progress

bidir/src/bidir.rs

@@ -15,12 +15,13 @@ pub fn app_ctx(ctx: &Context, ty: &Type) -> Result<Type> {
       None => bail!("existential variable {a} doesn't exist in context"),
     },
 
-    Type::Polytype(_, _) => todo!(),
+    Type::Polytype(a, t) => Ok(Type::Polytype(a.clone(), Box::new(app_ctx(ctx, t)?))),
+
     Type::Arrow(a, b) => Ok(Type::Arrow(
       Box::new(app_ctx(ctx, a)?),
       Box::new(app_ctx(ctx, b)?),
     )),
-    _ => todo!("shiiet"),
+    _ => todo!("shiiet ctx = {ctx:?}, ty = {ty:?}"),
   }
 }
 
@@ -152,28 +153,73 @@ pub fn synthesize(ctx: &Context, term: &Term) -> Result<(Type, Context)> {
       Ok((ty_a.clone(), ctx_delta))
     }
 
-    // →I⇒ rule
-    // > Rule →I⇒ corresponds to Decl→I⇒, one of the guessing rules, so we
-    // > create new existential variables ^α (for the function domain) and ^β (for
-    // > the codomain) and check the function body against ^β.  As in ∀App, we do
-    // > not place a marker before ^α, because ^α and ^β appear in the output type
-    // > (λx. e ⇒ ^α → ^β).
+    // →I⇒' rule
     Term::Lam(x, e) => {
       let ex_a_s = gensym_existential();
       let ex_b_s = gensym_existential();
+
+      let ex_gen = format!("{}->", ex_a_s);
+
       let ex_a = Type::Existential(ex_a_s.clone());
       let ex_b = Type::Existential(ex_b_s.clone());
+
       let aug_ctx = ctx.add(vec![
+        ContextEntry::Marker(ex_a_s.clone()),
         ContextEntry::ExistentialVar(ex_a_s.clone()),
         ContextEntry::ExistentialVar(ex_b_s.clone()),
         ContextEntry::TermAnnot(x.clone(), ex_a.clone()),
       ]);
 
       let wtf_ctx = typecheck(&aug_ctx, &e, &ex_b)?;
-      println!("the wtf ctx is {wtf_ctx:?}");
-      Ok((Type::Arrow(Box::new(ex_a), Box::new(ex_b)), ctx.clone()))
+      println!("WTF CTX {wtf_ctx:?}");
+
+      // Split back out at the marker
+      let (before_marker, after_marker) = {
+        let marker_idx = wtf_ctx
+          .0
+          .iter()
+          .position(|entry| match entry {
+            ContextEntry::Marker(m) if *m == ex_a_s => true,
+            _ => false,
+          })
+          .unwrap();
+
+        // println!("Marker index: {marker_idx}");
+        wtf_ctx.0.clone().split_at(marker_idx)
+      };
+      let before_marker = Context(before_marker);
+      let after_marker = Context(after_marker);
+
+      let mut tau = app_ctx(&after_marker, &Type::Arrow(Box::new(ex_a), Box::new(ex_b)))?;
+      for name in after_marker.unsolved_existentials() {
+        tau = tau.subst(name, &Type::Var(ex_gen.clone()));
       }
 
+      Ok((Type::Polytype(ex_gen, Box::new(tau)), before_marker))
+    }
+
+    // // →I⇒ rule
+    // // > Rule →I⇒ corresponds to Decl→I⇒, one of the guessing rules, so we
+    // // > create new existential variables ^α (for the function domain) and ^β (for
+    // // > the codomain) and check the function body against ^β.  As in ∀App, we do
+    // // > not place a marker before ^α, because ^α and ^β appear in the output type
+    // // > (λx. e ⇒ ^α → ^β).
+    // Term::Lam(x, e) => {
+    //   let ex_a_s = gensym_existential();
+    //   let ex_b_s = gensym_existential();
+    //   let ex_a = Type::Existential(ex_a_s.clone());
+    //   let ex_b = Type::Existential(ex_b_s.clone());
+    //   let aug_ctx = ctx.add(vec![
+    //     ContextEntry::ExistentialVar(ex_a_s.clone()),
+    //     ContextEntry::ExistentialVar(ex_b_s.clone()),
+    //     ContextEntry::TermAnnot(x.clone(), ex_a.clone()),
+    //   ]);
+
+    //   let wtf_ctx = typecheck(&aug_ctx, &e, &ex_b)?;
+    //   println!("the wtf ctx is {wtf_ctx:?}");
+    //   Ok((Type::Arrow(Box::new(ex_a), Box::new(ex_b)), ctx.clone()))
+    // }
+
     // →E rule
     Term::App(e1, e2) => {
       let (ty_a, ctx_theta) = synthesize(ctx, e1)?;

bidir/src/data.rs

@@ -1,4 +1,4 @@
-use std::{fmt, hash::Hash};
+use std::{fmt, hash::Hash, mem::replace};
 
 use im::{HashSet, Vector};
 
@@ -38,7 +38,7 @@ impl fmt::Debug for Type {
       Self::Unit => write!(f, "𝟙"),
       Self::Var(arg0) => write!(f, "{}", arg0),
       Self::Existential(arg0) => write!(f, "{}", arg0),
-      Self::Polytype(arg0, arg1) => write!(f, "(∀{}.{:?})", arg0, arg1),
+      Self::Polytype(arg0, arg1) => write!(f, "(∀ {} . {:?})", arg0, arg1),
       Self::Arrow(arg0, arg1) => write!(f, "({:?} -> {:?})", arg0, arg1),
     }
   }
@@ -93,6 +93,21 @@ impl Type {
 
     free_vars_with_context(&Context::default(), self)
   }
+
+  pub fn subst(&self, var: impl AsRef<str>, replacement: &Type) -> Type {
+    let var = var.as_ref();
+    match self {
+      Type::Unit => Type::Unit,
+      Type::Var(n) if n == var => replacement.clone(),
+      Type::Var(n) => Type::Var(n.clone()),
+      Type::Existential(s) => Type::Existential(s.clone()),
+      Type::Polytype(a, t) => Type::Polytype(a.clone(), Box::new(t.subst(var, replacement))),
+      Type::Arrow(a, b) => Type::Arrow(
+        Box::new(a.subst(var, replacement)),
+        Box::new(b.subst(var, replacement)),
+      ),
+    }
+  }
 }
 
 #[derive(Clone)]
@@ -214,4 +229,19 @@ impl Context {
   pub fn has_existential(&self, name: impl AsRef<str>) -> bool {
     self.lookup_existential(name).is_some()
   }
+
+  pub fn unsolved_existentials(&self) -> HashSet<String> {
+    let mut unsolved = HashSet::new();
+
+    for entry in self.0.iter() {
+      match entry {
+        ContextEntry::ExistentialVar(n) => {
+          unsolved.insert(n.clone());
+        }
+        _ => {}
+      }
+    }
+
+    unsolved
+  }
 }

bidir/src/tests.rs

@@ -16,8 +16,8 @@ fn test_id() -> Result<()> {
   let id = id_term!();
   let ctx = Context::default();
   let (ty, out_ctx) = synthesize(&ctx, &id)?;
-  let ty2 = app_ctx(&out_ctx, &ty)?;
-  println!("Result: {:?}", ty2);
+  println!("Synthesis result: {ty:?} | {out_ctx:?}");
+
   Ok(())
 }
 
@@ -26,6 +26,7 @@ fn test_id_of_unit() -> Result<()> {
   let id = id_term!();
   let id_of_unit = Term::App(Box::new(id), Box::new(Term::Unit));
   let ctx = Context::default();
+
   bail!("Result: {:?}", synthesize(&ctx, &id_of_unit));
   Ok(())
 }