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Reduction in X does not agree with Intersection and Union Types
, 2008
"... This paper defines intersection and union type assignment for the calculus X, a substitution free language that enjoys the Curry-Howard correspondence with respect to Gentzen’s sequent calculus for classical logic. We show that this notion is the minimal one closed for subject-expansion, and show th ..."
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This paper defines intersection and union type assignment for the calculus X, a substitution free language that enjoys the Curry-Howard correspondence with respect to Gentzen’s sequent calculus for classical logic. We show that this notion is the minimal one closed for subject-expansion, and show that it needs to be restricted to satisfy subject-reduction as well, making it unsuitable to define a semantics.
Sound and Complete Typing for λµ
"... In this paper we define intersection and union type assignment for Parigot’s calculus λµ. We show that this notion is complete (i.e. closed under subject-expansion), and show also that it is sound (i.e. closed under subject-reduction). This implies that this notion of intersectionunion type assignme ..."
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In this paper we define intersection and union type assignment for Parigot’s calculus λµ. We show that this notion is complete (i.e. closed under subject-expansion), and show also that it is sound (i.e. closed under subject-reduction). This implies that this notion of intersectionunion type assignment is suitable to define a semantics.
