Safe Agda

By using the option --safe (as a pragma option, or on the command-line), a user can specify that Agda should ensure that features leading to possible inconsistencies should be disabled.

Here is a list of the features --safe is incompatible with:

• postulate; can be used to assume any axiom.

• --allow-unsolved-metas; forces Agda to accept unfinished proofs.

• --allow-incomplete-matches; forces Agda to accept unfinished proofs.

• --no-positivity-check; makes it possible to write non-terminating programs by structural “induction” on non strictly positive datatypes.

• --no-termination-check; gives loopy programs any type.

• --type-in-type and --omega-in-omega; allow the user to encode the Girard-Hurken paradox.

• --injective-type-constructors; together with excluded middle leads to an inconsistency via Chung-Kil Hur’s construction.

• --guardedness together with --sized-types; currently can be used to define a type which is both inductive and coinductive, which leads to an inconsistency. This might be fixed in the future.

• --experimental-irrelevance and --irrelevant-projections; enables potentially unsound irrelevance features (irrelevant levels, irrelevant data matching, and projection of irrelevant record fields, respectively).

• --rewriting; turns any equation into one that holds definitionally. It can at the very least break convergence.

• --cubical together with --with-K; the univalence axiom is provable using cubical constructions, which falsifies the K axiom.

• The primEraseEquality primitive together with --without-K; using primEraseEquality, one can derive the K axiom.

• --allow-exec; allows system calls during type checking.

• --no-load-primitives; allows the user to bind the sort and level primitives manually.

The option --safe is coinfective (see Checking options for consistency); if a module is declared safe, then all its imported modules must also be declared safe.