Add check for inhabited datatypes

Strata/DL/Lambda/LTy.lean

@@ -173,6 +173,10 @@ theorem LMonoTy.size_gt_zero :
   unfold LMonoTys.size; split
   simp_all; omega
 
+theorem LMonoTy.size_lt_of_mem {ty: LMonoTy} {tys: LMonoTys} (h: ty ∈ tys):
+  ty.size <= tys.size := by
+  induction tys <;> simp only[LMonoTys.size]<;> grind
+
 /--
 Boolean equality for `LMonoTy`.
 -/

Strata/DL/Lambda/Lambda.lean

@@ -44,6 +44,7 @@ def typeCheckAndPartialEval
   Except Std.Format (LExpr T.mono) := do
   let E := TEnv.default
   let C := LContext.default.addFactoryFunctions f
+  let _ ← TypeFactory.checkInhab t
   let C ← C.addTypeFactory t
   let (et, _T) ← LExpr.annotate C E e
   dbg_trace f!"Annotated expression:{Format.line}{et}{Format.line}"

Strata/DL/Lambda/TypeFactory.lean

@@ -7,6 +7,7 @@
 import Strata.DL.Lambda.LExprWF
 import Strata.DL.Lambda.LTy
 import Strata.DL.Lambda.Factory
+import Strata.DL.Util.List
 
 /-!
 ## Lambda's Type Factory
@@ -428,6 +429,144 @@ def TypeFactory.addDatatype (t: @TypeFactory IDMeta) (d: LDatatype IDMeta) : Exc
               Existing Type: {d'}\n\
               New Type:{d}"
 
+---------------------------------------------------------------------
+
+-- Inhabited types
+
+/-
+Because we generate destructors, it is vital to ensure that every datatype
+is inhabited. Otherwise, we can have the following:
+```
+type Empty :=.
+type List := Nil | Cons (hd: Empty) (tl: List)
+```
+The only element of `List` is `Nil`, but we also create the destructor
+`hd : List → Empty`, which means `hd Nil` has type `Empty`, contradicting the
+fact that `Empty` is uninhabited.
+
+However, checking type inhabitation is complicated for several reasons:
+1. Datatypes can refer to other datatypes. E.g. `type Bad = B(x: Empty)` is
+uninhabited
+2. These dependencies need not be linear. For example,
+the following datatypes are uninhabited:
+```
+type Bad1 := B1(x: Bad2)
+type Bad2 := B2(x: Bad1)
+```
+3. Instantiated type parameters matter: `List Empty` is
+inhabited, but `Either Empty Empty` is not. Our check is conservative and will
+not allow either of these types.
+
+We determine if all types in a TypeFactory are inhabited simulataneously,
+memoizing the results.
+-/
+
+abbrev typeMap : Type := Map String Bool
+
+mutual
+
+/--
+Prove that type symbol `ts` is inhabited, assuming
+that types `seen` are unknown. All other types are assumed inhabited.
+The `List.Nodup` and `⊆` hypotheses are only used to prove termination.
+-/
+def typesym_inhab (adts: @TypeFactory IDMeta) (seen: List String)
+  (hnodup: List.Nodup seen)
+  (hsub: seen ⊆ (List.map (fun x => x.name) adts.toList))
+  (ts: String) : StateM typeMap (Option String) := do
+  let knowType (b: Bool) : StateM typeMap (Option String) := do
+    -- Only add false if not in a cycle, it may resolve later
+    if b || seen.isEmpty then
+      let m ← get
+      set (m.insert ts b)
+    if b then pure none else pure (some ts)
+  -- Check if type is already known to be inhabited
+  let m ← get
+  match m.find? ts with
+  | some true => pure none
+  | some false => pure (some ts)
+  | none =>
+    -- If type in `seen`, it is unknown, so we return false
+    if hin: List.elem ts seen then pure (some ts)
+    else
+      match ha: adts.getType ts with
+      | none => pure none -- Assume all non-datatypes are inhabited
+      | some l =>
+        -- A datatype is inhabited if it has an inhabited constructor
+        let res ← (l.constrs.foldlM (fun accC c => do
+          -- A constructor is inhabited if all of its arguments are inhabited
+          let constrInhab ← (c.args.foldlM
+            (fun accA ty1 =>
+                do
+                  have hn: List.Nodup (l.name :: seen) := by
+                    rw[List.nodup_cons]; constructor
+                    . have := Array.find?_some ha; grind
+                    . assumption
+                  have hsub' : (l.name :: seen) ⊆ (List.map (fun x => x.name) adts.toList) := by
+                    apply List.cons_subset.mpr
+                    constructor <;> try assumption
+                    rw[List.mem_map]; exists l; constructor <;> try grind
+                    have := Array.mem_of_find?_eq_some ha; grind
+                  let b1 ← ty_inhab adts (l.name :: seen) hn hsub' ty1.2
+                  pure (accA && b1)
+              ) true)
+          pure (accC || constrInhab)
+          ) false)
+        knowType res
+  termination_by (adts.size - seen.length, 0)
+  decreasing_by
+    apply Prod.Lex.left; simp only[List.length]
+    apply Nat.sub_succ_lt_self
+    have hlen := List.subset_nodup_length hn hsub'; simp_all; omega
+
+def ty_inhab (adts: @TypeFactory IDMeta) (seen: List String)
+  (hnodup: List.Nodup seen) (hsub: seen ⊆  (List.map (fun x => x.name) adts.toList))
+  (t: LMonoTy) : StateM typeMap Bool :=
+  match t with
+  | .tcons name args => do
+      -- name(args) is inhabited if name is inhabited as a typesym
+      -- and all args are inhabited as types (note this is conservative)
+      let checkTy ← typesym_inhab adts seen hnodup hsub name
+      if checkTy.isNone then
+        args.foldrM (fun ty acc => do
+          let x ← ty_inhab adts seen hnodup hsub ty
+          pure (x && acc)
+        ) true
+      else pure false
+  | _ => pure true -- Type variables and bitvectors are inhabited
+termination_by (adts.size - seen.length, t.size)
+decreasing_by
+  . apply Prod.Lex.right; simp only[LMonoTy.size]; omega
+  . rename_i h; have := LMonoTy.size_lt_of_mem h;
+    apply Prod.Lex.right; simp only[LMonoTy.size]; omega
+end
+
+/--
+Prove that ADT with name `a` is inhabited. All other types are assumed inhabited.
+-/
+def adt_inhab  (adts: @TypeFactory IDMeta) (a: String) : StateM typeMap (Option String) :=
+  typesym_inhab adts [] (by grind) (by grind) a
+
+/--
+Check that all ADTs in TypeFactory `adts` are inhabited. This uses memoization
+to avoid computing the intermediate results more than once. Returns `none` if
+all datatypes are inhabited, `some a` for some uninhabited type `a`
+-/
+def TypeFactory.all_inhab (adts: @TypeFactory IDMeta) : Option String :=
+  let x := (Array.foldlM (fun (x: Option String) (l: LDatatype IDMeta) =>
+    do
+      match x with
+      | some a => pure (some a)
+      | none => adt_inhab adts l.name) none adts)
+  (StateT.run x []).1
+
+/--
+Check that all ADTs in TypeFactory `adts` are inhabited.
+-/
+def TypeFactory.checkInhab (adts: @TypeFactory IDMeta) : Except Format Unit :=
+  match adts.all_inhab with
+  | none => .ok ()
+  | some a => .error f!"Error: datatype {a} not inhabited"
 
 ---------------------------------------------------------------------
 

Strata/DL/Util/List.lean

@@ -411,4 +411,15 @@ theorem length_dedup_of_subset_le {α : Type} [DecidableEq α] (l₁ l₂ : List
       simp_all [dedup]
       omega
 
+theorem subset_nodup_length {α} {s1 s2: List α} (hn: s1.Nodup) (hsub: s1 ⊆ s2) : s1.length ≤ s2.length := by
+  induction s1 generalizing s2 with
+  | nil => simp
+  | cons x t IH =>
+    simp only[List.length]
+    have xin: x ∈ s2 := by apply hsub; grind
+    rw[List.mem_iff_append] at xin
+    rcases xin with ⟨l1, ⟨l2, hs2⟩⟩; subst_vars
+    have hsub1: t ⊆ (l1 ++ l2) := by grind
+    grind
+
 end List