Implementing mathematics with the Nuprl proof development system
Implementing mathematics with the Nuprl proof development system
Programming in Martin-Lo¨f's type theory: an introduction
Programming in Martin-Lo¨f's type theory: an introduction
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Theoretical Computer Science
Let's see how things unfold: reconciling the infinite with the intensional
CALCO'09 Proceedings of the 3rd international conference on Algebra and coalgebra in computer science
Interfaces as games, programs as strategies
TYPES'04 Proceedings of the 2004 international conference on Types for Proofs and Programs
Programming and reasoning with algebraic effects and dependent types
Proceedings of the 18th ACM SIGPLAN international conference on Functional programming
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We introduce the notion of state dependent interactive programs for Martin-Lof Type Theory. These programs are elements of coalgebras of certain endofunctors on the presheaf category S-Set. We prove the existence of final coalgebras for these functors. This shows as well the consistency of type theory plus rules expressing the existence of weakly final coalgebras for these functors, which represents the type of interactive programs. We define in this type theory the bisimulation relation, and give some simple examples for interactive programs. A generalised monad operation is defined by corecursion on interactive programs with return value, and a generalised version of the monad laws for this operation is proved. The correctness of the monad laws has been verified in the theorem prover Agda which is based on intensional type theory.