Unifying Theories Execution History Tony Hoare In honour of Manfred Broy 30 October 2009

Manfred Broy and Tony Hoare at Marktoberdorf.

Unifying… Memory – shared/private, weakly/strongly consistent Communication – synchronised/buffered, reliable/unreliable Resource management – dynamic/nested, disposed/collected

Unifying… Sequential programming – C, Java, C#,... Process algebras and calculi – stream processing functions – CCS, CSP, pi Shared memory, threads – fine-grained, coarse-grained, transactions – weakly consistent memory

Labelled graphs Trace semantics(Mazurkiewicz) Regular expressions(Kleene) Causal nets(Petri) Event structure configurations(Winskel) Message Sequence Charts(UML) INSIGHT! They are all labeled graphs

A labeled Graph E: a set of nodes (events) A: a set of arrows (denoting data flow) L: a set of labels (to be determined) source, target: A -> E label: A -> L (labelling the arrow) label: E -> L (labelling the events)

Program Execution is recorded as a trace of all events that have occurred – drawn as boxes all dependencies between them – drawn as arrows source target – the target could not occur before source

Program Execution is recorded as a trace of: all events that have occurred – drawn as boxes – with labels naming the executed command all dependencies between them – drawn as arrows source target – with labels naming resource.value, etc. x := 3 x.3 x := 3x = 3

A Sequential Resource begin end next

Implementation begin end next allocated globally/on stack/in heap/… disposed from stack/by command/by collector/by OS

Fork fanout all arrows of the graph have the same source

Join fanin all arrows of the graph have the same target

Shared Resource faninfanout begin end

Publication faninfanout publish next

Assignment fanin fanout := 3 := 7 next =3

A variable begin end next := fanin fanout = = ==

A variable begin end next := fanin fanout = = ==

A variable begin end next := fanin fanout = = ==

A variable begin end next := fanin fanout = = ==

A variable begin end next := fanin fanout = = ==

A variable begin end next := fanin fanout = = ==

A variable begin end next := fanin fanout = = ==

Unassigned fetch begin end next := fanin fanout fanin fanout

Communication !!! ? ?? send

Ordering next !!! ? ?? send

Channel next !!! ? ?? end begin next send

Single-buffered Channel next !!! ? ?? end begin next send sync

Synchronised next !!! ? ?? end begin next send sync

Lossy channel next !!! ? ? send

Stuttering channel next !! ? ?? send

Fraudulent channel next !! ? ?? send

Overtaking next !! ?? send

Reliable channel reliable =  loss &  fraud &  stutter &  merge &  overtaking

Threads fork begin end next begin next join begin next end fork join

An Atomic Assignment x := x + y x = 3 y= 4 x := 7

An Atomic Assignment x := x + y x = 3 y= 4 x := 7 x.fanout.3x.fanin y.fanout.4 y.fanin x.next x.fanout.7 x.fanin t.next

An Atomic Assignment x := x + y x = 3 y= 4 x := 7 x.fanout.3x.fanin y.fanout.4 y.fanin x.next x.fanout.7 x.fanin t.next

Events and atomic actions Each occurrence of an event in the trace of program execution belongs to the trace of exactly one resource (thread, variable, channel,…) Atomic actions are groups of synchronised events, including exactly one from the thread which invoked the action, and one (or more) from every resource used by it.

v.fanout v:= 4 v := 3v:= 6 v.next v.fanin v.fanout v.fanin =3 = 4= 6 v.next A variable (fully labelled) v.fanout

t.next v:= 4 v := 3v:= 6 thread t interfering thread v.next =3 = 4= 6 v.next A shared variable v.next

Weakly consistent memory as implemented in multi-core architecture, is even more complicated to define … and more still to use! A common architecture is TSO

Total Store Ordering :=4 sync :=3 :=6global memory sync

Local memory next val next :=4 sync :=3 :=6 := 4:= 3:= 6 local memory global memory sync

Local memory access next val next :=4 sync :=3 :=6 := 4:= 3:= 6 local memory global memory = 3= 4= 6 local memory sync

next val next :=4 sync :=3 :=6 := 4:= 3:= 6 local memory global memory other thread :=4 = 3= 4= 6 local memory sync :=3

Memory Barrier next val next sync :=4 :=3 :=6 := 4:= 3:= 6bar local memory global memory

Summary Dependency and data flow are a primitive concepts adequate to describe the dynamic behaviour of many kinds of computing resource Labelled graphs provide a general framework adequate for a unifying theory of dependency