first attempt

This commit is contained in:
mehbark 2025-04-09 14:33:26 -04:00
parent 6c93d38e81
commit 61a7d2befb
4 changed files with 120 additions and 2 deletions

View file

@ -1 +1,99 @@
def hello := "world"
import Batteries.Data.Rat.Basic
import Batteries.Control.Lawful.MonadLift
inductive Ast
| lit (n : Rat)
| add (l r : Ast)
| sub (l r : Ast)
| mul (l r : Ast)
| div (l r : Ast)
instance : Coe Rat Ast where coe := .lit
instance : OfScientific Ast where
ofScientific a b c := .lit (.ofScientific a b c)
instance : OfNat Ast n where ofNat := .lit n
instance : Add Ast where add := .add
instance : Sub Ast where sub := .sub
instance : Mul Ast where mul := .mul
instance : Div Ast where div := .div
def Ast.interpret : Ast → Rat
| lit n => n
| add l r => l.interpret + r.interpret
| sub l r => l.interpret - r.interpret
| mul l r => l.interpret * r.interpret
| div l r => l.interpret / r.interpret
#eval Ast.interpret <| 3/2 + 0.5
inductive Op
| push (n : Rat)
| add
| sub
| mul
| div
deriving Repr
-- TODO: prove that the stack manip is all good throughout
def Op.pop_push : Op → Nat × Nat
| push _ => (0, 1)
| _ => (2, 1)
abbrev Ops := Array Op
def pushM (x : α) : StateM (Array α) Unit :=
modify <| (·.push x)
def popM? : StateM (Array α) (Option α) := do
let top ← Array.back? <$> get
modify Array.pop
return top
abbrev M := OptionT (StateM (Array Rat))
instance : LawfulMonad M := sorry
def Op.action (op : Op) : M Unit := do
match op with
| .push n => pushM n
| .add => pushM <| (← popM?) + (← popM?)
| .sub => pushM <| (← popM?) - (← popM?)
| .mul => pushM <| (← popM?) * (← popM?)
| .div => pushM <| (← popM?) / (← popM?)
def Ops.action (ops : Ops) : M Unit := ops.forM Op.action
def Ops.run (ops : Ops) : Option Rat :=
(do
ops.action
popM?
).run #[] |>.fst
def Ast.compile : Ast → Ops
| .lit n => #[.push n]
| .add l r => l.compile ++ r.compile ++ #[.add]
| .sub l r => l.compile ++ r.compile ++ #[.sub]
| .mul l r => l.compile ++ r.compile ++ #[.mul]
-- Note that l and r are flipped here. compilation!
| .div l r => r.compile ++ l.compile ++ #[.div]
#eval (3/2 + 0.5 : Ast) |>.compile.run
@[simp]
theorem Ops.append_action (a b : Ops)
: (a ++ b).action = (do a.action; b.action) := by
rw [action]
exact Array.forM_append
@[simp]
theorem Ops.push_action (ops : Ops) (op : Op)
: action (ops.push op) = (do ops.action; op.action) := by
rw [Array.push_eq_append, append_action]
have : op.action = action #[op] := by simp [action]
rw [this]
theorem Ast.compile_sound (ast : Ast)
: ast.compile.run = some ast.interpret := by
induction ast
· rfl
simp [compile]

15
lake-manifest.json Normal file
View file

@ -0,0 +1,15 @@
{"version": "1.1.0",
"packagesDir": ".lake/packages",
"packages":
[{"url": "https://github.com/leanprover-community/batteries",
"type": "git",
"subDir": null,
"scope": "leanprover-community",
"rev": "f1a7afdb343196b33bf9137b232eb69446065925",
"name": "batteries",
"manifestFile": "lake-manifest.json",
"inputRev": "main",
"inherited": false,
"configFile": "lakefile.toml"}],
"name": "bytecode",
"lakeDir": ".lake"}

View file

@ -8,3 +8,8 @@ name = "Bytecode"
[[lean_exe]]
name = "bytecode"
root = "Main"
[[require]]
name = "batteries"
scope = "leanprover-community"
rev = "main"

View file

@ -1 +1 @@
leanprover/lean4:v4.16.0-rc2
leanprover/lean4:v4.19.0-rc2