Davies, R. 1996. A temporal logic approach to binding-time analysis. In Symposium on Logic in Computer Science, LICS'96, E. Clarke, Ed. IEEE Computer Society Press, New Brunswick, New Jersey, 184--195.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....multi stage languages in the context of binding time analysis for offline partial evaluation. Important, early formal investigations into lanuages for staging computation were carried out by Rowan Davies and Frank Pfenning. They studied the typed multi stage languages MiniML O [20] and MiniML [19]. These languages explore type systems (and find connections to intuitionistic modal logic, and linear time constructive modal logic) for languages with type constructors for code. An important work relating these areas is the thesis of Walid Taha [74] His thesis explains the utility of program ....

....and when it will (finally) be fully compiled. Fabius. Fabius [42 44] is a compiler for a staged language. Fabius uses explicit annotations to stage a program in an ML like language. The staging annotations of Fabius are based upon the type systems devised by Frank Pfenning and Rowan Davies [20, 19]. Other than MetaML, Fabius is the only dynamic code generator that types object level code. The UW Dynamic Compilation Project. DyC [34,6,35] is a C based dynamic compilation system. In DyC regions of code are marked for specialization, and variables in those regions are declared either ....

R. Davies. A temporal-logic approach to binding-time analysis. In Proceedings, 11 th Annual IEEE Symposium on Logic in Computer Science, pages 184-195, New Brunswick, July 1996. IEEE Computer Society Press.

....v safely. 4 Type System The type system derives judgments of the following forms . i.e. # is a well formed context . n t, i.e. t is a well formed type at level n . n e: t, i.e. e is a well formed term of type t at level n Levels are typical of multi level languages (like # # of [Dav96] In a dynamically typed multistage language, like MetaKlaim (see also [SSP98] type variables get bound at di#erent stages of a computation, and thus well formedness is level dependent not only for terms, but also for types. The declarations in a context # have the following meaning: X ....

R. Davies. A temporal-logic approach to binding-time analysis. In the Symposium on Logic in Computer Science (LICS '96), pages 184--195, New Brunswick, 1996. IEEE Computer Society Press.

....existent and well established proof systems for lineartime temporal logic. In fact, from a recent personal communication with Frank Pfenning we learned that he has developed a proof system in the natural deduction style for a logic very similar to T I (related work to this proof system appears in [Dav96] Therefore, a line of research is to investigate the use of existent theorems provers, in particular [L.P94] for an implementation of T I . Nevertheless, linear time temporal specifications do not include sensitivity to the branching behavior of processes. Therefore, we plan to study the ....

Rowan Davies. A temporal-logic approach to binding-time analysis. In Proceedings, 11 th Annual IEEE Symposium on Logic in Computer Science, pages 184--195, New Brunswick, New Jersey, 27--30 July 1996. IEEE Computer Society Press.

....of open issues in meta programming can be found in [She01] Comparison with MetaML, # # and # . The motivation for looking at the interactions between computational e#ects and run time code generation comes from MetaML [MHP00, Tah99, TS00, CMSar] We borrow code types from MetaML (and # # of [Dav96] but use annotated term constructors as in # of [Dav96] see also [GJ95] so that simplification and computation rules are level insensitive. Indeed, the term constructors of MMML can be given by an alternative BNF c C: ret B doB #B B newB get B set B l B ....

....Comparison with MetaML, # # and # . The motivation for looking at the interactions between computational e#ects and run time code generation comes from MetaML [MHP00, Tah99, TS00, CMSar] We borrow code types from MetaML (and # # of [Dav96] but use annotated term constructors as in # of [Dav96] see also [GJ95] so that simplification and computation rules are level insensitive. Indeed, the term constructors of MMML can be given by an alternative BNF c C: ret B doB #B B newB get B set B l B upB dnB with B M # For instance, #B is # when B is ....

Rowan Davies. A temporal-logic approach to binding-time analysis. In the Symposium on Logic in Computer Science (LICS '96), pages 184--195, New Brunswick, 1996. IEEE Computer Society Press. 12

....polymorphic constants, and it enjoys similar properties (that we do not recall) In the rest of this section we discuss related work, design choices, variations, and open issues. A more general discussion of open issues in meta programming can be found in [She01] Comparison with # # and # of [Dav96] MMML borrows code types from # # (and MetaML) and annotated term constructors from # . In MMML an annotation is a sequence b M # , while in # is a natural number n, namely the length of b. The additional information provided by b says for each i n whether computation at that stage has ....

....The translation achieves two goals: 1. to make explicit the order of evaluation, by extending the CBV translation of a functional language into a monadic metalanguage [Mog97, BHM00] 2. to make explicit the binding time annotation in terms, by refining the translation from # # into # given in [Dav96] Davies defines also an inverse translation from # into # # , in our case there is no inverse because MMML is more expressive than MetaML) For instance, the translation x of a variable at level n has to make explicit that at all levels from 0 to n there is nothing to compute. To keep the ....

Rowan Davies. A temporal-logic approach to binding-time analysis. In the Symposium on Logic in Computer Science (LICS '96), pages 184--195, New Brunswick, 1996. IEEE Computer Society Press.

.... that by emphasizing the logical character of type based and operational semantics specifications, the correctness of a partial evaluator can be mechanically verified [35] Davies and Pfenning have developed a language for expressing staged computation based on the intuistionistic modal logic S4 [20, 19]. The type system of this language is strikingly similar to that of Moggi s computational metalanguage. A modality analogous to the e Delta construction of Moggi is used to type code objects (in our terminology, objects whose specialization type is dynamic) Their language also includes a let ....

Rowan Davies. A temporal-logic approach to binding-time analysis. In Proceedings of the Eleventh Annual IEEE Symposium on Logic in Computer Science, pages 184--195, New Brunswick, New Jersey, July 1996. IEEE Computer Society Press.

....it becomes hard (if not impossible) to type check macros before expansion and evaluation start. This paper argues that macro systems can be viewed formally and usefully as multi stage computations. Multi stage programming languages (including two level languages [28, 16] multi level languages [13, 14, 15, 8, 7], and MetaML [41, 39, 5] have been developed precisely to provide precise and usable models of such computations that occur in multiple distinct stages. Over the last few years, the study of MetaML and related systems has not only resulted in a good understanding of the types and semantics of ....

Davies, R. A temporal-logic approach to binding-time analysis. In 11 th Annual IEEE Symposium on Logic in Computer Science (LICS) (New Brunswick, 1996), IEEE Computer Society Press, pp. 184--195.

....( n e: hti n run e: t n 1 e: t n hei: hti n e: hti n 1 e: t n e: t n 1 e: t ; X n n e: t n X:e: 8X:t n e: 8X:t 2 n t 1 n eft 1 g: t 2 [X: t 1 ] n;g e: t n e: 2t n e: g n e: 2g n e: 2t n e: t Fig. 2. Type System languages (like of [6]) In a dynamically typed multi stage language, like MetaKlaim (see also [32] type variables get bound at di erent stages of a computation, and thus well formedness is level dependent not only for terms, but also for types. In MetaKlaim we consider two kinds of terms: local terms, classi ed by ....

Davies, R., A temporal-logic approach to binding-time analysis, in: the Symposium on Logic in Computer Science (LICS '96), IEEE Computer Society Press, New Brunswick, 1996, pp. 184-195.

....and J rgensen [12, 13] were the rst to generalize the techniques of two level languages to a multi level setting. Over the last six years, signi cant e orts have been invested in the development of a theory of multi stage computation, starting from the work of Davies on linear temporal logic [9] and Moggi on functor category and topos theoretic semantics [30, 31] then continuing as various studies on the semantics [47, 3, 43] and type systems for MetaML [32, 5, 4] and the use of monads for modeling meta computations [17, 18] Key contributions include the identi cation of a wide range ....

Davies, R. A temporal-logic approach to binding-time analysis. In the Symposium on Logic in Computer Science (LICS '96) (New Brunswick, 1996), IEEE Computer Society Press, pp. 184-195.

....multi stage languages in the context of binding time analysis for o ine partial evaluation. Important, early formal investigations into lanuages for staging computation were carried out by Rowan Davies and Frank Pfenning. They studied the typed multi stage languages MiniML ut [20] and MiniML [19]. These languages explore type systems (and nd connections to intuitionistic modal logic, and linear time constructive modal logic) for languages with type constructors for code. An important work relating these areas is the thesis of Walid Taha [74] His thesis explains the utility of program ....

....and when it will ( nally) be fully compiled. Fabius. Fabius [42 44] is a compiler for a staged language. Fabius uses explicit annotations to stage a program in an ML like language. The staging annotations of Fabius are based upon the type systems devised by Frank Pfenning and Rowan Davies [20, 19]. Other than MetaML, Fabius is the only dynamic code generator that types object level code. Accomplishments and Research Challenges in Meta Programming 39 The UW Dynamic Compilation Project. DyC [34, 6, 35] is a C based dynamic compilation system. In DyC regions of code are marked for ....

R. Davies. A temporal-logic approach to binding-time analysis. In Proceedings, 11 th Annual IEEE Symposium on Logic in Computer Science, pages 184-195, New Brunswick, July 1996. IEEE Computer Society Press.

....constructs Brackets obj e : t object level program fragment of type t meta hei : hti meta level representation of e Escape meta e : hti obj e : t such that hei e. These constructs are borrowed from MetaML (Taha Sheard, 1997; Taha et al. 1998) and the multi level language (Davies, 1996). Cross Stage Persistence CSP meta e : t obj e : t t object and meta level type allows the inclusion of meta level computations in object level programs, a similar construct is available in BN (Benaissa et al. 1999) and implicitly also in MetaML (Taha Sheard, 1997) A Closed ....

.... ; n e : c] closI2) n ; n e : t ; n e : t] closE) n e : t] n e : t Fig. 3. Type System for MiniML meta ref . signature for locations, and type and level assignments with disjoint domains. the level information, typical of multi level languages like (Davies, 1996); the splitting of type and level assignments in two parts ( and ) borrowed from (Davies Pfenning, 1996) The di erence between a declaration in and the same declaration in is expressed in the Substitution Lemma 3.4. The level information is essential to express the typing rules for ....

[Article contains additional citation context not shown here]

Davies, Rowan. (1996). A temporal-logic approach to binding-time analysis. Pages 184{ 195 of: the symposium on logic in computer science (LICS '96). IEEE Computer Society Press, New Brunswick.

....Semantically, the same type constructors are present in RT FRP, but they are made implicit in the types. This is achieved by having a specialized type system that only addresses the reactive part of FRP. Staging: Multi stage languages [12, 90, 92] are based on the key ideas of multilevel [25, 26, 33] and two level languages [52, 71] and provide mechanisms for building programs that execute in multiple distinct stages. This is achieved by providing constructs for building, combining, and executing code at runtime. The presence of these constructs provides both hygienic program generation and ....

Rowan Davies. A temporal-logic approach to binding-time analysis. In the Symposium on Logic in Computer Science (LICS '96), pages 184--195, New Brunswick, 1996. IEEE Computer Society Press.

....Brackets obj e : t object level program fragment of type t meta hei : hti meta level representation of e and Escape meta e : hti obj e : t such that hei e. These constructs are borrowed from MetaML (Taha Sheard, 1997; Taha et al. 1998) and the multi level language (Davies, 1996). Cross Stage Persistence meta e : t obj e : t t object and meta level type allows the inclusion of meta level computations in object level programs, a similar construct is available in BN (Benaissa et al. 1999) and implicitly also in MetaML (Taha Sheard, 1997) A Closed type ....

.... ; x : t m 1 n e 2 : t 2 ; n e 2 [x : e 1 ] t 2 subst. m ; m e 1 : c 1 ; x : c m 1 ; n e 2 : t 2 ; n e 2 [x : e 1 ] t 2 Remark 3. 7 (Comparison with MiniML ref ) The level information in typing judgments is typical of multi level languages, like (Davies, 1996). The splitting of type and level assignments in two parts ( and ) is borrowed from (Davies Pfenning, 1996) The di erence between a declaration in and the same declaration in is expressed in the Substitution Lemma. There are two typing rules, like those in , which exploit the ....

[Article contains additional citation context not shown here]

Davies, Rowan. (1996). A temporal-logic approach to binding-time analysis. Pages 184{ 195 of: 11 th annual IEEE symposium on logic in computer science (LICS). IEEE Computer Society Press, New Brunswick.

....it becomes hard (if not impossible) to type check macros before expansion and evaluation start. This paper argues that macro systems can be viewed formally and usefully as multi stage computations. Multi stage programming languages (including two level languages [28, 16] multi level languages [13, 14, 15, 8, 7], and MetaML [41, 39, 5] have been developed precisely to provide precise and usable models of such computations that occur in multiple distinct stages. Over the last few years, the study of MetaML and related systems has not only resulted in a good understanding of the types and semantics of ....

Davies, R. A temporal-logic approach to binding-time analysis. In 11 th Annual IEEE Symposium on Logic in Computer Science (LICS) (New Brunswick, 1996), IEEE Computer Society Press, pp. 184-195.

....after macro expansion, it becomes hard (if not impossible) to type check macros before expansion. This paper argues that macro systems can be viewed formally and usefully as multi stage computations. Multi stage programming languages (including two level languages [32, 16] multi level languages [13, 14, 15, 8, 7], and MetaML [48, 45, 4] have been developed to provide precise and usable models of such computations that occur in multiple distinct stages. Over the last few years, the study of MetaML and related systems has resulted in a good understanding of the types and semantics of multi stage systems. ....

Davies, R. A temporal-logic approach to binding-time analysis. In 11 th Annual IEEE Symposium on Logic in Computer Science (LICS) (New Brunswick, 1996), IEEE Computer Society Press, pp. 184-195.

....the laws of S4. The judgment M Xi A can be read as A is provable , hiding the proof object. It is similar to (but does not match exactly) the temporal modality hP iA which means A was true at some time in the past . Proof term calculi for temporal logic have been developed by Davies [Dav96] and Wansing [Wan00] but both have a very different character and computational meaning from the one considered here. In a type theory as a foundation for functional programming, irrelevant objects (that is, proofs) are erased before execution without affecting the observable outcome. From this ....

Rowan Davies. A temporal logic approach to binding-time analysis. In E. Clarke, editor, Proceedings of the Eleventh Annual Symposium on Logic in Computer Science, pages 184--195, New Brunswick, New Jersey, July 1996. IEEE Computer Society Press.

....the laws of S4. The judgment M A can be read as A is provable , hiding the proof object. It is similar to (but does not match exactly) the temporal modality #P#A which means A was true at some time in the past . Proof term calculi for temporal logic have been developed by Davies [Dav96] and Wansing [Wan00] but both have a very di#erent character and computational meaning from the one considered here. In a type theory as a foundation for functional programming, irrelevant objects (that is, proofs) are erased before execution without a#ecting the observable outcome. From this ....

Rowan Davies. A temporal logic approach to binding-time analysis. In E. Clarke, editor, Proceedings of the Eleventh Annual Symposium on Logic in Computer Science, pages 184--195, New Brunswick, New Jersey, July 1996. IEEE Computer Society Press.

....operational semantics presented here solves the problem with a binder for useless variables, introduced before storing a term. Relation to MiniML BN ref . There is a signi cant overlap between MiniML meta ref and MiniML BN ref . We refer to [CMT00] for a broader discussion of related work [DP96,Dav96,TS97,TBS98,MTBS99,BMTS99,Tah99,TS00]. For those familiar with MiniML BN ref (recalled in Appendix A) we summarize the di erences: MiniML meta ref has no closedness annotation [e] and the closed type constructor [ cannot be applied to a closed type c. These are cosmetic changes, motivated by the following remarks in [CMT00] ....

Rowan Davies. A temporal-logic approach to binding-time analysis. In Proceedings, 11 th Annual IEEE Symposium on Logic in Computer Science, pages 184-195, New Brunswick, July 1996. IEEE Computer Society Press.

....in the resulting dynamic value. This approach requires the programmer to perform complex type checking explicitly. It is also fairly verbose compared with our solution: apply : hi hi hi apply df dx = h df dx i Our approach is motivated by the recent work of Davies and Pfenning [11, 10] and Taha and Sheard [29] in staged computation. Our hi and operators correspond with the next and prev constructs of [11] extended to allow the cross stage persistence of [29] Our run operator corresponds to the unbox pop operation of [11] with an appropriate dynamic check for closure. 8 ....

R. Davies. A temporal logic approach to binding-time analysis. In E. Clarke, editor, Proceedings of the Eleventh Annual IEEE Symposium on Logic in Computer Science, New Brunswick, New Jersey, pages 184--195. IEEE Computer Society Press, Jul 1996.

.... be generalized to n levels for fixed n or even to an arbitrary number of levels (using for example the style of Gluck and Hatcliff [23] This gives rise to the type constructor prog (presented in the beginning of this report) that corresponds to the next operator from the modal lambda calculus [16, 17]. The generating extension in Figure 3.2 can be generalized to also handle types on form prog and produce n level terms. In its generalized form, the generating extension does incremental specialization. It also provides a connection with the second Futamura projection for type directed partial ....

Rowan Davies. A temporal-logic approach to binding-time analysis. In Proceedings of the Eleventh Annual IEEE Symposium on Logic in Computer Science, pages 184--195, New Brunswick, New Jersey, July 1996. IEEE Computer Society Press.

....either loops or it returns a specialized program, but it cannot fail due to type mismatches. There are many approaches to define the semantics of Lambdamix style specializers, based on denotational semantics [22, 21] operational semantics [27] logical frameworks [26] modal and temporal logics [16, 15], category theory [35] and higher order rewriting [14] We add a further color to this palette by employing type theory as a semantic foundation. Our plan is as follows: ffl define the static semantics by translating an annotated expression into a term in a suitable type theory; ffl obtain the ....

....for Standard ML. Crary [11] defines the semantics of a higher order kernel programming language with recursion, records, and modules using Nuprl [8] There is no other work that defines the semantics of specialization using type theory. The closest is probably Davies s and Pfenning s work [16, 15] that connects modal and temporal logics with specialization. There are also a number of investigations of the phase distinction in type theory [4, 5] The idea of duplicating certain values at the type level (and their types at the kind level) is inspired from this work. Cardelli [5] calls these ....

Rowan Davies. A temporal-logic approach to bindingtime analysis. In Proceedings, 11 th Annual IEEE Symposium on Logic in Computer Science, pages 184--195, New Brunswick, New Jersey, July 1996. IEEE Computer Society Press.

....no free variables. In a statically typed setting, open code and closed code have different properties, which we explain in the following section. Open and Closed Code A number of typed languages for manipulating code fragments have been proposed in the literature. Some have types for open code [9, 6, 3, 12], and others have types for closed code [4, 13] On one hand, languages with open code types play an important role in the study of partial evaluation. Typically, they provide two constructs, one for building a code fragment with free variables, and one for combining such fragments. Being able to ....

....of An Idealized MetaML (AIM) whose design is inspired by a categorical model for MetaML (such a model will be the subject of another paper) AIM is strictly more expressive than any known typed multi level language, and features: 1. An open code type hti, which corresponds to flt of fl [3] and hti of MetaML; 2. A closed code type [t] which corresponds to t of [4] 3. Cross stage persistence of MetaML; 4. A Run with construct, generalizing Run of MetaML. This work is the first to achieve a semantically sound integration of Davies and Pfenning s [4] and Davies fl [3] ....

[Article contains additional citation context not shown here]

Rowan Davies. A temporal-logic approach to binding-time analysis. In Proceedings, 11 th Annual IEEE Symposium on Logic in Computer Science, pages 184--195, New Brunswick, New Jersey, July 1996. IEEE Computer Society Press.

....at level 0 uses substitution, and Run at level 0 uses demotion. 11.4 Cross Stage Persistence Monolithic Variables Cross stage persistence can be relaxed by allowing variables to be available at exactly one stage. This seems to be the case in all multistage languages known to us to date [34, 7, 13, 9, 10, 6]. Intuitively, they use the following monolithic rule for variables (assume r = 0) Var (Monolithic) Delta x = n 0 Delta n x : when n 0 = n We allow the more general condition n 0 n, so an expression like val lift like = fn x = x is accepted, because inside the Brackets, ....

.... generation [43] The base language was statically typed, and dependent types were used to generate a wider class of programs than is possible by MetaML Facility Example Nielson Nielson [34] Gomard Jones [11] Gluck Jrgensen [9] Thiemann [50] Hatcliff Gluck [13] 7] fl [6] M Levels x.x 2 2 2 Static Typing Y 1 N N N Y Y Y Monolithic Var. x. f x ) Y Y Y Y Y N Y Y Reflection Run or eval N N N Y N Y N Y Persistence f. x.f x N N N N N N N Y Portability Y Y Y Y Y Y Y N Fig. 3. Comparative feature set restricted to two stages. Sheard and Shields ....

[Article contains additional citation context not shown here]

Rowan Davies. A temporal-logic approach to binding-time analysis. In Proceedings, 11 th Annual IEEE Symposium on Logic in Computer Science, pages 184--195, New Brunswick, New Jersey, 27--30 July 1996. IEEE Computer Society Press.

.... Tecniche formali per la specifica, l analisi, la verifica, la sintesi e la trasformazione di sistemi software , ESPRIT WG APPSEM. 1. The operational semantics and pragmatics of staged computation [15, 14, 11, 13] 2. Previous work on the applications of logical modalities to staged computation [5, 4], 3. Categorical models for multi stage languages [9, 1] Our study has been consolidated into a new language for multi stage programming called BN . 1.1 Multi Stage Programming The main steps of multi stage programming are: 1. Write the conventional program program: t S t D t where t S ....

....provide generic constructs building, combining and executing code fragments. The three languages we have studied have the following main features: ffl 2 [5] provides constructs for building and then executing closed code. Such a language is useful in machine code generation. ffl fl [4], provides constructs for building and combining open code fragments. Such a language is useful in high level program generation and in lining. ffl MetaML [15, 14] extends fl by providing an additional construct for the execution of code fragments, and cross stage persistence. Cross stage ....

[Article contains additional citation context not shown here]

R. Davies. A temporal-logic approach to bindingtime analysis. In 11 th LICS, New Brunswick, New Jersey, July 1996. IEEE Computer Society Press.

....doing so, we have identified a variety of subtleties related to multi stage programming, and provided solutions to a number of them. The results presented in this paper are based directly on Chapters 5 and 6. Davies and Pfenning propose two typed frameworks for staged computation, 6] and fl [5]. The latter is more directly related to MetaML because it allows evaluation under lambda (and therefore computation with open code) Davies uses a notion of expression family in the typed development of fl to classify values, but it is not used to impose restrictions in the notions of ....

Davies, R. A temporal-logic approach to binding-time analysis. In Proceedings, 11 th Annual IEEE Symposium on Logic in Computer Science (New Brunswick, July 1996), IEEE Computer Society Press, pp. 184--195.

....type constructor that guarantees that a given term will evaluate to a closed value at run time. We demonstrate our approach in the case of ML style references [MTHM97] We extend recent studies into the semantics and type systems for multi level and multi stage languages. Multi level languages [GJ91,GJ96,Mog98,Dav96] provide a mechanism for constructing and combining open code. Multi stage languages [TS97,TBS98,MTBS99,BMTS99,Tah99,Tah00] extend multi level languages with a construct for executing the code generated at run time. Multi stage programming can be illustrated using MetaML [TS97,Met00] an ....

....most features of SML and a host of novel meta programming constructs. In this release, safety is not guaranteed for meta programs that use Run or effects. We hope to incorporate the ideas presented in this paper into the next MetaML release. 2 The observation made here also applies to fl [Dav96]. language. We demonstrate this formally using a core language, that we call Mini ML BN ref , which extends Mini ML [CDDK86] with ML style references and 3 A code type constructor h i [TS97,TBS98,Dav96] A closed type constructor [ BMTS99] but with improved syntax borrowed from ....

[Article contains additional citation context not shown here]

Rowan Davies. A temporal-logic approach to binding-time analysis. In Proceedings, 11 th Annual IEEE Symposium on Logic in Computer Science, pages 184--195, New Brunswick, July 1996. IEEE Computer Society Press.

....at level 0 uses substitution, and Run at level 0 uses demotion. 11.4 Cross Stage Persistence Monolithic Variables Cross stage persistence can be relaxed by allowing variables to be available at exactly one stage. This seems to be the case in all multistage languages known to us to date [34, 7, 13, 9, 10, 6]. Intuitively, they use the following monolithic rule for variables (assume r = 0) Var (Monolithic) Delta x = n 0 Delta n x : when n 0 = n We allow the more general condition n 0 n, so an expression like val lift like = fn x ) hxi is accepted, because inside the Brackets, n ....

....to two stages. Sheard and Shields [44] investigate a dynamic type systems for multi staged programs where some type obligations of staged computations can be put off till run time. Davies and Pfenning present a statically typed multi stage language Mini ML , motivated by constructive modal logic [6]. A formal proof is presented for the equivalence of binding time correctness and modal correctness. MetaML typesystem was motivated primarily by operational considerations. Their language has two constructs, box and let box, which correspond roughly to Brackets and Run. Mini ML s type ....

[Article contains additional citation context not shown here]

Rowan Davies. A temporal-logic approach to binding-time analysis. In Proceedings, 11 th Annual IEEE Symposium on Logic in Computer Science, pages 184--195, New Brunswick, New Jersey, 27--30 July 1996. IEEE Computer Society Press.

No context found.

Davies, R. 1996. A temporal-logic approach to binding-time analysis. In E. Clarke Ed., Proceedings of the Eleventh Annual Symposium on Logic in Computer Science (LICS'96) (July 1996), pp. 184--195.

No context found.

Rowan Davies. A temporal-logic approach to binding-time analysis. In E. Clarke, editor, Proceedings of the Eleventh Annual Symposium on Logic in Computer Science, pages 184--195, July 1996.

No context found.

Davies, R. 1996. A temporal logic approach to binding-time analysis. In Symposium on Logic in Computer Science, LICS'96, E. Clarke, Ed. IEEE Computer Society Press, New Brunswick, New Jersey, 184--195.

No context found.

Davies, Rowan. (1996). A temporal logic approach to binding-time analysis. Pages 184-- 195 of: Symposium on Logic in Computer Science, LICS'96.

No context found.

Davies, R. A temporal-logic approach to binding-time analysis. In Symposium on Logic in Computer Science (1996), IEEE Computer Society Press, pp. 184--195.

No context found.

Rowan Davies. A temporal-logic approach to binding-time analysis. In Proceedings, 11 th Annual IEEE Symposium on Logic in Computer Science, pages 184--195, New Brunswick, New Jersey, July 1996. IEEE Computer Society Press.

No context found.

Rowan Davies. A temporal-logic approach to binding-time analysis. In the Symposium on Logic in Computer Science (LICS '96), pages 184-195, New Brunswick, 1996. IEEE Computer Society Press.

No context found.

Rowan Davies. A temporal-logic approach to binding-time analysis. In the Symposium on Logic in Computer Science (LICS '96), pages 184--195, New Brunswick, 1996. IEEE Computer Society Press.

No context found.

Rowan Davies. A temporal-logic approach to binding-time analysis. In Proceedings, 11 th Annual IEEE Symposium on Logic in Computer Science, pages 184--195, New Brunswick, July 1996. IEEE Computer Society Press.

No context found.

Davies, R. A temporal-logic approach to binding-time analysis. In the Symposium on Logic in Computer Science (LICS '96) (New Brunswick, 1996), IEEE Computer Society Press, pp. 184--195.

No context found.

R. Davies. A temporal logic approach to binding-time analysis. In Symposium on Logic in Computer Science (LICS '96), pages 184--195, 1996.

No context found.

Rowan Davies. A temporal logic approach to binding-time analysis. In E. Clarke, editor, Proceedings of the Eleventh Annual Symposium on Logic in Computer Science, pages 184--195, New Brunswick, New Jersey, July 1996. IEEE Computer Society Press.

No context found.

R. Davies. A temporal-logic approach to binding-time analysis. In the Symposium on Logic in Computer Science (LICS '96), pages 184--195, New Brunswick, 1996. IEEE Computer Society Press.

No context found.

Rowan Davies. A temporal-logic approach to binding-time analysis. In the Symposium on Logic in Computer Science (LICS '96), pages 184--195, New Brunswick, 1996. IEEE Computer Society Press.

No context found.

Davies, R. A temporal-logic approach to binding-time analysis. In the Symposium on Logic in Computer Science (LICS '96) (New Brunswick, 1996), IEEE Computer Society Press, pp. 184--195.

No context found.

R. Davies. A temporal-logic approach to binding-time analysis. In the Symposium on Logic in Computer Science (LICS '96), pages 184--195, New Brunswick, 1996. IEEE Computer Society Press.

No context found.

Davies, R.: A temporal-logic approach to binding-time analysis. In: Logic in Computer Science. (1996) 184-195

No context found.

Rowan Davies. A temporal-logic approach to binding-time analysis. In Proceedings, 11 th Annual IEEE Symposium on Logic in Computer Science, pages 184--195, New Brunswick, July 1996. IEEE Computer Society Press.

No context found.

Davies, R. A temporal-logic approach to binding-time analysis. In Symposium on Logic in Computer Science (1996), IEEE Computer Society Press, pp. 184--195.

No context found.

Davies, R. A temporal-logic approach to binding-time analysis. In the Symposium on Logic in Computer Science (LICS '96) (New Brunswick, 1996), IEEE Computer Society Press, pp. 184--195.

No context found.

Rowan Davies. A temporal logic approach to binding-time analysis. In E. Clarke, editor, Proceedings of the Eleventh Annual IEEE Symposium on Logic in Computer Science, New Brunswick, New Jersey, pages 184--195. IEEE Computer Society Press, July 1996.

No context found.

Rowan Davies. A temporal logic approach to binding-time analysis. In E. Clarke, editor, Proceedings of the Eleventh Annual IEEE Symposium on Logic in Computer Science, New Brunswick, New Jersey, pages 184--195. IEEE Computer Society Press, July 1996.

No context found.

Rowan Davies. A temporal-logic approach to binding-time analysis. In 11 th Annual IEEE Symposium on Logic in Computer Science (LICS), pages 184-- 195, New Brunswick, 1996. IEEE Computer Society Press.

First 50 documents  Next 50

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC