
We report on an experimental implementation in Haskell of a dependent type theory featuring an observational equality type, based on Pujet et al.’s CCobs. We use normalisation by evaluation to produce an efficient normalisation function, which is used to implement a bidirectional type checker. To allow for greater expressivity, we extend the core CCobs calculus with quotient types and inductive types. To make the system usable, we explore various proof-assistant features, notably a rudimentary version of a "hole" system similar to Agda’s. While rather crude, this experience should inform other, more substantial implementation efforts of observational equality.
Observational equality, Dependent type theory, Normalisation by evaluation, Bidirectional typing, ddc: ddc:004
Observational equality, Dependent type theory, Normalisation by evaluation, Bidirectional typing, ddc: ddc:004
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