Agda.TypeChecking.Rewriting

Rewriting with arbitrary rules.

The user specifies a relation symbol by the pragma {-# BUILTIN REWRITE rel #-} where rel should be of type Δ → (lhs rhs : A) → Set i.

Then the user can add rewrite rules by the pragma {-# REWRITE q #-} where q should be a closed term of type Γ → rel us lhs rhs.

We then intend to add a rewrite rule Γ ⊢ lhs ↦ rhs : B to the signature where B = A[us/Δ].

To this end, we normalize lhs, which should be of the form f ts for a Def-symbol f (postulate, function, data, record, constructor). Further, FV(ts) = dom(Γ). The rule q :: Γ ⊢ f ts ↦ rhs : B is added to the signature to the definition of f.

When reducing a term Ψ ⊢ f vs is stuck, we try the rewrites for f, by trying to unify vs with ts. This is for now done by substituting fresh metas Xs for the bound variables in ts and checking equality with vs Ψ ⊢ (f ts)[XsΓ] = f vs : B[XsΓ] If successful (no open metas/constraints), we replace f vs by rhs[Xs/Γ] and continue reducing.