R. Harper and F. Pfenning. On equivalence and canonical forms in the LF type theory. In A. Felty, editor, Proceedings of the Workshop on Logical Frameworks and MetaLanguages (LFM'99), Paris, France, Sept. 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....size of its input and thus no preserver. However, our proposed type system can e#ortlessly keep track of the amount of size change in insert. This information is successfully used to accept inssort as a terminating preserver. How to integrate approximation types into the underlying type theory LF [20] requires a careful investigation. Since dependent types are present in LF, Xi s type based termination check [36] might be more suitable. Our approach fits best to simply typed logic programming. 7.3 Resource Bound Certification Crary and Weirich [14] describe a language LXres for resource ....

R. Harper and F. Pfenning. On Equivalence and Canonical Forms in the LF Type Theory. Technical report, Carnegie Mellon University, July 2000.

....linear logical framework LLF [1] hereafter CP ) The typing rules of LLF forced wellformed terms into long form, making all well typed normal forms canonical and rendering any rules for de nitional equality unnecessary. Subsequent to the original de nition of LLF, Harper and Pfenning [6,7] (hereafter, HP ) gave an alternate formulation of ordinary LF that allowed a clean treatment of de nitional equality without having to restrict terms to precanonical form. Their approach was based on the use of a typed de nitional equality judgment as opposed to an untyped reduction ....

Robert Harper and Frank Pfenning. On equivalence and canonical forms in the LF type theory. Technical Report CMU-CS-00-148, Carnegie Mellon University, July 2000.

....linear logical framework LLF [1] hereafter CP ) The typing rules of LLF forced wellformed terms into long form, making all well typed normal forms canonical and rendering any rules for de nitional equality unnecessary. Subsequent to the original de nition of LLF, Harper and Pfenning [6,7] (hereafter, HP ) gave an alternate formulation of ordinary LF that allowed a clean treatment of de nitional equality without having to restrict terms to precanonical form. Their approach was based on the use of a typed de nitional equality judgment as opposed to an untyped reduction ....

Robert Harper and Frank Pfenning. On equivalence and canonical forms in the LF type theory. Technical Report CMU-CS-99-159, Carnegie Mellon University, September 1999.

....(Mk) to families, together with a wellfounded ordering on the non term constants in the domain of the mapping. We write S for the ordering associated with S. The judgement forms for LTT s static semantics are given in Figure 3. We follow Harper and Pfenning s treatment of the metatheory of LF [10], using typed equality judgements rather than ## conversion; equality judgements are required for all classes except terms, which alone cannot appear inside of types. The typing rules for LTT are the expected ones, and are given in Appendix B (for full LTT, including linearity) As usual, we ....

....typed lambda calculus) Theorem 4.2 Suppose S and R are well formed, #S # context, and # or not # A1 = A2 : K is derivable, and whether or not M1 = M2 : A is derivable. The proof [23] is based on a logical relations argument modeled after the analogous proof of Harper and Pfenning [10] for intuitionistic LF. From this it is easy to show decidability of LTT typechecking: Corollary 4.3 Suppose S and R are well formed, # context, and # or not #; # e : # . 5 Example: Memory Management In this section we present a strategy for using the linear constructs of LTT to ....

R. Harper and F. Pfenning. On equivalence and canonical forms in the LF type theory. Technical Report CMU-CS-00148, Carnegie Mellon University, School of Computer Science, July 2000.

....they then use a separate rule of conversion to reclassify N with type A, if indeed A . The test used for equivalence is the term directed, context independent one of [7] whose description is omitted here. It should be possible to extend the results to a context dependent test like that of [11]. I. Classi cations: v : A A = lookup(v; type) type : kind ; x : A M : B x : A: B : x : A: M : x : A: B 2 ftype; kindg M : x : A: B N : A (M N) B[x : N ] A A : type ; x : A B : x : A: B : 2 ftype; kindg II. Contexts: ctxemp) ....

R. Harper and F. Pfenning. On Equivalence and Canonical Forms in the LF Type Theory. Technical Report CMU-CS-00-148, Carnegie Mellon University, July 2000.

....omit formal statements of lemmas and their proofs when they follow standard techniques. For the sake of brevity we concentrate in the lemmas and theorems on objects and may omit analogous statements for the levels of families and kinds. Full details can be found in a forthcoming technical report [HP99]. 2 The LF Type Theory Syntactically, our formulation of the LF type theory follows the original proposal by Harper, Honsell and Plotkin [HHP93] except that we omit type level abstraction. This simplifies the proof of the soundness theorem considerably, since we can prove the injectivity of ....

Robert Harper and Frank Pfenning. On equivalence and canonical forms in the LF type theory. Technical Report CMU-CS-99-159, Department of Computer Science, Carnegie Mellon University, 1999. Forthcoming.

....the linear logical framework LLF [1] hereafter CP ) The typing rules of LLF forced well formed terms into long form, making all well typed normal forms canonical and rendering any rules for de nitional equality unnecessary. Subsequent to the original de nition of LLF, Harper and Pfenning [6, 7] (hereafter, HP ) gave an alternate formulation of ordinary LF that allowed a clean treatment of de nitional equality without having to restrict terms to pre canonical form. Their approach was based on the use of a typed de nitional equality judgment as opposed to an untyped reduction ....

Robert Harper and Frank Pfenning. On equivalence and canonical forms in the LF type theory. Technical Report CMU-CS-00-148, Carnegie Mellon University, July 2000.

....the linear logical framework LLF [1] hereafter CP ) The typing rules of LLF forced well formed terms into long form, making all well typed normal forms canonical and rendering any rules for de nitional equality unnecessary. Subsequent to the original de nition of LLF, Harper and Pfenning [6, 7] (hereafter, HP ) gave an alternate formulation of ordinary LF that allowed a clean treatment of de nitional equality without having to restrict terms to pre canonical form. Their approach was based on the use of a typed de nitional equality judgment as opposed to an untyped reduction ....

Robert Harper and Frank Pfenning. On equivalence and canonical forms in the LF type theory. Technical Report CMU-CS-99-159, Carnegie Mellon University, September 1999.

No context found.

R. Harper and F. Pfenning. On equivalence and canonical forms in the LF type theory. In A. Felty, editor, Proceedings of the Workshop on Logical Frameworks and MetaLanguages (LFM'99), Paris, France, Sept. 1999.

No context found.

Harper, R. and Pfenning, F. 1999. On equivalence and canonical forms in the LF type theory. Tech. Rep. CMU-CS-99-159, Department of Computer Science, Carnegie Mellon University.

No context found.

R. Harper and F. Pfenning. On equivalence and canonical forms in the LF type theory. Transactions on Computational Logic, 2003.

No context found.

R. Harper and F. Pfenning. On equivalence and canonical forms in the LF type theory. Transactions on Computational Logic, 2003. To appear. Preliminary version available as Technical Report CMU-CS-00-148.

No context found.

R. Harper and F. Pfenning. On equivalence and canonical forms in the LF type theory. Transactions on Computational Logic, 2003.

No context found.

Robert Harper and Frank Pfenning. On equivalence and canonical forms in the LF type theory. Technical Report CMU-CS-00-148, Department of Computer Science, Carnegie Mellon University, July 2000.

No context found.

R. Harper and F. Pfenning. On equivalence and canonical forms in the LF type theory. Transactions on Computational Logic, 2003. To appear. Preliminary version available as Technical Report CMU-CS-00-148.

....and every well formed term can be regarded as canonical. Definition 3 (Objects) The rst two categories of object are the normal objects N and the atomic objects R. These correspond to the quasi canonical and quasi atomic forms of LF object, respectively, as described by Harper and Pfenning [HP00]. A normal object is a series of constructors applied to atomic objects, while an atomic object is a series of natural deduction style destructors applied to a variable x or constant c. They include all the constructors and destructors of LF and LLF: the unrestricted function constructor x: N and ....

....their adequacy. Ghani [Gha97] uses a typed rewriting relation similar to Goguen s operational semantics but with expansion rather than reduction. This leads to a more pleasant theory, especially given that normal forms with respect to Ghani s rewrite rule are canonical. Harper and Pfenning [HP00] also adopt an approach similar to Goguen s, in that equality is de ned axiomatically and shown to be equivalent to a decision procedure. Their method improves on Goguen s in that the decision procedure is based on transforming a pair of terms simultaneously into canonical form. It o ers the ....

Robert Harper and Frank Pfenning. On equivalence and canonical forms in the LF type theory. Technical Report CMU-CS-00-148, Department of Computer Science, Carnegie Mellon University, July 2000.

....the theories required for reasoning about safety properties such as arithmetic modulo 2 32 or memory update and access from the underlying mechanism of checking proofs. It is also simple, since it is based on a pure, dependently typed # calculus whose properties have been deeply investigated [9,10]. Proofs in a logic designed for reasoning about safety properties are represented as terms in LF. Checking that a proof is valid is reduced to checking that its representation in the logical framework is well typed. This can be carried out e#ectively even for very large proof objects. ....

R. Harper, F. Pfenning, On equivalence and canonical forms in the LF type theory, Tech. Rep. CMU-CS-00-148, Department of Computer Science, Carnegie Mellon University (Jul. 2000).

....how to encode MSR, a rich, strongly typed framework for representing cryptographic protocols. Finally, we conclude with section 7. 2 The Concurrent Logical Framework CLF In contrast to prior presentations of the logical framework LF, all terms are represented in normal, long form what in [HP00] are called quasi canonical forms. The strategy based entirely on canonical forms also simpli es adequacy proofs for representations of other theories within CLF because such representations are always de ned in terms of canonical forms. This new presentation also simpli es the proof that type ....

Robert Harper and Frank Pfenning. On equivalence and canonical forms in the LF type theory. Technical Report CMU-CS-00-148, Department of Computer Science, Carnegie Mellon University, July 2000. 82

....as canonical. Definition 3 (Objects) The first two categories of object are the normal objects N and the atomic objects R. These correspond to the quasi canonical and quasi atomic forms of LF object, respectively, as described by Harper and Pfenning [HP00]. A normal object is a series of constructors applied to atomic objects, while an atomic object is a series of natural deduction style destructors applied to a variable x or constant c. They include all the constructors and destructors of LF and LLF: the unrestricted function constructor #x. N and ....

....their adequacy. Ghani [Gha97] uses a typed rewriting relation similar to Goguen s operational semantics but with # expansion rather than # reduction. This leads to a more pleasant theory, especially given that normal forms with respect to Ghani s rewrite rule are canonical. Harper and Pfenning [HP00] also adopt an approach similar to Goguen s, in that equality is defined axiomatically and shown to be equivalent to a decision procedure. Their method improves on Goguen s in that the decision procedure is based on transforming a pair of terms simultaneously into canonical form. It o#ers the ....

Robert Harper and Frank Pfenning. On equivalence and canonical forms in the LF type theory. Technical Report CMU-CS-00-148, Department of Computer Science, Carnegie Mellon University, July 2000.

....how to encode MSR, a rich, strongly typed framework for representing cryptographic protocols. Finally, we conclude with section 7. 2 The Concurrent Logical Framework CLF In contrast to prior presentations of the logical framework LF, all terms are represented in # normal, # long form what in [HP00] are called quasi canonical forms. The strategy based entirely on canonical forms also simplifies adequacy proofs for representations of other theories within CLF because such representations are always defined in terms of canonical forms. This new presentation also simplifies the proof that type ....

Robert Harper and Frank Pfenning. On equivalence and canonical forms in the LF type theory. Technical Report CMU-CS-00-148, Department of Computer Science, Carnegie Mellon University, July 2000. 82

....both of which are based on the erased types. The first author and Stone [SH00] have concurrently developed a variant of the technique presented here to handle a form of subtyping and singleton kinds. A number of papers subsequent to the original 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 ....

Robert Harper and Frank Pfenning. On equivalence and canonical forms in the LF type theory. Technical Report CMU-CS-99-159, Department of Computer Science, Carnegie Mellon University, 1999.

No context found.

Harper, Robert, & Pfenning, Frank. (2005). On equivalence and canonical forms in the LF type theory. Transactions on Computational Logic, 6, 61--101.

No context found.

Robert Harper and Frank Pfenning. On the equivalence and canonical forms in the LF type theory. Technical report, Carnegie Mellon University, 2001.

No context found.

Robert Harper and Frank Pfenning. On Equivalence and Canonical Forms in the LF Type Theory. Technical report, Carnegie Mellon University, July 2000.

No context found.

Robert Harper and Frank Pfenning. On equivalence and canonical forms in the LF type theory. (Submitted for publication.), October 2001.

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