160 research outputs found
Decidable structures between Church-style and Curry-style
It is well-known that the type-checking and type-inference problems are undecidable for second order lambda-calculus in Curry-style, although those for Church-style are decidable. What causes the differences in decidability and undecidability on the problems? We examine crucial conditions on terms for the (un)decidability property from the viewpoint of partially typed terms, and what kinds of type annotations are essential for (un)decidability of type-related problems. It is revealed that there exists an intermediate structure of second order lambda-terms, called a style of hole-application, between Church-style and Curry-style, such that the type-related problems are decidable under the structure. We also extend this idea to the omega-order polymorphic calculus F-omega, and show that the type-checking and type-inference problems then become undecidable
A Light Modality for Recursion
We investigate the interplay between a modality for controlling the behaviour
of recursive functional programs on infinite structures which are completely
silent in the syntax. The latter means that programs do not contain "marks"
showing the application of the introduction and elimination rules for the
modality. This shifts the burden of controlling recursion from the programmer
to the compiler. To do this, we introduce a typed lambda calculus a la Curry
with a silent modality and guarded recursive types. The typing discipline
guarantees normalisation and can be transformed into an algorithm which infers
the type of a program.Comment: 32 pages 1 figure in pdf forma
Filter models: non-idempotent intersection types, orthogonality and polymorphism - long version
This paper revisits models of typed lambda-calculus based on filters of intersection types: By using non-idempotent intersections, we simplify a methodology that produces modular proofs of strong normalisation based on filter models. Non-idempotent intersections provide a decreasing measure proving a key termination property, simpler than the reducibility techniques used with idempotent intersections. Such filter models are shown to be captured by orthogonality techniques: we formalise an abstract notion of orthogonality model inspired by classical realisability, and express a filter model as one of its instances, along with two term-models (one of which captures a now common technique for strong normalisation). Applying the above range of model constructions to Curry-style System F describes at different levels of detail how the infinite polymorphism of System F can systematically be reduced to the finite polymorphism of intersection types
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