U. Reddy. Global state considered unnecessary: Introduction to object-based semantics. In P. O'Hearn and R. Tennent, editors, Algol-like Languages, volume 2, Progress in Theoretical Computer Science, chapter 19, pages 227--295. Birkhauser, 1997.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....calculational, algebraic style. We also obtain a decidability result for equivalence of programs in this fragment. The approach of game semantics, and therefore of this paper, has little in common with the traditional semantics of IA. Intuitively it comes closest to Reddy s object semantics [9] and Brookes s trace semantics for sharedvariable concurrent Algol [10] Although the language has assignment, a semantic notion of store is not used; although the language has procedures, a semantic notion of function is not used. Instead, we are primarily concerned with behaviour, with all the ....

....of each side will be identical because of the locality of v, as seen above. The rst model to correctly address this issue was O Hearn and Reynolds s interpretation of IA using the polymorphic linear lambda calculus [6] Reddy also addressed this issue using a novel object semantics approach [9], but in a particular avour of IA known as interference controlled Algol [26] A further development of the model, which also satis es this equivalence, is O Hearn and Reddy s [27] a model fully abstract for the second order subset. PROOF. We proceed in a bottom up fashion. The following ....

U. S. Reddy, Global state considered unnecessary: Introduction to object-based semantics, Lisp and Symbolic Computation 9 (1) (1996) 7-76, published also as Chapter 19 of [2].

....form of Contraction for , in addition to the general Contraction for ; These rules can all be interpreted using the bire ective subcategory structure found in Tennent s model [10, 4] 7.2 Implicit State Models A very di erent semantics of SCI can be obtained using ideas of Uday Reddy. In [21], Reddy presents a novel semantics of SCI in which the state is implicit in a history of events. The model is not cartesian closed, but it was subsequently shown in [11] how a Yoneda embedding could be used to obtain not only in a semantics of simply typed calculus but also of Idealized Algol. ....

U. S. Reddy. Global states considered unnecessary: introduction to objectbased semantics. Lisp and Symbolic Computation, February 1996. Special issue on State in Programming Languages. Also in [14], vol 2, pages 227-296.

....improves upon their system in two important ways. First, the promote and derelict operators are explicit in the term syntax of SCIRK , but they were implicit in Reynolds s original proposal. Intuitively, these operations do not affect any change of meaning; i.e. the implicit language is coherent [15]. In this paper, we devise type inference algorithms that allow many of these coercion operators to be left implicit. Second, there is no provision for polymorphism in SCIRK . Traditional type inference techniques for let terms, such as using type quantification [3] or substitution [12] do not ....

....that they do not change global variables. For this purpose, we add a new type constructor where the type represents values of type that do not change global variables. The type of c: c; c then, would be (comm comm) 2 1 This intuition is formalized by the semantic models of [15, 13]. 2 Our types ( 0 ) correspond to the passive function We extend the type syntax of our language with and define the passive types OE: ffi j var[ffi] j comm j 1 Theta 2 j 1 2 j OE : ffi j OE 1 Theta OE 2 j OE j We formalize the above intuitions in ....

[Article contains additional citation context not shown here]

U. S. Reddy. Global state considered unnecessary: An introduction to object-based semantics. J. Lisp and Symbolic Computation, 9:7--76, 1996. (Reprinted as Chapter 19 of [14]).

....calculational, algebraic style. We also obtain a decidability result for equivalence of programs in this fragment. The approach of game semantics, and therefore of this paper, has little in common with the traditional semantics of IA. Intuitively it comes closest to Reddy s object semantics [22] and Brookes s trace semantics for sharedvariable concurrent Algol [3] Although the language has assignment, a semantic notion of store is not used; although the language has procedures a semantic notion of function is not used. Instead, we are primarily concerned with behaviour, with all the ....

....each side will be identical because of the locality of x, as seen above. The rst model to correctly address this issue was O Hearn and Reynolds s interpretation of IA using the polymorphic linear lambda calculus [16] Reddy 20 also addressed this issue using a novel object semantics approach [22], but in a particular avour of IA known as interference controlled Algol [14] A further development of the model, which also satis es this equivalence, is O Hearn and Reddy s [15] a model fully abstract for the second order subset. p : comm comm new x in p(x : 1) if x = 1 then diverge ....

U. S. Reddy. Global state considered unnecessary: Introduction to object-based semantics. Lisp and Symbolic Computation, 9(1):7-76, 1996. Published also as Chapter 19 of [18].

....properties of classes. The formula Inst C x:OE(x) is understood to mean that all instances of class C satisfy the formula OE(x) The author then presents semantics in two different styles. The first is a parametricity style of semantics[37] The second is referred to as object based semantics[34] for a subset of IA , restricted by a type theoretic notion called Syntactic Control of Interference[35] The parametricity semantics elegantly handles locally allocated (also described as stack allocated) objects. The object based semantics uses notions similar to that of process in CCS[13] ....

Uday S. Reddy. Global state considered unnecessary: An introduction to object-based semantics. Lisp and Symbolic Computation, 9(1):7--76, February 1996.

....to formally express a notion of method extension which corresponds to the intuition that, usually, operations which change the state affect only a limited part of it. This intuition is not reflected in usual denotational models of imperative languages, causing some inadequateness (see, e.g. [41, 35, 39, 40] for a discussion and proposals of solution) In our approach, the problem is solved assuming to define methods only on the involved part of the state and then extending them to richer states in a uniform way, fixed for any given language we are dealing with. The overall categorical framework ....

Reddy, U. S.: 1996, `Global State Considered Unnecessary: An Introduction to Object-Based Semantics'. Journ. of Lisp and Symbolic Computation 9, 7--76.

....a purely functional language with a type structure able to capture both representation independence and irreversibility. 9. Stateless Models The semantic problems raised by storage are attacked from an entirely different point of view by recent behavioural models based on interacting objects [46] or games [1, 2] These models of storage are more intensional and operational than the state oriented models considered so far. They are concerned only with how programs behave; stores do not appear explicitly in the semantics because they are not directly observable. It is noteworthy that Park s ....

U. S. Reddy. Global state considered unnecessary: Introduction to object-based semantics. Lisp and Symbolic Computation, 9(1):7--76, 1996. Reprinted as Chapter 19 of [37].

....style, using our semantics. We also obtain a decidability result for equivalence of programs in this fragment. The approach of game semantics, and therefore of this paper, has little in common with the traditional semantics of IA. Intuitively it comes closest to Reddy s object semantics [13] and Brookes s trace semantics for sharedvariable concurrent Algol [2] Identifiers are not interpreted using an environment, variables are not interpreted using a notion of store and functions in the language are not interpreted using a mathematical notion of function. Instead, we are primarily ....

....of each side will be identical because of the locality of x, as seen above. The first model to address this issue correctly was O Hearn and Reynolds s interpretation of IA using the polymorphic linear lambda calculus [8] Reddy also addressed this issue using a novel object semantics approach [13], but in a particular flavour of IA known as interference controlled Algol [6] A further development of this model, that also satisfies this equivalence, is O Hearn and Reddy s [7] a model fully abstract for the second order subset. P : comm comm new x in P (x : 1) if x = 1 then Omega ....

U. S. Reddy. Global state considered unnecessary: Introduction to object-based semantics. Lisp and Symbolic Computation, 9(1):7--76, 1996. Published also as Chapter 19 of [10].

....properties of states. In this respect, the work we have presented is related with some research aimed at refining usual denotational models of imperative programming languages (functions on global states) trying to capture the fact that a function can usually modify only some part of the state [15,11,14,16]. Anyway, in these papers the main aim is the treatment of locality of variables and the issue of structured data types is not tackled. Another non standard approach to modeling store is [10] where the main aim is to describe in an abstract way sharing of subcomponents. Finally, in [12] store ....

U. S. Reddy. Global state considered unnecessary: An introduction to objectbased semantics. Journ. of Lisp and Symbolic Computation, 9:7--76, 1996.

....scoped and are executed using a stack discipline. The subtleties of the externally observable behaviour of such locally declared Research partially supported by the EU HCM Research Network on Lambda Calcul Type . state are such that, despite the considerable efforts of a number of researchers [5, 11, 10, 16, 8, 20], no concrete denotational model of Algol has yet been constructed which exactly captures observational equivalence for n th order procedures beyond n = 2 or 3 (depending upon how one counts orders) Nevertheless, useful semantical ideas and techniques have emerged from the effort to construct ....

U. S. Reddy. Global state considered unnecessary: Introduction to object-based semantics. Lisp and Symbolic Computation, 1995. special issue on State in Programming Languages, to appear.

....structuring programs so that it is clear where interference might occur, making reasoning about programs much easier. O Hearn et al. later developed SCIR [OPTT95] an elegant type system and semantics for SCI. Interference free Algol also became the foundation for Reddy s object based semantics [Red96]. The techniques of SCI can be adapted to a variety of languages. We believe that it can serve as a foundation for the design and study of more advanced languages, such as those which address references or synchronization. But for SCI to gain wider acceptance, practical type inference algorithms ....

....OE : ffi j OE 1 Theta OE 2 j OE j We formalize the above intuitions in SCIR, whose type rules are shown in Figure 2. The system we discuss is similar to the one presented in [OPTT95] but extended with the new type constructor 1 This intuition is formalized by the semantic models of [OPTT95, Red96]. 2 Our types ( 0 ) correspond to the passive function types p 0 in Reynolds s presentation [Rey78] Adding a generic constructor is a useful notational convenience. Axiom j x: x: Pi j Gamma; x: M : OE Passification Pi; x: j Gamma M : OE Pi; x: j ....

U. S. Reddy. Global state considered unnecessary: An introduction to object-based semantics. J. Lisp and Symbolic Computation, 9:7--76, 1996.

....3.4 Discussion: Non Bireflective Models We have included the qualification bireflective in Definition 3.2 because there are models of the SCIR type system in which the left and right adjoints to the inclusion do not coincide. The first, and foremost, examples are given by the models in [35,36]. Others are given, for example, by arrow categories C . The models that we know of have the form of two categories and three functors between them, like so: P C I L i R 6 j with I fully faithful and L a I a R. Additional conditions that a more general (not necessarily ....

....ha; bi 2 (A Omega B) W ) the naturality requirement for OE(X; Y ) ensures that j(W )ha; bi is uniquely determined. It is a routine exercise to verify that the mappings j 7 OE and OE 7 j just given are mutual inverses. Uday Reddy has launched a criticism at semantics based on global states [36], and developed an alternate approach in which different identifiers denote independent objects, where the state is implicitly represented in histories of observations. We would claim that functor category models, though they are not stateless, also represent a move away from the viewpoint of ....

U. S. Reddy. Global states considered unnecessary: introduction to object-based semantics. Lisp and Symbolic Computation, February 1996. Special issue on State in Programming Languages. Also in [29], pages 227--296.

.... 0 ; c 1 i s = s if c 0 s 6= and c 1 s 6= otherwise This doubly offensive operation exhibits both snapback and the kind of determinate parallelism found in the continuous function model of PCF, and it does exist in the models found in [8, 7, 15] It does not exist in the models found in [10, 6]. Example 6. Our final example is for Basic SCI. comm comm comm) I = 8fi : 8ff : fi Gammaffi fi) Theta (ff Gammaffi ff) fi Omega ff Gammaffi fi Omega ff) N Omega N Here, a pair (n; m) corresponds to c 1 c 2 : c m 1 k c n 2 , which is in fact equal to c 1 c 2 : ....

....of result can be pushed to higher types. We immediately obtain that each of these first order types is an algebraic cpo. It is interesting that the domain equation has something of the flavour of resumptions, thus suggesting a connection to more process oriented semantics (especially that of Reddy [10, 6]) Given Proposition 3 and the argument in [6] Proposition 5.2, we obtain. Proposition 4 If b 1 ; b n ; b are primitive Algol types then every finite element of [ b 1 Theta Delta Delta Delta b n b) I ] is definable by a closed Idealize Algol term of type b 1 Theta Delta Delta ....

U. S. Reddy. Global states considered unnecessary: introduction to object-based semantics. To appear in Lisp and Symbolic Computation, special issue on State in Programming Languages, 1995.

....2 Peter W. O Hearn languages. It turns out that standard models of Algol like languages are not suitable because they contain what Reynolds calls snapback operations, which cause backtracking of state changes that require copying of the entire state (cf. O Hearn and Tennent, 1995; O Hearn and Reddy, 1995) for discussion) These operations violate the intuitive property of irreversibility of state changes, and Section 3 shows an example of where snapback invalidates an equivalence true in the assignmentfree sublanguage. Thus, conservativity fails for the standard models. The main step in the proof ....

....x denotes ) because the change to during evaluation of f(1) is temporary. We now present a semantic model that overcomes this specific difficulty pertaining to conservativity. The model does not address the general problem of irreversibility of state change; see (O Hearn and Tennent, 1995; Reddy, 1995; O Hearn and Reddy, 1995) for discussion of this. The aim is to provide a simple (though ad hoc) work around, that is just enough to achieve conservativity. The main idea of the new semantics C[ Delta] is to push the state as far outward as possible, by interpreting the PPCF fragment in a way ....

[Article contains additional citation context not shown here]

Reddy, U. S. 1995. Global states considered unnecessary: Introduction to object-based semantics. Lisp and Symbolic Computation. Special issue on State in Programming Languages. To appear.

....Indeed, the cuts, i.e. the computation to be performed, are also involved in the partial order, and therefore a concurrent strategy is described within the syntax itself. This ts in with the computational interpretation of linear logic of [1] and is the starting point of the use [4, 5] and [26, 27] made of this calculus. Computational meaning of before and of partial orders. As usual cut links may be viewed as particular nal times links, which allows us to make them appear in the partial order. This partial order may thus be viewed as a strategy for computing the proof net, which is ....

....to the aforementioned elds: In [4, 5] the authors consider proof nets as processes, and show that the correctness of the proof net corresponds to freedom from deadlock. The connectives are interpreted as follows: parallel composition, Omega internal choice, and sequential composition. In [26, 27] the author makes use of the calculus to model by local means state change in imperative programming. For instance, a buoeer of type A has the type (A A) thus it forces that it rst get something of type A (write) and then produce something of type A (read) In [15] the author suggests ....

U. S. Reddy. Global state considered unnecessary: An introduction to object-based semantics. Journal of Lisp and Symbolic Computation, 1996. (to appear).

....the author [56, 32] a global state based semantics was de ned for stateful object oriented programs. Being a global state based semantics, it does not handle the state encapsulation issues of objects adequately. The de ciencies of the global state set up have been discussed in a number of papers [39, 51, 58]. Work on speci cation of stateful objects includes [6, 34, 35, 36] in addressing subtyping issues and [3, 7] in addressing self reference issues. A number of recent papers [1, 8, 11, 19, 18] discuss object oriented type systems for languages with side e ects, but this work does not address ....

....5. SEMANTICS The denotational semantics of IA brings out important properties of classes and objects. We consider two styles of semantics: parametricity semantics along the lines of [51] which highlights the data abstraction aspects of classes, and object based semantics along the lines of [58], which highlights the class instance relationship. 5.1. Parametricity semantics Recall, from Sec. 2, that objects can be regarded as state machines with a state set Q and operations that act on the state set Q. Since these operations correspond to methods written in IA , it follows that IA ....

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U. S. Reddy. Global state considered unnecessary: An introduction to object-based semantics. J. Lisp and Symbolic Computation, 9:7-76, 1996. (Reprinted as Chapter 19 of [52]).

....3 Semantics The denotational semantics of IA brings out important properties of classes and objects. We consider two styles of semantics: parametricity semantics along the lines of [42] which highlights the data abstraction aspects of classes, and object based semantics along the lines of [49], which highlights the class instance relationship. 3.1 Parametricity semantics As pointed by Reynolds [53] parametricity has to do fundamentally with data abstraction. Since classes incorporate data abstraction, one expects parametricity to play a role in their interpretation. We follow the ....

....axiom. The two sides of the equation denote the respective state transformations: q; ha; f; ri) q; ha[1 x] 1; 1i) q; ha; f; ri) q; ha; 0; 0i) It is clear that they are equivalent by the relation [EQ Theta EZ EQ Theta EZ ] 3. 2 Object based semantics The object based semantics [49, 39] (see also [4] treats objects as state machines and describes them purely by their observable behavior. The observable behavior is given in terms of event traces whose structure is determined by the type of the object. This is similar to how processes are described in the semantics of CSP or CCS. ....

[Article contains additional citation context not shown here]

Reddy, U. S. Global state considered unnecessary: An introduction to object-based semantics. J. Lisp and Symbolic Computation 9 (1996), 7--76. (Reprinted as Chapter 19 of

....Syracuse University Uday S. Reddy 2 University of Illinois at Urbana Champaign Dedicated to John C. Reynolds, in honor of his 60th birthday. Abstract We present a new semantics for Algol like languages that combines methods from two prior lines of development: ffl the object based approach of [28,29], where the meaning of an imperative program is described in terms of sequences of observable actions, and ffl the functor category approach initiated by Reynolds [31] where the varying nature of the run time stack is explained using functors from a category of store shapes to a category of ....

.... program for the semantics of imperative languages was further developed by Oles and Tennent [22,23,38 40] and continued and expanded in a number of works [13,16,24,18,20,36,17,35] In a separate line of development, a model based more explicitly on a notion of objects has been formulated in [28,29]. Reynolds s conception of imperative programming expressed above formed an important pre theoretic motivation for this work, though its theoretical development also draws inspiration from linear logic, syntactic control of interference, and the relation between them. In this paper we obtain a new ....

[Article contains additional citation context not shown here]

U. S. Reddy. Global states considered unnecessary: introduction to object-based semant ics. Lisp and Symbolic Computation, February 1996. Special issue on State in Programming Languages.

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U. Reddy. Global state considered unnecessary: Introduction to object-based semantics. In P. O'Hearn and R. Tennent, editors, Algol-like Languages, volume 2, Progress in Theoretical Computer Science, chapter 19, pages 227--295. Birkhauser, 1997.

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