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- W2091240930 abstract "The aim of this paper is to investigate the soundness and completeness of the intersection type discipline (for terms of the (untyped λ-calculus) with respect to the F -semantics ( F -soundness and F -completeness). As pointed out by Scott, if D is the domain of a γ-model, there is a subset F of D whose elements are the ‘canonical’ representatives of functions. The F -semantics of types takes into account that theintuitive meaning of “σ→τ” is ‘the type of functions with domain σ and range τ’ and interprets σ→τ as a subset of F . The type theories which induce F -complete type assignments are characterized. It follows that a type assignment is F -complete iff equal terms get equal types and, whenever M has a type ϕ ∧ ω n , where ϕ is a type variable and ϕ is the ‘universal’ type, the term λz 1… z n … Mz 1 … z n has type ϕ. Here we assume that z 1 … z . n do not occur free in M ." @default.
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- W2091240930 date "1986-01-01" @default.
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- W2091240930 title "A characterization of F-complete type assignments" @default.
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- W2091240930 doi "https://doi.org/10.1016/0304-3975(86)90043-5" @default.
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