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TUNA Project Meeting York University 5 th. December, 2005 occam-pi Multiway Sync Models Peter Welch (Kent University) (updated 12 th. December, 2005)
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This looks at directly modeling Steve Schneider’s FDR script in occam-pi: clump1d2d3dtock-2005-12-06.fdr2 clump1d2d3dtock-2005-12-06.fdr2
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A CELL process holds at most one platelet and imposes a speed limit: channel tock channel enterCell, exitCell CELL = enterCell -> tock -> FCELL [] tock -> CELL FCELL = exitCell -> CELL [] tock -> FCELL channel enterCell, exitCell CELL = enterCell -> tock -> FCELL [] tock -> CELL FCELL = exitCell -> CELL [] tock -> FCELL channel pass : {0..N} AC (i) = {pass.i, pass.i+1, tock} channel pass : {0..N} AC (i) = {pass.i, pass.i+1, tock} LINE = || i:{0..N-1} @ [AC (i)] C (i) C (i) = CELL [[enterCell <- pass.i, exitCell <- pass.i+1]]
![A CELL process holds at most one platelet and imposes a speed limit: channel tock channel enterCell, exitCell CELL = enterCell -> tock -> FCELL [] tock -> CELL FCELL = exitCell -> CELL [] tock -> FCELL channel enterCell, exitCell CELL = enterCell -> tock -> FCELL [] tock -> CELL FCELL = exitCell -> CELL [] tock -> FCELL channel pass : {0..N} AC (i) = {pass.i, pass.i+1, tock} channel pass : {0..N} AC (i) = {pass.i, pass.i+1, tock} LINE = || [AC (i)] C (i) C (i) = CELL [[enterCell <- pass.i, exitCell <- pass.i+1]]](http://images.slideplayer.com/16/5135876/slides/slide_3.jpg "A CELL process holds at most one platelet and imposes a speed limit: channel tock channel enterCell, exitCell CELL = enterCell -> tock -> FCELL [] tock -> CELL FCELL = exitCell -> CELL [] tock -> FCELL channel enterCell, exitCell CELL = enterCell -> tock -> FCELL [] tock -> CELL FCELL = exitCell -> CELL [] tock -> FCELL channel pass : {0..N} AC (i) = {pass.i, pass.i+1, tock} channel pass : {0..N} AC (i) = {pass.i, pass.i+1, tock} LINE = || [AC (i)] C (i) C (i) = CELL [[enterCell <- pass.i, exitCell <- pass.i+1]]")
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STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA channel enterA, exitA, enterB STICKYAB models the sticking of one platelet to another: delete this line and we won’t need the CELL processes!
![STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA channel enterA, exitA, enterB STICKYAB models the sticking of one platelet to another: delete this line and we won’t need the CELL processes!](http://images.slideplayer.com/16/5135876/slides/slide_4.jpg "STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA channel enterA, exitA, enterB STICKYAB models the sticking of one platelet to another: delete this line and we won’t need the CELL processes!")
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AF (i) = {pass.i, pass.i+1, pass.i+2, tock} F (i) = STICKYAB [[enterA <- pass.i, exitA <- pass.i+1, enterB <- pass.i+2]] FS = || i:{0..N-2} @ [AF (i)] F (i) SYS1D = LINE |{|pass, tock|}| FS In 1-D, STICKYAB controls three adjacent cells (where “ A ” is cell “ i ” and “ B ” is cell “ i+2 ”):
![AF (i) = {pass.i, pass.i+1, pass.i+2, tock} F (i) = STICKYAB [[enterA <- pass.i, exitA <- pass.i+1, enterB <- pass.i+2]] FS = || [AF (i)] F (i) SYS1D = LINE |{|pass, tock|}| FS In 1-D, STICKYAB controls three adjacent cells (where A is cell i and B is cell i+2 ):](http://images.slideplayer.com/16/5135876/slides/slide_5.jpg "AF (i) = {pass.i, pass.i+1, pass.i+2, tock} F (i) = STICKYAB [[enterA <- pass.i, exitA <- pass.i+1, enterB <- pass.i+2]] FS = || [AF (i)] F (i) SYS1D = LINE |{|pass, tock|}| FS In 1-D, STICKYAB controls three adjacent cells (where A is cell i and B is cell i+2 ):")
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What we are aiming for:
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PROC sticky.ab (ALT.BARRIER enter.a, exit.a, enter.b, tock) enter.b, tock): STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA
![PROC sticky.ab (ALT.BARRIER enter.a, exit.a, enter.b, tock) enter.b, tock): STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA](http://images.slideplayer.com/16/5135876/slides/slide_7.jpg "PROC sticky.ab (ALT.BARRIER enter.a, exit.a, enter.b, tock) enter.b, tock): STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA")
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PROC sticky.ab (ALT.BARRIER enter.a, exit.a, enter.b, tock) enter.b, tock) VAL INT EMPTY.A IS 0: VAL INT EMPTY.A IS 0: VAL INT ALMOST.A IS 1: VAL INT ALMOST.A IS 1: VAL INT FULL.A IS 2: VAL INT FULL.A IS 2: INITIAL INT state IS EMPTY.A: INITIAL INT state IS EMPTY.A: : PROC sticky.ab (ALT.BARRIER enter.a, exit.a, enter.b, tock) enter.b, tock) VAL INT EMPTY.A IS 0: VAL INT EMPTY.A IS 0: VAL INT ALMOST.A IS 1: VAL INT ALMOST.A IS 1: VAL INT FULL.A IS 2: VAL INT FULL.A IS 2: INITIAL INT state IS EMPTY.A: INITIAL INT state IS EMPTY.A: : STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA
![PROC sticky.ab (ALT.BARRIER enter.a, exit.a, enter.b, tock) enter.b, tock) VAL INT EMPTY.A IS 0: VAL INT EMPTY.A IS 0: VAL INT ALMOST.A IS 1: VAL INT ALMOST.A IS 1: VAL INT FULL.A IS 2: VAL INT FULL.A IS 2: INITIAL INT state IS EMPTY.A: INITIAL INT state IS EMPTY.A: : PROC sticky.ab (ALT.BARRIER enter.a, exit.a, enter.b, tock) enter.b, tock) VAL INT EMPTY.A IS 0: VAL INT EMPTY.A IS 0: VAL INT ALMOST.A IS 1: VAL INT ALMOST.A IS 1: VAL INT FULL.A IS 2: VAL INT FULL.A IS 2: INITIAL INT state IS EMPTY.A: INITIAL INT state IS EMPTY.A: : STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA](http://images.slideplayer.com/16/5135876/slides/slide_8.jpg "PROC sticky.ab (ALT.BARRIER enter.a, exit.a, enter.b, tock) enter.b, tock) VAL INT EMPTY.A IS 0: VAL INT EMPTY.A IS 0: VAL INT ALMOST.A IS 1: VAL INT ALMOST.A IS 1: VAL INT FULL.A IS 2: VAL INT FULL.A IS 2: INITIAL INT state IS EMPTY.A: INITIAL INT state IS EMPTY.A: : PROC sticky.ab (ALT.BARRIER enter.a, exit.a, enter.b, tock) enter.b, tock) VAL INT EMPTY.A IS 0: VAL INT EMPTY.A IS 0: VAL INT ALMOST.A IS 1: VAL INT ALMOST.A IS 1: VAL INT FULL.A IS 2: VAL INT FULL.A IS 2: INITIAL INT state IS EMPTY.A: INITIAL INT state IS EMPTY.A: : STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA")
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PROC sticky.ab (ALT.BARRIER enter.a, exit.a, enter.b, tock) enter.b, tock) VAL INT EMPTY.A IS 0: VAL INT EMPTY.A IS 0: VAL INT ALMOST.A IS 1: VAL INT ALMOST.A IS 1: VAL INT FULL.A IS 2: VAL INT FULL.A IS 2: INITIAL INT state IS EMPTY.A: INITIAL INT state IS EMPTY.A: WHILE TRUE WHILE TRUE CASE state CASE state... EMPTY.A case... EMPTY.A case... ALMOST.A case... ALMOST.A case... FULL.A case... FULL.A case: PROC sticky.ab (ALT.BARRIER enter.a, exit.a, enter.b, tock) enter.b, tock) VAL INT EMPTY.A IS 0: VAL INT EMPTY.A IS 0: VAL INT ALMOST.A IS 1: VAL INT ALMOST.A IS 1: VAL INT FULL.A IS 2: VAL INT FULL.A IS 2: INITIAL INT state IS EMPTY.A: INITIAL INT state IS EMPTY.A: WHILE TRUE WHILE TRUE CASE state CASE state... EMPTY.A case... EMPTY.A case... ALMOST.A case... ALMOST.A case... FULL.A case... FULL.A case: STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA
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{{{ FULL.A case FULL.A ALT ALT SYNC exit.a SYNC exit.a state := EMPTY.A state := EMPTY.A SYNC enter.b SYNC enter.b SEQ SEQ SYNC exit.a SYNC exit.a state := EMPTY.A state := EMPTY.A SYNC tock SYNC tock SKIP SKIP}}} {{{ FULL.A case FULL.A ALT ALT SYNC exit.a SYNC exit.a state := EMPTY.A state := EMPTY.A SYNC enter.b SYNC enter.b SEQ SEQ SYNC exit.a SYNC exit.a state := EMPTY.A state := EMPTY.A SYNC tock SYNC tock SKIP SKIP}}} FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA
![{{{ FULL.A case FULL.A ALT ALT SYNC exit.a SYNC exit.a state := EMPTY.A state := EMPTY.A SYNC enter.b SYNC enter.b SEQ SEQ SYNC exit.a SYNC exit.a state := EMPTY.A state := EMPTY.A SYNC tock SYNC tock SKIP SKIP}}} {{{ FULL.A case FULL.A ALT ALT SYNC exit.a SYNC exit.a state := EMPTY.A state := EMPTY.A SYNC enter.b SYNC enter.b SEQ SEQ SYNC exit.a SYNC exit.a state := EMPTY.A state := EMPTY.A SYNC tock SYNC tock SKIP SKIP}}} FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA](http://images.slideplayer.com/16/5135876/slides/slide_10.jpg "{{{ FULL.A case FULL.A ALT ALT SYNC exit.a SYNC exit.a state := EMPTY.A state := EMPTY.A SYNC enter.b SYNC enter.b SEQ SEQ SYNC exit.a SYNC exit.a state := EMPTY.A state := EMPTY.A SYNC tock SYNC tock SKIP SKIP}}} {{{ FULL.A case FULL.A ALT ALT SYNC exit.a SYNC exit.a state := EMPTY.A state := EMPTY.A SYNC enter.b SYNC enter.b SEQ SEQ SYNC exit.a SYNC exit.a state := EMPTY.A state := EMPTY.A SYNC tock SYNC tock SKIP SKIP}}} FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA")
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What we can (just about) do: using the “oracle” process …
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PROC sticky.ab (VAL INT id, VAL INT enter.a, exit.a, enter.b, tock, VAL INT enter.a, exit.a, enter.b, tock, SHARED CHAN ALT.SYNC.START to.oracle!, SHARED CHAN ALT.SYNC.START to.oracle!, CHAN ALT.SYNC.FINISH from.oracle?) CHAN ALT.SYNC.FINISH from.oracle?): PROC sticky.ab (VAL INT id, VAL INT enter.a, exit.a, enter.b, tock, VAL INT enter.a, exit.a, enter.b, tock, SHARED CHAN ALT.SYNC.START to.oracle!, SHARED CHAN ALT.SYNC.START to.oracle!, CHAN ALT.SYNC.FINISH from.oracle?) CHAN ALT.SYNC.FINISH from.oracle?): STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA
![PROC sticky.ab (VAL INT id, VAL INT enter.a, exit.a, enter.b, tock, VAL INT enter.a, exit.a, enter.b, tock, SHARED CHAN ALT.SYNC.START to.oracle!, SHARED CHAN ALT.SYNC.START to.oracle!, CHAN ALT.SYNC.FINISH from.oracle ) CHAN ALT.SYNC.FINISH from.oracle ): PROC sticky.ab (VAL INT id, VAL INT enter.a, exit.a, enter.b, tock, VAL INT enter.a, exit.a, enter.b, tock, SHARED CHAN ALT.SYNC.START to.oracle!, SHARED CHAN ALT.SYNC.START to.oracle!, CHAN ALT.SYNC.FINISH from.oracle ) CHAN ALT.SYNC.FINISH from.oracle ): STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA](http://images.slideplayer.com/16/5135876/slides/slide_12.jpg "PROC sticky.ab (VAL INT id, VAL INT enter.a, exit.a, enter.b, tock, VAL INT enter.a, exit.a, enter.b, tock, SHARED CHAN ALT.SYNC.START to.oracle!, SHARED CHAN ALT.SYNC.START to.oracle!, CHAN ALT.SYNC.FINISH from.oracle ) CHAN ALT.SYNC.FINISH from.oracle ): PROC sticky.ab (VAL INT id, VAL INT enter.a, exit.a, enter.b, tock, VAL INT enter.a, exit.a, enter.b, tock, SHARED CHAN ALT.SYNC.START to.oracle!, SHARED CHAN ALT.SYNC.START to.oracle!, CHAN ALT.SYNC.FINISH from.oracle ) CHAN ALT.SYNC.FINISH from.oracle ): STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA")
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PROC sticky.ab (VAL INT id, VAL INT enter.a, exit.a, enter.b, tock, VAL INT enter.a, exit.a, enter.b, tock, SHARED CHAN ALT.SYNC.START to.oracle!, SHARED CHAN ALT.SYNC.START to.oracle!, CHAN ALT.SYNC.FINISH from.oracle?) CHAN ALT.SYNC.FINISH from.oracle?)... VAL INT EMPTY.A, ALMOST.A, FULL.A... VAL INT EMPTY.A, ALMOST.A, FULL.A... VAL OFFER emtpy.a, almost.a, full.a, full.a.b... VAL OFFER emtpy.a, almost.a, full.a, full.a.b INITIAL INT state IS EMPTY.A: INITIAL INT state IS EMPTY.A:: PROC sticky.ab (VAL INT id, VAL INT enter.a, exit.a, enter.b, tock, VAL INT enter.a, exit.a, enter.b, tock, SHARED CHAN ALT.SYNC.START to.oracle!, SHARED CHAN ALT.SYNC.START to.oracle!, CHAN ALT.SYNC.FINISH from.oracle?) CHAN ALT.SYNC.FINISH from.oracle?)... VAL INT EMPTY.A, ALMOST.A, FULL.A... VAL INT EMPTY.A, ALMOST.A, FULL.A... VAL OFFER emtpy.a, almost.a, full.a, full.a.b... VAL OFFER emtpy.a, almost.a, full.a, full.a.b INITIAL INT state IS EMPTY.A: INITIAL INT state IS EMPTY.A:: STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA
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PROC sticky.ab (VAL INT id, VAL INT enter.a, exit.a, enter.b, tock, VAL INT enter.a, exit.a, enter.b, tock, SHARED CHAN ALT.SYNC.START to.oracle!, SHARED CHAN ALT.SYNC.START to.oracle!, CHAN ALT.SYNC.FINISH from.oracle?) CHAN ALT.SYNC.FINISH from.oracle?)... VAL INT EMPTY.A, ALMOST.A, FULL.A... VAL INT EMPTY.A, ALMOST.A, FULL.A... VAL OFFER emtpy.a, almost.a, full.a, full.a.b... VAL OFFER emtpy.a, almost.a, full.a, full.a.b INITIAL INT state IS EMPTY.A: INITIAL INT state IS EMPTY.A: WHILE TRUE WHILE TRUE CASE state CASE state... EMPTY.A case... EMPTY.A case... ALMOST.A case... ALMOST.A case... FULL.A case... FULL.A case: PROC sticky.ab (VAL INT id, VAL INT enter.a, exit.a, enter.b, tock, VAL INT enter.a, exit.a, enter.b, tock, SHARED CHAN ALT.SYNC.START to.oracle!, SHARED CHAN ALT.SYNC.START to.oracle!, CHAN ALT.SYNC.FINISH from.oracle?) CHAN ALT.SYNC.FINISH from.oracle?)... VAL INT EMPTY.A, ALMOST.A, FULL.A... VAL INT EMPTY.A, ALMOST.A, FULL.A... VAL OFFER emtpy.a, almost.a, full.a, full.a.b... VAL OFFER emtpy.a, almost.a, full.a, full.a.b INITIAL INT state IS EMPTY.A: INITIAL INT state IS EMPTY.A: WHILE TRUE WHILE TRUE CASE state CASE state... EMPTY.A case... EMPTY.A case... ALMOST.A case... ALMOST.A case... FULL.A case... FULL.A case: STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA
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{{{ VAL OFFER emtpy.a, almost.a, full.a, full.a.b VAL OFFER empty.a IS [enter.a, enter.b, tock]: VAL OFFER almost.a IS [tock, enter.b, exit.a]: VAL OFFER full.a IS [exit.a, enter.b, tock]: VAL OFFER full.a.b IS [exit.a]: }}} {{{ VAL OFFER emtpy.a, almost.a, full.a, full.a.b VAL OFFER empty.a IS [enter.a, enter.b, tock]: VAL OFFER almost.a IS [tock, enter.b, exit.a]: VAL OFFER full.a IS [exit.a, enter.b, tock]: VAL OFFER full.a.b IS [exit.a]: }}} STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA
![{{{ VAL OFFER emtpy.a, almost.a, full.a, full.a.b VAL OFFER empty.a IS [enter.a, enter.b, tock]: VAL OFFER almost.a IS [tock, enter.b, exit.a]: VAL OFFER full.a IS [exit.a, enter.b, tock]: VAL OFFER full.a.b IS [exit.a]: }}} {{{ VAL OFFER emtpy.a, almost.a, full.a, full.a.b VAL OFFER empty.a IS [enter.a, enter.b, tock]: VAL OFFER almost.a IS [tock, enter.b, exit.a]: VAL OFFER full.a IS [exit.a, enter.b, tock]: VAL OFFER full.a.b IS [exit.a]: }}} STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA](http://images.slideplayer.com/16/5135876/slides/slide_15.jpg "{{{ VAL OFFER emtpy.a, almost.a, full.a, full.a.b VAL OFFER empty.a IS [enter.a, enter.b, tock]: VAL OFFER almost.a IS [tock, enter.b, exit.a]: VAL OFFER full.a IS [exit.a, enter.b, tock]: VAL OFFER full.a.b IS [exit.a]: }}} {{{ VAL OFFER emtpy.a, almost.a, full.a, full.a.b VAL OFFER empty.a IS [enter.a, enter.b, tock]: VAL OFFER almost.a IS [tock, enter.b, exit.a]: VAL OFFER full.a IS [exit.a, enter.b, tock]: VAL OFFER full.a.b IS [exit.a]: }}} STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA")
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PROC sticky.ab (VAL INT id, VAL INT enter.a, exit.a, enter.b, tock, VAL INT enter.a, exit.a, enter.b, tock, SHARED CHAN ALT.SYNC.START to.oracle!, SHARED CHAN ALT.SYNC.START to.oracle!, CHAN ALT.SYNC.FINISH from.oracle?) CHAN ALT.SYNC.FINISH from.oracle?)... VAL INT EMPTY.A, ALMOST.A, FULL.A... VAL INT EMPTY.A, ALMOST.A, FULL.A... VAL OFFER emtpy.a, almost.a, full.a, full.a.b... VAL OFFER emtpy.a, almost.a, full.a, full.a.b INITIAL INT state IS EMPTY.A: INITIAL INT state IS EMPTY.A: WHILE TRUE WHILE TRUE CASE state CASE state... EMPTY.A case... EMPTY.A case... ALMOST.A case... ALMOST.A case... FULL.A case... FULL.A case: PROC sticky.ab (VAL INT id, VAL INT enter.a, exit.a, enter.b, tock, VAL INT enter.a, exit.a, enter.b, tock, SHARED CHAN ALT.SYNC.START to.oracle!, SHARED CHAN ALT.SYNC.START to.oracle!, CHAN ALT.SYNC.FINISH from.oracle?) CHAN ALT.SYNC.FINISH from.oracle?)... VAL INT EMPTY.A, ALMOST.A, FULL.A... VAL INT EMPTY.A, ALMOST.A, FULL.A... VAL OFFER emtpy.a, almost.a, full.a, full.a.b... VAL OFFER emtpy.a, almost.a, full.a, full.a.b INITIAL INT state IS EMPTY.A: INITIAL INT state IS EMPTY.A: WHILE TRUE WHILE TRUE CASE state CASE state... EMPTY.A case... EMPTY.A case... ALMOST.A case... ALMOST.A case... FULL.A case... FULL.A case: STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA STICKAB = EMPTYA EMPTYA = enterA -> ALMOSTA [] enterB -> EMPTYA [] tock -> EMPTYA ALMOSTA = tock -> FULLA [] enterB -> ALMOSTA [] exitA -> EMPTYA FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA
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{{{ FULL.A case FULL.A INT result: INT result: SEQ SEQ CLAIM to.oracle! CLAIM to.oracle! to.oracle ! id; full.a to.oracle ! id; full.a from.oracle ? result; full.a from.oracle ? result; full.a CASE result CASE result... exit.a... exit.a... enter.b... enter.b... tock... tock}}} {{{ FULL.A case FULL.A INT result: INT result: SEQ SEQ CLAIM to.oracle! CLAIM to.oracle! to.oracle ! id; full.a to.oracle ! id; full.a from.oracle ? result; full.a from.oracle ? result; full.a CASE result CASE result... exit.a... exit.a... enter.b... enter.b... tock... tock}}} [exit.a, enter.b, tock] FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA
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{{{ exit.a exit.a state := EMPTY.A state := EMPTY.A}}} {{{ exit.a exit.a state := EMPTY.A state := EMPTY.A}}} {{{ tock tock SKIP SKIP}}} {{{ tock tock SKIP SKIP}}} FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA
![{{{ exit.a exit.a state := EMPTY.A state := EMPTY.A}}} {{{ exit.a exit.a state := EMPTY.A state := EMPTY.A}}} {{{ tock tock SKIP SKIP}}} {{{ tock tock SKIP SKIP}}} FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA](http://images.slideplayer.com/16/5135876/slides/slide_18.jpg "{{{ exit.a exit.a state := EMPTY.A state := EMPTY.A}}} {{{ exit.a exit.a state := EMPTY.A state := EMPTY.A}}} {{{ tock tock SKIP SKIP}}} {{{ tock tock SKIP SKIP}}} FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA")
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{{{ enter.b enter.b SEQ SEQ CLAIM to.oracle! CLAIM to.oracle! to.oracle ! id; full.a.b to.oracle ! id; full.a.b from.oracle ? result; full.a.b from.oracle ? result; full.a.b state := EMPTY.A state := EMPTY.A}}} {{{ enter.b enter.b SEQ SEQ CLAIM to.oracle! CLAIM to.oracle! to.oracle ! id; full.a.b to.oracle ! id; full.a.b from.oracle ? result; full.a.b from.oracle ? result; full.a.b state := EMPTY.A state := EMPTY.A}}} [exit.a] exit.a FULLA = exitA -> EMPTYA [] enterB -> exitA -> EMPTYA [] tock -> FULLA
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channel tock channel enterCell, exitCell CELL = enterCell -> tock -> FCELL [] tock -> CELL FCELL = exitCell -> CELL [] tock -> FCELL channel enterCell, exitCell CELL = enterCell -> tock -> FCELL [] tock -> CELL FCELL = exitCell -> CELL [] tock -> FCELL channel pass : {0..N} AC (i) = {pass.i, pass.i+1, tock} channel pass : {0..N} AC (i) = {pass.i, pass.i+1, tock} LINE = || i:{0..N-1} @ [AC (i)] C (i) C (i) = CELL [[enterCell <- pass.i, exitCell <- pass.i+1]] Let’s use the CELL processes to synchronise visualisation (after a tock ) of their state:
![channel tock channel enterCell, exitCell CELL = enterCell -> tock -> FCELL [] tock -> CELL FCELL = exitCell -> CELL [] tock -> FCELL channel enterCell, exitCell CELL = enterCell -> tock -> FCELL [] tock -> CELL FCELL = exitCell -> CELL [] tock -> FCELL channel pass : {0..N} AC (i) = {pass.i, pass.i+1, tock} channel pass : {0..N} AC (i) = {pass.i, pass.i+1, tock} LINE = || [AC (i)] C (i) C (i) = CELL [[enterCell <- pass.i, exitCell <- pass.i+1]] Let’s use the CELL processes to synchronise visualisation (after a tock ) of their state:](http://images.slideplayer.com/16/5135876/slides/slide_20.jpg "channel tock channel enterCell, exitCell CELL = enterCell -> tock -> FCELL [] tock -> CELL FCELL = exitCell -> CELL [] tock -> FCELL channel enterCell, exitCell CELL = enterCell -> tock -> FCELL [] tock -> CELL FCELL = exitCell -> CELL [] tock -> FCELL channel pass : {0..N} AC (i) = {pass.i, pass.i+1, tock} channel pass : {0..N} AC (i) = {pass.i, pass.i+1, tock} LINE = || [AC (i)] C (i) C (i) = CELL [[enterCell <- pass.i, exitCell <- pass.i+1]] Let’s use the CELL processes to synchronise visualisation (after a tock ) of their state:")
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channel tock channel enterCell, exitCell CELL = enterCell -> tock -> FCELL [] tock -> CELL FCELL = exitCell -> CELL [] tock -> FCELL channel enterCell, exitCell CELL = enterCell -> tock -> FCELL [] tock -> CELL FCELL = exitCell -> CELL [] tock -> FCELL channel pass : {0..N} AC (i) = {pass.i, pass.i+1, tock} channel pass : {0..N} AC (i) = {pass.i, pass.i+1, tock} LINE = || i:{0..N-1} @ [AC (i)] C (i) C (i) = CELL [[enterCell <- pass.i, exitCell <- pass.i+1]] For each CELL process, we add a draw event which always follows a tock :
![channel tock channel enterCell, exitCell CELL = enterCell -> tock -> FCELL [] tock -> CELL FCELL = exitCell -> CELL [] tock -> FCELL channel enterCell, exitCell CELL = enterCell -> tock -> FCELL [] tock -> CELL FCELL = exitCell -> CELL [] tock -> FCELL channel pass : {0..N} AC (i) = {pass.i, pass.i+1, tock} channel pass : {0..N} AC (i) = {pass.i, pass.i+1, tock} LINE = || [AC (i)] C (i) C (i) = CELL [[enterCell <- pass.i, exitCell <- pass.i+1]] For each CELL process, we add a draw event which always follows a tock :](http://images.slideplayer.com/16/5135876/slides/slide_21.jpg "channel tock channel enterCell, exitCell CELL = enterCell -> tock -> FCELL [] tock -> CELL FCELL = exitCell -> CELL [] tock -> FCELL channel enterCell, exitCell CELL = enterCell -> tock -> FCELL [] tock -> CELL FCELL = exitCell -> CELL [] tock -> FCELL channel pass : {0..N} AC (i) = {pass.i, pass.i+1, tock} channel pass : {0..N} AC (i) = {pass.i, pass.i+1, tock} LINE = || [AC (i)] C (i) C (i) = CELL [[enterCell <- pass.i, exitCell <- pass.i+1]] For each CELL process, we add a draw event which always follows a tock :")
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channel tock, draw channel enterCell, exitCell CELL = enterCell -> tock -> draw ->FCELL [] tock -> draw ->CELL CELL = enterCell -> tock -> draw -> FCELL [] tock -> draw -> CELL FCELL = exitCell -> CELL [] tock -> draw ->FCELL FCELL = exitCell -> CELL [] tock -> draw -> FCELL channel enterCell, exitCell CELL = enterCell -> tock -> draw ->FCELL [] tock -> draw ->CELL CELL = enterCell -> tock -> draw -> FCELL [] tock -> draw -> CELL FCELL = exitCell -> CELL [] tock -> draw ->FCELL FCELL = exitCell -> CELL [] tock -> draw -> FCELL channel pass : {0..N} AC (i) = {pass.i, pass.i+1, tock, draw} channel pass : {0..N} AC (i) = {pass.i, pass.i+1, tock, draw} LINE = || i:{0..N-1} @ [AC (i)] tock -> draw ->C (i) LINE = || i:{0..N-1} @ [AC (i)] tock -> draw -> C (i) C (i) = CELL [[enterCell <- pass.i, exitCell <- pass.i+1]] For each CELL process, we add a draw event which always follows a tock :
![channel tock, draw channel enterCell, exitCell CELL = enterCell -> tock -> draw ->FCELL [] tock -> draw ->CELL CELL = enterCell -> tock -> draw -> FCELL [] tock -> draw -> CELL FCELL = exitCell -> CELL [] tock -> draw ->FCELL FCELL = exitCell -> CELL [] tock -> draw -> FCELL channel enterCell, exitCell CELL = enterCell -> tock -> draw ->FCELL [] tock -> draw ->CELL CELL = enterCell -> tock -> draw -> FCELL [] tock -> draw -> CELL FCELL = exitCell -> CELL [] tock -> draw ->FCELL FCELL = exitCell -> CELL [] tock -> draw -> FCELL channel pass : {0..N} AC (i) = {pass.i, pass.i+1, tock, draw} channel pass : {0..N} AC (i) = {pass.i, pass.i+1, tock, draw} LINE = || [AC (i)] tock -> draw ->C (i) LINE = || [AC (i)] tock -> draw -> C (i) C (i) = CELL [[enterCell <- pass.i, exitCell <- pass.i+1]] For each CELL process, we add a draw event which always follows a tock :](http://images.slideplayer.com/16/5135876/slides/slide_22.jpg "channel tock, draw channel enterCell, exitCell CELL = enterCell -> tock -> draw ->FCELL [] tock -> draw ->CELL CELL = enterCell -> tock -> draw -> FCELL [] tock -> draw -> CELL FCELL = exitCell -> CELL [] tock -> draw ->FCELL FCELL = exitCell -> CELL [] tock -> draw -> FCELL channel enterCell, exitCell CELL = enterCell -> tock -> draw ->FCELL [] tock -> draw ->CELL CELL = enterCell -> tock -> draw -> FCELL [] tock -> draw -> CELL FCELL = exitCell -> CELL [] tock -> draw ->FCELL FCELL = exitCell -> CELL [] tock -> draw -> FCELL channel pass : {0..N} AC (i) = {pass.i, pass.i+1, tock, draw} channel pass : {0..N} AC (i) = {pass.i, pass.i+1, tock, draw} LINE = || [AC (i)] tock -> draw ->C (i) LINE = || [AC (i)] tock -> draw -> C (i) C (i) = CELL [[enterCell <- pass.i, exitCell <- pass.i+1]] For each CELL process, we add a draw event which always follows a tock :")
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channel tock, draw channel enterCell, exitCell CELL = enterCell -> tock -> draw -> FCELL [] tock -> draw -> CELL FCELL = exitCell -> CELL [] tock -> draw -> FCELL channel enterCell, exitCell CELL = enterCell -> tock -> draw -> FCELL [] tock -> draw -> CELL FCELL = exitCell -> CELL [] tock -> draw -> FCELL channel pass : {0..N} AC (i) = {pass.i, pass.i+1, tock, draw} channel pass : {0..N} AC (i) = {pass.i, pass.i+1, tock, draw} LINE = || i:{0..N-1} @ [AC (i)] tock -> draw -> C (i) C (i) = CELL [[enterCell <- pass.i, exitCell <- pass.i+1]] Visualisation will take place between a tockand a draw – when the cells can’t change state: Visualisation will take place between a tock and a draw – when the cells can’t change state:
![channel tock, draw channel enterCell, exitCell CELL = enterCell -> tock -> draw -> FCELL [] tock -> draw -> CELL FCELL = exitCell -> CELL [] tock -> draw -> FCELL channel enterCell, exitCell CELL = enterCell -> tock -> draw -> FCELL [] tock -> draw -> CELL FCELL = exitCell -> CELL [] tock -> draw -> FCELL channel pass : {0..N} AC (i) = {pass.i, pass.i+1, tock, draw} channel pass : {0..N} AC (i) = {pass.i, pass.i+1, tock, draw} LINE = || [AC (i)] tock -> draw -> C (i) C (i) = CELL [[enterCell <- pass.i, exitCell <- pass.i+1]] Visualisation will take place between a tockand a draw – when the cells can’t change state: Visualisation will take place between a tock and a draw – when the cells can’t change state:](http://images.slideplayer.com/16/5135876/slides/slide_23.jpg "channel tock, draw channel enterCell, exitCell CELL = enterCell -> tock -> draw -> FCELL [] tock -> draw -> CELL FCELL = exitCell -> CELL [] tock -> draw -> FCELL channel enterCell, exitCell CELL = enterCell -> tock -> draw -> FCELL [] tock -> draw -> CELL FCELL = exitCell -> CELL [] tock -> draw -> FCELL channel pass : {0..N} AC (i) = {pass.i, pass.i+1, tock, draw} channel pass : {0..N} AC (i) = {pass.i, pass.i+1, tock, draw} LINE = || [AC (i)] tock -> draw -> C (i) C (i) = CELL [[enterCell <- pass.i, exitCell <- pass.i+1]] Visualisation will take place between a tockand a draw – when the cells can’t change state: Visualisation will take place between a tock and a draw – when the cells can’t change state:")
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DISPLAY = (tock -> RENDER_CELLS); (draw -> DISPLAY) A DISPLAY process also synchronises on tock and draw, rendering the full or empty states of the cells in between: RENDER_CELLS =... The CELL processes share state variables with DISPLAY, which observes them only during RENDER_CELLS. These state variables could be easily modeled as processes with load and store channels.
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Note also that all process commit to the draw event – it is never offered as an option! channel enterCell, exitCell CELL = enterCell -> tock -> draw -> FCELL [] tock -> draw -> CELL FCELL = exitCell -> CELL [] tock -> draw -> FCELL channel enterCell, exitCell CELL = enterCell -> tock -> draw -> FCELL [] tock -> draw -> CELL FCELL = exitCell -> CELL [] tock -> draw -> FCELL LINE = || i:{0..N-1} @ [AC (i)] tock -> draw -> C (i) C (i) = CELL [[enterCell <- pass.i, exitCell <- pass.i+1]] DISPLAY = (tock -> RENDER_CELLS); (draw -> DISPLAY)
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PROC cell (ALT.BARRIER enter, exit, tock, BARRIER draw, BYTE pixel) BARRIER draw, BYTE pixel) : PROC cell (ALT.BARRIER enter, exit, tock, BARRIER draw, BYTE pixel) BARRIER draw, BYTE pixel) INITIAL BOOL empty IS TRUE: INITIAL BOOL empty IS TRUE: SEQ SEQ pixel := empty.colour pixel := empty.colour SYNC tock SYNC tock SYNC draw SYNC draw WHILE TRUE WHILE TRUE IF IF empty empty... empty... empty TRUE TRUE... full... full: CELL = enter -> tock -> draw -> FCELL [] tock -> draw -> CELL FCELL = exit -> CELL [] tock -> draw -> FCELL CELL = enter -> tock -> draw -> FCELL [] tock -> draw -> CELL FCELL = exit -> CELL [] tock -> draw -> FCELL pixel rendering takes place between these SYNC s
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{{{ empty case ALT SYNC enter SYNC enter SEQ SEQ pixel := full.colour pixel := full.colour empty := FALSE empty := FALSE SYNC tock SYNC tock SYNC draw SYNC draw SYNC tock SYNC tock SYNC draw SYNC draw}}} pixel rendering takes place between these SYNC s … and between these SYNC s CELL = enter -> tock -> draw -> FCELL [] tock -> draw -> CELL FCELL = exit -> CELL [] tock -> draw -> FCELL CELL = enter -> tock -> draw -> FCELL [] tock -> draw -> CELL FCELL = exit -> CELL [] tock -> draw -> FCELL
![{{{ empty case ALT SYNC enter SYNC enter SEQ SEQ pixel := full.colour pixel := full.colour empty := FALSE empty := FALSE SYNC tock SYNC tock SYNC draw SYNC draw SYNC tock SYNC tock SYNC draw SYNC draw}}} pixel rendering takes place between these SYNC s … and between these SYNC s CELL = enter -> tock -> draw -> FCELL [] tock -> draw -> CELL FCELL = exit -> CELL [] tock -> draw -> FCELL CELL = enter -> tock -> draw -> FCELL [] tock -> draw -> CELL FCELL = exit -> CELL [] tock -> draw -> FCELL](http://images.slideplayer.com/16/5135876/slides/slide_27.jpg "{{{ empty case ALT SYNC enter SYNC enter SEQ SEQ pixel := full.colour pixel := full.colour empty := FALSE empty := FALSE SYNC tock SYNC tock SYNC draw SYNC draw SYNC tock SYNC tock SYNC draw SYNC draw}}} pixel rendering takes place between these SYNC s … and between these SYNC s CELL = enter -> tock -> draw -> FCELL [] tock -> draw -> CELL FCELL = exit -> CELL [] tock -> draw -> FCELL CELL = enter -> tock -> draw -> FCELL [] tock -> draw -> CELL FCELL = exit -> CELL [] tock -> draw -> FCELL")
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{{{ full case ALT SYNC exit SYNC exit SEQ SEQ pixel := empty.colour pixel := empty.colour empty := TRUE empty := TRUE SYNC tock SYNC tock SYNC draw SYNC draw}}} pixel rendering takes place between these SYNC s CELL = enter -> tock -> draw -> FCELL [] tock -> draw -> CELL FCELL = exit -> CELL [] tock -> draw -> FCELL CELL = enter -> tock -> draw -> FCELL [] tock -> draw -> CELL FCELL = exit -> CELL [] tock -> draw -> FCELL
![{{{ full case ALT SYNC exit SYNC exit SEQ SEQ pixel := empty.colour pixel := empty.colour empty := TRUE empty := TRUE SYNC tock SYNC tock SYNC draw SYNC draw}}} pixel rendering takes place between these SYNC s CELL = enter -> tock -> draw -> FCELL [] tock -> draw -> CELL FCELL = exit -> CELL [] tock -> draw -> FCELL CELL = enter -> tock -> draw -> FCELL [] tock -> draw -> CELL FCELL = exit -> CELL [] tock -> draw -> FCELL](http://images.slideplayer.com/16/5135876/slides/slide_28.jpg "{{{ full case ALT SYNC exit SYNC exit SEQ SEQ pixel := empty.colour pixel := empty.colour empty := TRUE empty := TRUE SYNC tock SYNC tock SYNC draw SYNC draw}}} pixel rendering takes place between these SYNC s CELL = enter -> tock -> draw -> FCELL [] tock -> draw -> CELL FCELL = exit -> CELL [] tock -> draw -> FCELL CELL = enter -> tock -> draw -> FCELL [] tock -> draw -> CELL FCELL = exit -> CELL [] tock -> draw -> FCELL")
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Alternatively, we could equip each CELL process with a drawing channel to which it would output its state (if changed) immediately following a tock. The DISPLAY process could then monitor the drawing channels and promise to service them – i.e. always accept them. It would not have to engage with tock. Many other scenarios for visualisation are possible … The described method of giving each CELL process direct access to the pixel used for rendering may be the most efficient.
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