author | paulson |
Sat, 23 Sep 2000 16:02:01 +0200 | |
changeset 10064 | 1a77667b21ef |
parent 9403 | aad13b59b8d9 |
permissions | -rw-r--r-- |
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(* Title: HOL/UNITY/AllocImpl |
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ID: $Id$ |
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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Copyright 1998 University of Cambridge |
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Implementation of a multiple-client allocator from a single-client allocator |
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*) |
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AllocImpl = AllocBase + Follows + PPROD + |
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(** State definitions. OUTPUT variables are locals **) |
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(*Type variable 'b is the type of items being merged*) |
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record 'b merge = |
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In :: nat => 'b list (*merge's INPUT histories: streams to merge*) |
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Out :: 'b list (*merge's OUTPUT history: merged items*) |
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iOut :: nat list (*merge's OUTPUT history: origins of merged items*) |
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record ('a,'b) merge_d = |
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'b merge + |
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dummy :: 'a (*dummy field for new variables*) |
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constdefs |
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non_dummy :: ('a,'b) merge_d => 'b merge |
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"non_dummy s == (|In = In s, Out = Out s, iOut = iOut s|)" |
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record 'b distr = |
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In :: 'b list (*items to distribute*) |
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iIn :: nat list (*destinations of items to distribute*) |
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Out :: nat => 'b list (*distributed items*) |
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record ('a,'b) distr_d = |
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'b distr + |
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dummy :: 'a (*dummy field for new variables*) |
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record allocState = |
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giv :: nat list (*OUTPUT history: source of tokens*) |
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ask :: nat list (*INPUT: tokens requested from allocator*) |
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rel :: nat list (*INPUT: tokens released to allocator*) |
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record 'a allocState_d = |
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allocState + |
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dummy :: 'a (*dummy field for new variables*) |
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record 'a systemState = |
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allocState + |
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mergeRel :: nat merge |
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mergeAsk :: nat merge |
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distr :: nat distr |
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dummy :: 'a (*dummy field for new variables*) |
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constdefs |
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(** Merge specification (the number of inputs is Nclients) ***) |
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(*spec (10)*) |
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merge_increasing :: ('a,'b) merge_d program set |
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"merge_increasing == |
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UNIV guarantees (Increasing merge.Out) Int (Increasing merge.iOut)" |
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(*spec (11)*) |
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merge_eqOut :: ('a,'b) merge_d program set |
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"merge_eqOut == |
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UNIV guarantees |
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Always {s. length (merge.Out s) = length (merge.iOut s)}" |
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(*spec (12)*) |
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merge_bounded :: ('a,'b) merge_d program set |
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"merge_bounded == |
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UNIV guarantees |
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Always {s. ALL elt : set (merge.iOut s). elt < Nclients}" |
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(*spec (13)*) |
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merge_follows :: ('a,'b) merge_d program set |
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"merge_follows == |
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(INT i : lessThan Nclients. Increasing (sub i o merge.In)) |
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guarantees |
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(INT i : lessThan Nclients. |
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(%s. sublist (merge.Out s) |
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{k. k < size(merge.iOut s) & merge.iOut s! k = i}) |
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Fols (sub i o merge.In))" |
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(*spec: preserves part*) |
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merge_preserves :: ('a,'b) merge_d program set |
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"merge_preserves == preserves merge.In Int preserves merge_d.dummy" |
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(*environmental constraints*) |
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merge_allowed_acts :: ('a,'b) merge_d program set |
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"merge_allowed_acts == |
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{F. AllowedActs F = |
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insert Id (UNION (preserves (funPair merge.Out merge.iOut)) Acts)}" |
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merge_spec :: ('a,'b) merge_d program set |
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"merge_spec == merge_increasing Int merge_eqOut Int merge_bounded Int |
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merge_follows Int merge_allowed_acts Int merge_preserves" |
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(** Distributor specification (the number of outputs is Nclients) ***) |
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(*spec (14)*) |
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distr_follows :: ('a,'b) distr_d program set |
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"distr_follows == |
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Increasing distr.In Int Increasing distr.iIn Int |
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Always {s. ALL elt : set (distr.iIn s). elt < Nclients} |
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guarantees |
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(INT i : lessThan Nclients. |
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(sub i o distr.Out) Fols |
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(%s. sublist (distr.In s) |
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{k. k < size(distr.iIn s) & distr.iIn s ! k = i}))" |
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distr_allowed_acts :: ('a,'b) distr_d program set |
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"distr_allowed_acts == |
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{D. AllowedActs D = insert Id (UNION (preserves distr.Out) Acts)}" |
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distr_spec :: ('a,'b) distr_d program set |
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"distr_spec == distr_follows Int distr_allowed_acts" |
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(** Single-client allocator specification (required) ***) |
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(*spec (18)*) |
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alloc_increasing :: 'a allocState_d program set |
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"alloc_increasing == UNIV guarantees Increasing giv" |
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(*spec (19)*) |
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alloc_safety :: 'a allocState_d program set |
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"alloc_safety == |
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Increasing rel |
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guarantees Always {s. tokens (giv s) <= NbT + tokens (rel s)}" |
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(*spec (20)*) |
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alloc_progress :: 'a allocState_d program set |
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"alloc_progress == |
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Increasing ask Int Increasing rel Int |
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Always {s. ALL elt : set (ask s). elt <= NbT} |
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Int |
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(INT h. {s. h <= giv s & h pfixGe (ask s)} |
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LeadsTo |
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{s. tokens h <= tokens (rel s)}) |
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guarantees (INT h. {s. h <= ask s} LeadsTo {s. h pfixLe giv s})" |
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(*spec: preserves part*) |
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alloc_preserves :: 'a allocState_d program set |
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"alloc_preserves == preserves rel Int |
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preserves ask Int |
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preserves allocState_d.dummy" |
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(*environmental constraints*) |
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alloc_allowed_acts :: 'a allocState_d program set |
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"alloc_allowed_acts == |
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{F. AllowedActs F = insert Id (UNION (preserves giv) Acts)}" |
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alloc_spec :: 'a allocState_d program set |
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"alloc_spec == alloc_increasing Int alloc_safety Int alloc_progress Int |
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alloc_allowed_acts Int alloc_preserves" |
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locale Merge = |
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fixes |
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M :: ('a,'b::order) merge_d program |
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assumes |
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Merge_spec "M : merge_spec" |
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locale Distrib = |
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fixes |
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D :: ('a,'b::order) distr_d program |
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assumes |
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Distrib_spec "D : distr_spec" |
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(**** |
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# (** Network specification ***) |
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# (*spec (9.1)*) |
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# network_ask :: 'a systemState program set |
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# "network_ask == INT i : lessThan Nclients. |
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# Increasing (ask o sub i o client) |
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# guarantees[ask] |
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# (ask Fols (ask o sub i o client))" |
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# (*spec (9.2)*) |
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# network_giv :: 'a systemState program set |
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# "network_giv == INT i : lessThan Nclients. |
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# Increasing giv |
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# guarantees[giv o sub i o client] |
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# ((giv o sub i o client) Fols giv )" |
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# (*spec (9.3)*) |
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# network_rel :: 'a systemState program set |
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# "network_rel == INT i : lessThan Nclients. |
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191 |
# Increasing (rel o sub i o client) |
1a77667b21ef
added compatibility relation: AllowedActs, Allowed, ok,
paulson
parents:
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diff
changeset
|
192 |
# guarantees[rel] |
1a77667b21ef
added compatibility relation: AllowedActs, Allowed, ok,
paulson
parents:
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diff
changeset
|
193 |
# (rel Fols (rel o sub i o client))" |
9027 | 194 |
|
10064
1a77667b21ef
added compatibility relation: AllowedActs, Allowed, ok,
paulson
parents:
9403
diff
changeset
|
195 |
# (*spec: preserves part*) |
1a77667b21ef
added compatibility relation: AllowedActs, Allowed, ok,
paulson
parents:
9403
diff
changeset
|
196 |
# network_preserves :: 'a systemState program set |
1a77667b21ef
added compatibility relation: AllowedActs, Allowed, ok,
paulson
parents:
9403
diff
changeset
|
197 |
# "network_preserves == preserves giv Int |
1a77667b21ef
added compatibility relation: AllowedActs, Allowed, ok,
paulson
parents:
9403
diff
changeset
|
198 |
# (INT i : lessThan Nclients. |
1a77667b21ef
added compatibility relation: AllowedActs, Allowed, ok,
paulson
parents:
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diff
changeset
|
199 |
# preserves (funPair rel ask o sub i o client))" |
9027 | 200 |
|
10064
1a77667b21ef
added compatibility relation: AllowedActs, Allowed, ok,
paulson
parents:
9403
diff
changeset
|
201 |
# network_spec :: 'a systemState program set |
1a77667b21ef
added compatibility relation: AllowedActs, Allowed, ok,
paulson
parents:
9403
diff
changeset
|
202 |
# "network_spec == network_ask Int network_giv Int |
1a77667b21ef
added compatibility relation: AllowedActs, Allowed, ok,
paulson
parents:
9403
diff
changeset
|
203 |
# network_rel Int network_preserves" |
9027 | 204 |
|
205 |
||
10064
1a77667b21ef
added compatibility relation: AllowedActs, Allowed, ok,
paulson
parents:
9403
diff
changeset
|
206 |
# (** State mappings **) |
1a77667b21ef
added compatibility relation: AllowedActs, Allowed, ok,
paulson
parents:
9403
diff
changeset
|
207 |
# sysOfAlloc :: "((nat => merge) * 'a) allocState_d => 'a systemState" |
1a77667b21ef
added compatibility relation: AllowedActs, Allowed, ok,
paulson
parents:
9403
diff
changeset
|
208 |
# "sysOfAlloc == %s. let (cl,xtr) = allocState_d.dummy s |
1a77667b21ef
added compatibility relation: AllowedActs, Allowed, ok,
paulson
parents:
9403
diff
changeset
|
209 |
# in (| giv = giv s, |
1a77667b21ef
added compatibility relation: AllowedActs, Allowed, ok,
paulson
parents:
9403
diff
changeset
|
210 |
# ask = ask s, |
1a77667b21ef
added compatibility relation: AllowedActs, Allowed, ok,
paulson
parents:
9403
diff
changeset
|
211 |
# rel = rel s, |
1a77667b21ef
added compatibility relation: AllowedActs, Allowed, ok,
paulson
parents:
9403
diff
changeset
|
212 |
# client = cl, |
1a77667b21ef
added compatibility relation: AllowedActs, Allowed, ok,
paulson
parents:
9403
diff
changeset
|
213 |
# dummy = xtr|)" |
9027 | 214 |
|
215 |
||
10064
1a77667b21ef
added compatibility relation: AllowedActs, Allowed, ok,
paulson
parents:
9403
diff
changeset
|
216 |
# sysOfClient :: "(nat => merge) * 'a allocState_d => 'a systemState" |
1a77667b21ef
added compatibility relation: AllowedActs, Allowed, ok,
paulson
parents:
9403
diff
changeset
|
217 |
# "sysOfClient == %(cl,al). (| giv = giv al, |
1a77667b21ef
added compatibility relation: AllowedActs, Allowed, ok,
paulson
parents:
9403
diff
changeset
|
218 |
# ask = ask al, |
1a77667b21ef
added compatibility relation: AllowedActs, Allowed, ok,
paulson
parents:
9403
diff
changeset
|
219 |
# rel = rel al, |
1a77667b21ef
added compatibility relation: AllowedActs, Allowed, ok,
paulson
parents:
9403
diff
changeset
|
220 |
# client = cl, |
1a77667b21ef
added compatibility relation: AllowedActs, Allowed, ok,
paulson
parents:
9403
diff
changeset
|
221 |
# systemState.dummy = allocState_d.dummy al|)" |
9027 | 222 |
****) |
223 |
||
224 |
end |