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Observational Equality, Now! Thorsten Altenkirch Conor McBride Wouter Swierstra

Summary: Observational Equality, Now!
Thorsten Altenkirch Conor McBride Wouter Swierstra
University of Nottingham, UK
This paper has something new and positive to say about propo-
sitional equality in programming and proof systems based on the
Curry-Howard correspondence between propositions and types. We
have found a way to present a propositional equality type
which is substitutive, allowing us to reason by replacing equal
for equal in propositions;
which reflects the observable behaviour of values rather than
their construction: in particular, we have extensionality--
functions are equal if they take equal inputs to equal outputs;
which retains strong normalisation, decidable typechecking and
canonicity--the property that closed normal forms inhabiting
datatypes have canonical constructors;
which allows inductive data structures to be expressed in terms
of a standard characterisation of well-founded trees;
which is presented syntactically--you can implement it di-


Source: Altenkirch, Thorsten - School of Computer Science, University of Nottingham


Collections: Computer Technologies and Information Sciences