author | Tony Garnock-Jones <tonyg@kcbbs.gen.nz> |
Thu, 31 Mar 2005 01:25:02 +1200 | |
changeset 0 | ea4e1a00864c |
permissions | -rw-r--r-- |
0
ea4e1a00864c
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Tony Garnock-Jones <tonyg@kcbbs.gen.nz>
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1 |
#LyX 1.3 created this file. For more info see http://www.lyx.org/ |
ea4e1a00864c
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\lyxformat 221 |
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\textclass article |
ea4e1a00864c
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4 |
\language english |
ea4e1a00864c
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\inputencoding auto |
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\fontscheme palatino |
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\graphics default |
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\paperfontsize default |
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\spacing single |
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\papersize a4paper |
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\paperpackage widemarginsa4 |
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\use_geometry 0 |
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\use_amsmath 0 |
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\use_natbib 0 |
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\use_numerical_citations 0 |
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\paperorientation portrait |
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\secnumdepth 3 |
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\tocdepth 3 |
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\paragraph_separation indent |
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\defskip medskip |
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\quotes_language english |
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\quotes_times 2 |
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\papercolumns 2 |
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\papersides 1 |
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\paperpagestyle default |
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\layout Title |
ea4e1a00864c
Initial version, from TLA arch@eighty-twenty.org--2004/smalltalk-tng--main--0--version-0
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ea4e1a00864c
Initial version, from TLA arch@eighty-twenty.org--2004/smalltalk-tng--main--0--version-0
Tony Garnock-Jones <tonyg@kcbbs.gen.nz>
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29 |
Pseudo-ambients |
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\layout Author |
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Tony Garnock-Jones <tonyg@kcbbs.gen.nz> |
ea4e1a00864c
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\layout Date |
ea4e1a00864c
Initial version, from TLA arch@eighty-twenty.org--2004/smalltalk-tng--main--0--version-0
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ea4e1a00864c
Initial version, from TLA arch@eighty-twenty.org--2004/smalltalk-tng--main--0--version-0
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35 |
1 November 2004 |
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\layout Standard |
ea4e1a00864c
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|
ea4e1a00864c
Initial version, from TLA arch@eighty-twenty.org--2004/smalltalk-tng--main--0--version-0
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38 |
The idea is to take a calculus much like Cardelli's Mobile Ambients, and |
ea4e1a00864c
Initial version, from TLA arch@eighty-twenty.org--2004/smalltalk-tng--main--0--version-0
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39 |
short-circuit the routing so that paths are one element long and always |
ea4e1a00864c
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40 |
take you directly to the given port. |
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|
ea4e1a00864c
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\begin_inset Formula $\nu$ |
ea4e1a00864c
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\end_inset |
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|
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is interpreted as allocation; the store holds allocated ports. |
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46 |
Ports/locations have exactly one parent, except for the top location, |
ea4e1a00864c
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47 |
\begin_inset Formula $\top$ |
ea4e1a00864c
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48 |
\end_inset |
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49 |
|
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50 |
, which has no parent. |
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51 |
The parent of a location is the location at which the |
ea4e1a00864c
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\begin_inset Formula $\nu$ |
ea4e1a00864c
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53 |
\end_inset |
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54 |
|
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55 |
was executed. |
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This gives rise to a tree of locations. |
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Ports do not move once they are defined, and are garbage collected when |
ea4e1a00864c
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no longer referenced, in the usual manner. |
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\layout Standard |
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60 |
|
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|
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\begin_inset Formula \begin{eqnarray*} |
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\nu x.P & & \textrm{allocation}\\ |
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P\vert Q & & \textrm{par}\\ |
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\left\langle \tilde{x}\right\rangle & & \textrm{output message}\\ |
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(\widetilde{x}).P & & \textrm{input message}\\ |
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!(\widetilde{x}).P & & \textrm{replicated input}\\ |
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x[P] & & \textrm{relocation}\\ |
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\mathbf{lift}\, x(y).P & & \textrm{reflection}\\ |
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\mathbf{eval}\, x & & \textrm{evaluation}\end{eqnarray*} |
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|
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72 |
\end_inset |
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73 |
|
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74 |
|
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\layout Standard |
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76 |
|
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77 |
Processes are written with an environment |
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\begin_inset Formula \[ |
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\mathcal{E}\subset\{ x\mapsto a\,\vert\, x,a\in\mathcal{L}\}\] |
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80 |
|
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81 |
\end_inset |
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82 |
|
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83 |
with ports/locations |
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\begin_inset Formula $a,b,c,\top\in\mathcal{L}$ |
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85 |
\end_inset |
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86 |
|
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87 |
, and processes |
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88 |
\begin_inset Formula $P$ |
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89 |
\end_inset |
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90 |
|
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91 |
, |
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92 |
\begin_inset Formula $Q$ |
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93 |
\end_inset |
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94 |
|
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95 |
, |
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96 |
\begin_inset Formula $R$ |
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97 |
\end_inset |
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98 |
|
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99 |
: |
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100 |
\layout Standard |
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101 |
|
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102 |
|
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103 |
\begin_inset Formula \[ |
ea4e1a00864c
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104 |
\mathcal{E}\vdash a[P]\,\Vert\, b[Q]\,\Vert\, c[R]\] |
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105 |
|
ea4e1a00864c
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106 |
\end_inset |
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107 |
|
ea4e1a00864c
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108 |
|
ea4e1a00864c
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109 |
\layout Standard |
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110 |
|
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111 |
so reduction proceeds as in figure |
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112 |
\begin_inset LatexCommand \ref{cap:Reduction-rules} |
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113 |
|
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114 |
\end_inset |
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115 |
|
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116 |
, where |
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117 |
\begin_inset Formula $\sigma$ |
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118 |
\end_inset |
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119 |
|
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120 |
are appropriate substitutions. |
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121 |
Note that the rule for lift is currently not very well defined. |
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122 |
\layout Standard |
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123 |
|
ea4e1a00864c
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124 |
|
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125 |
\begin_inset Float figure |
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126 |
wide true |
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127 |
collapsed false |
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128 |
|
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129 |
\layout Standard |
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130 |
|
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131 |
|
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132 |
\begin_inset Formula \begin{align*} |
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133 |
\mathcal{E}\vdash a[\nu x.P] & \rightarrow\mathcal{E}\cup\{ x\mapsto a\}\vdash a[P] & \textrm{R-alloc}\\ |
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134 |
\mathcal{E}\vdash a[P\vert Q] & \rightarrow\mathcal{E}\vdash a[P]\Vert a[Q] & \textrm{R-par}\\ |
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135 |
\mathcal{E}\vdash a[\langle\tilde{x}\rangle]\,\Vert\, a[(\tilde{y}).P] & \rightarrow\mathcal{E}\vdash a[P\sigma] & \textrm{R-comm}\\ |
ea4e1a00864c
Initial version, from TLA arch@eighty-twenty.org--2004/smalltalk-tng--main--0--version-0
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136 |
\mathcal{E}\vdash a[\langle\tilde{x}\rangle]\,\Vert\, a[!(\tilde{y}).P] & \rightarrow\mathcal{E}\vdash a[P\sigma]\,\Vert\, a[!(\tilde{y}).P] & \textrm{R-repcomm}\\ |
ea4e1a00864c
Initial version, from TLA arch@eighty-twenty.org--2004/smalltalk-tng--main--0--version-0
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137 |
\mathcal{E}\vdash a[x[P]] & \rightarrow\mathcal{E}\vdash x[P] & \textrm{R-reloc}\\ |
ea4e1a00864c
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138 |
\frac{\alpha=\{ a\vert a\mapsto x\in\mathcal{E}\},\,\mathbf{P}=x[P_{0}]\,\Vert\,{\displaystyle \prod_{a\in\alpha}}a[P_{a}]}{\mathcal{E}\lyxlock\vdash a[\mathbf{lift\,}x(y).P]\,\Vert\,\mathbf{P}} & \rightarrow\mathcal{E}\cup\{ y\mapsto a\}\vdash a[P\sigma]\,\Vert\,\left\lceil \mathbf{P}\right\rceil ^{y} & \textrm{R-reflect}\end{align*} |
ea4e1a00864c
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139 |
|
ea4e1a00864c
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140 |
\end_inset |
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141 |
|
ea4e1a00864c
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142 |
|
ea4e1a00864c
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143 |
\layout Caption |
ea4e1a00864c
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144 |
|
ea4e1a00864c
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145 |
|
ea4e1a00864c
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146 |
\begin_inset LatexCommand \label{cap:Reduction-rules} |
ea4e1a00864c
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147 |
|
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148 |
\end_inset |
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149 |
|
ea4e1a00864c
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150 |
Reduction rules |
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151 |
\end_inset |
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152 |
|
ea4e1a00864c
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153 |
|
ea4e1a00864c
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154 |
\the_end |