Nominal Coalgebraic Data Types with Applications to Lambda Calculus

We investigate final coalgebras in nominal sets. This allows us to define types of infinite data with binding for which all constructions automatically respect alpha equivalence. We give applications to the infinitary lambda calculus

A new coinductive confluence proof for infinitary lambda calculus

We present a new and formal coinductive proof of confluence and normalisation of B\"ohm reduction in infinitary lambda calculus. The proof is simpler than previous proofs of this result. The technique of the proof is new, i.e., it is not merely a coinductive reformulation of any earlier proofs. We formalised the proof in the Coq proof assistant.Comment: arXiv admin note: text overlap with arXiv:1501.0435

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

Nominal Coalgebraic Data Types with Applications to Lambda Calculus

We investigate final coalgebras in nominal sets. This allows us to define types of infinite data with binding for which all constructions automatically respect alpha equivalence. We give applications to the infinitary lambda calculus