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A Semantics for Static Type Inference
 Information and Computation
, 1993
"... Curry's system for Fdeducibility is the basis for static type inference algorithms for programming languages such as ML. If a natural "preservation of types by conversion" rule is added to Curry's system, it becomes undecidable, but complete relative to a variety of model classes. We show compl ..."
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Curry's system for Fdeducibility is the basis for static type inference algorithms for programming languages such as ML. If a natural "preservation of types by conversion" rule is added to Curry's system, it becomes undecidable, but complete relative to a variety of model classes. We show completeness for Curry's system itself, relative to an extended notion of model that validates reduction but not conversion.
Combinators and Structurally Free Logic
 LOGIC JOURNAL OF THE IGPL
, 1997
"... A "Kripkestyle" semantics is given for combinatory logic using frames with a ternary accessibility relation, much as in the RoutleyMeyer semantics for relevance logic. We prove by algebraic means a completeness theorem for combinatory logic, by proving a representation theorem for "combinatory pos ..."
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A "Kripkestyle" semantics is given for combinatory logic using frames with a ternary accessibility relation, much as in the RoutleyMeyer semantics for relevance logic. We prove by algebraic means a completeness theorem for combinatory logic, by proving a representation theorem for "combinatory posets." A philosophical interpretation is given of the models, showing that an element of a combinatory poset can be understood simultaneously as a set of states and as a set of (untyped) actions on states. This double interpretation allows for one such element to be applied to another (including itself). Application turns out to be modeled the same way as "fusion" in relevance logic. We also introduce "dual combinators" that apply from the right. We then explore relationships to some wellknown substructural logics, showing that each can be embedded into the structurally free, nonassociative Lambek calculus, with the embedding taking a theorem # to a statement of the form # # #, where # i...