Preparing for coq-metacoq.1.0~beta2+8.12
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…ndP- Move syntactic equality checking to a separate safechecker library- move monadic combinators to monad_utils
…their right place
…ack fixing of universes, still needed in 8.11
Cleanup safechecker
The safe checker was destructing the inferred type of predicates directly as an arity, which was not complete. It meant that the following example was not accepted by the safe checker: Definition WrappedType := Type. Definition WrappedNat : WrappedType := nat. Definition foo : nat := match 0 return WrappedNat with | 0 => 0 | S n => 0 end. To fix we now use reduction for the predicate type.
Primitive integers and floats
…than anticipated: one really has to do surgeryon the binary applications derivation to produce onewhere applications are n-ary *without* relying on transitivity of cumulativityanywhere. This requires to use induction on the size of derivations (includingnon-principal/paranoid hypotheses).
Template <-> PCUIC proofs
In PCUIC we treated axioms as values, but we did not consistently treat eg. fixpoints and cases stuck on axioms as values. This removes the evaluation of axioms in PCUIC and gets rid of the axiom_free assumption that was needed for erasure because of it.
Remove evaluation of axioms from wcbv and add proof of consistency using safe reduction + canonicity
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