1. Interface Theories in Ptolemy II
Ben Lickly
Stavros Tripakis
Interface Theories in Ptolemy II
Interface Theories
Checking Compositions
Composition by feedback
Acknowledgement
This work was supported in part by the Center for Hybrid and Embedded Software Systems (CHESS) at UC Berkeley, which receives support from the National Science Foundation (NSF awards # (CSR-EHS:PRET) and # (CSR-CPS)), the U. S. Army Research Office (ARO#W911NF ), the U. S. Air Force Office of Scientific Research (MURI #FA ), the Air Force Research Lab (AFRL), the State of California Micro Program, and the following companies: Agilent, Bosch, HSBC, Lockheed-Martin, National Instruments, and Toyota.
In addition, compositions of interfaces are also defined formally. Thus we should be able to compose and check compositions of interfaces automatically with Yices as well. B A A’ B’
(1) If A’  A and B’  B, then A’ • B’  A • B.
(2) If A’  A and A satisfies P then A’ satisfies P.
satisfaction
composition
Interface theory defines how to abstract and prove properties about components and their compositions.
This allows for modular and reusable designs. x
A, φ1 y
Composition by connection
A must be Moore with respect to input x:
i.e., the contract of A does not depend on x
Input assumptions: set of legal input assignments
composite
interface x y
Theoretical results x
A, φ1 y z
B, φ2 w
Interface Definition
Refinement preserved by composition:
If A’ ≤ A and B’ ≤ B then θ(A’,B’) ≤ θ(A,B)
θ is a composition by connection
If A’ ≤ A then κ(A’) ≤ κ(A)
κ is a composition by feedback
Both A and A’ must be Moore
Refinement does not necessarily preserve Mooreness
E.g., (y = 2x) refines (y mod 2 = 0)
Refinement characterizes pluggability:
A’ ≤ A iff for all environments E, pluggable(A,E) implies pluggable(A’,E)
Note that this is iff I
Set of input variables
Contract
Contract is relation between input and output assignments
Set of output variables
Connection example
A(X)
A(Y)
Set of all assignments
of variables in X
Set of all assignments
of variables in Y
Future Work
Implementation
Extend the theory
More flexibility in feedback
Use Ptolemy models to record different theories
Improve the Ptolemy implementation
Infer the order of compositions in a large graph.
Express and check refinement relationships.
In this project, we connect Ptolemy II to the Yices SMT solver. Here, interfaces can be expressed as Ptolemy expressions, which are parsed and converted into a form that Yices accepts. The interfaces can then be checked for satisfiability.
Division example
Divide x y z
composite
interface x y z w
February 11, 2010
Center for Hybrid and Embedded Software Systems