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Undecidability of typechecking in domainfree typed lambdacalculi with existence
 In the 17th EACSL Annual Conference on Computer Science Logic (CSL 2008), LNCS 5213
, 2008
"... Abstract. This paper shows undecidability of typechecking and typeinference problems in domainfree typed lambdacalculi with existential types: a negation and conjunction fragment, and an implicational fragment. These are proved by reducing typechecking and typeinference problems of the domainf ..."
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Abstract. This paper shows undecidability of typechecking and typeinference problems in domainfree typed lambdacalculi with existential types: a negation and conjunction fragment, and an implicational fragment. These are proved by reducing typechecking and typeinference problems of the domainfree polymorphic typed lambdacalculus to those of the lambdacalculi with existential types by continuation passing style translations.
Union of reducibility candidates for orthogonal constructor rewriting
 In CiE’08
, 2008
"... Abstract. We revisit Girard’s reducibility candidates by proposing a general of the notion of neutral terms. They are the terms which do not interact with some contexts called elimination contexts. We apply this framework to constructor rewriting, and show that for orthogonal constructor rewriting, ..."
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Abstract. We revisit Girard’s reducibility candidates by proposing a general of the notion of neutral terms. They are the terms which do not interact with some contexts called elimination contexts. We apply this framework to constructor rewriting, and show that for orthogonal constructor rewriting, Girard’s reducibility candidates are stable by union. 1
Type checking and inference are equivalent in lambda calculi with existential types
 In WFLP ’09: 18th International Workshop on Functional and (Constraint) Logic Programming
, 2009
"... Abstract. This paper shows that typechecking and typeinference problems are equivalent in domainfree lambda calculi with existential types, that is, typechecking problem is Turing reducible to typeinference problem and vice versa. In this paper, the equivalence is proved for two variants of doma ..."
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Abstract. This paper shows that typechecking and typeinference problems are equivalent in domainfree lambda calculi with existential types, that is, typechecking problem is Turing reducible to typeinference problem and vice versa. In this paper, the equivalence is proved for two variants of domainfree lambda calculi with existential types: one is an implication and existence fragment, and the other is a negation, conjunction and existence fragment. This result gives another proof of undecidability of type inference in the domainfree calculi with existence.
Type Checking and Inference for Polymorphic and Existential Types
"... This paper proves undecidability of type checking and type inference problems in some variants of typed lambda calculi with polymorphic and existential types. First, type inference in the domainfree polymorphic lambda calculus is proved to be undecidable, and then it is proved that type inference i ..."
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This paper proves undecidability of type checking and type inference problems in some variants of typed lambda calculi with polymorphic and existential types. First, type inference in the domainfree polymorphic lambda calculus is proved to be undecidable, and then it is proved that type inference is undecidable in the negation, conjunction, and existence fragment of the domainfree typed lambda calculus. Secondly, their variants with multiple quantifier rules are introduced, and their type checking and type inference are proved to be undecidable. Finally, it is proved that we can reduce undecidability of type checking and type inference problems in the Currystyle lambda calculus in negation, conjunction, and existential fragment to undecidability of those problems in another variant of the domainfree polymorphic lambda calculus.
Short proofs of strong normalization
"... Abstract. This paper presents simple, syntactic strong normalization proofs for the simplytyped λcalculus and the polymorphic λcalculus (system F) with the full set of logical connectives, and all the permutative reductions. The normalization proofs use translations of terms and types of λ→,∧,∨, ..."
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Abstract. This paper presents simple, syntactic strong normalization proofs for the simplytyped λcalculus and the polymorphic λcalculus (system F) with the full set of logical connectives, and all the permutative reductions. The normalization proofs use translations of terms and types of λ→,∧,∨, ⊥ to terms and types of λ → and from F∀,∃,→,∧,∨, ⊥ to F∀,→. 1
CALLBYVALUE AND CALLBYNAME DUAL CALCULI WITH INDUCTIVE AND COINDUCTIVE TYPES ∗
, 2010
"... Vol. 9(1:14)2013, pp. 1–38 www.lmcsonline.org ..."
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On the Values of Reducibility Candidates
, 2013
"... Abstract. The straightforward elimination of union types is known to break subject reduction, and for some extensions of the lambdacalculus, to break strong normalization as well. Similarly, the straightforward elimination of implicit existential types breaks subject reduction. We propose eliminati ..."
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Abstract. The straightforward elimination of union types is known to break subject reduction, and for some extensions of the lambdacalculus, to break strong normalization as well. Similarly, the straightforward elimination of implicit existential types breaks subject reduction. We propose elimination rules for union types and implicit existential quantification which use a form callbyvalue issued from Girard’s reducibility candidates. We show that these rules remedy the above mentioned difficulties, for strong normalization and, for the existential quantification, for subject reduction as well. Moreover, for extensions of the lambdacalculus based on intuitionistic logic, we show that the obtained existential quantification is equivalent to its usual impredicative encoding w.r.t. provability in realizability models built from reducibility candidates and biorthogonals. 1
Strong normalization results by translation
"... We prove the strong normalization of full classical natural deduction (i.e. with conjunction, disjunction and permutative conversions) by using a translation into the simply typed λµcalculus. We also extend Mendler’s result on recursive equations to this system. 1 ..."
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We prove the strong normalization of full classical natural deduction (i.e. with conjunction, disjunction and permutative conversions) by using a translation into the simply typed λµcalculus. We also extend Mendler’s result on recursive equations to this system. 1