F. Honsell and D. Sannella. Pre-logical relations. In Proc. Computer Science Logic, volume 1683 of LNCS, pages 546--561. Springer, 1999. An extended version is in Information and Computation 178:23--43,2002.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....morphisms are terms up to conversion is the free CCC with a strong monad over the set B. Accordingly, our study will rest on categorical principles. While there is a urry of generalizations of logical relations (Kripke logical relations [13] lax logical relations [18] pre logical relations [7], etc. we use subscones [14] as a unifying framework for de ning logical relations. Recall that subscones over Set Set Set al..low us to de ne logical relations, and subscones over the presheaf category lead to I indexed Kripke logical relations [14] The important property of logical ....

....2 ) 2 R, therefore b 1 2 fxj(x; y) 2 Rg; so B 1 fxj(x; y) 2 Rg. The reverse inclusion is obvious, so B 1 = fxj(x; y) 2 Rg. The other equality B 2 = fyj(x; y) 2 Rg is by symmetry. That logical relations on powersets de ne bisimulations was conjectured in [11] and, for pre logical relations, in [7]. 6.1 Labelled transition systems and bisimulations The case TA = P n (A) de nes labelled transition systems as elements of (TA) with labels in L and states in A, as functions mapping states a and labels to the set of states a such that a a . Our monad lifting S in this case ....

F. Honsell and D. Sannella. Pre-logical relations. In CSL'99, pages 546-561. Springer Verlag LNCS 1683, 1999.

.... abstraction is closely related to data re nement, and the fundamental notion of this paper, that of being linked by a logical relation , is closely related to the notion of L relation in [6] see also [18] The work of that paper, and of this paper, and those on lax and pre logical relations [4, 13] clearly need to be combined at some point. An obvious direction for further work is to address models of call by value lambda calculi such as the computational lambda calculus [12] Such analysis would probably best be done by moving from cartesian closed categories to some form of closed ....

F. Honsell and D. Sannella. Pre-logical relations. In Proc CSL 99, LNCS 1683, pages 546-562, 1999.

....extensional collapses. Moreover, extensional collapses (i.e. logical relations) are not even closed under composition, and this is one reason for favouring our definition of morphism over the concept of logical relation. In fact, our morphisms correspond to pre logical relations as studied in [HS99], where the reader may find further details arguments for the advantages of pre logical over logical relations. We also have the following simple facts: Proposition 1.18 Suppose A is an extensional PTS over X. Then (i) Any morphism A # B over X is discrete. ii) The only morphism A # A ....

F. Honsell and D. Sannella. Pre-logical relations. In Proc. Computer Science Logic, CSL'99, volume 1683 of Lecture Notes in Computer Science, pages 546--561. Springer, 1999.

.... devise an alternative notion of simulation relation in the logic [12] This notion composes at higher order, thus relating the syntactic level to on going work on the semantic level remedying the fact that logical relations traditionally used to describe refinement do not compose at higher order [15, 16, 19, 18, 31]. Now, using an alternative simulation relation means that parametricity is not applicable in the needed form. This is solved soundly w.r.t. the parametric PER model by augmenting the logical language with a new basic predicate Closed with predefined semantics, so as to restrict observable ....

....a(T[R] # C )b # # D#Obs #f:#X. T[X ] # D) Closed # In (f) # (fA a) fB b) 11 We regain not only transitivity of the existence of simulation relations, but also composability of simulation relations. This is akin to recent notions on the semantic level, i.e. pre logical relations [15, 16], lax logical relations [31, 19] and L relations [18] Theorem 12 (Composability of Simulation Relations) For T[X ] adhering to adt, let # = A, B, a, b, # # = B, C, b, c, # ## = A, C, a, c. Given spParamC, #A, B, C, R#AB,S#BC, a:T[A] b:T[B] c: T[C] a(T[R] # C )b # b(T[S] # # C )c ....

F. Honsell and D. Sannella. Pre-logical relations. In Proc. CSL'99, volume 1683 of LNCS, pages 546--561, 1999.

....of simulation relation based on a weaker arrow type relation. This notion composes at higher order, thus relating the syntactic level to recent and on going work on the semantic level remedying the fact that logical relations traditionally used to describe refinement do not compose at higher order [17, 18, 21, 20, 32]. In [12] an account of algebraic specification refinement [38, 37] is mapped to the first order type theoretic refinement notion, and the two accounts of refinement are shown to coincide. Important issues in algebraic specification refinement, such as the choice of input sorts [36] and the ....

....(fB b) b:g y) For this we display f above. 2 We also regain not only transitivity of the existence of simulation relations, but also composability of simulation relations. This relates the syntactic level to recent and on going work on the semantic level, namely the pre logical relations of [17, 18], the lax logical relations of [32, 21] and the L relations of [20] Theorem 10 (Composability of Simulation Relations) Given spParam, for T[X ] adhering to adt, we can derive 8A; B; G; R aeA Theta B; S aeB Theta G; a: T[A] b:T[B] g: T[G] a(T[R] b b(T[S] g ) a(T[S ffi R] ....

F. Honsell and D. Sannella. Pre-logical relations. In Proc. CSL'99, volume 1683 of LNCS, pages 546--561, 1999.

....a relation that explicitly restricts arguments to be definable, namely the relation R in the proof of Lemma 4. At higher order, one could try altering the relational proof criteria by incorporating explicit definability clauses. This is reminiscent of recent approaches on the semantical level [15, 13]. Acknowledgements Thanks are due to Martin Hofmann, Don Sannella, and the referees for helpful comments and suggestions. This research has been supported by EPSRC grant GR K63795, and NFR (Norwegian Research Council) grant 110904 41. ....

F. Honsell and D. Sannella. Pre-logical relations. In Proc. CSL'99, LNCS, 1999.

....Basic Lemma is easily proved and (binary) algebraic relations compose. But Mitchell concludes that, because logical relations are easily constructed by induction on types, they seem to be the important special case for proving properties of typed lambda calculi. Recently, Honsell and Sannella [HS99] have shown that such relation families, which they term pre logical relations, are both the largest class of conventional relations on Henkin models that satisfy the Basic Lemma, and the smallest class that both includes logical relations and is closed under composition. They give a number of ....

....closed under composition. They give a number of examples and applications, and study their closure properties. We briey sketch two of their applications. The composite of (binary) logical relations need not be logical. It is an easy exercise to construct a counter example; see, for instance, HS99] But the composite of binary pre logical relations is a pre logical relation. Mitchell [Mi91] showed that the use of logical relations to verify data representations in typed lambda calculi is complete, provided that all of the primitive functions are rst order. In [HS99] this is ....

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F. Honsell and D. Sannella. Pre-logical relations. In Flum and RodriguezArtalejo

.... of the category of signatures in [65] We have also discussed some possible extensions of Casl, notably by higher order operations, where a complete formal proposal is under development on the basis of [32] and the work on behavioural equivalence of higher order models is also relevant [33] also [34]) An important stream of work addressed the issues of a careful, semanticsbased comparison of Casl with other specifications formalism [46] 9] With the semantics essentially ready, we have started to work on making it fully institution independent [44] 40] and on proof systems and proof ....

....projects. Libraries of specifications. A library of basic datatypes is being developed at Bremen [58, 59, 57, 51, 61] Formal software development based on algebraic specifications. In particular work has been done on architectural specifications [14, 15] and on various concepts of refinement [33, 34, 35, 62], see also [7] Additional CoFI related publications by the Methodology task group are [30, 31, 13] 1.4 Tools A L A T E X package for formatting Casl specifications has been developed [52] The aim is to facilitate the pretty printing and uniform formatting of Casl specifications, and the ....

F. Honsell and D. Sannella. Pre-logical relations. Submitted for journal publication, 1999.

.... details of the category of signatures in [65] We have also discussed some possible extensions of Casl, notably by higher order operations, where a complete formal proposal is under development on the basis of [32] and the work on behavioural equivalence of higher order models is also relevant [33] (also [34] An important stream of work addressed the issues of a careful, semanticsbased comparison of Casl with other specifications formalism [46] 9] With the semantics essentially ready, we have started to work on making it fully institution independent [44] 40] and on proof systems ....

....projects. Libraries of specifications. A library of basic datatypes is being developed at Bremen [58, 59, 57, 51, 61] Formal software development based on algebraic specifications. In particular work has been done on architectural specifications [14, 15] and on various concepts of refinement [33, 34, 35, 62], see also [7] Additional CoFI related publications by the Methodology task group are [30, 31, 13] 1.4 Tools A L A T E X package for formatting Casl specifications has been developed [52] The aim is to facilitate the pretty printing and uniform formatting of Casl specifications, and the ....

F. Honsell and D. Sannella. Pre-logical relations. In Proc. Computer Science Logic, CSL'99, volume 1683 of Lecture Notes in Computer Science, pages 546--561. Springer, 1999.

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F. Honsell and D. Sannella. Pre-logical relations. In Proc. Computer Science Logic, volume 1683 of LNCS, pages 546--561. Springer, 1999. An extended version is in Information and Computation 178:23--43,2002.

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F. Honsell and D. Sannella. Pre-logical relations. In Proc. 13rd Int. Workshop Computer Science Logic (CSL), volume 1683 of Lecture Notes in Computer Science, pages 546--561, 1999.

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F. Honsell and D. Sannella. Pre-logical relations. In Proc. CSL'99, volume 1683 of LNCS, 1999.

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F. Honsell and D. Sannella. Pre-logical relations. In Proc. 13rd Int. Workshop Computer Science Logic (CSL), volume 1683 of Lecture Notes in Computer Science, pages 546--561, 1999.

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Furio Honsell and Donald Sannella. Pre-logical relations. In Proc. Computer Science Logic, CSL'99, volume 1683 of Lecture Notes in Computer Science, pages 546--561. Springer, 1999. URL ftp://ftp.dcs.ed.ac.uk/pub/dts/prelogrel.ps.

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F. Honsell and D. Sannella. Pre-logical relations. In Computer Science Logic, CSL'99, volume 1683 of Lecture Notes in Computer Science, pages 546--561. Springer Verlag, 1999.

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