(Case _ of/ _)" 10) |
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108 "_Case1" :: "['a, 'b] => Case_syn" ("(2_ =>/ _)" 10) |
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109 "" :: "Case_syn => Cases_syn" ("_") |
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110 "_Case2" :: "[Case_syn, Cases_syn] => Cases_syn" ("_/ | _") |
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111 |
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112 syntax (xsymbols) |
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113 "_Case1" :: "['a, 'b] => Case_syn" ("(2_ \<Rightarrow>/ _)" 10) |
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114 |
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115 translations |
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116 "_Case_syntax x ms" == "CONST cases\<cdot>(ms\<cdot>x)" |
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117 "_Case2 m ms" == "m \<parallel> ms" |
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118 |
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119 text {* Parsing Case expressions *} |
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120 |
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121 syntax |
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122 "_pat" :: "'a" |
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123 "_variable" :: "'a" |
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124 "_noargs" :: "'a" |
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125 |
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126 translations |
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127 "_Case1 p r" => "CONST branch (_pat p)\<cdot>(_variable p r)" |
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128 "_variable (_args x y) r" => "CONST csplit\<cdot>(_variable x (_variable y r))" |
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129 "_variable _noargs r" => "CONST unit_when\<cdot>r" |
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130 |
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131 parse_translation {* |
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132 (* rewrite (_pat x) => (succeed) *) |
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133 (* rewrite (_variable x t) => (Abs_cfun (%x. t)) *) |
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134 [(@{syntax_const "_pat"}, fn _ => Syntax.const @{const_syntax Fixrec.succeed}), |
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135 mk_binder_tr (@{syntax_const "_variable"}, @{const_syntax Abs_cfun})]; |
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136 *} |
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137 |
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138 text {* Printing Case expressions *} |
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139 |
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140 syntax |
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141 "_match" :: "'a" |
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142 |
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143 print_translation {* |
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144 let |
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145 fun dest_LAM (Const (@{const_syntax Rep_cfun},_) $ Const (@{const_syntax unit_when},_) $ t) = |
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146 (Syntax.const @{syntax_const "_noargs"}, t) |
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147 | dest_LAM (Const (@{const_syntax Rep_cfun},_) $ Const (@{const_syntax csplit},_) $ t) = |
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148 let |
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149 val (v1, t1) = dest_LAM t; |
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150 val (v2, t2) = dest_LAM t1; |
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151 in (Syntax.const @{syntax_const "_args"} $ v1 $ v2, t2) end |
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152 | dest_LAM (Const (@{const_syntax Abs_cfun},_) $ t) = |
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153 let |
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154 val abs = |
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155 case t of Abs abs => abs |
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156 | _ => ("x", dummyT, incr_boundvars 1 t $ Bound 0); |
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157 val (x, t') = atomic_abs_tr' abs; |
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158 in (Syntax.const @{syntax_const "_variable"} $ x, t') end |
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159 | dest_LAM _ = raise Match; (* too few vars: abort translation *) |
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160 |
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161 fun Case1_tr' [Const(@{const_syntax branch},_) $ p, r] = |
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162 let val (v, t) = dest_LAM r in |
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163 Syntax.const @{syntax_const "_Case1"} $ |
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164 (Syntax.const @{syntax_const "_match"} $ p $ v) $ t |
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165 end; |
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166 |
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167 in [(@{const_syntax Rep_cfun}, Case1_tr')] end; |
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168 *} |
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169 |
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170 translations |
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171 "x" <= "_match (CONST succeed) (_variable x)" |
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172 |
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173 |
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174 subsection {* Pattern combinators for data constructors *} |
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175 |
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176 types ('a, 'b) pat = "'a \<rightarrow> 'b match" |
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177 |
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178 definition |
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179 cpair_pat :: "('a, 'c) pat \<Rightarrow> ('b, 'd) pat \<Rightarrow> ('a \<times> 'b, 'c \<times> 'd) pat" where |
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180 "cpair_pat p1 p2 = (\<Lambda>(x, y). |
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181 match_bind\<cdot>(p1\<cdot>x)\<cdot>(\<Lambda> a. match_bind\<cdot>(p2\<cdot>y)\<cdot>(\<Lambda> b. succeed\<cdot>(a, b))))" |
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182 |
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183 definition |
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184 spair_pat :: |
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185 "('a, 'c) pat \<Rightarrow> ('b, 'd) pat \<Rightarrow> ('a::pcpo \<otimes> 'b::pcpo, 'c \<times> 'd) pat" where |
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186 "spair_pat p1 p2 = (\<Lambda>(:x, y:). cpair_pat p1 p2\<cdot>(x, y))" |
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187 |
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188 definition |
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189 sinl_pat :: "('a, 'c) pat \<Rightarrow> ('a::pcpo \<oplus> 'b::pcpo, 'c) pat" where |
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190 "sinl_pat p = sscase\<cdot>p\<cdot>(\<Lambda> x. fail)" |
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191 |
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192 definition |
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193 sinr_pat :: "('b, 'c) pat \<Rightarrow> ('a::pcpo \<oplus> 'b::pcpo, 'c) pat" where |
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194 "sinr_pat p = sscase\<cdot>(\<Lambda> x. fail)\<cdot>p" |
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195 |
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196 definition |
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197 up_pat :: "('a, 'b) pat \<Rightarrow> ('a u, 'b) pat" where |
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198 "up_pat p = fup\<cdot>p" |
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199 |
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200 definition |
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201 TT_pat :: "(tr, unit) pat" where |
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202 "TT_pat = (\<Lambda> b. If b then succeed\<cdot>() else fail)" |
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203 |
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204 definition |
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205 FF_pat :: "(tr, unit) pat" where |
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206 "FF_pat = (\<Lambda> b. If b then fail else succeed\<cdot>())" |
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207 |
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208 definition |
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209 ONE_pat :: "(one, unit) pat" where |
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210 "ONE_pat = (\<Lambda> ONE. succeed\<cdot>())" |
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211 |
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212 text {* Parse translations (patterns) *} |
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213 translations |
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214 "_pat (XCONST Pair x y)" => "CONST cpair_pat (_pat x) (_pat y)" |
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215 "_pat (XCONST spair\<cdot>x\<cdot>y)" => "CONST spair_pat (_pat x) (_pat y)" |
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216 "_pat (XCONST sinl\<cdot>x)" => "CONST sinl_pat (_pat x)" |
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217 "_pat (XCONST sinr\<cdot>x)" => "CONST sinr_pat (_pat x)" |
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218 "_pat (XCONST up\<cdot>x)" => "CONST up_pat (_pat x)" |
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219 "_pat (XCONST TT)" => "CONST TT_pat" |
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220 "_pat (XCONST FF)" => "CONST FF_pat" |
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221 "_pat (XCONST ONE)" => "CONST ONE_pat" |
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222 |
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223 text {* CONST version is also needed for constructors with special syntax *} |
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224 translations |
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225 "_pat (CONST Pair x y)" => "CONST cpair_pat (_pat x) (_pat y)" |
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226 "_pat (CONST spair\<cdot>x\<cdot>y)" => "CONST spair_pat (_pat x) (_pat y)" |
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227 |
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228 text {* Parse translations (variables) *} |
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229 translations |
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230 "_variable (XCONST Pair x y) r" => "_variable (_args x y) r" |
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231 "_variable (XCONST spair\<cdot>x\<cdot>y) r" => "_variable (_args x y) r" |
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232 "_variable (XCONST sinl\<cdot>x) r" => "_variable x r" |
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233 "_variable (XCONST sinr\<cdot>x) r" => "_variable x r" |
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234 "_variable (XCONST up\<cdot>x) r" => "_variable x r" |
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235 "_variable (XCONST TT) r" => "_variable _noargs r" |
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236 "_variable (XCONST FF) r" => "_variable _noargs r" |
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237 "_variable (XCONST ONE) r" => "_variable _noargs r" |
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238 |
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239 translations |
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240 "_variable (CONST Pair x y) r" => "_variable (_args x y) r" |
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241 "_variable (CONST spair\<cdot>x\<cdot>y) r" => "_variable (_args x y) r" |
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242 |
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243 text {* Print translations *} |
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244 translations |
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245 "CONST Pair (_match p1 v1) (_match p2 v2)" |
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246 <= "_match (CONST cpair_pat p1 p2) (_args v1 v2)" |
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247 "CONST spair\<cdot>(_match p1 v1)\<cdot>(_match p2 v2)" |
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248 <= "_match (CONST spair_pat p1 p2) (_args v1 v2)" |
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249 "CONST sinl\<cdot>(_match p1 v1)" <= "_match (CONST sinl_pat p1) v1" |
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250 "CONST sinr\<cdot>(_match p1 v1)" <= "_match (CONST sinr_pat p1) v1" |
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251 "CONST up\<cdot>(_match p1 v1)" <= "_match (CONST up_pat p1) v1" |
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252 "CONST TT" <= "_match (CONST TT_pat) _noargs" |
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253 "CONST FF" <= "_match (CONST FF_pat) _noargs" |
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254 "CONST ONE" <= "_match (CONST ONE_pat) _noargs" |
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255 |
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256 lemma cpair_pat1: |
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257 "branch p\<cdot>r\<cdot>x = \<bottom> \<Longrightarrow> branch (cpair_pat p q)\<cdot>(csplit\<cdot>r)\<cdot>(x, y) = \<bottom>" |
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258 apply (simp add: branch_def cpair_pat_def) |
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259 apply (cases "p\<cdot>x", simp_all) |
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260 done |
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261 |
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262 lemma cpair_pat2: |
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263 "branch p\<cdot>r\<cdot>x = fail \<Longrightarrow> branch (cpair_pat p q)\<cdot>(csplit\<cdot>r)\<cdot>(x, y) = fail" |
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264 apply (simp add: branch_def cpair_pat_def) |
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265 apply (cases "p\<cdot>x", simp_all) |
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266 done |
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267 |
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268 lemma cpair_pat3: |
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269 "branch p\<cdot>r\<cdot>x = succeed\<cdot>s \<Longrightarrow> |
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270 branch (cpair_pat p q)\<cdot>(csplit\<cdot>r)\<cdot>(x, y) = branch q\<cdot>s\<cdot>y" |
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271 apply (simp add: branch_def cpair_pat_def) |
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272 apply (cases "p\<cdot>x", simp_all) |
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273 apply (cases "q\<cdot>y", simp_all) |
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274 done |
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275 |
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276 lemmas cpair_pat [simp] = |
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277 cpair_pat1 cpair_pat2 cpair_pat3 |
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278 |
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279 lemma spair_pat [simp]: |
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280 "branch (spair_pat p1 p2)\<cdot>r\<cdot>\<bottom> = \<bottom>" |
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281 "\<lbrakk>x \<noteq> \<bottom>; y \<noteq> \<bottom>\<rbrakk> |
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282 \<Longrightarrow> branch (spair_pat p1 p2)\<cdot>r\<cdot>(:x, y:) = |
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283 branch (cpair_pat p1 p2)\<cdot>r\<cdot>(x, y)" |
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284 by (simp_all add: branch_def spair_pat_def) |
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285 |
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286 lemma sinl_pat [simp]: |
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287 "branch (sinl_pat p)\<cdot>r\<cdot>\<bottom> = \<bottom>" |
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288 "x \<noteq> \<bottom> \<Longrightarrow> branch (sinl_pat p)\<cdot>r\<cdot>(sinl\<cdot>x) = branch p\<cdot>r\<cdot>x" |
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289 "y \<noteq> \<bottom> \<Longrightarrow> branch (sinl_pat p)\<cdot>r\<cdot>(sinr\<cdot>y) = fail" |
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290 by (simp_all add: branch_def sinl_pat_def) |
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291 |
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292 lemma sinr_pat [simp]: |
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293 "branch (sinr_pat p)\<cdot>r\<cdot>\<bottom> = \<bottom>" |
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294 "x \<noteq> \<bottom> \<Longrightarrow> branch (sinr_pat p)\<cdot>r\<cdot>(sinl\<cdot>x) = fail" |
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295 "y \<noteq> \<bottom> \<Longrightarrow> branch (sinr_pat p)\<cdot>r\<cdot>(sinr\<cdot>y) = branch p\<cdot>r\<cdot>y" |
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296 by (simp_all add: branch_def sinr_pat_def) |
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297 |
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298 lemma up_pat [simp]: |
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299 "branch (up_pat p)\<cdot>r\<cdot>\<bottom> = \<bottom>" |
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300 "branch (up_pat p)\<cdot>r\<cdot>(up\<cdot>x) = branch p\<cdot>r\<cdot>x" |
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301 by (simp_all add: branch_def up_pat_def) |
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302 |
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303 lemma TT_pat [simp]: |
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304 "branch TT_pat\<cdot>(unit_when\<cdot>r)\<cdot>\<bottom> = \<bottom>" |
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305 "branch TT_pat\<cdot>(unit_when\<cdot>r)\<cdot>TT = succeed\<cdot>r" |
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306 "branch TT_pat\<cdot>(unit_when\<cdot>r)\<cdot>FF = fail" |
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307 by (simp_all add: branch_def TT_pat_def) |
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308 |
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309 lemma FF_pat [simp]: |
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310 "branch FF_pat\<cdot>(unit_when\<cdot>r)\<cdot>\<bottom> = \<bottom>" |
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311 "branch FF_pat\<cdot>(unit_when\<cdot>r)\<cdot>TT = fail" |
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312 "branch FF_pat\<cdot>(unit_when\<cdot>r)\<cdot>FF = succeed\<cdot>r" |
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313 by (simp_all add: branch_def FF_pat_def) |
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314 |
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315 lemma ONE_pat [simp]: |
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316 "branch ONE_pat\<cdot>(unit_when\<cdot>r)\<cdot>\<bottom> = \<bottom>" |
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317 "branch ONE_pat\<cdot>(unit_when\<cdot>r)\<cdot>ONE = succeed\<cdot>r" |
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318 by (simp_all add: branch_def ONE_pat_def) |
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319 |
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320 |
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321 subsection {* Wildcards, as-patterns, and lazy patterns *} |
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322 |
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323 definition |
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324 wild_pat :: "'a \<rightarrow> unit match" where |
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325 "wild_pat = (\<Lambda> x. succeed\<cdot>())" |
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326 |
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327 definition |
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328 as_pat :: "('a \<rightarrow> 'b match) \<Rightarrow> 'a \<rightarrow> ('a \<times> 'b) match" where |
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329 "as_pat p = (\<Lambda> x. match_bind\<cdot>(p\<cdot>x)\<cdot>(\<Lambda> a. succeed\<cdot>(x, a)))" |
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330 |
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331 definition |
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332 lazy_pat :: "('a \<rightarrow> 'b::pcpo match) \<Rightarrow> ('a \<rightarrow> 'b match)" where |
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333 "lazy_pat p = (\<Lambda> x. succeed\<cdot>(cases\<cdot>(p\<cdot>x)))" |
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334 |
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335 text {* Parse translations (patterns) *} |
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336 translations |
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337 "_pat _" => "CONST wild_pat" |
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338 |
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339 text {* Parse translations (variables) *} |
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340 translations |
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341 "_variable _ r" => "_variable _noargs r" |
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342 |
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343 text {* Print translations *} |
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344 translations |
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345 "_" <= "_match (CONST wild_pat) _noargs" |
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346 |
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347 lemma wild_pat [simp]: "branch wild_pat\<cdot>(unit_when\<cdot>r)\<cdot>x = succeed\<cdot>r" |
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348 by (simp add: branch_def wild_pat_def) |
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349 |
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350 lemma as_pat [simp]: |
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351 "branch (as_pat p)\<cdot>(csplit\<cdot>r)\<cdot>x = branch p\<cdot>(r\<cdot>x)\<cdot>x" |
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352 apply (simp add: branch_def as_pat_def) |
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353 apply (cases "p\<cdot>x", simp_all) |
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354 done |
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355 |
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356 lemma lazy_pat [simp]: |
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357 "branch p\<cdot>r\<cdot>x = \<bottom> \<Longrightarrow> branch (lazy_pat p)\<cdot>r\<cdot>x = succeed\<cdot>(r\<cdot>\<bottom>)" |
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358 "branch p\<cdot>r\<cdot>x = fail \<Longrightarrow> branch (lazy_pat p)\<cdot>r\<cdot>x = succeed\<cdot>(r\<cdot>\<bottom>)" |
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359 "branch p\<cdot>r\<cdot>x = succeed\<cdot>s \<Longrightarrow> branch (lazy_pat p)\<cdot>r\<cdot>x = succeed\<cdot>s" |
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360 apply (simp_all add: branch_def lazy_pat_def) |
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361 apply (cases "p\<cdot>x", simp_all)+ |
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362 done |
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363 |
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364 subsection {* Examples *} |
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365 |
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366 term "Case t of (:up\<cdot>(sinl\<cdot>x), sinr\<cdot>y:) \<Rightarrow> (x, y)" |
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367 |
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368 term "\<Lambda> t. Case t of up\<cdot>(sinl\<cdot>a) \<Rightarrow> a | up\<cdot>(sinr\<cdot>b) \<Rightarrow> b" |
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369 |
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370 term "\<Lambda> t. Case t of (:up\<cdot>(sinl\<cdot>_), sinr\<cdot>x:) \<Rightarrow> x" |
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371 |
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372 subsection {* ML code for generating definitions *} |
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373 |
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374 ML {* |
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375 local open HOLCF_Library in |
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376 |
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377 infixr 6 ->>; |
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378 infix 9 ` ; |
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379 |
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380 val beta_rules = |
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381 @{thms beta_cfun cont_id cont_const cont2cont_APP cont2cont_LAM'} @ |
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382 @{thms cont2cont_fst cont2cont_snd cont2cont_Pair}; |
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383 |
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384 val beta_ss = HOL_basic_ss addsimps (simp_thms @ beta_rules); |
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385 |
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386 fun define_consts |
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387 (specs : (binding * term * mixfix) list) |
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388 (thy : theory) |
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389 : (term list * thm list) * theory = |
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390 let |
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391 fun mk_decl (b, t, mx) = (b, fastype_of t, mx); |
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392 val decls = map mk_decl specs; |
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393 val thy = Cont_Consts.add_consts decls thy; |
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394 fun mk_const (b, T, mx) = Const (Sign.full_name thy b, T); |
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395 val consts = map mk_const decls; |
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396 fun mk_def c (b, t, mx) = |
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397 (Binding.suffix_name "_def" b, Logic.mk_equals (c, t)); |
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398 val defs = map2 mk_def consts specs; |
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399 val (def_thms, thy) = |
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400 Global_Theory.add_defs false (map Thm.no_attributes defs) thy; |
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401 in |
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402 ((consts, def_thms), thy) |
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403 end; |
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404 |
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405 fun prove |
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406 (thy : theory) |
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407 (defs : thm list) |
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408 (goal : term) |
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409 (tacs : {prems: thm list, context: Proof.context} -> tactic list) |
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410 : thm = |
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411 let |
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412 fun tac {prems, context} = |
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413 rewrite_goals_tac defs THEN |
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414 EVERY (tacs {prems = map (rewrite_rule defs) prems, context = context}) |
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415 in |
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416 Goal.prove_global thy [] [] goal tac |
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417 end; |
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418 |
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419 fun get_vars_avoiding |
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420 (taken : string list) |
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421 (args : (bool * typ) list) |
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422 : (term list * term list) = |
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423 let |
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424 val Ts = map snd args; |
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425 val ns = Name.variant_list taken (Datatype_Prop.make_tnames Ts); |
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426 val vs = map Free (ns ~~ Ts); |
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427 val nonlazy = map snd (filter_out (fst o fst) (args ~~ vs)); |
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428 in |
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429 (vs, nonlazy) |
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430 end; |
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431 |
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432 (******************************************************************************) |
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433 (************** definitions and theorems for pattern combinators **************) |
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434 (******************************************************************************) |
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435 |
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436 fun add_pattern_combinators |
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437 (bindings : binding list) |
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438 (spec : (term * (bool * typ) list) list) |
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439 (lhsT : typ) |
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440 (exhaust : thm) |
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441 (case_const : typ -> term) |
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442 (case_rews : thm list) |
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443 (thy : theory) = |
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444 let |
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445 |
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446 (* utility functions *) |
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447 fun mk_pair_pat (p1, p2) = |
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448 let |
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449 val T1 = fastype_of p1; |
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450 val T2 = fastype_of p2; |
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451 val (U1, V1) = apsnd dest_matchT (dest_cfunT T1); |
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452 val (U2, V2) = apsnd dest_matchT (dest_cfunT T2); |
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453 val pat_typ = [T1, T2] ---> |
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454 (mk_prodT (U1, U2) ->> mk_matchT (mk_prodT (V1, V2))); |
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455 val pat_const = Const (@{const_name cpair_pat}, pat_typ); |
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456 in |
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457 pat_const $ p1 $ p2 |
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458 end; |
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459 fun mk_tuple_pat [] = succeed_const HOLogic.unitT |
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460 | mk_tuple_pat ps = foldr1 mk_pair_pat ps; |
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461 fun branch_const (T,U,V) = |
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462 Const (@{const_name branch}, |
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463 (T ->> mk_matchT U) --> (U ->> V) ->> T ->> mk_matchT V); |
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464 |
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465 (* define pattern combinators *) |
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466 local |
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467 val tns = map (fst o dest_TFree) (snd (dest_Type lhsT)); |
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468 |
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469 fun pat_eqn (i, (bind, (con, args))) : binding * term * mixfix = |
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470 let |
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471 val pat_bind = Binding.suffix_name "_pat" bind; |
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472 val Ts = map snd args; |
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473 val Vs = |
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474 (map (K "'t") args) |
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475 |> Datatype_Prop.indexify_names |
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476 |> Name.variant_list tns |
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477 |> map (fn t => TFree (t, @{sort pcpo})); |
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478 val patNs = Datatype_Prop.indexify_names (map (K "pat") args); |
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479 val patTs = map2 (fn T => fn V => T ->> mk_matchT V) Ts Vs; |
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480 val pats = map Free (patNs ~~ patTs); |
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481 val fail = mk_fail (mk_tupleT Vs); |
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482 val (vs, nonlazy) = get_vars_avoiding patNs args; |
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483 val rhs = big_lambdas vs (mk_tuple_pat pats ` mk_tuple vs); |
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484 fun one_fun (j, (_, args')) = |
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485 let |
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486 val (vs', nonlazy) = get_vars_avoiding patNs args'; |
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487 in if i = j then rhs else big_lambdas vs' fail end; |
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488 val funs = map_index one_fun spec; |
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489 val body = list_ccomb (case_const (mk_matchT (mk_tupleT Vs)), funs); |
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490 in |
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491 (pat_bind, lambdas pats body, NoSyn) |
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492 end; |
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493 in |
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494 val ((pat_consts, pat_defs), thy) = |
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495 define_consts (map_index pat_eqn (bindings ~~ spec)) thy |
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496 end; |
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497 |
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498 (* syntax translations for pattern combinators *) |
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499 local |
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500 open Syntax |
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501 fun syntax c = Syntax.mark_const (fst (dest_Const c)); |
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502 fun app s (l, r) = Syntax.mk_appl (Constant s) [l, r]; |
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503 val capp = app @{const_syntax Rep_cfun}; |
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504 val capps = Library.foldl capp |
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505 |
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506 fun app_var x = Syntax.mk_appl (Constant "_variable") [x, Variable "rhs"]; |
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507 fun app_pat x = Syntax.mk_appl (Constant "_pat") [x]; |
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508 fun args_list [] = Constant "_noargs" |
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509 | args_list xs = foldr1 (app "_args") xs; |
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510 fun one_case_trans (pat, (con, args)) = |
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511 let |
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512 val cname = Constant (syntax con); |
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513 val pname = Constant (syntax pat); |
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514 val ns = 1 upto length args; |
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515 val xs = map (fn n => Variable ("x"^(string_of_int n))) ns; |
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516 val ps = map (fn n => Variable ("p"^(string_of_int n))) ns; |
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517 val vs = map (fn n => Variable ("v"^(string_of_int n))) ns; |
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518 in |
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519 [ParseRule (app_pat (capps (cname, xs)), |
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520 mk_appl pname (map app_pat xs)), |
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521 ParseRule (app_var (capps (cname, xs)), |
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522 app_var (args_list xs)), |
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523 PrintRule (capps (cname, ListPair.map (app "_match") (ps,vs)), |
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524 app "_match" (mk_appl pname ps, args_list vs))] |
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525 end; |
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526 val trans_rules : Syntax.ast Syntax.trrule list = |
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527 maps one_case_trans (pat_consts ~~ spec); |
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528 in |
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529 val thy = Sign.add_trrules_i trans_rules thy; |
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530 end; |
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531 |
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532 (* prove strictness and reduction rules of pattern combinators *) |
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533 local |
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534 val tns = map (fst o dest_TFree) (snd (dest_Type lhsT)); |
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535 val rn = Name.variant tns "'r"; |
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536 val R = TFree (rn, @{sort pcpo}); |
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537 fun pat_lhs (pat, args) = |
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538 let |
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539 val Ts = map snd args; |
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540 val Vs = |
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541 (map (K "'t") args) |
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542 |> Datatype_Prop.indexify_names |
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543 |> Name.variant_list (rn::tns) |
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544 |> map (fn t => TFree (t, @{sort pcpo})); |
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545 val patNs = Datatype_Prop.indexify_names (map (K "pat") args); |
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546 val patTs = map2 (fn T => fn V => T ->> mk_matchT V) Ts Vs; |
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547 val pats = map Free (patNs ~~ patTs); |
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548 val k = Free ("rhs", mk_tupleT Vs ->> R); |
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549 val branch1 = branch_const (lhsT, mk_tupleT Vs, R); |
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550 val fun1 = (branch1 $ list_comb (pat, pats)) ` k; |
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551 val branch2 = branch_const (mk_tupleT Ts, mk_tupleT Vs, R); |
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552 val fun2 = (branch2 $ mk_tuple_pat pats) ` k; |
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553 val taken = "rhs" :: patNs; |
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554 in (fun1, fun2, taken) end; |
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555 fun pat_strict (pat, (con, args)) = |
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556 let |
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557 val (fun1, fun2, taken) = pat_lhs (pat, args); |
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558 val defs = @{thm branch_def} :: pat_defs; |
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559 val goal = mk_trp (mk_strict fun1); |
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560 val rules = @{thms match_bind_simps} @ case_rews; |
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561 val tacs = [simp_tac (beta_ss addsimps rules) 1]; |
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562 in prove thy defs goal (K tacs) end; |
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563 fun pat_apps (i, (pat, (con, args))) = |
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564 let |
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565 val (fun1, fun2, taken) = pat_lhs (pat, args); |
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566 fun pat_app (j, (con', args')) = |
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567 let |
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568 val (vs, nonlazy) = get_vars_avoiding taken args'; |
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569 val con_app = list_ccomb (con', vs); |
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570 val assms = map (mk_trp o mk_defined) nonlazy; |
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571 val rhs = if i = j then fun2 ` mk_tuple vs else mk_fail R; |
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572 val concl = mk_trp (mk_eq (fun1 ` con_app, rhs)); |
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573 val goal = Logic.list_implies (assms, concl); |
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574 val defs = @{thm branch_def} :: pat_defs; |
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575 val rules = @{thms match_bind_simps} @ case_rews; |
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576 val tacs = [asm_simp_tac (beta_ss addsimps rules) 1]; |
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577 in prove thy defs goal (K tacs) end; |
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578 in map_index pat_app spec end; |
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579 in |
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580 val pat_stricts = map pat_strict (pat_consts ~~ spec); |
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581 val pat_apps = flat (map_index pat_apps (pat_consts ~~ spec)); |
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582 end; |
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583 |
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584 in |
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585 (pat_stricts @ pat_apps, thy) |
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586 end |
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587 |
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588 end |
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589 *} |
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590 |
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591 (* |
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592 Cut from HOLCF/Tools/domain_constructors.ML |
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593 in function add_domain_constructors: |
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594 |
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595 ( * define and prove theorems for pattern combinators * ) |
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596 val (pat_thms : thm list, thy : theory) = |
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597 let |
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598 val bindings = map #1 spec; |
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599 fun prep_arg (lazy, sel, T) = (lazy, T); |
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600 fun prep_con c (b, args, mx) = (c, map prep_arg args); |
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601 val pat_spec = map2 prep_con con_consts spec; |
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602 in |
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603 add_pattern_combinators bindings pat_spec lhsT |
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604 exhaust case_const cases thy |
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605 end |
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606 |
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607 *) |
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608 |
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609 end |