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of the program's equations by using the initial algebra semantics? Why do
we obtain a unique solution of a flattened guarded system of program's equa-
tions?
7. What is the operational meaning
[ p k ]
of a process (program) p k at the state
ass(p k ) ? Why is the finite branching LTS of the
obtained update processes fundamental w.r.t. the Peter Aczel's anti-foundation
axiom, and which solution is adopted here? How are the abstract behavior func-
tor and its final co-algebra semantics defined, and what is the greatest fixed
point of it? What is a bisimulation relation and how is the observational equiv-
alence for the processes defined? Explain the unique solution based on the final
semantics and coinductive principle, and explain the meaning of the observa-
tional comonad.
8. What is the meaning of the “specification versus solution”, that is, duality of
the initial and final semantics? Define a table of dual concepts obtained from a
combined diagram:
(an instance database) A =
9. How are we able to combine the initial and final semantics diagrams in order
to express the semantic adequateness of a denotational algebra (model) for the
operational behavior? Can we use the final semantics of the abstract behav-
ior endofunctor
B P instead of the final semantics of the flattened guarded set
of equations for the processes, and how (explain the commutative diagram in
Proposition 39 )? What are the terms of the DB-denotational semantics for the
abstract Σ P -algebras, and their relationship with DB category? How can we
represent the LTS trees in
D P S (the greatest fixed point of the behavior endo-
functor) by the subcategories of DB ? Based on this representation, define the
adequate DB-denotational semantics for the operational semantics based on the
DB category.
10. What is the Structural Operational Semantics (SOS), the Functorial Operational
Semantics (FOS) for a syntax monad
B P , and what is its dual
semantics? Explain the relationship between the abstract SOS-denotational se-
mantics and the DB-denotational semantics given by the following commutative
diagram
T P and a behavior
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