Monotone Fixed-Point Types and Strong Normalization
Several systems of fixed-point types (also called retract types or recursive types with explicit isomorphisms) extending system F are considered. The seemingly strongest systems have monotonicity witnesses and use them in the definition of beta reduction for those types. A more naïve approach leads to non-normalizing terms. All the other systems are strongly normalizing because they embed in a reduction-preserving way into the system of non-interleaved positive fixed-point types which can be shown to be strongly normalizing by an easy extension of some proof of strong normalization for system F.
KeywordsNatural Deduction Elimination Rule Inductive Type Type Construct Introduction Rule
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