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␈↓␈↓↓␈↓α␈↓β␈↓∧␈↓ ↓H
␈↓ α,␈β↓H␈↓␈↓␈↓ α,
␈↓ α,␈β↓k␈↓␈↓α␈↓&OVERVIEW OF THE AL COMPILER␈↓)βλ␈↓␈↓ α,
␈↓ α,␈βα∞␈↓␈↓ α,
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␈↓ α,␈βαT␈↓␈↓ α,
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of␈α
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SAIL␈α
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¬␈↓␈↓ α|trajectories␈α∞are␈α∞written␈α
into␈α
output␈α
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Similarly,␈α
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␈↓ α,␈β⊃␈↓␈↓ α,AIM-243␈αare␈αthe␈αinput␈αsyntax,␈αfor␈αwhich␈αa␈αmuch␈αsimpler␈αform␈αis␈αcurrently␈αbeing␈αused,␈αand␈↓ α,
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a␈α
PDP-11␈α
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more␈α
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For␈α
instance,␈α
the␈α
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simple␈α
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that␈α
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from␈α
work␈αon␈αthe␈αrest␈αof␈αthe␈αcompiler,␈αthus␈↓ α,
␈↓ α,␈β∧l␈↓␈↓ α,keeping␈α⊃bugs␈α⊃occuring␈α⊃in␈α⊃one␈α⊂part␈α⊂from␈α⊂holding␈α⊂up␈α⊂work␈α⊂in␈α⊂the␈α⊂other.␈α⊂The␈α⊂danger,␈α⊂of␈↓ α,
␈↓ α,␈β¬∂␈↓␈↓ α,course,␈α
is␈α
that␈α
the␈α
structures␈αbuilt␈αby␈αthe␈αparser␈αmay␈αbe␈αsubtly␈αdifferent␈αfrom␈αthose␈αused␈αin␈↓ α,
␈↓ α,␈β¬2␈↓␈↓ α,the␈α
compiler,␈α
thus␈αmaking␈αit␈αvery␈αdifficult␈αto␈αdo␈αaway␈αeventually␈αwith␈αthe␈αintermediate␈αfile.␈↓ α,
␈↓ α,␈β¬U␈↓␈↓ α,We␈αare␈αaware␈αof␈αthis,␈αand␈αare␈αtaking␈αcare␈αto␈αminimize␈αany␈αsuch␈αdifficulties.␈αIn␈αany␈αevent,␈αit␈↓ α,
␈↓ α,␈β¬x␈↓␈↓ α,is␈αfelt␈αthat␈αthe␈αpossible␈αcosts␈αof␈αlater␈αmerging␈αare␈αmore␈αthan␈αcompensated␈αby␈αthe␈αbenefits␈αof␈↓ α,
␈↓ α,␈βε≠␈↓␈↓ α,increased␈α
insulation␈α
during␈α
program␈α
development.␈↓ α,
␈↓ α,␈βε>␈↓␈↓ α,
␈↓ α,␈βεa␈↓␈↓&Internal Representation of AL Programs␈↓)βλ␈↓ α,
␈↓ α,␈βπ∧␈↓␈↓ α,
␈↓ α,␈βπ'␈↓␈↓ α,Internally,␈αAL␈αprogram␈αgraphs␈αare␈αbuilt␈αas␈αSAIL␈αrecord␈αstructures.␈αEssentially,␈αthe␈αcompiler␈↓ α,
␈↓ α,␈βπJ␈↓␈↓ α,associates␈α
a␈α
record␈α
"class"␈α
with␈α
each␈α
major␈α
semantic␈α
entity␈α
in␈α
AL.␈α
For␈α
example:␈↓ α,
␈↓ α,␈βπt␈↓␈↓β␈↓ α,
␈↓ α,␈βλ↔␈↓β␈↓ βRECORD_CLASS V3ECT(REAL X,Y,Z);␈↓ α,
␈↓ α,␈βλ:␈↓β␈↓ βRECORD_CLASS ASSIGNMENT(POINTER(VARIABLE) VAR;POINTER(EXPRESSION) VAL);␈↓ α,
␈↓ α,␈βλV␈↓β␈↓␈↓ α,
␈↓ α,␈βλy␈↓␈↓ α,are␈αused␈αfor␈αvector␈αconstants␈αand␈αassignment␈α
statements,␈α
respectively.␈α
Component␈α
elements␈α
of␈↓ α,
␈↓ α,␈β	≤␈↓␈↓ α,the␈α
records␈α
can␈α
then␈α
be␈α
accessed␈α
by␈α
name,␈α
as␈α
with:␈↓ α,
␈↓ α,␈β	F␈↓␈↓β␈↓ α,
␈↓ α,␈β	i␈↓β␈↓ βQ←V3ECT:X[V1]*V3ECT:X[V2];␈↓ α,
␈↓ α,␈β
¬␈↓β␈↓␈↓ α,
␈↓ α,␈β
(␈↓␈↓ α,A␈α⊃large␈α⊃number␈α⊃of␈α⊃"service"␈α⊃routines␈α⊃have␈α⊃been␈α⊃provided␈α⊃to␈α⊃aid␈α⊃in␈α⊃manipulating␈α⊂these␈↓ α,
␈↓ α,␈β
K␈↓␈↓ α,structures.␈α
For␈α
instance,␈↓ α,
␈↓ α,␈β
u␈↓␈↓β␈↓ α,
␈↓ α,␈β_␈↓β␈↓ βHALPRN(<structure>) -- produces "pretty printed" output of <structure>␈↓ α,
␈↓ α,␈β;␈↓β␈↓ βV3DOT(V1,V2) -- computes the vector dot product of V1 and V2␈↓ α,
␈↓ α,␈βW␈↓β␈↓␈↓ α,
␈↓ α,␈βz␈↓␈↓ α,This␈αapproach␈α
has␈α
allowed␈α
considerable␈α
flexibility␈α
in␈α
implementation,␈α
since␈α
SAIL␈α
handles␈α
all␈↓ α,
␈↓ α,␈β≥␈↓␈↓ α,free-storage␈α⊂management␈α⊂and␈α⊂since␈α⊂new␈α⊂attributes␈α⊂can␈α⊂be␈α⊂added␈α⊂to␈α∂the␈α∂various␈α∂semantic␈↓ α,
␈↓ α,␈β@␈↓␈↓ α,entities␈α
without␈α
recoding␈α
previously␈α
debugged␈α
programs.␈↓ α,
␈↓ α,␈βc␈↓␈↓ α,
␈↓ α,␈β
ε␈↓␈↓ α,Currently,␈αthere␈α
are␈α
in␈α
excess␈α
of␈α
50␈α
such␈α
class␈α
declarations,␈α
new␈α
ones␈α
being␈α
added␈α
at␈α
a␈α
rate␈α
of␈↓ α,
␈↓ α,␈β
)␈↓␈↓ α,(very)␈α
roughly␈α
two␈α
a␈α
week.␈↓ α,
␈↓ α,␈β
L␈↓␈↓ α,
␈↓ α,␈β
o␈↓␈↓ α,The␈α⊃principal␈α⊃structural␈α⊃entities␈α⊃used␈α⊃in␈α⊃representing␈α⊂an␈α⊂AL␈α⊂program␈α⊂are␈α⊂BLOCK␈α⊂and␈↓ α,
␈↓ α,␈β∞∩␈↓␈↓ α,STMNT␈α
records.␈α
Simpilfied,␈α
their␈α
declarations␈α
look␈α
like␈α
this:␈↓ α,
␈↓ α,␈β∞<␈↓␈↓β␈↓ α,
␈↓ α,␈β∞←␈↓β␈↓ βRECORD_CLASS BLOCK(LIST CODE,VARS);␈↓ α,
␈↓ α,␈β∂α␈↓β␈↓ βRECORD_CLASS STMNT(ITEM IW,OW;POINTER(ANY_CLASS) SEMANTICS);␈↓ α,
␈↓ α,␈β∂≡␈↓β␈↓␈↓ α,
␈↓ A␈β↓␈↓α[4]
␈↓ α,␈β↓H␈↓␈↓ α,In␈α
a␈α
BLOCK,␈α
VARS␈α
is␈α
a␈α
list␈α
of␈α
variables␈α
declared␈α
within␈αthat␈αblock,␈αand␈αcode␈αis␈αa␈αlist␈αof␈↓ α,
␈↓ α,␈β↓k␈↓␈↓ α,STMNT␈αrecords␈αfor␈αthe␈αexecutable␈αstatements␈αin␈αthe␈αblock.␈αIn␈αa␈αstatement,␈αIW␈α
and␈α
OW␈α
are␈↓ α,
␈↓ α,␈βα∞␈↓␈↓ α,context␈α⊂pointers␈α⊂into␈α⊂the␈α⊂simulation␈α⊂model's␈α⊂data␈α⊂base,␈α⊂corresponding,␈α∂respectively,␈α∂to␈α∂the␈↓ α,
␈↓ α,␈βα1␈↓␈↓ α,expected␈α∂state␈α∂before␈α∞and␈α∞after␈α∞the␈α∞statement␈α∞is␈α∞executed.␈α∞Figure␈α∞1␈α∞illustrates␈α∞the␈α∞program␈↓ α,
␈↓ α,␈βαT␈↓␈↓ α,graph␈α
built␈α
for␈α
our␈α
sample␈α
program.␈↓ α,
␈↓ C␈β↓␈↓α[5]
␈↓ α,␈β↓H␈↓␈↓&Preprocessor␈↓)βλ␈↓ α,
␈↓ α,␈β↓k␈↓␈↓ α,
␈↓ α,␈βα∞␈↓␈↓ α,The␈α∂principal␈α∂duty␈α∂of␈α∂the␈α∂preprocessor␈α∂is␈α∂to␈α∂produce␈α∞a␈α∞"planning␈α∞model"␈α∞of␈α∞the␈α∞expected␈↓ α,
␈↓ α,␈βα1␈↓␈↓ α,program␈α⊃state␈α⊃at␈α⊃each␈α⊃point␈α⊃in␈α⊃the␈α⊃program␈α⊃graph.␈α⊃This␈α⊃model␈α⊃is␈α⊃then␈α⊃used␈α⊃to␈α⊂supply␈↓ α,
␈↓ α,␈βαT␈↓␈↓ α,planning␈αvalues␈αfor␈αuse␈αby␈αthe␈αtrajectory␈αcalculator,␈αto␈αdetermine␈αwhich␈αarm␈αis␈αto␈αbe␈αused␈α
in␈↓ α,
␈↓ α,␈βαw␈↓␈↓ α,motion␈α
statements,␈α
and␈α
other␈α
similar␈α
purposes.␈↓ α,
␈↓ α,␈ββ~␈↓␈↓ α,
␈↓ α,␈ββ=␈↓␈↓ α,The␈αplanning␈αmodel␈αis␈αkept␈αin␈αa␈α
data␈α
base␈α
of␈α
assertional␈α
forms,␈α
the␈α
most␈α
important␈α
of␈α
which␈↓ α,
␈↓ α,␈ββ`␈↓␈↓ α,(for␈α∪our␈α∪present␈α∪purposes)␈α∪are␈α∪those␈α∪dealing␈α∪with␈α∪expected␈α∪values␈α∪and␈α∩affixments,␈α∩for␈↓ α,
␈↓ α,␈β∧β␈↓␈↓ α,example:␈↓ α,
␈↓ α,␈β∧-␈↓␈↓β␈↓ α,
␈↓ α,␈β∧P␈↓β␈↓ β(VALUE_OF_YARM,FRAME(NILROT,VECTOR(0,31.2,23.7))␈↓ α,
␈↓ α,␈β∧s␈↓β␈↓ β(AFFIXED,f1,YARM,t,NONRIGIDLY)␈↓ α,
␈↓ α,␈β¬∂␈↓β␈↓␈↓ α,
␈↓ α,␈β¬2␈↓␈↓ α,With␈α∪each␈α∪such␈α∪assertion,␈α∪the␈α∩database␈α∩routines␈α∩keep␈α∩a␈α∩list␈α∩of␈α∩"worlds"␈α∩in␈α∩which␈α∩that␈↓ α,
␈↓ α,␈β¬U␈↓␈↓ α,assertion␈α⊃is␈α⊃assumed␈α⊃to␈α⊃be␈α⊃"true".␈α⊃Currently,␈α⊃the␈α⊂data␈α⊂base␈α⊂routines␈α⊂include␈α⊂facilities␈α⊂for␈↓ α,
␈↓ α,␈β¬x␈↓␈↓ α,addition,␈αdeletion,␈αand␈αassociative␈αretrieval␈αof␈αfacts␈αfrom␈αthe␈αdata␈α
base␈α
and␈α
for␈α
manipulating␈↓ α,
␈↓ α,␈βε≠␈↓␈↓ α,worlds␈α
as␈α
if␈α
they␈α
were␈α
sets␈α
of␈α
facts.␈α
The␈α
principal␈α
routines␈α
include:␈↓ α,
␈↓ α,␈βεE␈↓␈↓β␈↓ α,
␈↓ α,␈βεh␈↓β␈↓ βASRTPF(<world>,<form>) -- adds assertional form to <world>␈↓ α,
␈↓ α,␈βπ␈↓β␈↓ βDENYPF(<world>,<form>) -- removes assertional form from <world>␈↓ α,
␈↓ α,␈βπ.␈↓β␈↓ βPMATCH(<world>,<form>) -- retrieves all forms that match <form> in <world>␈↓ α,
␈↓ α,␈βπQ␈↓β␈↓ βCPYWLD(<world 1>,<world 2>) -- makes a fact true in <world 2> if and only if it is true in <world 1>␈↓ α,
␈↓ α,␈βπt␈↓β␈↓ βANDWLD(<world 1>,<world 2>,<world 3>) -- sets <world 2> to the intersection of <world 1> and <world 2>.␈↓ α,
␈↓ α,␈βλ↔␈↓β␈↓ βANDWLD(<world 1>,<world 2>,<world 3>) -- sets <world 2> to the union of <world 1> and <world 2>.␈↓ α,
␈↓ α,␈βλ3␈↓β␈↓␈↓ α,
␈↓ α,␈βλV␈↓␈↓ α,Other␈α∪routines␈α∪provide␈α∪a␈α∪"demon"␈α∪facility␈α∪that␈α∩allows␈α∩a␈α∩pattern␈α∩to␈α∩be␈α∩flagged␈α∩so␈α∩that␈↓ α,
␈↓ α,␈βλy␈↓␈↓ α,additional␈α
book-keeping␈α
procedures␈α
are␈α
called␈α
whenever␈α
that␈α
pattern␈α
is␈α
asserted␈α
or␈α
denied.␈↓ α,
␈↓ α,␈β	≤␈↓␈↓ α,
␈↓ α,␈β	?␈↓␈↓ α,Subroutines␈α
for␈α
simulating␈α
the␈α
effects␈α
of␈α
graph␈α
structure␈α
are␈αbuilt␈α"on␈αtop␈αof"␈αthe␈αdatabase␈↓ α,
␈↓ α,␈β	b␈↓␈↓ α,routines.␈α
These␈α
include:␈↓ α,
␈↓ α,␈β
␈↓␈↓β␈↓ α,
␈↓ α,␈β
/␈↓β␈↓ βGETVALUE(<variable>,<world>) -- returns planning value of <variable> in <world>␈↓ α,
␈↓ α,␈β
R␈↓β␈↓ βVCHANGE(<variable>,<value>,<world>) -- sets the planning value of <variable> to <value> in <world>␈↓ α,
␈↓ α,␈β
u␈↓β␈↓ βEVALEXPR(<expression>,<world>) -- computes planning value for <expression> in <world>.␈↓ α,
␈↓ α,␈β⊃␈↓β␈↓␈↓ α,
␈↓ α,␈β4␈↓␈↓ α,which␈αare␈αused␈αby␈αboth␈αthe␈αsimulator␈αand␈αthe␈αtrajectory␈αcalculator␈αto␈αfetch␈αplanning␈αvalues.␈↓ α,
␈↓ α,␈βW␈↓␈↓ α,Other␈α↔important␈α↔graph␈α↔structure␈α↔routines␈α↔in␈α↔EXPRS␈α↔include␈α↔ADDCLC,␈α⊗KILLCLC,␈↓ α,
␈↓ α,␈βz␈↓␈↓ α,ADDCHG,␈α
and␈α
KILLCHG,␈α
which␈α
are␈α
used␈α
in␈α
simulating␈α
graph␈α
structure␈α
modifications.␈↓ α,
␈↓ α,␈β≥␈↓␈↓ α,
␈↓ α,␈β@␈↓␈↓ α,The␈α
actual␈α
simulation␈α
proceeds␈α
in␈α
two␈α
phases:␈↓ α,
␈↓ α|␈βc␈↓␈↓ α|
␈↓ α|␈β
ε␈↓␈↓ α|1.␈↓&initialization␈↓)βλ␈α↔Procedure␈α↔WLDASG␈α↔is␈α⊗called␈α⊗to␈α⊗assign␈α⊗input␈α⊗and␈α⊗output␈↓ α|
␈↓ α|␈β
)␈↓␈↓ α|planning␈α∞worlds␈α∞to␈α∞every␈α∞statement␈α∞in␈α∞the␈α∞program␈α∞graph.␈α∞Usually,␈α
the␈α
output␈↓ α|
␈↓ α|␈β
L␈↓␈↓ α|world␈α
of␈αone␈αstatement␈αwill␈αbe␈αthe␈αinput␈αworld␈αof␈αthe␈αnext␈αstatement.␈αTo␈αavoid␈↓ α|
␈↓ α|␈β
o␈↓␈↓ α|needless␈α
proliferation␈α
of␈α
worlds,␈α
WLDASG␈αtreats␈αsequences␈αof␈αassignments␈αand␈↓ α|
␈↓ α|␈β∞∩␈↓␈↓ α|affixments␈α
as␈α
a␈α
single␈α
statement.␈α
In␈α
addition,␈α
initial␈α
planning␈αvalues␈αare␈αset␈αup␈↓ α|
␈↓ α|␈β∞5␈↓␈↓ α|for␈α∞certain␈α∞predeclared␈α∞variables␈α∞(such␈α∞as␈α∞YARM).␈α∞World␈α∞assignments␈α∞for␈α
our␈↓ α|
␈↓ α|␈β∞X␈↓␈↓ α|sample␈α
program␈α
are␈α
indicated␈α
below.␈↓ α|
␈↓ 
t␈β↓␈↓α[6]
␈↓ βL␈β↓H␈↓␈↓β␈↓ βL
␈↓ βL␈β↓k␈↓β(PR␈↓ βL
␈↓ βL␈βα∞␈↓β  (BL (FVAR a b)(RVAR r)(TVAR t)␈↓ βL
␈↓ βL␈βα1␈↓β    (AS r (RMAKE YHAT (SSMUL 180 DEG))) [IW = W0, OW = W1]␈↓ βL
␈↓ βL␈βαT␈↓β    (AS a (FMAKE r (VMAKE 0 0 2))) [IW = W1, OW = W1]␈↓ βL
␈↓ βL␈βαw␈↓β    (MO YARM (FMAKE r (VMAKE 1 0 2))) [IW = W1, OW = W2]␈↓ βL
␈↓ βL␈ββ~␈↓β    (AS b (FMAKE r (VMAKE 0 0 3))) [IW = W2, OW = W3]␈↓ βL
␈↓ βL␈ββ=␈↓β    (AFFIX a YARM t () RIGIDLY) [IW = W3, OW = W3]␈↓ βL
␈↓ βL␈ββ`␈↓β    (MO a b) [IW = W3, OW = W4]␈↓ βL
␈↓ βL␈β∧β␈↓β    (MO a (TTMUL b (TMAKE (AXW_ROTN XHAT (SSMUL 90 DEG))(VMAKE 1 1 1)))) [IW = W4, OW = W5]␈↓ βL
␈↓ βL␈β∧&␈↓β    (UNFIX a YARM) [IW = W5, OW = W6]␈↓ βL
␈↓ βL␈β∧I␈↓β    (MO YARM YPARK) [IW = W6, OW = W7]␈↓ βL
␈↓ βL␈β∧l␈↓β  )[IW = W0, OW = W7]␈↓ βL
␈↓ βL␈β¬∂␈↓β )␈↓ βL
␈↓ α|␈β¬+␈↓β␈↓␈↓ α|
␈↓ α|␈β¬N␈↓␈↓ α|2.␈↓&simulation␈↓)βλ␈α⊂Recursive␈α⊂procedure␈α⊂STINTERP␈α⊂is␈α⊂called␈α⊂to␈α⊂perform␈α⊂the␈α⊂actual␈↓ α|
␈↓ α|␈β¬q␈↓␈↓ α|smulation.␈αThis␈αprocedure␈αconsists␈αof␈αa␈αbig␈α
IF-THEN-ELSE␈α
chain␈α
that␈α
looks␈α
at␈↓ α|
␈↓ α|␈βε∀␈↓␈↓ α|the␈αsemantics␈αof␈αeach␈αstatement␈αand␈αperforms␈αthe␈αappropriate␈αactions␈αto␈αupdate␈↓ α|
␈↓ α|␈βε7␈↓␈↓ α|the␈α∂planning␈α∂model.␈α∂Typically,␈α∂this␈α∂involves␈α∂copying␈α∂the␈α∞input␈α∞world␈α∞into␈α∞the␈↓ α|
␈↓ α|␈βεZ␈↓␈↓ α|output␈α∀world␈α∪and␈α∪then␈α∪modifying␈α∪the␈α∪output␈α∪world␈α∪to␈α∪reflect␈α∪any␈α∪changes␈↓ α|
␈↓ α|␈βε⎇␈↓␈↓ α|introduced␈α⊃by␈α⊃the␈α⊃statement.␈α⊃STINTERP␈α⊃is␈α⊃capable␈α⊃of␈α⊂handling␈α⊂all␈α⊂the␈α⊂AL␈↓ α|
␈↓ α|␈βπ ␈↓␈↓ α|control␈α⊃structures␈α⊂currently␈α⊂implemented,␈α⊂including␈α⊂conditionals,␈α⊂coblocks,␈α⊂and␈↓ α|
␈↓ α|␈βπC␈↓␈↓ α|loops.␈αIn␈αaddition␈αto␈αbuilding␈αthe␈αplanning␈αmodel,␈α
STINTERP␈α
makes␈α
a␈α
number␈↓ α|
␈↓ α|␈βπf␈↓␈↓ α|of␈α∀minor␈α∀modifications␈α∀to␈α∀the␈α∀program␈α∀graph.␈α∀These␈α∪include␈α∪invention␈α∪of␈↓ α|
␈↓ α|␈βλ	␈↓␈↓ α|temporary␈α∪variables,␈α∪translation␈α∪of␈α∪AFFIX␈α∪and␈α∩UNFIX␈α∩statements␈α∩into␈α∩the␈↓ α|
␈↓ α|␈βλ,␈↓␈↓ α|corresponding␈α∞graph␈α∞modification␈α∞statements,␈α∞and␈α
rewriting␈α
MOVE␈α
statements␈↓ α|
␈↓ α|␈βλO␈↓␈↓ α|to␈α∂always␈α∂be␈α∞in␈α∞terms␈α∞of␈α∞an␈α∞arm.␈α∞Procedures␈α∞for␈α∞larger␈α∞modifications,␈α∞such␈α∞as␈↓ α|
␈↓ α|␈βλr␈↓␈↓ α|"unrolling"␈α→of␈α→loops␈α→or␈α→translation␈α→of␈α→"very␈α→high␈α→level"␈α→statements␈α→into␈↓ α|
␈↓ α|␈β	∃␈↓␈↓ α|manipulator␈αcommands,␈αare␈αnot␈αincluded␈αin␈αthe␈αversion␈α
presently␈α
integrated␈α
into␈↓ α|
␈↓ α|␈β	8␈↓␈↓ α|the␈α
compiler.␈↓ α|
␈↓ α,␈β	[␈↓␈↓ α,
␈↓ α,␈β	}␈↓␈↓ α,Once␈αpreprocessing␈αis␈αcomplete,␈αthe␈αplanning␈αmodel's␈αdata␈αbase␈αwill␈αcontain␈αthe␈αdata␈αneeded␈↓ α,
␈↓ α,␈β
!␈↓␈↓ α,by␈αthe␈αtrajectory␈αcalculator.␈αFor␈αour␈αtest␈αcase,␈αthe␈αdata␈αbase␈αwill␈αcontain␈αassertions␈αthat␈αlook␈↓ α,
␈↓ α,␈β
D␈↓␈↓ α,roughly␈α
like␈α
the␈α
following:␈↓ α,
␈↓ α|␈β
n␈↓␈↓β␈↓ α|
␈↓ α|␈β⊃␈↓β(AFFIXED,a,YARM,t,RIGIDLY) in W3,W4,W5␈↓ α|
␈↓ α|␈β4␈↓β(AFFIXED,YARM,a,(TINVRT t),RIGIDLY) in W3,W4,W5␈↓ α|
␈↓ α|␈βW␈↓β␈↓ β\...␈↓ α|
␈↓ α|␈βz␈↓β(COMPUTES_a,(TTMUL YARM t)) in W3,W4,W5␈↓ α|
␈↓ α|␈β≥␈↓β␈↓ β\...␈↓ α|
␈↓ α|␈β@␈↓β(VALUE_OF_a,FRAME(ROT(YHAT,180*DEG),VECTOR(0,0,2)) in W1,W2,W3␈↓ α|
␈↓ α|␈βc␈↓β(VALUE_OF_a,FRAME(ROT(YHAT,180*DEG),VECTOR(0,0,3)) in W4␈↓ α|
␈↓ α|␈β
ε␈↓β␈↓ β\...␈↓ α|
␈↓ α,␈β
"␈↓β␈↓␈↓ α,
␈↓ α,␈β
E␈↓␈↓ α,In␈α∂addition,␈α∂the␈α∂AFFIX␈α∂statement␈α∂will␈α∂have␈α∂been␈α∂annotated␈α∂to␈α∂indicate␈α∂that␈α∂it␈α∞should␈α∞be␈↓ α,
␈↓ α,␈β
h␈↓␈↓ α,compiled␈α
as:␈↓ α,
␈↓ α|␈β∞∩␈↓␈↓β␈↓ α|
␈↓ α|␈β∞5␈↓β(AS t (TTMUL (TINVRT YARM) a))␈↓ α|
␈↓ α|␈β∞X␈↓β(GAS a = (g001 CLC (TTMUL YARM t)))␈↓ α|
␈↓ α|␈β∞{␈↓β(GAS YARM = (g002 CLC (TTMUL a (TINVRT t))))␈↓ α|
␈↓ α,␈β∂↔␈↓β␈↓␈↓ α,
␈↓ D␈β↓␈↓α[7]
␈↓ α,␈β↓H␈↓The UNFIX will be annotated for expansion as ␈↓ α,
␈↓ α|␈β↓r␈↓␈↓β␈↓ α|
␈↓ α|␈βα∃␈↓β(GAS a ≠ g001)␈↓ α|
␈↓ α|␈βα8␈↓β(GAS YARM ≠ g002)␈↓ α|
␈↓ α,␈βαT␈↓β␈↓␈↓ α,
␈↓ α,␈βαw␈↓␈↓ α,and␈αthe␈αmove␈αstatements␈αwill␈αbe␈αrewritten␈αexplicitly␈αin␈αterms␈αof␈αthe␈αyellow␈αarm.␈α
For␈α
instance,␈↓ α,
␈↓ α,␈ββ~␈↓␈↓ α,(MO␈α
a␈α
b)␈α
in␈α
our␈α
example␈α
would␈α
be␈α
rewritten␈α
as␈α
(MO␈α
YARM␈α
(TTMUL␈α
b␈α
(TINVRT␈α
t))).␈↓ α,
␈↓ α,␈ββ=␈↓␈↓ α,
␈↓ α,␈ββ`␈↓␈↓&Code Emitter␈↓)βλ␈↓ α,
␈↓ α,␈β∧β␈↓␈↓ α,
␈↓ α,␈β∧&␈↓␈↓ α,There␈α⊃are␈α⊃three␈α⊂major␈α⊂components␈α⊂in␈α⊂the␈α⊂code␈α⊂emission␈α⊂phase:␈α⊂a␈α⊂code␈α⊂generator,␈α⊂which␈↓ α,
␈↓ α,␈β∧I␈↓␈↓ α,translates␈α~internal␈α→structures␈α→into␈α→the␈α→proper␈α→interpreter␈α→pseudo-code,␈α→the␈α→trajectory␈↓ α,
␈↓ α,␈β∧l␈↓␈↓ α,calculator,␈α
and␈α
a␈α
function␈α
that␈α
does␈α
the␈α
actual␈α
work␈α
of␈α
writing␈α
the␈α
output␈α
file.␈↓ α,
␈↓ α,␈β¬∂␈↓␈↓ α,
␈↓ α,␈β¬2␈↓␈↓↓␈↓&code generator␈↓)βλ␈↓ α,
␈↓ α,␈β¬U␈↓↓␈↓ α,
␈↓ α,␈β¬x␈↓↓␈↓␈↓ α,The␈αprincipal␈αroutine␈αis␈αTSCAN,␈αwhich␈αgenerates␈αcode␈αfor␈αthe␈αroot␈αof␈αthe␈αbound␈αparse␈αtree␈↓ α,
␈↓ α,␈βε≠␈↓␈↓ α,and␈αcalls␈αitself␈αrecursively␈αfor␈αthe␈αrest.␈αTSCAN␈α
is␈α
a␈α
large␈α
IF-THEN-ELSE-IF-THEN␈α
chain␈↓ α,
␈↓ α,␈βε>␈↓␈↓ α,which␈α∞determines␈α∞which␈α∞of␈α∞the␈α∞various␈α∞possible␈α∞structures␈α∞is␈α∞present.␈α
If␈α
it␈α
is␈α
some␈α
kind␈α
of␈↓ α,
␈↓ α,␈βεa␈↓␈↓ α,statement,␈α∪then␈α∪appropriate␈α∪pseudo-code␈α∪is␈α∪emitted.␈α∪The␈α∪preparation␈α∪of␈α∪this␈α∩code␈α∩may␈↓ α,
␈↓ α,␈βπ∧␈↓␈↓ α,require␈αthat␈αcode␈αfor␈αthe␈αevaluation␈αof␈αan␈αexpression.␈α
Such␈α
code␈α
is␈α
prepared␈α
in␈α
the␈α
recursive␈↓ α,
␈↓ α,␈βπ'␈↓␈↓ α,procedure␈αEMITEXPR,␈αwhich␈αperforms␈αtype-consistency␈αchecking␈α(but␈αnot␈αconstant␈α
folding,␈↓ α,
␈↓ α,␈βπJ␈↓␈↓ α,which␈α
could␈α
be␈α
done␈α
here).␈α
Code␈α
for␈α
boolean␈α
tests␈α
is␈α
prepared␈α
by␈α
EMITBOOL.␈↓ α,
␈↓ α,␈βπm␈↓␈↓ α,
␈↓ α,␈βλ⊂␈↓␈↓↓␈↓&trajectory calculator␈↓)βλ␈↓ α,
␈↓ α,␈βλ3␈↓↓␈↓ α,
␈↓ α,␈βλV␈↓↓␈↓␈↓ α,The␈αtrajectory␈αcalculator␈αturns␈αmotion␈αspecifications␈αinto␈αinterpretable␈αtables.␈αAt␈αthe␈α
moment␈↓ α,
␈↓ α,␈βλy␈↓␈↓ α,it␈α⊂allows␈α⊂any␈α⊂one␈α⊂mechanism,␈α⊂that␈α⊂is,␈α⊂one␈α∂arm␈α∂or␈α∂one␈α∂hand.␈α∂Future␈α∂work␈α∂will␈α∂allow␈α∂any␈↓ α,
␈↓ α,␈β	≤␈↓␈↓ α,combination␈α
of␈α
mechanisms.␈α
The␈α
tables␈α
are␈α
calculated␈α
by␈α
the␈α
following␈α
method:␈↓ α,
␈↓ α,␈β	?␈↓␈↓ α,
␈↓ α|␈β	b␈↓␈↓ α|A␈αthread␈αis␈αmade,␈αwith␈αa␈αnode␈αfor␈α
each␈α
place␈α
in␈α
the␈α
motion␈α
specification,␈α
that␈α
is,␈↓ α|
␈↓ α|␈β
¬␈↓␈↓ α|the␈α∞initial␈α
point,␈α
the␈α
departure,␈α
if␈α
any,␈α
the␈α
via␈α
points,␈α
the␈α
approach␈α
point,␈α
and␈↓ α|
␈↓ α|␈β
(␈↓␈↓ α|the␈α
destination.␈α
Arm␈α
or␈α
hand␈α
solutions␈α
are␈α
calculated␈α
for␈α
each␈α
node.␈αIt␈αmay␈αbe␈↓ α|
␈↓ α|␈β
K␈↓␈↓ α|that␈α⊂this␈α⊂serial␈α⊂calculation␈α⊂will␈α⊂lead␈α⊂to␈α⊂flips␈α⊂of␈α⊂the␈α⊂arm.␈α⊂If␈α⊂this␈α∂happens,␈α∂the␈↓ α|
␈↓ α|␈β
n␈↓␈↓ α|proper␈α∪order␈α∩is␈α∩outside-in.␈α∩This␈α∩is␈α∩because␈α∩the␈α∩ARMSOL␈α∩routine␈α∩uses␈α∩the␈↓ α|
␈↓ α|␈β⊃␈↓␈↓ α|previous␈α
solution␈α
to␈α
resolve␈α
ambiguities␈α
in␈α
joint␈α
4␈α
of␈α
the␈α
Scheinman␈α
arms.␈↓ α|
␈↓ α,␈β4␈↓␈↓ α,␈↓ α,
␈↓ α|␈βW␈↓␈↓ α|Any␈α⊃deproach␈α⊃points␈α⊂or␈α⊂calculated␈α⊂via␈α⊂points␈α⊂or␈α⊂calculated␈α⊂destinations␈α⊂must␈↓ α|
␈↓ α|␈βz␈↓␈↓ α|have␈αcode␈αemitted␈αto␈αmake␈αa␈αcell␈αfor␈αthem␈αin␈αthe␈αgraph␈αstructure.␈αThe␈αcell␈αfor␈αa␈↓ α|
␈↓ α|␈β≥␈↓␈↓ α|departure␈α∞is␈α∞marked␈α∞permanently␈α∞invalid.␈α∞Its␈α∞calculator␈α
uses␈α
the␈α
hand␈α
position␈↓ α|
␈↓ α|␈β@␈↓␈↓ α|itself,␈αnot␈αthe␈αplace␈αwhere␈αthe␈αarm␈αwas␈αto␈αbe␈αat␈αthe␈α
start␈α
of␈α
the␈α
motion.␈α
The␈α
cells␈↓ α|
␈↓ α|␈βc␈↓␈↓ α|for␈αthe␈αcalculated␈αvia␈αpoints␈αand␈αthe␈αapproach␈αpoint␈αare␈αin␈αthe␈αgraph␈αstructure␈↓ α|
␈↓ α|␈β
ε␈↓␈↓ α|in␈αthe␈αusual␈α
way.␈α
This␈α
code␈α
must␈α
be␈α
emmitted␈α
at␈α
the␈α
outermost␈α
practical␈α
point␈α
in␈↓ α|
␈↓ α|␈β
)␈↓␈↓ α|the␈αprogram:␈αIf␈αit␈αis␈αtoo␈αfar␈αin,␈αthen␈αit␈αgets␈αredone␈αtoo␈αoften,␈αand␈αif␈αit␈αis␈αtoo␈αfar␈↓ α|
␈↓ α|␈β
L␈↓␈↓ α|out,␈α∂it␈α∂might␈α∂cause␈α∂graph␈α∂structure␈α∞to␈α∞hang␈α∞around␈α∞associated␈α∞to␈α∞non-existent␈↓ α|
␈↓ α|␈β
o␈↓␈↓ α|nodes.␈α
In␈α
any␈α
case,␈α
it␈α
is␈α
necessary␈α
to␈α
put␈α
such␈α
code␈α
at␈α
a␈α
block␈α
entry,␈α
and␈α
to␈α
be␈↓ α|
␈↓ α|␈β∞∩␈↓␈↓ α|sure␈α∞to␈α
get␈α
rid␈α
of␈α
the␈α
resulting␈α
graph␈α
structure␈α
at␈α
block␈α
exit.␈α
The␈α
current␈α
code␈↓ α|
␈↓ α|␈β∞5␈↓␈↓ α|does␈α
not␈α
handle␈α
any␈α
of␈α
this.␈↓ α|
␈↓ α,␈β∞X␈↓␈↓ α,␈↓ α,
␈↓ α|␈β∞{␈↓␈↓ α|At␈αthis␈α
time,␈α
the␈α
fourth␈α
degree␈α
polynomials␈α
for␈α
deproach␈α
segments␈α
are␈α
calculated,␈↓ α|
␈↓ α|␈β∂≡␈↓␈↓ α|and␈α⊗any␈α⊗given␈α∃velocity␈α∃constraints␈α∃are␈α∃noted.␈α∃The␈α∃presence␈α∃of␈α∃a␈α∃velocity␈↓ α|
␈↓ C␈β↓␈↓α[8]
␈↓ α|␈β↓H␈↓␈↓ α|constraint␈α⊂implies␈α⊂that␈α⊂the␈α∂acceleration␈α∂is␈α∂constrained␈α∂to␈α∂zero.␈α∂If␈α∂the␈α∂user␈α∂has␈↓ α|
␈↓ α|␈β↓k␈↓␈↓ α|supplied␈αa␈αtime,␈αit␈αis␈αput␈αin␈αUTIME,␈αand␈αSTIME␈αis␈αcomputed␈αby␈αthe␈αsystem.␈αIf␈↓ α|
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modified␈α
to␈α
the␈α
final␈α
decision␈α
on␈α
the␈α
time␈α
for␈α
the␈↓ α|
␈↓ α|␈βα1␈↓␈↓ α|segment.␈↓ α|
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insure␈α
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to␈α
insert␈α
one␈↓ α|
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POLY␈α
is␈↓ α|
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resulting␈α
trajectory␈α
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emitted.␈↓ α|
␈↓ α,␈βπ∧␈↓␈↓ α,␈↓ α,
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The␈α
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told␈α
which␈α
mechanism␈α
to␈α
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by␈α
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the␈α
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when␈α
the␈↓ α,
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attempted.␈↓ α,
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modules.␈↓ α,
␈↓ α,␈β
ε␈↓␈↓ α,
␈↓ D␈β↓␈↓α[9]