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Algorithmic subtyping\n\n/// Under input context Γ , type A is a subtype of B, with output context ∆\npub fn subtype(ctx: \u0026Context, a: \u0026Type, b: \u0026Type) -\u003e Result\u003cContext\u003e {\n  println!(\"subtype(ctx = {ctx:?}, a = {a:?}, b = {b:?})\");\n  match (a, b) {\n    // \u003c:Unit rule\n    (Type::Unit, Type::Unit) =\u003e Ok(ctx.clone()),\n\n    // \u003c:Var rule\n    (Type::Var(x), Type::Var(y)) if x == y =\u003e {\n      // Ensure that the name exists in the context\n      if !ctx.iter().any(|entry| match entry {\n        ContextEntry::ExistentialVar(z) if x == z =\u003e true,\n        _ =\u003e false,\n      }) {\n        bail!(\"name {x} not in context\");\n      }\n\n      Ok(ctx.clone())\n    }\n\n    (Type::Existential(_), Type::Unit) =\u003e todo!(),\n    (Type::Existential(_), Type::Var(_)) =\u003e todo!(),\n    (Type::Existential(_), Type::Existential(_)) =\u003e todo!(),\n    (Type::Existential(_), Type::Polytype(_, _)) =\u003e todo!(),\n    (Type::Existential(_), Type::Arrow(_, _)) =\u003e todo!(),\n    (Type::Polytype(_, _), Type::Unit) =\u003e todo!(),\n    (Type::Polytype(_, _), Type::Var(_)) =\u003e todo!(),\n    (Type::Polytype(_, _), Type::Existential(_)) =\u003e todo!(),\n    (Type::Polytype(_, _), Type::Polytype(_, _)) =\u003e todo!(),\n    (Type::Polytype(_, _), Type::Arrow(_, _)) =\u003e todo!(),\n    (Type::Arrow(_, _), Type::Unit) =\u003e todo!(),\n    (Type::Arrow(_, _), Type::Var(_)) =\u003e todo!(),\n    (Type::Arrow(_, _), Type::Existential(_)) =\u003e todo!(),\n    (Type::Arrow(_, _), Type::Polytype(_, _)) =\u003e todo!(),\n    (Type::Arrow(_, _), Type::Arrow(_, _)) =\u003e todo!(),\n\n    _ =\u003e bail!(\"subtyping relation failed\"),\n  }\n}\n\n// Figure 10. 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Algorithmic typing\n\npub fn typecheck(ctx: \u0026Context, term: \u0026Term, ty: \u0026Type) -\u003e Result\u003cContext\u003e {\n  println!(\"typecheck(ctx = {ctx:?}, term = {term:?}, ty = {ty:?})\");\n  match (term, ty) {\n    // 1I rule\n    (Term::Unit, Type::Unit) =\u003e Ok(ctx.clone()),\n\n    // ∀I rule\n    (e, Type::Polytype(x, tyA)) =\u003e todo!(),\n\n    // →I rule\n    (Term::Lam(x, e), Type::Arrow(ty_a, ty_b)) =\u003e {\n      let mut aug_ctx = ctx.clone();\n      todo!()\n    }\n\n    // Sub rule\n    (term, ty) =\u003e {\n      let (ty_a, ctx_theta) = synthesize(ctx, term)?;\n      let a = app_ctx(\u0026ctx_theta, \u0026ty_a);\n      let b = app_ctx(\u0026ctx_theta, ty);\n      let ctx_delta = subtype(\u0026ctx_theta, \u0026a, \u0026b)?;\n      Ok(ctx_delta)\n    }\n  }\n}\n\npub fn synthesize(ctx: \u0026Context, term: \u0026Term) -\u003e Result\u003c(Type, Context)\u003e {\n  println!(\"synthesize(ctx = {ctx:?}, term = {term:?}\");\n  match term {\n    // Var rule\n    Term::Var(name) =\u003e {\n      let ty = match ctx_lookup_type(ctx, name) {\n        Some(v) =\u003e v,\n        None =\u003e bail!(\"could not find name {name}\"),\n      };\n      Ok((ty, ctx.clone()))\n    }\n\n    // 1I⇒ rule\n    Term::Unit =\u003e Ok((Type::Unit, ctx.clone())),\n\n    // Anno rule\n    Term::Annot(_, _) =\u003e todo!(),\n\n    // →I⇒ rule\n    Term::Lam(x, e) =\u003e {\n      let mut aug_ctx = ctx.clone();\n      let ex_a = gensym_prefix(\"ex\");\n      let ex_b = gensym_prefix(\"ex\");\n      aug_ctx.push_back(ContextEntry::TypeVar(ex_a.clone()));\n      aug_ctx.push_back(ContextEntry::TypeVar(ex_b.clone()));\n      aug_ctx.push_back(ContextEntry::TermAnnot(x.clone(), Type::Var(ex_a.clone())));\n\n      let res = typecheck(\u0026aug_ctx, \u0026e, \u0026Type::Var(ex_b.clone()));\n      Ok((\n        Type::Arrow(\n          Box::new(Type::Existential(ex_a)),\n          Box::new(Type::Existential(ex_b)),\n        ),\n        ctx.clone(),\n      ))\n    }\n\n    // →E rule\n    Term::App(e1, e2) =\u003e {\n      let (tyA, out_ctx) = synthesize(ctx, e1)?;\n      todo!()\n    }\n  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im::Vector;\n\n#[derive(Debug, Clone)]\npub enum Term {\n  Unit,\n  Var(String),\n  Lam(String, Box\u003cTerm\u003e),\n  App(Box\u003cTerm\u003e, Box\u003cTerm\u003e),\n  Annot(Box\u003cTerm\u003e, Type),\n}\n\n#[derive(Debug, Clone)]\npub enum Type {\n  Unit,\n  Var(String),\n  Existential(String),\n  Polytype(String, Box\u003cType\u003e),\n  Arrow(Box\u003cType\u003e, Box\u003cType\u003e),\n}\n\n#[derive(Debug, Clone)]\npub enum Monotype {\n  Unit,\n  Var(String),\n  Existential(String),\n  Arrow(Box\u003cMonotype\u003e, Box\u003cMonotype\u003e),\n}\n\npub type Context = Vector\u003cContextEntry\u003e;\n\n#[derive(Debug, Clone)]\npub enum ContextEntry {\n  TypeVar(String),\n  TermAnnot(String, Type),\n  ExistentialVar(String),\n  ExistentialSolved(String, Monotype),\n  Marker(String),\n}\n\n#[derive(Debug, Clone)]\npub enum CompleteContextEntry {\n  TypeVar(String),\n  TermAnnot(String, Type),\n  ExistentialSolved(String, Monotype),\n  Marker(String),\n}\n\npub fn ctx_lookup_type(ctx: \u0026Context, name: impl AsRef\u003cstr\u003e) -\u003e Option\u003cType\u003e {\n  ctx.iter().find_map(|entry| match entry {\n    ContextEntry::TermAnnot(n, t) if n == name.as_ref() =\u003e Some(t.clone()),\n    _ =\u003e None,\n  })\n}\n","traces":[{"line":48,"address":[],"length":0,"stats":{"Line":1},"fn_name":null},{"line":49,"address":[],"length":0,"stats":{"Line":2},"fn_name":null},{"line":50,"address":[],"length":0,"stats":{"Line":2},"fn_name":null},{"line":51,"address":[],"length":0,"stats":{"Line":2},"fn_name":null}],"covered":4,"coverable":4},{"path":["/","Users","michael","Projects","school","csci8980-f23","bidir","src","gensym.rs"],"content":"use lazy_static::lazy_static;\nuse parking_lot::Mutex;\n\nlazy_static! {\n  static ref CTR: Mutex\u003cusize\u003e = Mutex::new(0);\n}\n\npub fn gensym() -\u003e String {\n  gensym_prefix(\"var\")\n}\n\npub fn gensym_prefix(prefix: impl AsRef\u003cstr\u003e) -\u003e String {\n  let mut g = CTR.lock();\n  let ctr = 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Result};\nuse im::Vector;\n\nuse crate::{bidir::synthesize, data::Term};\n\n#[test]\nfn test_id() -\u003e Result\u003c()\u003e {\n  let id = Term::Lam(\"x\".to_owned(), Box::new(Term::Var(\"x\".to_owned())));\n  let ctx = Vector::new();\n  let (ty, out_ctx) = synthesize(\u0026ctx, \u0026id)?;\n  //   bail!(\"Output: {ty:?} in context {out_ctx:?}\");\n  Ok(())\n}\n","traces":[],"covered":0,"coverable":0}]};
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