luau/prototyping/Luau/Syntax.agda
2022-03-02 15:26:58 -08:00

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module Luau.Syntax where
open import Agda.Builtin.Equality using (_≡_)
open import Agda.Builtin.Bool using (Bool; true; false)
open import Agda.Builtin.Float using (Float)
open import Agda.Builtin.String using (String)
open import Luau.Var using (Var)
open import Luau.Addr using (Addr)
open import Luau.Type using (Type)
open import FFI.Data.Maybe using (Maybe; just; nothing)
infixr 5 _∙_
data Annotated : Set where
maybe : Annotated
yes : Annotated
data VarDec : Annotated Set where
var : Var VarDec maybe
var_∈_ : {a} Var Type VarDec a
name : {a} VarDec a Var
name (var x) = x
name (var x T) = x
data FunDec : Annotated Set where
_⟨_⟩∈_ : {a} Var VarDec a Type FunDec a
_⟨_⟩ : Var VarDec maybe FunDec maybe
fun : {a} FunDec a VarDec a
fun (f x ⟩∈ T) = (var f T)
fun (f x ) = (var f)
arg : {a} FunDec a VarDec a
arg (f x ⟩∈ T) = x
arg (f x ) = x
data BinaryOperator : Set where
+ : BinaryOperator
- : BinaryOperator
* : BinaryOperator
/ : BinaryOperator
< : BinaryOperator
> : BinaryOperator
== : BinaryOperator
~= : BinaryOperator
<= : BinaryOperator
>= : BinaryOperator
·· : BinaryOperator
data Value : Set where
nil : Value
addr : Addr Value
number : Float Value
bool : Bool Value
string : String Value
data Block (a : Annotated) : Set
data Stat (a : Annotated) : Set
data Expr (a : Annotated) : Set
data Block a where
_∙_ : Stat a Block a Block a
done : Block a
data Stat a where
function_is_end : FunDec a Block a Stat a
local_←_ : VarDec a Expr a Stat a
return : Expr a Stat a
data Expr a where
var : Var Expr a
val : Value Expr a
_$_ : Expr a Expr a Expr a
function_is_end : FunDec a Block a Expr a
block_is_end : VarDec a Block a Expr a
binexp : Expr a BinaryOperator Expr a Expr a
isAnnotatedᴱ : {a} Expr a Maybe (Expr yes)
isAnnotatedᴮ : {a} Block a Maybe (Block yes)
isAnnotatedᴱ (var x) = just (var x)
isAnnotatedᴱ (val v) = just (val v)
isAnnotatedᴱ (M $ N) with isAnnotatedᴱ M | isAnnotatedᴱ N
isAnnotatedᴱ (M $ N) | just M | just N = just (M $ N)
isAnnotatedᴱ (M $ N) | _ | _ = nothing
isAnnotatedᴱ (function f var x T ⟩∈ U is B end) with isAnnotatedᴮ B
isAnnotatedᴱ (function f var x T ⟩∈ U is B end) | just B = just (function f var x T ⟩∈ U is B end)
isAnnotatedᴱ (function f var x T ⟩∈ U is B end) | _ = nothing
isAnnotatedᴱ (function _ is B end) = nothing
isAnnotatedᴱ (block var b T is B end) with isAnnotatedᴮ B
isAnnotatedᴱ (block var b T is B end) | just B = just (block var b T is B end)
isAnnotatedᴱ (block var b T is B end) | _ = nothing
isAnnotatedᴱ (block _ is B end) = nothing
isAnnotatedᴱ (binexp M op N) with isAnnotatedᴱ M | isAnnotatedᴱ N
isAnnotatedᴱ (binexp M op N) | just M | just N = just (binexp M op N)
isAnnotatedᴱ (binexp M op N) | _ | _ = nothing
isAnnotatedᴮ (function f var x T ⟩∈ U is C end B) with isAnnotatedᴮ B | isAnnotatedᴮ C
isAnnotatedᴮ (function f var x T ⟩∈ U is C end B) | just B | just C = just (function f var x T ⟩∈ U is C end B)
isAnnotatedᴮ (function f var x T ⟩∈ U is C end B) | _ | _ = nothing
isAnnotatedᴮ (function _ is C end B) = nothing
isAnnotatedᴮ (local var x T M B) with isAnnotatedᴱ M | isAnnotatedᴮ B
isAnnotatedᴮ (local var x T M B) | just M | just B = just (local var x T M B)
isAnnotatedᴮ (local var x T M B) | _ | _ = nothing
isAnnotatedᴮ (local _ M B) = nothing
isAnnotatedᴮ (return M B) with isAnnotatedᴱ M | isAnnotatedᴮ B
isAnnotatedᴮ (return M B) | just M | just B = just (return M B)
isAnnotatedᴮ (return M B) | _ | _ = nothing
isAnnotatedᴮ done = just done