open import 1Lab.Type

module Meta.Brackets where

Semantic bracket notation🔗

In many of our developments (primarily, but not limited to, those in logic), we have a notion of a type $T$ being a syntactic presentation for some other, semantic, type $S\text{.}$ In keeping with convention, we want to overload the notation $[[e]]$ to mean “the semantic value of $e\text{.}$” This can be achieved with a simple notation class:

record ⟦⟧-notation {ℓ} (A : Type ℓ) : Typeω where
  constructor brackets
  field
    {lvl} : Level
    Sem : Type lvl
    ⟦_⟧ : A → Sem

open ⟦⟧-notation ⦃...⦄ using (⟦_⟧) public
{-# DISPLAY ⟦⟧-notation.⟦_⟧ _ x = ⟦ x ⟧ #-}