> The tactic system then basically build the actual proof by putting everything on a stack and applying in reverse: once you've proved both goals, it knows it can apply the forward-reasoning induction proof function to construct a proof of the original statements from the two proofs you gave.
In Agda, you would type something like `nat-ind ?x ?y` into a hole of type (forall m -> P m). Then ?x becomes a hole of type (P zero) and ?y becomes a hole of type (forall n -> P n -> P (suc n)), and you can fill these holes with proofs at your own leisure. It does not feel all that different from using `induction m` in Coq. In Agda, you'd normally implement your "reflective tactics" as functions, or you'd write macros if you really need them (e.g. for ring solvers), but there is no separate tactic language and proofs are never tactic scripts.
In Agda, you would type something like `nat-ind ?x ?y` into a hole of type (forall m -> P m). Then ?x becomes a hole of type (P zero) and ?y becomes a hole of type (forall n -> P n -> P (suc n)), and you can fill these holes with proofs at your own leisure. It does not feel all that different from using `induction m` in Coq. In Agda, you'd normally implement your "reflective tactics" as functions, or you'd write macros if you really need them (e.g. for ring solvers), but there is no separate tactic language and proofs are never tactic scripts.