they work

prototyping/Examples/Run.agda

@@ -3,7 +3,7 @@
 module Examples.Run where
 
 open import Agda.Builtin.Equality using (_≡_; refl)
-open import Luau.Syntax using (nil; var; _$_; function_is_end; return; _∙_; done; _⟨_⟩; number)
+open import Luau.Syntax using (nil; var; _$_; function_is_end; return; _∙_; done; _⟨_⟩; number; binexp; +)
 open import Luau.Value using (nil; number)
 open import Luau.Run using (run; return)
 open import Luau.Heap using (lookup-next; next-emp; lookup-next-emp)
@@ -16,3 +16,6 @@ ex1 = refl
 
 ex2 : (run (function "fn" ⟨ var "x" ⟩ is return (number 123.0) ∙ done end ∙ return (var "fn" $ nil) ∙ done) ≡ return (number 123.0) _)
 ex2 = refl
+
+ex3 : (run (function "fn" ⟨ var "x" ⟩ is return (binexp (number 1.0) + (number 2.0)) ∙ done end ∙ return (var "fn" $ nil) ∙ done) ≡ return (number 3.0) _)
+ex3 = refl

prototyping/Luau/OpSem.agda

@@ -66,10 +66,22 @@ data _⊢_⟶ᴱ_⊣_  where
     ---------------------------------
     H ⊢ (block b is done end) ⟶ᴱ nil ⊣ H
   
-  binOp :
+  binOpEval :
     ∀ {H x op y} →
     --------------------------------------------------------------------------
     H ⊢ (binexp (number x) op (number y)) ⟶ᴱ (number (evalBinOp x op y)) ⊣ H
+  
+  binOp₁ :
+    ∀ {H H′ x x′ op y} →
+    H ⊢ x ⟶ᴱ x′ ⊣ H′ →
+    ---------------------------------------------
+    H ⊢ (binexp x op y) ⟶ᴱ (binexp x′ op y) ⊣ H′
+  
+  binOp₂ :
+    ∀ {H H′ x op y y′} →
+    H ⊢ y ⟶ᴱ y′ ⊣ H′ →
+    ---------------------------------------------
+    H ⊢ (binexp x op y) ⟶ᴱ (binexp x op y′) ⊣ H′
 
   
 data _⊢_⟶ᴮ_⊣_  where

prototyping/Luau/RuntimeError.agda

@@ -4,7 +4,7 @@ open import Agda.Builtin.Equality using (_≡_)
 open import Luau.Heap using (Heap; _[_])
 open import FFI.Data.Maybe using (just; nothing)
 open import FFI.Data.String using (String)
-open import Luau.Syntax using (Block; Expr; nil; var; addr; block_is_end; _$_; local_←_; return; done; _∙_; number)
+open import Luau.Syntax using (Block; Expr; nil; var; addr; block_is_end; _$_; local_←_; return; done; _∙_; number; binexp)
 open import Luau.RuntimeType using (RuntimeType; valueType)
 open import Luau.Value using (val)
 open import Properties.Equality using (_≢_)
@@ -19,6 +19,8 @@ data RuntimeErrorᴱ H where
   app₁ : ∀ {M N} → RuntimeErrorᴱ H M → RuntimeErrorᴱ H (M $ N)
   app₂ : ∀ {M N} → RuntimeErrorᴱ H N → RuntimeErrorᴱ H (M $ N)
   block : ∀ b {B} → RuntimeErrorᴮ H B → RuntimeErrorᴱ H (block b is B end)
+  bin₁ : ∀ {M N op} → RuntimeErrorᴱ H M → RuntimeErrorᴱ H (binexp M op N)
+  bin₂ : ∀ {M N op} → RuntimeErrorᴱ H N → RuntimeErrorᴱ H (binexp M op N)
 
 data RuntimeErrorᴮ H where
   local : ∀ x {M B} → RuntimeErrorᴱ H M → RuntimeErrorᴮ H (local x ← M ∙ B)

prototyping/Luau/RuntimeError/ToString.agda

@@ -2,23 +2,25 @@ module Luau.RuntimeError.ToString where
 
 open import Agda.Builtin.Float using (primShowFloat)
 open import FFI.Data.String using (String; _++_)
-open import Luau.RuntimeError using (RuntimeErrorᴮ; RuntimeErrorᴱ; local; return; NilIsNotAFunction; NumberIsNotAFunction; UnboundVariable; SEGV; app₁; app₂; block; ValueIsNotANumber)
+open import Luau.RuntimeError using (RuntimeErrorᴮ; RuntimeErrorᴱ; local; return; TypeMismatch; UnboundVariable; SEGV; app₁; app₂; block; bin₁; bin₂)
+open import Luau.RuntimeType.ToString using (runtimeTypeToString)
 open import Luau.Addr.ToString using (addrToString)
 open import Luau.Syntax.ToString using (exprToString)
 open import Luau.Var.ToString using (varToString)
+open import Luau.Value.ToString using (valueToString)
 open import Luau.Syntax using (name; _$_)
 
 errToStringᴱ : ∀ {a H B} → RuntimeErrorᴱ {a} H B → String
 errToStringᴮ : ∀ {a H B} → RuntimeErrorᴮ {a} H B → String
 
-errToStringᴱ NilIsNotAFunction = "nil is not a function"
-errToStringᴱ (NumberIsNotAFunction n) = "number " ++ primShowFloat n ++ " is not a function"
 errToStringᴱ (UnboundVariable x) = "variable " ++ varToString x ++ " is unbound"
 errToStringᴱ (SEGV a x) = "address " ++ addrToString a ++ " is unallocated"
 errToStringᴱ (app₁ E) = errToStringᴱ E
 errToStringᴱ (app₂ E) = errToStringᴱ E
+errToStringᴱ (bin₁ E) = errToStringᴱ E
+errToStringᴱ (bin₂ E) = errToStringᴱ E
 errToStringᴱ (block b E) = errToStringᴮ E ++ "\n  in call of function " ++ varToString b
-errToStringᴱ (ValueIsNotANumber v) = exprToString v ++ " is not a number"
+errToStringᴱ (TypeMismatch t v _) = "value " ++ valueToString v ++ " is not a " ++ runtimeTypeToString t
 
 errToStringᴮ (local x E) = errToStringᴱ E ++ "\n  in definition of " ++ varToString (name x) 
 errToStringᴮ (return E) = errToStringᴱ E ++ "\n  in return statement"

prototyping/Luau/RuntimeType/ToString.agda

@@ -0,0 +1,9 @@
+module Luau.RuntimeType.ToString where
+
+open import FFI.Data.String using (String)
+open import Luau.RuntimeType using (RuntimeType; function; number; nil)
+
+runtimeTypeToString : RuntimeType → String
+runtimeTypeToString function = "function"
+runtimeTypeToString number = "number"
+runtimeTypeToString nil = "nil"

prototyping/Properties/Step.agda

@@ -5,8 +5,9 @@ open import Agda.Builtin.Float using (primFloatPlus; primFloatMinus; primFloatTi
 open import FFI.Data.Maybe using (just; nothing)
 open import Luau.Heap using (Heap; _[_]; alloc; ok; function_is_end)
 open import Luau.Syntax using (Block; Expr; nil; var; addr; function_is_end; block_is_end; _$_; local_←_; return; done; _∙_; name; fun; arg; number; binexp; +)
-open import Luau.OpSem using (_⊢_⟶ᴱ_⊣_; _⊢_⟶ᴮ_⊣_; app₁ ; app₂ ; beta; function; block; return; done; local; subst; binOp; evalBinOp)
-open import Luau.RuntimeError using (RuntimeErrorᴱ; RuntimeErrorᴮ; TypeMismatch; UnboundVariable; SEGV; app; block; local; return)
+open import Luau.OpSem using (_⊢_⟶ᴱ_⊣_; _⊢_⟶ᴮ_⊣_; app₁ ; app₂ ; beta; function; block; return; done; local; subst; binOpEval; evalBinOp; binOp₁; binOp₂)
+open import Luau.RuntimeError using (RuntimeErrorᴱ; RuntimeErrorᴮ; TypeMismatch; UnboundVariable; SEGV; app₁; app₂; block; local; return; bin₁; bin₂)
+open import Luau.RuntimeType using (function; number)
 open import Luau.Substitution using (_[_/_]ᴮ)
 open import Luau.Value using (nil; addr; val; number)
 open import Properties.Remember using (remember; _,_)
@@ -36,8 +37,8 @@ stepᴱ H (M $ N) with stepᴱ H M
 stepᴱ H (M $ N) | step H′ M′ D = step H′ (M′ $ N) (app₁ D)
 stepᴱ H (_ $ N) | value V refl with stepᴱ H N
 stepᴱ H (_ $ N) | value V refl | step H′ N′ s = step H′ (val V $ N′) (app₂ s)
-stepᴱ H (_ $ _) | value nil refl | value W refl = error NilIsNotAFunction
-stepᴱ H (_ $ _) | value (number n) refl | value W refl = error (NumberIsNotAFunction n)
+stepᴱ H (_ $ _) | value nil refl | value W refl = error (app₁ (TypeMismatch function nil λ()))
+stepᴱ H (_ $ _) | value (number n) refl | value W refl = error (app₁ (TypeMismatch function (number n) λ()))
 stepᴱ H (_ $ _) | value (addr a) refl | value W refl with remember (H [ a ])
 stepᴱ H (_ $ _) | value (addr a) refl | value W refl  | (nothing , p) = error (app₁ (SEGV a p))
 stepᴱ H (_ $ _) | value (addr a) refl | value W refl  | (just(function F is B end) , p) = step H (block fun F is B [ W / name (arg F) ]ᴮ end) (beta p)
@@ -50,8 +51,17 @@ stepᴱ H (block b is done end) | done refl = step H nil done
 stepᴱ H (block b is B end) | error E = error (block b E)
 stepᴱ H (function F is C end) with alloc H (function F is C end)
 stepᴱ H function F is C end | ok a H′ p = step H′ (addr a) (function p)
-stepᴱ H (binexp x op y) with stepᴱ H x | stepᴱ H y
-stepᴱ H (binexp x op y) | value (number x′) refl | value (number y′) refl = step H (number (evalBinOp x′ op y′)) binOp
+stepᴱ H (binexp x op y) with stepᴱ H x
+stepᴱ H (binexp x op y) | value x′ refl with stepᴱ H y
+stepᴱ H (binexp x op y) | value (number x′) refl | value (number y′) refl = step H (number (evalBinOp x′ op y′)) binOpEval
+stepᴱ H (binexp x op y) | value (number x′) refl | step H′ y′ s = step H′ (binexp (number x′) op y′) (binOp₂ s)
+stepᴱ H (binexp x op y) | value (number x′) refl | error E = error (bin₂ E)
+stepᴱ H (binexp x op y) | value nil refl | _ = error (bin₁ (TypeMismatch number nil λ()))
+stepᴱ H (binexp x op y) | _ | value nil refl = error (bin₂ (TypeMismatch number nil λ()))
+stepᴱ H (binexp x op y) | value (addr a) refl | _ = error (bin₁ (TypeMismatch number (addr a) λ()))
+stepᴱ H (binexp x op y) | _ | value (addr a) refl = error (bin₂ (TypeMismatch number (addr a) λ()))
+stepᴱ H (binexp x op y) | step H′ x′ s = step H′ (binexp x′ op y) (binOp₁ s)
+stepᴱ H (binexp x op y) | error E = error (bin₁ E)
 
 stepᴮ H (function F is C end ∙ B) with alloc H (function F is C end)
 stepᴮ H (function F is C end ∙ B) | ok a H′ p = step H′ (B [ addr a / fun F ]ᴮ) (function p)
@@ -64,4 +74,3 @@ stepᴮ H (return M ∙ B) | step H′ M′ D = step H′ (return M′ ∙ B) (r
 stepᴮ H (return _ ∙ B) | value V refl = return V refl
 stepᴮ H (return M ∙ B) | error E = error (return E)
 stepᴮ H done = done refl
-