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[ papers ] Tidy the Peterson's Prop type

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Inspired by `Search/Properties.Pythagoras.formula`, having the CSP as
its own type allows for some better docs+understanding than `Prop ? ?`.
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Thomas E. Hansen 2022-09-22 13:33:52 +02:00 committed by CodingCellist
parent d5c9253e7e
commit c5b114209e
1 changed files with 24 additions and 12 deletions
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libs/papers/Search/GCL.idr
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@ -296,13 +296,33 @@ public export
tree : CT (GCL State, GCL State) State
tree = model (GCL State, GCL State) State petersons init
||| The Critical Section Problem:
||| 1) a process's critical section (CS) is only ever accessed by that process
||| and no other
||| 2) any process which wishes to gain access to its CS eventually
||| does so
||| 3) the composition of the processes is deadlock free
||| (we use a stronger requirement: that all process composition must
||| terminate successfully)
public export
CSP : Type
CSP = (arg : Nat **
AND' (GCL State, GCL State) State
(\depth, tree => Mutex depth tree) -- mutually exclusive
(\depth, tree =>
AND' (GCL State, GCL State) State
(\depth, tree => SF depth tree) -- starvation free
(\depth, tree => Termination depth tree) -- completed
depth tree)
arg GCL.tree)
||| A `Prop` (property) containing all the conditions necessary for proving that
||| Peterson's Algorithm is a correct solution to the Critical Section Problem.
||| When evaluated (e.g. through the `auto` search in a `Properties.check`
||| call; specifically `runProp`), it will produce the required proof (which is
||| **very** big).
public export
checkPetersons : Prop ? ?
checkPetersons : Prop ? CSP
checkPetersons = exists $
(mcAND' (GCL State, GCL State) State
checkMutex
@ -315,17 +335,9 @@ checkPetersons = exists $
||| /!\ CAUTION: THIS IS **VERY** SLOW + RESOURCE INTENSIVE /!\
|||
||| Prove that Peterson's Algorithm is a solution to the Critical Section
||| Problem; i.e.:
||| 1) a process's critical section (CS) is only ever accessed by that process
||| and no other
||| 2) any process which wishes to gain access to its CS eventually
||| does so
||| 3) the composition of the processes is deadlock free
||| (we use a stronger requirement: that all process composition must
||| terminate successfully)
|||
||| This evaluates the `checkPetersons` property to obtain a proof (at a search
||| depth of 1000!), at which point we can show that it is depth-invariant.
||| Problem. This evaluates the `checkPetersons` property to obtain a proof (at
||| a search depth of 1000!), at which point we can show that it is
||| depth-invariant.
public export
petersonsCorrect : Models ? ?
GCL.tree