-- The Agda standard library
-- Environments (heterogeneous collections)

module Data.Star.Environment (Ty : Set) where

open import Data.Star
open import Data.Star.List
open import Data.Star.Decoration
open import Data.Star.Pointer as Pointer hiding (lookup)
open import Data.Unit
open import Relation.Binary.PropositionalEquality

-- Contexts, listing the types of all the elements in an environment.

Ctxt : Set
Ctxt = List Ty

-- Variables (de Bruijn indices); pointers into environments.

infix 4 _∋_

_∋_ : Ctxt  Ty  Set
Γ  σ = Any  _  ) (_≡_ σ) Γ

vz :  {Γ σ}  Γ  σ  σ
vz = this refl

vs :  {Γ σ τ}  Γ  τ  Γ  σ  τ
vs = that tt

-- Environments. The T function maps types to element types.

Env : (Ty  Set)  Ctxt  Set
Env T Γ = All T Γ

-- A safe lookup function for environments.

lookup :  {Γ σ} {T : Ty  Set}  Γ  σ  Env T Γ  T σ
lookup i ρ with Pointer.lookup i ρ
... | result refl x = x