Iliano Cervesato and Frank Pfenning. A linear logical framework. Information and Computation, 1999. To appear in the special issue with invited papers from LICS'96, E. Clarke, editor.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....hypothetical judgments in deductions. Moreover, proofs are rei ed as objects which allows properties of or relations between proofs to be expressed within the framework [Pfe91] Representations of systems involving state remained cumbersome until the design of the linear logical framework LLF [CP98] and its close relative RLF [IP98] For example, LLF allows an elegant representation of Mini ML with mutable references that rei es imperative computations as objects. LLF is a conservative extension of LF with the linear function type A B, the additive product type A B, and the additive unit ....

....freely generated fragment of intuitionistic linear logic [HM94, Bar96] whose proofs admit long normal forms without any commuting conversions. This allows a relatively simple type directed equality checking algorithm which is critical in the proof of decidability of type checking for the framework [CP98, VC00]. While LLF solved many problems associated with the representation of stateful computations, the encoding of concurrent computations remained unsatisfactory. In this report, we demonstrate that the limitations of LLF can be overcome by extending the framework with a monad that incorporates the ....

Iliano Cervesato and Frank Pfenning. A linear logical framework. Information and Computation, 1998. To appear in a special issue with invited papers from LICS'96, E. Clarke, editor.

....by the underlying type theory. In particular, we can achieve a bijection between hypothetical deductions of a judgment and canonical objects of the corresponding type. Representations in this style of systems involving state remained cumbersome until the design of the linear logical framework LLF [CP98] and its close relative RLF [IP98] LLF is a conservative extension of LF with selected constructs from linear logic. The representation principles behind LLF are state as linear hypotheses and imperative computations as linear functions . Again, we can achieve a bijection between imperative ....

....we do here. The method of de ning a type theory by a typed operational semantics goes back to the Automath languages [dB93] and has been applied to LF by Felty [Fel91] Our canonical formulation signi cantly extends and streamlines the ideas behind Felty s canonical LF and its extension to LLF [CP98]; the need for con uence and normalization results is eliminated. 5 Conclusion In this paper, we have presented the basic design of a logical framework that internalizes parametric and hypothetical judgments, linear hypothetical judgments, and true concurrency. This supports representation of a ....

Iliano Cervesato and Frank Pfenning. A linear logical framework. Information and Computation, 1998. To appear in a special issue with invited papers from LICS'96, E. Clarke, editor.

....the store. If the store is modeled by a set of assumptions, say contains C V, where C is a cell and V a value, then linear logic [9] o#ers the right setting, since updates will consume and add resources. This is one of the motivations for investigating frameworks based on linear logics such as LLF [4]. On the other hand, work on the automation of reasoning in such frameworks is still in its infancy [10] The methodology which enriches, in a conservative way, a logical framework so as to capture, at the right level of abstraction, di#erent object level phenomena can be pushed further. In this ....

....1 (lam # x. e) e 2 ## K ev e[e 2 x] In order to prove type preservation of this machine we need to consider sequences of transitions by taking the reflexive transitive closure ## # of the above relation. Further we add typing judgments for expressions, values, instructions and continuations [4]. We report here only the last two, but their complete encoding can be found in Subsection 4.2. 4 v1 : # # e2 : # # ofI app 1 i app 1 v1 e2 : # e : # ofI ev i ev e : # v : # ofI return i return v : # ofK init init : # #, x:#1 i i : # # K : # ofK K ....

[Article contains additional citation context not shown here]

I. Cervesato and F. Pfenning. A linear logical framework. Information and Computation, 1998. To appear in a special issue with invited papers from LICS'96, E. Clarke, editor.

....hypothetical judgments in deductions. Moreover, proofs are rei ed as objects which allows properties of or relations between proofs to be expressed within the framework [Pfe91] Representations of systems involving state remained cumbersome until the design of the linear logical framework LLF [CP98] and its close relative RLF [IP98] For example, LLF allows an elegant representation of Mini ML with mutable references that rei es imperative computations as objects. LLF is a conservative extension of LF with the linear function type A B, the additive product type A B, and the additive unit ....

....freely generated fragment of intuitionistic linear logic [HM94, Bar96] whose proofs admit long normal forms without any commuting conversions. This allows a relatively simple type directed equality checking algorithm which is critical in the proof of decidability of type checking for the framework [CP98, VC00]. While LLF solved many problems associated with stateful computation, the encoding of concurrent computations remained unsatisfactory. In this report, we demonstrate that the limitations of LLF can be overcome by extending the framework with a monad that incorporates the synchronous ....

[Article contains additional citation context not shown here]

Iliano Cervesato and Frank Pfenning. A linear logical framework. Information and Computation, 1998. To appear in a special issue with invited papers from LICS'96, E. Clarke, editor.

....hypothetical judgments in deductions. Moreover, proofs are reified as objects which allows properties of or relations between proofs to be expressed within the framework [Pfe91] Representations of systems involving state remained cumbersome until the design of the linear logical framework LLF [CP98] and its close relative RLF [IP98] For example, LLF allows an elegant representation of Mini ML with mutable references that reifies imperative computations as objects. LLF is a conservative extension of LF with the linear function type B, the additive product type A B, and the additive unit ....

....freely generated fragment of intuitionistic linear logic [HM94, Bar96] whose proofs admit long normal forms without any commuting conversions. This allows a relatively simple type directed equality checking algorithm which is critical in the proof of decidability of type checking for the framework [CP98, VC00]. While LLF solved many problems associated with the representation of stateful computations, the encoding of concurrent computations remained unsatisfactory. In this report, we demonstrate that the limitations of LLF can be overcome by extending the framework with a monad that incorporates the ....

Iliano Cervesato and Frank Pfenning. A linear logical framework. Information and Computation, 1998. To appear in a special issue with invited papers from LICS'96, E. Clarke, editor.

....hypothetical judgments in deductions. Moreover, proofs are reified as objects which allows properties of or relations between proofs to be expressed within the framework [Pfe91] Representations of systems involving state remained cumbersome until the design of the linear logical framework LLF [CP98] and its close relative RLF [IP98] For example, LLF allows an elegant representation of Mini ML with mutable references that reifies imperative computations as objects. LLF is a conservative extension of LF with the linear function type B, the additive product type A B, and the additive unit ....

....freely generated fragment of intuitionistic linear logic [HM94, Bar96] whose proofs admit long normal forms without any commuting conversions. This allows a relatively simple type directed equality checking algorithm which is critical in the proof of decidability of type checking for the framework [CP98, VC00]. While LLF solved many problems associated with stateful computation, the encoding of concurrent computations remained unsatisfactory. In this report, we demonstrate that the limitations of LLF can be overcome by extending the framework with a monad that incorporates the synchronous ....

[Article contains additional citation context not shown here]

Iliano Cervesato and Frank Pfenning. A linear logical framework. Information and Computation, 1998. To appear in a special issue with invited papers from LICS'96, E. Clarke, editor.

....by the underlying type theory. In particular, we can achieve a bijection between hypothetical deductions of a judgment and canonical objects of the corresponding type. Representations in this style of systems involving state remained cumbersome until the design of the linear logical framework LLF [CP98] and its close relative RLF [IP98] LLF is a conservative extension of LF with selected constructs from linear logic. The representation principles behind LLF are state as linear hypotheses and imperative computations as linear functions . Again, we can achieve a bijection between imperative ....

....we do here. The method of defining a type theory by a typed operational semantics goes back to the Automath languages [dB93] and has been applied to LF by Felty [Fel91] Our canonical formulation significantly extends and streamlines the ideas behind Felty s canonical LF and its extension to LLF [CP98]; the need for confluence and # normalization results is eliminated. 5 Conclusion In this paper, we have presented the basic design of a logical framework that internalizes parametric and hypothetical judgments, linear hypothetical judgments, and true concurrency. This supports representation of ....

Iliano Cervesato and Frank Pfenning. A linear logical framework. Information and Computation, 1998. To appear in a special issue with invited papers from LICS'96, E. Clarke, editor.

....side stepped in the original paper on the LF logical framework [HHP93] by restricting attention to # conversion for definitional equality. This is su#cient if we also restrict attention to # long forms [FM90, Cer96] This restriction is somewhat unsatisfactory, especially in linear variants of LF [CP98]. More recently, # expansion has been studied in its own right, using modification of standard techniques from rewriting theory to overcome the lack of strong normalization when expansion is not restricted [JG95, Gha97] In the dependently typed case, even the definition of long normal form is ....

....technical report describing our construction [HP99] have clearly demonstrated that the proposed technique is widely applicable. Vanderwaart and Crary [VC01] have adapted the ideas with minor modifications to give a proof of the decidability for linear LF that is stronger than the original one [CP98] since it does not require # long forms from the start. The further adaptation to the case of an ordered linear type theory [Pol01] provides further evidence. Finally, the second author has adapted the technique to prove decidability and existence of canonical forms for a type theory with an ....

[Article contains additional citation context not shown here]

Iliano Cervesato and Frank Pfenning. A linear logical framework. Information and Computation, 1998. To appear in a special issue with invited papers from LICS'96, E. Clarke, editor.

.... in the original paper on the LF logical framework [HHP93] by restricting attention to fi conversion for definitional equality, which is sufficient if we also restrict attention to j long forms [FM90, Cer96] This restriction is somewhat unsatisfactory, especially in linear variants of LF [CP98]. More recently, j expansion has been studied in its own right, using modification of standard techniques from rewriting theory to overcome the lack of strong normalization when expansion is not restricted [JG95, Gha97] In the dependently typed case, even the definition of long normal form is ....

....theorem for the type directed equality algorithm. That is, if two terms are definitionally equal, the algorithm will succeed. The goal is to present a flexible and modular technique which can be adapted easily to related type theories, such as the one underlying the linear logical framework [CP98], one based on non commutative linear logic [PP99] or one including subtyping [Pfe93] Other techniques presented in the literature, particularly those based on a notion of j reduction, do not seem to adapt well to these richer theories. The central idea is to proceed by an argument via logical ....

Iliano Cervesato and Frank Pfenning. A linear logical framework. Information and Computation, 1998. To appear in a special issue with invited papers from LICS'96, E. Clarke, editor.

....can act as a logical data structure and hold information which must be accessed in a constrained fashion. It remains to clarify the order in which the clauses in a context are considered when the goal has become atomic. We employ here the same strategy as the Lolli language [9] and linear LF [5] by dividing the hypotheses into a static program and dynamic assumptions made during search. We first scan all dynamic assumptions from right to left, where R , Gammaffi R , iR add assumptions on the right, and aeR adds assumptions on the left. Then we attempt each formula in the static ....

....present in splitting mixed contexts. We conjecture that the techniques discussed in this paper can be extended to mixed contexts. Finally, the existence of canonical forms for the natural deduction system of OLL [14] means that it might be possible to add it to the linear logical framework [5] in a conservative manner. However, we have not yet considered such issues as type reconstruction or unification. 7. ACKNOWLEDGEMENTS We would like to thank Frank Pfenning for valuable contributions to this paper. 8. ....

I. Cervesato and F. Pfenning. A linear logical framework. Information and Computation, 1999. To appear in the special issue with invited papers from LICS'96, E. Clarke, editor.

....syntax, and parametric and hypothetical judgments through dependently typed functions. In previous work, I. Cervesato and the second author have investigated a conservative extension of LF which allows the natural representation of systems with state via linear functions and additive pairs [CP98, Cer96]. In this paper we explore a further conservative extension with an intrinsic notion of order. The impetus for the development of such a framework came from the observation of certain analogies between ordering properties of CPS terms [DP95, DDP99] and substitution properties of linear calculi. ....

....at well formed type A. The existence of canonical forms for this simple implicational fragment of OLL provides a basis for an ordered logical framework. We conjecture that an ordered logical framework based on a full type theory can be constructed along the lines of the linear logical framework [CP98]. In this paper we only need a two level fragment as explained in Section 5. 3 CPS terms In this section we review CPS terms and their ordering properties as investigated in [DP95, DDP99] We use the following syntax for direct style (DS) terms: DS Terms r : e DS Expressions e : e 1 e 2 j ....

Iliano Cervesato and Frank Pfenning. A linear logical framework. Information and Computation, 1998. To appear in a special issue with invited papers from LICS'96, E. Clarke, editor.

....where these judgments are considered primarily as hypotheses. Instead of internalizing them as modal operators, we internalize the corresponding hypothetical judgment as function types. Such a restriction is not new it goes back to similar treatments of linear logic [9] and linear type theory [3] with similar motivations. In the remainder of the paper we present our type theory, investigate its properties, and sketch some further developments and potential applications. 2 A Modal Type Theory Our modal type theory is a conservative extension of LF [7] Our approach follows the outline ....

I. Cervesato and F. Pfenning. A linear logical framework. Information and Computation, 1998. To appear in a special issue with invited papers from LICS'96, E. Clarke, editor.

....these judgments are considered primarily as hypotheses. Instead of internalizing them as modal operators, we internalize the corresponding hypothetical judgment as function types. Such a restriction is not new it goes back to similar treatments of linear logic [HM94] and linear type theory [CP98, VC00] with similar motivations. 2 In the remainder of the paper we present our type theory, investigate its properties, and sketch some further developments and potential applications. 2 A Modal Type Theory Our modal type theory is a conservative extension of LF [HHP93] Our approach follows ....

Iliano Cervesato and Frank Pfenning. A linear logical framework. Information and Computation, 1998. To appear in a special issue with invited papers from LICS'96, E. Clarke, editor.

....these judgments are considered primarily as hypotheses. Instead of internalizing them as modal operators, we internalize the corresponding hypothetical judgment as function types. Such a restriction is not new it goes back to similar treatments of linear logic [HM94] and linear type theory [CP98, VC00] with similar motivations. 2 In the remainder of the paper we present our type theory, investigate its properties, and sketch some further developments and potential applications. 2 A Modal Type Theory Our modal type theory is a conservative extension of LF [HHP93] Our approach follows ....

Iliano Cervesato and Frank Pfenning. A linear logical framework. Information and Computation, 1998. To appear in a special issue with invited papers from LICS'96, E. Clarke, editor.

....since represented CPS terms correspond to actual CPS terms satisfying the stackability judgements. Finally, we give a conclusion with some related and future work in section 7. 2 Ordered Logical Framework OLF is a logical framework in the tradition of LF [HHP93] and its linear extension LLF [CP99] Thus OLF is essentially a dependent type theory 1 for which type checking is decidable and canonical forms exist. Since OLF has come under study quite recently, the remainder of this section provides the necessary background information to follow our proof. OLF should be thought of as ordered ....

....more canonical objects. The existence of canonical forms for this simple implicational fragment of OLL provides a basis for an ordered logical framework. We conjecture that an ordered logical framework based on a full type theory can be constructed along the lines of the linear logical framework [CP99] In this paper we only need a two level fragment as explained in subsection 2.2. 2.2 Two Level Framework We extend the ordered calculus from subsection 2.1 to a simple two level logical framework where level 2 types will be allowed to depend upon level 1 objects. Thus level 2 type families p ....

Iliano Cervesato and Frank Pfenning. A linear logical framework. Information and Computation, 1999. To appear in the special issue with invited papers from LICS'96, E. Clarke, editor.

....in the original paper on the LF logical framework [HHP93] by restricting attention to fi conversion for definitional equality. This is sufficient if we also restrict attention to j long forms [FM90, Cer96] This restriction is somewhat unsatisfactory, especially in linear variants of LF [CP98]. More recently, j expansion has been studied in its own right, using modification of standard techniques from rewriting theory to overcome the lack of strong normalization when expansion is not restricted [JG95, Gha97] In the dependently typed case, even the definition of long normal form is not ....

....theorem for the type directed equality algorithm. That is, if two terms are definitionally equal, the algorithm will succeed. The goal is to present a flexible and modular technique which can be adapted easily to related type theories, such as the one underlying the linear logical framework [CP98], one based on non commutative linear logic [PP99] or one including subtyping [Pfe93] Other techniques presented in the literature, particularly those based on a notion of j reduction, do not seem to adapt well to these richer theories. The central idea is to proceed by an argument via logical ....

Iliano Cervesato and Frank Pfenning. A linear logical framework. Information and Computation, 1998. To appear in a special issue with invited papers from LICS'96, E. Clarke, editor.

....syntax, and parametric and hypothetical judgments through dependently typed functions. In previous work, I. Cervesato and the second author have investigated a conservative extension of LF which allows the natural representation of systems with state via linear functions and additive pairs [CP98, Cer96]. In this paper we explore a further conservative extension with an intrinsic notion of order. The impetus for the development of such a framework came from the observation of certain analogies between ordering properties of CPS terms [DP95, DDP99] and substitution properties of linear calculi. ....

....at well formed type A. The existence of canonical forms for this simple implicational fragment of OLL provides a basis for an ordered logical framework. We conjecture that an ordered logical framework based on a full type theory can be constructed along the lines of the linear logical framework [CP98]. In this paper we only need a two level fragment as explained in Section 5. 3 CPS terms In this section we review CPS terms and their ordering properties as investigated in [DP95, DDP99] We use the following syntax for direct style (DS) terms: DS Terms r : e DS Expressions e : e 1 e 2 j ....

Iliano Cervesato and Frank Pfenning. A linear logical framework. Information and Computation, 1998. To appear in a special issue with invited papers from LICS'96, E. Clarke, editor.

No context found.

Iliano Cervesato and Frank Pfenning. A linear logical framework. Information and Computation, 1999. To appear in the special issue with invited papers from LICS'96, E. Clarke, editor.

No context found.

Iliano Cervesato and Frank Pfenning. A linear logical framework. Information and Computation, 1998. To appear in a special issue with invited papers from LICS'96, E. Clarke, editor.

No context found.

Iliano Cervesato and Frank Pfenning. A linear logical framework. Information and Computation, 1998. To appear in a special issue with invited papers from LICS'96, E. Clarke, editor.

No context found.

Iliano Cervesato and Frank Pfenning. A linear logical framework. Information and Computation, 1998. To appear in a special issue with invited papers from LICS'96, E. Clarke, editor.

No context found.

Iliano Cervesato and Frank Pfenning. A linear logical framework. Information and Computation, 1998. To appear in a special issue with invited papers from LICS'96, E. Clarke, editor.

No context found.

Iliano Cervesato and Frank Pfenning. A linear logical framework. Information and Computation, 1998. To appear in a special issue with invited papers from LICS'96, E. Clarke, editor.

No context found.

Iliano Cervesato and Frank Pfenning. A linear logical framework. Information and Computation, 1998. To appear in a special issue with invited papers from LICS'96, E. Clarke, editor.

No context found.

I. Cervesato and F. Pfenning. A linear logical framework. Information and Computation, 1998. To appear in a special issue with invited papers from LICS'96, E. Clarke, editor.

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