Examples of decidable

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In general, the set of valid flow judgments for a program is not decidable.
Any set with decidable identities has collapsed identity sets.
This suggests that decidable restrictions of our framework may be successfully defined with applications in program transformation.
To keep the calculus decidable, one has to settle for internal representations of the definitional equalities in object languages.
Similarly, we ignore issues related to the decidability of equality and do not require equality to be decidable.
This new reconstruction avoids elaboration and is decidable in theory.
However, this does not in itself lead to the conclusion that isomorphism of our invariants is decidable.
In this paper we prove that the isomorphism problem in this setting is decidable, even when the assumption of non-singularity is removed.
The emphasis is on achieving maximum expressiveness whilst maintaining sound, decidable and understandable typechecking.
And even though we get decidable unification problems by removing the distributivity axiom, it is not clear that the algorithms can be made efficient enough.
We also deduce that the parameterised model-checking problem of the universal disjunction-free fragment of the -calculus is decidable.
From this, we deduce that the -calculus model-checking problem is decidable for this class of systems.
As a direct consequence of this result, we obtain that provability is decidable in the considered fragment.
The only known class of infinite-state processes where simulation preorder/equivalence remains decidable are one-counter nets.
Consider, for example, the property of both believing something, and not believing anything, which entails that arithmetic is decidable.
Then one defines a larger, and still decidable, class of queries that can easily be rewritten in this 'hereditarily finite' form.
Equivalence is straightforward between constants, but not between in-line functions or macro definitions; some decidable approximation must be agreed upon.
Depending on the nature of the concepts, the presence or absence of such inconsistencies may not be decidable or tractable.

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