Analysis of dependencies on non-deterministic operations
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This analysis is useful if some operation has a non-deterministic
behavior and one wants to find the reason for this behavior.
For this purpose, the analysis computes for each operation the set of
operations with a non-deterministic definition that might be called
by this operation. An operation has a non-deterministic definition
if its definition contains overlapping left-hand sides or free variables.
Non-deterministic operations that are called by other
non-deterministic operations are ignored so that only the first
(w.r.t. the call sequence) non-deterministic operations are returned.
Moreover, if the non-determinism of an operation is encapsulated by a
set function or an encapsulated search operation of the module
`AllSolutions`, it is considered as deterministic.
For instance, consider the operations
last xs | _ ++ [x] == xs = x where x free
coin = 0 ? 1
lastCoin = id (last [coin])
Then the operation `lastCoin` depends on the non-deterministic
operations `last` and `coin`. Now consider the operations
f x = x ? lastCoin
g x = f x
Then the operation `g` depends on the non-deterministic operation `f`,
but the dependency on the non-deterministic
operations `last` and `coin` is not reported.
In the long analysis output (produced by CASS in batch mode),
the non-deterministic operations are shown together with
the operation which directly calls the non-deterministic operation.