On the Meaning of Message Sequence Charts

Transcription

1 On the Meaning of Message Sequence Chats Manfed Boy Institut fü Infomatik Technische Univesität München Topics: We discuss Message Sequence Chats (MSCs) as a technique to descibe pattens of the inteaction between the components of a inteactive system as a technique to specify the behavio of the components of a system thei systematic use in the softwae development pocess Questions: What is the fomal meaning of a MSC fo the components of a system? How can MSCs be combined? What is the fomal meaning of a set of MSCs? How fa can MSCs seve as a pecise and compehensive mean of specification? What type of systems do MSCs efe to and what popeties do they specify pecisely? What is the methodological ole of MSCs and how do they fit into the development pocess? Pof. D. Manfed Boy: MeanMSC The Pupose of Message Sequence Chats LSTORE location c unlocked lock(p, c) location c unlocked MSCs as logical popeties of systems. locked(p, c) MSCs as pedicates on system components. location c locked fo pocess p Example: Component x: StoeIn y: StoeOut location c locked fo pocess p Reading and witing location c unlock(p, c) unlocked(p, c) location c locked fo pocess p LSTORE location c unlocked Pof. D. Manfed Boy: MeanMSC Successful Access to the Stoe Pof. D. Manfed Boy: MeanMSC

2 ENVIRONMENT x": StoeIn CACHE y": StoeOut CACHE x : StoeIn MANAGER x" s : StoeIn z : StoeIn y : StoeOut :StoeIn t : StoeOut s: StoeIn z: StoeOut LSTORE intenal Cache as a Data Flow Node LSTORE extenal Cache as a Netwok of Data Flow Nodes Pof. D. Manfed Boy: MeanMSC Pof. D. Manfed Boy: MeanMSC location c unlocked location c locked fo pocess p in extenal stoe location c locked fo pocess p in intenal stoe location c ead fom extenal stoe Scenaios lock(p, c) Manage lock(p, c) locked(p, c) lock(p, c) locked(p, c) ead(p, c) ead(p, c, d) wite(p, c, d) LST ORE intenal LSTORE extenal Selected System Model Components x1: S1 f y1: S1' xn: Sn ym: Sm' location c updated in intenal stoe location c locked fo pocess p and updated locked(p, c) witten(p, c) Message Sequence Chat fo Successful Locking I be the set of input channels O be the set of output channels. With evey channel in the cannel set I O we associate a data type (I, O) is the syntactic inteface of a system component is given. Pof. D. Manfed Boy: MeanMSC Pof. D. Manfed Boy: MeanMSC

3 Steams Valuations of channels Mω = Μ Μ steams of messages of set M C set of channels finite o infinite sequences of elements fom M type: C S types assigned to channels Mϖ set of infinite steams fom set M { } with an infinite numbe of time ticks. [s] caie set of data elements M = U{[s]: s S} M be the univese of all messages x: C Mϖ valuations of C Mϖ N M { }. whee fo each c C: x(c) [s]ϖ C set of valuations Pof. D. Manfed Boy: MeanMSC Pof. D. Manfed Boy: MeanMSC Black box behavio of a component Composed Systems by data flow nets f : I ( O) x k = z k {y k+1: y f(x)} = {y k+1: y f(z)} I/O-functions timing popety. N set of identifies fo components (I M ω ) (O M ω ) time abstaction f.x = {y O M ω : z I: z = x y f.z} (ν, O) distibuted system with syntactic inteface (I, O) ν: N Com Com[I, O] set of I/O-functions with input channels I and output channels O. Black box view: f Com[I, O] whee f(x) = {y O: y I = x i N: y Out(ν(i)) ν(i)(y In(ν(i)) ) } Pof. D. Manfed Boy: MeanMSC Pof. D. Manfed Boy: MeanMSC

4 Towads a Meaning of MSCs Questions Given a netwok of inteacting components with syntactic inteface (I, O) (ν: N Com, O) MSCs define (1) Is the component p descibed by the theads of the MSCs deteministic? (2) Is the component, afte a patten of behavio as specified, in a state whee again MSCs ae available to descibe the behavio? (3) Ae the MSCs dense pefixes, pojections, o fee selections of instances of inteactions? a pedicate Q p : I p ( O p ) (4) Is the set of MSCs meant as a loose sample o a compehensive set of equiements? fo each component p N epesented by a thead in the MSC. Pof. D. Manfed Boy: MeanMSC Pof. D. Manfed Boy: MeanMSC Syntax and Stuctued Pesentation of MSCs t 1 t 2... t i... t n A MSC is a diagam with n vetical lines, called the theads, one fo each component of the system, that symbolize the flow of time fo each component time flows fom the top to the bottom. (1) i 1 (1) o 1 (1) i 2 (1) o 2 i 1 (2) (k) i 1 (2) o 1 M (j) o 1 (2) i 2 o 2 (2) M M M Pof. D. Manfed Boy: MeanMSC Pof. D. Manfed Boy: MeanMSC

5 Causal consistency of MSCs t i A MSC is called consistent, if fo all its events thee is i o a patial odeing that contains the linea odeings of all the theads as subodeings (fo a compehensive discussion see [Alu et al. 96]). This means: no cycles in the causality flow of the events (no "causal loops"). Geneal Fom of a Thead in a MSC with Clusteed Input/Output An input o output patten is a finite channel valuation C * fo the channels in C which is defined as a mapping C (M { }) *. Pof. D. Manfed Boy: MeanMSC Pof. D. Manfed Boy: MeanMSC Semantics of Sets of MSCs Specifying Deteministic Systems The Semantics of MSCs fo Nondeteministic Systems Behavio of a deteministic system component A nondeteministic system component is intepeted by a set valued function I O I ( O) The MSC is epesented by the equation f(i) = o and the specifying fomula o f(i) We call a function f compehensive with espect to a set of MSCs if it fulfills the specifying fomulas. Pof. D. Manfed Boy: MeanMSC Pof. D. Manfed Boy: MeanMSC

6 Intoducing Contol and Data States f The Univese of Unfilteed Scenaios We get a set of conditional fomulas of the geneal foms i o χ: P(σ) o condition(x, y) y f σ χ (x) χ': Q(σ, σ ) condition(x, y) y = f χ σ (x) By choosing all instantiations fo the input histoy x and the output histoy y o f σ χ (i) P(σ) fo 1 k < n χ o ˆf σ (x) f χ σ (iˆx) P(σ) Q(σ, σ') This leads to a system of specifications of the function f σ χ. y f χ σ (x) o y = f χ σ (x) fo concete histoies y O and x I. Pof. D. Manfed Boy: MeanMSC Pof. D. Manfed Boy: MeanMSC MSCs as Pojections Closed Wold Assumptions - A Canonical Behavio with a Set of MSCs Given pojection functions fo a steam x witten in the fom x N We specify then a set of MSCs by the fomulas i = x N y f(x): o = y N intepetion of the theads of a component: pojection: a MSC descibes a pefix of a pojection of the input and output, loose selection: a MSC descibes a loose selection of messages. This set of the pattens is called the filteed univese of inteaction pattens. An I/O-function I ( O) connects infinite input histoies with infinite output histoies. We define the meaning of a set of theads fo the function f by f * : I * ( O * ) whee fo a set of channels C we define C * as the set of valuations C (M * ) * (M * ) pefix odeing ffi Pof. D. Manfed Boy: MeanMSC Pof. D. Manfed Boy: MeanMSC

7 DCS( O * ) = {Z C * : Z z C : z ffi x x Z z Z} * The patial odeing that we use on the set DCS is simply set inclusion. We define the function f * such that f * : I * DCS( O * ) Fo set of fomulas R = {Φ k : k K} whee each Φ k is of the fom y k f(x k ) o f(x kˆx') y kˆf(x') we specify the function f * as the -least time guaded function whee y k f * (x k ) Closues on the Canonical Behavio The function f * is completed into an I/O-function I ( O) by the following equation: f.x = {y O: k N: y k f * (x) k N: y k f * (x) y' f * (x): y k ffi y' y k = y'} f * (x kˆx') y kˆf * (x') Pof. D. Manfed Boy: MeanMSC Pof. D. Manfed Boy: MeanMSC The constuction of the chaotic closue The Methodological Role of MSCs The function f is the inclusion lagest function with the following popeties: (1) f is time guaded, (2) if thee is a MSC that talks about the input x, then f(x) contains exactly those outputs explicitly descibed in one of the MSCs. (3) if fo an input x we can decompose x into x'ˆx'' such that exactly fo the input patten in x' output is specified by the MSCs we define the output fo x'' as being abitay. (1) In the ealy phases of equiements engineeing to get a fist idea which sevices the system should povide. (2) In the late phases of equiements engineeing as desciption techniques as pat of a fomal specification. (3) In the design phase illustation of the inteaction between the system pats (key technique fo the decomposition of a system, design pattens). (4) In the implementation phase we use MSCs to epesent test cases. In paticula, wheneve fo some input an input patten is not contained in a set of MSCs, the output can be abitay (chaos). Pof. D. Manfed Boy: MeanMSC Pof. D. Manfed Boy: MeanMSC

8 Popety efinement Fist answe [Klein 98] ˆ I ( O) is called a popety efinement of a component with a behavio Let us undestand a set of scenaios as I ( O) the specification of the components if fo all input steams x I we have: ˆf(x) f(x) Conflict between efinement and equiements captue by sets of MSCs: # efinement steps that allow us to get id of nondeteministic altenatives, # the sets of MSCs that ae assumed to descibe all behavios that all should be possible. that shows fo input pattens coveed by scenaios exactly the behavio descibed by the scenaios and fo the input pattens not coveed abitay behavio. See "closed wold assumption". Pof. D. Manfed Boy: MeanMSC Pof. D. Manfed Boy: MeanMSC Second Answe to the Conflict Refinement/Sets of MSCs Conclusion Distinguishing two kinds of MSCs Seveal ways to intepet sets of MSCs - Good MSCs: MSCs that descibe the intended behavio and inteaction, Bad MSCs: MSCs that descibe unwanted behavio, modeling failue cases that, howeve, have to be toleated, but should be avoided wheneve possible. Negative scenaios may be eliminated in efinement steps wheneve feasible. Suggested concepts: distinction between input messages and output messages essential. leads to a concept of causality. MSCs as component specifications MSCs in that way do not only descibe by an MSC vey loosely what may happen in a system but also quite stictly what must happen. Pof. D. Manfed Boy: MeanMSC Pof. D. Manfed Boy: MeanMSC