Domain-Free<i>λµ</i>-Calculus

Fujita, Ken-etsu

doi:10.1051/ita:2000102

Cited by 10 publications

(18 citation statements)

References 42 publications

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“…(U 1 → · · · → U n+1 → o). From derivability for y B 1 x B 1 and y B 1 (x G [] n ) as well as from derivability for y B 2 x B 2 and y B 2 (x G [] n ) we obtain respectively that S(B 1 ) = S(G)D 1 · · · D n and S(B 2 ) = S(G)D 1 · · · D n (5) for some D 1 , . .…”

Section: Such That S Solves E and That S Differs From S Onlymentioning

confidence: 98%

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The undecidability of type related problems in the type-free style System F with finitely stratified polymorphic types

Fujita

Schubert

2012

Information and Computation

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We consider here a number of variations on System F that are predicative second-order systems whose terms are intermediate between the Curry style and the Church style. As in the Church style, the terms we deal with here contain the information on where universal quantifier elimination and introduction in the type inference process must take place. However, they omit the information on what types are involved in the rules, which is similar to Curry forms. This can be viewed as a version of the partial type reconstruction problem considered by Boehm and Pfenning in which type erasure is done in a systematic way. In this paper we prove the undecidability of the type checking, type inference, and typability problems for the system. This demonstrates that the reason for undecidability is not the absence of the information where the second-order rules should be applied but the actual shape of the polymorphic types to be used in the derivation. Moreover, the proof works for the predicative version of the system with finitely stratified polymorphic types. The result includes bounds on the Leivant levels of types used in the instances leading to undecidability.

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Section: Such That S Solves E and That S Differs From S Onlymentioning

confidence: 98%

“…It emerged in [4,5] as a good target language for CPS transformations. This style corresponds to removing from the terms the information on which types were involved in the application of the λ abstraction rule.…”

Section: Introductionmentioning

confidence: 99%

The undecidability of type related problems in the type-free style System F with finitely stratified polymorphic types

Fujita

Schubert

2012

Information and Computation

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“…There have been many attempts to prove strong normalization of calculi with control operators by reducing them to that of the simply typed λ-calculus by CPS-translations, such as [4,18,7,5]. We say that a translation preserves reduction when the translation of M reduces to the translation of N with some steps if M reduces to N with one step.…”

Section: Erasing-continuation and Augmentationsmentioning

confidence: 99%

“…Normalization of classical proofs is an important subject in the research area, and there are many papers on the issue [4,18,7,5,23,1,3,11,12,15].…”

Section: Introductionmentioning

confidence: 99%

Strong normalization of classical natural deduction with disjunctions

Nakazawa

Tatsuta

2008

Annals of Pure and Applied Logic

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This paper proves the strong normalization of classical natural deduction with disjunction and permutative conversions, by using CPS-translation and augmentations. Using them, this paper also proves the strong normalization of classical natural deduction with general elimination rules for implication and conjunction, and their permutative conversions. This paper also proves that natural deduction can be embedded into natural deduction with general elimination rules, strictly preserving proof normalization.

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“…Because of erasing-continuations, reduction relations of one or more steps are not necessarily preserved, which makes it difficult to prove strong normalization. All proofs by CPS-translations in [13,3,5,2] fail because of the same erasing-continuation problem.…”

Section: Introductionmentioning

confidence: 94%