Ëøóöý Ó Ö Áòù Blockinøóò Ò Aeùôöð Îò Blockinòø Êðð 1⋆¸ååö Óö 2 ¸ Òò Êóöø ĺ Óò×øøøðð 2

Abstra t. In order to turn Nuprl's logi into a fully intuitionisti logi , we are urrently experimenting with versions of Brouwer's bar indu tion prin iple. Using our formalization of Nuprl's metatheory in Coq, we have proved the lassi al validity of two su h prin iples: one for sequen es of numbers that involved little hanges to the system, and a more general one for sequen es of losed terms without names that involved adding a limit onstru tor to Nuprl's term syntax. We have also proved that these additions preserve Nuprl's key metatheoreti al properties su h as onsisten y. Finally, we show some new insights on bar indu tion that were made possible thanks to Nuprl's quotient types.