1. Defining A Formal Semantics For The Rosetta Specification Language

2. Overview Introduction Definitions Basic Semantics
Denoting Units of Semantics
State based model
Event based model
Ongoing work
Conclusion
2/18/2019
ECBS'03

3. Next … Introduction Definitions Basic Semantics
Denoting Units of Semantics
State based model
Event based model
Ongoing Work
Conclusion
2/18/2019
ECBS'03

4. Introduction Rosetta systems level design language
Supports different computation models
Addresses integration of information across domains
Uses domains to define semantics of models – there is no unique semantics for all domains
All languages have syntax and semantics
Rosetta has a fixed syntax, but different semantics
Use of denotational functions for interpreting Rosetta syntax
Decomposition of semantics into modules - each module has a different set of denotational functions from another
2/18/2019
ECBS'03

5. Next … Introduction Definitions Basic Semantics
Denoting Units of Semantics
State based model
Event based model
Ongoing Work
Conclusion
2/18/2019
ECBS'03

6. Definitions Model of computation Semantic domain
Distinctive paradigm for computation, communication, …
Semantic domain
Set of mathematical objects used to model agents
Unifying semantic domain
Semantic domain that can be used to represent a variety of different computation paradigms
Unit of semantics
A unifying semantic domain
Denotational semantics
Use of valuation functions to map syntactic constructs to abstract values denoted
2/18/2019
ECBS'03

7. Next … Introduction Definitions Basic Semantics
Denoting Units of Semantics
State based model
Event based model
Ongoing Work
Conclusion
2/18/2019
ECBS'03

8. Basic Semantics – Semantic modules
Static (prelude)
state-based-semantics
signal-based-semantics
continuous
discrete
discrete-time
continuous-time
CSP
trace-based
Unit of semantics
Event-based
State-based
Discrete
Cont.
CSP
SDF
Rosetta logical framework / prelude
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9. Basic Semantics – Denotational semantics
Denotation in the sense of The Scott-Strachey Approach to Programming Language
Define a semantic function that maps symbols from a language to a “known” object
E.g. Let N be such a function for numerals
N1 = 1
None = 1
where ‘’ and ‘’ are semantic brackets, and the element enclosed by them is an object from the language being defined
2/18/2019
ECBS'03

10. Basic Semantics – Evaluation functions
Following Allison’s approach (A Practical Introduction to denotational semantics), we identify 4 semantic functions
Expression evaluation function – given a store, maps an expression to a value
E: Store  Values
Constant evaluation function – maps constants and literals to their values in the abstract value space
V: constants  Values
Function evaluation function – maps binary operators to the corresponding function
O: Values  Values  Values
Term evaluation function – maps terms to a boolean function
T: Terms  Store  boolFnc
where boolFnc:Vars  boolean is a function of any number of parameters to a boolean value
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11. Basic Semantics – Specific evaluation functions
E st = (st_value )
Ev st = Vv
E  ’ st = O E st, E’ st
O= = v1, v2. If v1 = v2 then True else False
: univ  univ  boolean
where
 is an expression  represents identifiers
st is the store v represents constants
 is a binary operator (st_value x) indicates value of x in store st
param.body:typeFnc is a lambda expression of type typeFnc
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12. Basic semantics – Term evaluation examples
Assuming store st contains:
x  2
myFnc  x:int . x + 1
Tx=2 st
 O= (Ex st) V2
 (v1, v2. If v1 = v2 then True else False) 2 2
 if (2 = 2) then True else False
 True
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13. Basic semantics – Term evaluation examples
T(myFnc 1) = 2 st
 O= ((x:int . (x + 1) V1) V2)
 O= ((x:int . (x + 1) 1) 2
 True
T(undefFnc x) = 2 st
 O= ((EundefFnc st) 2) 2
 if ((EundefFnc st) 2) = 2 then True else False
For a facet/model to be consistent, terms always need to be true
 ((EundefFnc st) 2) = 2
a boolean equation with one unknown (EundefFnc st) is the result of the evaluation
2/18/2019
ECBS'03

14. Next … Introduction Definitions Basic Semantics
Denoting Units of Semantics
State based model
Event based model
Ongoing Work
Conclusion
2/18/2019
ECBS'03

15. Denoting Units of Semantics – State based
Denotation of model is a relation over states
Vocabulary of state based models
States – set of states, finite or infinite, denumerable or nondenumerable
 - the current state
next – the state transformation function
@ - the apply function used for dereferencing labels
Semantics of vocabulary
States= {Var  Values} – set of functions from variables to values
: States = Var  Values – current state, particular function
Next = States  States – the transformation function
@: Label  States  Values – the apply function
T: Terms  BoolFnc
E   : Values where  is an expression
2/18/2019
ECBS'03

16. Denoting Units of Semantics – State based
In Rosetta, no sequential execution
x := x + 1 is expressed as + 1
Change of state made explicit
Elements of vocabulary apparent
Definition of additional valuation functions
= v1, fnc . fnc v1
: Label  (Label  univ)  univ
st = E st y = (st_value ) ‘y’
st = (st_value next) (st_value ) ‘y’
2/18/2019
ECBS'03

17. Next … Introduction Definitions Basic Semantics
Denoting Units of Semantics
State based model
Event based model
Ongoing Work
Conclusion
2/18/2019
ECBS'03

18. Denoting Units of Semantics – Event based
Notion started with Lee and Sangiovanni-Vincentelli’s Tagged Signal model
Denotation of a process is partial function or relation on signals
Vocabulary
Tags – set of tags
Values – set of values
Events – set of events, i.e. set of T x V
States – set of states, each state uniquely mapping to an event
Signals – set of signals, each signal being a set of events
@ - the apply function, dereferencing signals in states indexed by events
2/18/2019
ECBS'03

19. Denoting Units of Semantics – Event based
Semantics associated with vocabulary
Events: {Tags x Values} – set of pairs of tags and values
previousEvt: Events – used as index to last state of process
evt: Events – refers to current state and is event being processed
Signals: Events – set of sets of events
sig: Signals = {Events} – particular set of events
getEvent: Signals  Events – next event to be processed
States: {SignalLabel  SignalValue} – states are dependent on events and are used to keep track of signals
EventBasedState: Events  States – each state uniquely referred to by an event
@: SignalLabel  Events  ((Events  States)  SignalValue) – the dereferencing of a signal label is obtained by first finding state corresponding to event and then applying state function to signal label to find signal value
2/18/2019
ECBS'03

20. Denoting Units of Semantics – Event based
Modified Valuation function
= v1, evt . (fnc . (fnc evt) v1)
: SignalLabels Events  (Events  States)  SignalValue
An example
st =
sig (Eevnt st) (st_value EventBasedState) =
sig (st_value evnt) (st_value EventBasedState) =
(fnc . (fnc (st_value evnt)) sig) (st_value EventBasedState) =
((st_value EventBasedState) (st_value evt)) sig
2/18/2019
ECBS'03

21. Next … Introduction Definitions Basic Semantics
Denoting Units of Semantics
State based model
Event based model
Ongoing Work
Conclusion
2/18/2019
ECBS'03

22. Ongoing work Where are we going with this ?
Result of the denotation is a language (lambda) which allows us to do interpretation, evaluation and verification of a facet
However, need to ensure correct and safe semantics
Use of co-algebra as semantic basis for a facet model
Show that
Rosetta Facet
Facet Co-algebra
d, p, f : S
where f; d
Elaborated Facet Semantics (-language)  
 elaboration
2/18/2019
ECBS'03

23. Next … Introduction Definitions Basic Semantics
Denoting Units of Semantics
State based model
Event based model
Ongoing Work
Conclusion
2/18/2019
ECBS'03

24. Conclusion
Rosetta provides a framework where different semantics may be defined
Use of domain specific denotational semantics
Also denote a facet by a monad to allow for facet composition
Moggi – uses monads to modularize semantics
Hudak and Liang – use monad transformers
Wadler – uses monads to add interaction into a purely declarative language
2/18/2019
ECBS'03