chore(users): grfn -> aspen r/7511

Change-Id: I6c6847fac56f0a9a1a2209792e00a3aec5e672b9
Reviewed-on: https://cl.tvl.fyi/c/depot/+/10809
Autosubmit: aspen <root@gws.fyi>
Reviewed-by: sterni <sternenseemann@systemli.org>
Tested-by: BuildkiteCI
Reviewed-by: lukegb <lukegb@tvl.fyi>

2 files changed, 848 insertions, 0 deletions

diff --git a/users/aspen/achilles/src/ast/hir.rs b/users/aspen/achilles/src/ast/hir.rs
new file mode 100644
index 000000000000..cdfaef567d7a
--- /dev/null
+++ b/users/aspen/achilles/src/ast/hir.rs
@@ -0,0 +1,364 @@
+use std::collections::HashMap;
+
+use itertools::Itertools;
+
+use super::{BinaryOperator, Ident, Literal, UnaryOperator};
+
+#[derive(Debug, PartialEq, Eq, Clone)]
+pub enum Pattern<'a, T> {
+    Id(Ident<'a>, T),
+    Tuple(Vec<Pattern<'a, T>>),
+}
+
+impl<'a, T> Pattern<'a, T> {
+    pub fn to_owned(&self) -> Pattern<'static, T>
+    where
+        T: Clone,
+    {
+        match self {
+            Pattern::Id(id, t) => Pattern::Id(id.to_owned(), t.clone()),
+            Pattern::Tuple(pats) => {
+                Pattern::Tuple(pats.into_iter().map(Pattern::to_owned).collect())
+            }
+        }
+    }
+
+    pub fn traverse_type<F, U, E>(self, f: F) -> Result<Pattern<'a, U>, E>
+    where
+        F: Fn(T) -> Result<U, E> + Clone,
+    {
+        match self {
+            Pattern::Id(id, t) => Ok(Pattern::Id(id, f(t)?)),
+            Pattern::Tuple(pats) => Ok(Pattern::Tuple(
+                pats.into_iter()
+                    .map(|pat| pat.traverse_type(f.clone()))
+                    .collect::<Result<Vec<_>, _>>()?,
+            )),
+        }
+    }
+}
+
+#[derive(Debug, PartialEq, Eq, Clone)]
+pub struct Binding<'a, T> {
+    pub pat: Pattern<'a, T>,
+    pub body: Expr<'a, T>,
+}
+
+impl<'a, T> Binding<'a, T> {
+    fn to_owned(&self) -> Binding<'static, T>
+    where
+        T: Clone,
+    {
+        Binding {
+            pat: self.pat.to_owned(),
+            body: self.body.to_owned(),
+        }
+    }
+}
+
+#[derive(Debug, PartialEq, Eq, Clone)]
+pub enum Expr<'a, T> {
+    Ident(Ident<'a>, T),
+
+    Literal(Literal<'a>, T),
+
+    Tuple(Vec<Expr<'a, T>>, T),
+
+    UnaryOp {
+        op: UnaryOperator,
+        rhs: Box<Expr<'a, T>>,
+        type_: T,
+    },
+
+    BinaryOp {
+        lhs: Box<Expr<'a, T>>,
+        op: BinaryOperator,
+        rhs: Box<Expr<'a, T>>,
+        type_: T,
+    },
+
+    Let {
+        bindings: Vec<Binding<'a, T>>,
+        body: Box<Expr<'a, T>>,
+        type_: T,
+    },
+
+    If {
+        condition: Box<Expr<'a, T>>,
+        then: Box<Expr<'a, T>>,
+        else_: Box<Expr<'a, T>>,
+        type_: T,
+    },
+
+    Fun {
+        type_args: Vec<Ident<'a>>,
+        args: Vec<(Ident<'a>, T)>,
+        body: Box<Expr<'a, T>>,
+        type_: T,
+    },
+
+    Call {
+        fun: Box<Expr<'a, T>>,
+        type_args: HashMap<Ident<'a>, T>,
+        args: Vec<Expr<'a, T>>,
+        type_: T,
+    },
+}
+
+impl<'a, T> Expr<'a, T> {
+    pub fn type_(&self) -> &T {
+        match self {
+            Expr::Ident(_, t) => t,
+            Expr::Literal(_, t) => t,
+            Expr::Tuple(_, t) => t,
+            Expr::UnaryOp { type_, .. } => type_,
+            Expr::BinaryOp { type_, .. } => type_,
+            Expr::Let { type_, .. } => type_,
+            Expr::If { type_, .. } => type_,
+            Expr::Fun { type_, .. } => type_,
+            Expr::Call { type_, .. } => type_,
+        }
+    }
+
+    pub fn traverse_type<F, U, E>(self, f: F) -> Result<Expr<'a, U>, E>
+    where
+        F: Fn(T) -> Result<U, E> + Clone,
+    {
+        match self {
+            Expr::Ident(id, t) => Ok(Expr::Ident(id, f(t)?)),
+            Expr::Literal(lit, t) => Ok(Expr::Literal(lit, f(t)?)),
+            Expr::UnaryOp { op, rhs, type_ } => Ok(Expr::UnaryOp {
+                op,
+                rhs: Box::new(rhs.traverse_type(f.clone())?),
+                type_: f(type_)?,
+            }),
+            Expr::BinaryOp {
+                lhs,
+                op,
+                rhs,
+                type_,
+            } => Ok(Expr::BinaryOp {
+                lhs: Box::new(lhs.traverse_type(f.clone())?),
+                op,
+                rhs: Box::new(rhs.traverse_type(f.clone())?),
+                type_: f(type_)?,
+            }),
+            Expr::Let {
+                bindings,
+                body,
+                type_,
+            } => Ok(Expr::Let {
+                bindings: bindings
+                    .into_iter()
+                    .map(|Binding { pat, body }| {
+                        Ok(Binding {
+                            pat: pat.traverse_type(f.clone())?,
+                            body: body.traverse_type(f.clone())?,
+                        })
+                    })
+                    .collect::<Result<Vec<_>, E>>()?,
+                body: Box::new(body.traverse_type(f.clone())?),
+                type_: f(type_)?,
+            }),
+            Expr::If {
+                condition,
+                then,
+                else_,
+                type_,
+            } => Ok(Expr::If {
+                condition: Box::new(condition.traverse_type(f.clone())?),
+                then: Box::new(then.traverse_type(f.clone())?),
+                else_: Box::new(else_.traverse_type(f.clone())?),
+                type_: f(type_)?,
+            }),
+            Expr::Fun {
+                args,
+                type_args,
+                body,
+                type_,
+            } => Ok(Expr::Fun {
+                args: args
+                    .into_iter()
+                    .map(|(id, t)| Ok((id, f.clone()(t)?)))
+                    .collect::<Result<Vec<_>, E>>()?,
+                type_args,
+                body: Box::new(body.traverse_type(f.clone())?),
+                type_: f(type_)?,
+            }),
+            Expr::Call {
+                fun,
+                type_args,
+                args,
+                type_,
+            } => Ok(Expr::Call {
+                fun: Box::new(fun.traverse_type(f.clone())?),
+                type_args: type_args
+                    .into_iter()
+                    .map(|(id, ty)| Ok((id, f.clone()(ty)?)))
+                    .collect::<Result<HashMap<_, _>, E>>()?,
+                args: args
+                    .into_iter()
+                    .map(|e| e.traverse_type(f.clone()))
+                    .collect::<Result<Vec<_>, E>>()?,
+                type_: f(type_)?,
+            }),
+            Expr::Tuple(members, t) => Ok(Expr::Tuple(
+                members
+                    .into_iter()
+                    .map(|t| t.traverse_type(f.clone()))
+                    .try_collect()?,
+                f(t)?,
+            )),
+        }
+    }
+
+    pub fn to_owned(&self) -> Expr<'static, T>
+    where
+        T: Clone,
+    {
+        match self {
+            Expr::Ident(id, t) => Expr::Ident(id.to_owned(), t.clone()),
+            Expr::Literal(lit, t) => Expr::Literal(lit.to_owned(), t.clone()),
+            Expr::UnaryOp { op, rhs, type_ } => Expr::UnaryOp {
+                op: *op,
+                rhs: Box::new((**rhs).to_owned()),
+                type_: type_.clone(),
+            },
+            Expr::BinaryOp {
+                lhs,
+                op,
+                rhs,
+                type_,
+            } => Expr::BinaryOp {
+                lhs: Box::new((**lhs).to_owned()),
+                op: *op,
+                rhs: Box::new((**rhs).to_owned()),
+                type_: type_.clone(),
+            },
+            Expr::Let {
+                bindings,
+                body,
+                type_,
+            } => Expr::Let {
+                bindings: bindings.iter().map(|b| b.to_owned()).collect(),
+                body: Box::new((**body).to_owned()),
+                type_: type_.clone(),
+            },
+            Expr::If {
+                condition,
+                then,
+                else_,
+                type_,
+            } => Expr::If {
+                condition: Box::new((**condition).to_owned()),
+                then: Box::new((**then).to_owned()),
+                else_: Box::new((**else_).to_owned()),
+                type_: type_.clone(),
+            },
+            Expr::Fun {
+                args,
+                type_args,
+                body,
+                type_,
+            } => Expr::Fun {
+                args: args
+                    .iter()
+                    .map(|(id, t)| (id.to_owned(), t.clone()))
+                    .collect(),
+                type_args: type_args.iter().map(|arg| arg.to_owned()).collect(),
+                body: Box::new((**body).to_owned()),
+                type_: type_.clone(),
+            },
+            Expr::Call {
+                fun,
+                type_args,
+                args,
+                type_,
+            } => Expr::Call {
+                fun: Box::new((**fun).to_owned()),
+                type_args: type_args
+                    .iter()
+                    .map(|(id, t)| (id.to_owned(), t.clone()))
+                    .collect(),
+                args: args.iter().map(|e| e.to_owned()).collect(),
+                type_: type_.clone(),
+            },
+            Expr::Tuple(members, t) => {
+                Expr::Tuple(members.into_iter().map(Expr::to_owned).collect(), t.clone())
+            }
+        }
+    }
+}
+
+#[derive(Debug, Clone, PartialEq, Eq)]
+pub enum Decl<'a, T> {
+    Fun {
+        name: Ident<'a>,
+        type_args: Vec<Ident<'a>>,
+        args: Vec<(Ident<'a>, T)>,
+        body: Box<Expr<'a, T>>,
+        type_: T,
+    },
+
+    Extern {
+        name: Ident<'a>,
+        arg_types: Vec<T>,
+        ret_type: T,
+    },
+}
+
+impl<'a, T> Decl<'a, T> {
+    pub fn name(&self) -> &Ident<'a> {
+        match self {
+            Decl::Fun { name, .. } => name,
+            Decl::Extern { name, .. } => name,
+        }
+    }
+
+    pub fn set_name(&mut self, new_name: Ident<'a>) {
+        match self {
+            Decl::Fun { name, .. } => *name = new_name,
+            Decl::Extern { name, .. } => *name = new_name,
+        }
+    }
+
+    pub fn type_(&self) -> Option<&T> {
+        match self {
+            Decl::Fun { type_, .. } => Some(type_),
+            Decl::Extern { .. } => None,
+        }
+    }
+
+    pub fn traverse_type<F, U, E>(self, f: F) -> Result<Decl<'a, U>, E>
+    where
+        F: Fn(T) -> Result<U, E> + Clone,
+    {
+        match self {
+            Decl::Fun {
+                name,
+                type_args,
+                args,
+                body,
+                type_,
+            } => Ok(Decl::Fun {
+                name,
+                type_args,
+                args: args
+                    .into_iter()
+                    .map(|(id, t)| Ok((id, f(t)?)))
+                    .try_collect()?,
+                body: Box::new(body.traverse_type(f.clone())?),
+                type_: f(type_)?,
+            }),
+            Decl::Extern {
+                name,
+                arg_types,
+                ret_type,
+            } => Ok(Decl::Extern {
+                name,
+                arg_types: arg_types.into_iter().map(f.clone()).try_collect()?,
+                ret_type: f(ret_type)?,
+            }),
+        }
+    }
+}
diff --git a/users/aspen/achilles/src/ast/mod.rs b/users/aspen/achilles/src/ast/mod.rs
new file mode 100644
index 000000000000..5438d29d2cf7
--- /dev/null
+++ b/users/aspen/achilles/src/ast/mod.rs
@@ -0,0 +1,484 @@
+pub(crate) mod hir;
+
+use std::borrow::Cow;
+use std::collections::HashMap;
+use std::convert::TryFrom;
+use std::fmt::{self, Display, Formatter};
+
+use itertools::Itertools;
+
+#[derive(Debug, PartialEq, Eq)]
+pub struct InvalidIdentifier<'a>(Cow<'a, str>);
+
+#[derive(Debug, PartialEq, Eq, Hash, Clone)]
+pub struct Ident<'a>(pub Cow<'a, str>);
+
+impl<'a> From<&'a Ident<'a>> for &'a str {
+    fn from(id: &'a Ident<'a>) -> Self {
+        id.0.as_ref()
+    }
+}
+
+impl<'a> Display for Ident<'a> {
+    fn fmt(&self, f: &mut Formatter<'_>) -> fmt::Result {
+        write!(f, "{}", self.0)
+    }
+}
+
+impl<'a> Ident<'a> {
+    pub fn to_owned(&self) -> Ident<'static> {
+        Ident(Cow::Owned(self.0.clone().into_owned()))
+    }
+
+    /// Construct an identifier from a &str without checking that it's a valid identifier
+    pub fn from_str_unchecked(s: &'a str) -> Self {
+        debug_assert!(is_valid_identifier(s));
+        Self(Cow::Borrowed(s))
+    }
+
+    pub fn from_string_unchecked(s: String) -> Self {
+        debug_assert!(is_valid_identifier(&s));
+        Self(Cow::Owned(s))
+    }
+}
+
+pub fn is_valid_identifier<S>(s: &S) -> bool
+where
+    S: AsRef<str> + ?Sized,
+{
+    s.as_ref()
+        .chars()
+        .any(|c| !c.is_alphanumeric() || !"_".contains(c))
+}
+
+impl<'a> TryFrom<&'a str> for Ident<'a> {
+    type Error = InvalidIdentifier<'a>;
+
+    fn try_from(s: &'a str) -> Result<Self, Self::Error> {
+        if is_valid_identifier(s) {
+            Ok(Ident(Cow::Borrowed(s)))
+        } else {
+            Err(InvalidIdentifier(Cow::Borrowed(s)))
+        }
+    }
+}
+
+impl<'a> TryFrom<String> for Ident<'a> {
+    type Error = InvalidIdentifier<'static>;
+
+    fn try_from(s: String) -> Result<Self, Self::Error> {
+        if is_valid_identifier(&s) {
+            Ok(Ident(Cow::Owned(s)))
+        } else {
+            Err(InvalidIdentifier(Cow::Owned(s)))
+        }
+    }
+}
+
+#[derive(Debug, PartialEq, Eq, Copy, Clone)]
+pub enum BinaryOperator {
+    /// `+`
+    Add,
+
+    /// `-`
+    Sub,
+
+    /// `*`
+    Mul,
+
+    /// `/`
+    Div,
+
+    /// `^`
+    Pow,
+
+    /// `==`
+    Equ,
+
+    /// `!=`
+    Neq,
+}
+
+#[derive(Debug, PartialEq, Eq, Copy, Clone)]
+pub enum UnaryOperator {
+    /// !
+    Not,
+
+    /// -
+    Neg,
+}
+
+#[derive(Debug, PartialEq, Eq, Clone)]
+pub enum Literal<'a> {
+    Unit,
+    Int(u64),
+    Bool(bool),
+    String(Cow<'a, str>),
+}
+
+impl<'a> Literal<'a> {
+    pub fn to_owned(&self) -> Literal<'static> {
+        match self {
+            Literal::Int(i) => Literal::Int(*i),
+            Literal::Bool(b) => Literal::Bool(*b),
+            Literal::String(s) => Literal::String(Cow::Owned(s.clone().into_owned())),
+            Literal::Unit => Literal::Unit,
+        }
+    }
+}
+
+#[derive(Debug, PartialEq, Eq, Clone)]
+pub enum Pattern<'a> {
+    Id(Ident<'a>),
+    Tuple(Vec<Pattern<'a>>),
+}
+
+impl<'a> Pattern<'a> {
+    pub fn to_owned(&self) -> Pattern<'static> {
+        match self {
+            Pattern::Id(id) => Pattern::Id(id.to_owned()),
+            Pattern::Tuple(pats) => Pattern::Tuple(pats.iter().map(Pattern::to_owned).collect()),
+        }
+    }
+}
+
+#[derive(Debug, PartialEq, Eq, Clone)]
+pub struct Binding<'a> {
+    pub pat: Pattern<'a>,
+    pub type_: Option<Type<'a>>,
+    pub body: Expr<'a>,
+}
+
+impl<'a> Binding<'a> {
+    fn to_owned(&self) -> Binding<'static> {
+        Binding {
+            pat: self.pat.to_owned(),
+            type_: self.type_.as_ref().map(|t| t.to_owned()),
+            body: self.body.to_owned(),
+        }
+    }
+}
+
+#[derive(Debug, PartialEq, Eq, Clone)]
+pub enum Expr<'a> {
+    Ident(Ident<'a>),
+
+    Literal(Literal<'a>),
+
+    UnaryOp {
+        op: UnaryOperator,
+        rhs: Box<Expr<'a>>,
+    },
+
+    BinaryOp {
+        lhs: Box<Expr<'a>>,
+        op: BinaryOperator,
+        rhs: Box<Expr<'a>>,
+    },
+
+    Let {
+        bindings: Vec<Binding<'a>>,
+        body: Box<Expr<'a>>,
+    },
+
+    If {
+        condition: Box<Expr<'a>>,
+        then: Box<Expr<'a>>,
+        else_: Box<Expr<'a>>,
+    },
+
+    Fun(Box<Fun<'a>>),
+
+    Call {
+        fun: Box<Expr<'a>>,
+        args: Vec<Expr<'a>>,
+    },
+
+    Tuple(Vec<Expr<'a>>),
+
+    Ascription {
+        expr: Box<Expr<'a>>,
+        type_: Type<'a>,
+    },
+}
+
+impl<'a> Expr<'a> {
+    pub fn to_owned(&self) -> Expr<'static> {
+        match self {
+            Expr::Ident(ref id) => Expr::Ident(id.to_owned()),
+            Expr::Literal(ref lit) => Expr::Literal(lit.to_owned()),
+            Expr::Tuple(ref members) => {
+                Expr::Tuple(members.into_iter().map(Expr::to_owned).collect())
+            }
+            Expr::UnaryOp { op, rhs } => Expr::UnaryOp {
+                op: *op,
+                rhs: Box::new((**rhs).to_owned()),
+            },
+            Expr::BinaryOp { lhs, op, rhs } => Expr::BinaryOp {
+                lhs: Box::new((**lhs).to_owned()),
+                op: *op,
+                rhs: Box::new((**rhs).to_owned()),
+            },
+            Expr::Let { bindings, body } => Expr::Let {
+                bindings: bindings.iter().map(|binding| binding.to_owned()).collect(),
+                body: Box::new((**body).to_owned()),
+            },
+            Expr::If {
+                condition,
+                then,
+                else_,
+            } => Expr::If {
+                condition: Box::new((**condition).to_owned()),
+                then: Box::new((**then).to_owned()),
+                else_: Box::new((**else_).to_owned()),
+            },
+            Expr::Fun(fun) => Expr::Fun(Box::new((**fun).to_owned())),
+            Expr::Call { fun, args } => Expr::Call {
+                fun: Box::new((**fun).to_owned()),
+                args: args.iter().map(|arg| arg.to_owned()).collect(),
+            },
+            Expr::Ascription { expr, type_ } => Expr::Ascription {
+                expr: Box::new((**expr).to_owned()),
+                type_: type_.to_owned(),
+            },
+        }
+    }
+}
+
+#[derive(Debug, PartialEq, Eq, Clone)]
+pub struct Arg<'a> {
+    pub ident: Ident<'a>,
+    pub type_: Option<Type<'a>>,
+}
+
+impl<'a> Arg<'a> {
+    pub fn to_owned(&self) -> Arg<'static> {
+        Arg {
+            ident: self.ident.to_owned(),
+            type_: self.type_.as_ref().map(Type::to_owned),
+        }
+    }
+}
+
+impl<'a> TryFrom<&'a str> for Arg<'a> {
+    type Error = <Ident<'a> as TryFrom<&'a str>>::Error;
+
+    fn try_from(value: &'a str) -> Result<Self, Self::Error> {
+        Ok(Arg {
+            ident: Ident::try_from(value)?,
+            type_: None,
+        })
+    }
+}
+
+#[derive(Debug, PartialEq, Eq, Clone)]
+pub struct Fun<'a> {
+    pub args: Vec<Arg<'a>>,
+    pub body: Expr<'a>,
+}
+
+impl<'a> Fun<'a> {
+    pub fn to_owned(&self) -> Fun<'static> {
+        Fun {
+            args: self.args.iter().map(|arg| arg.to_owned()).collect(),
+            body: self.body.to_owned(),
+        }
+    }
+}
+
+#[derive(Debug, PartialEq, Eq, Clone)]
+pub enum Decl<'a> {
+    Fun {
+        name: Ident<'a>,
+        body: Fun<'a>,
+    },
+    Ascription {
+        name: Ident<'a>,
+        type_: Type<'a>,
+    },
+    Extern {
+        name: Ident<'a>,
+        type_: FunctionType<'a>,
+    },
+}
+
+////
+
+#[derive(Debug, PartialEq, Eq, Clone)]
+pub struct FunctionType<'a> {
+    pub args: Vec<Type<'a>>,
+    pub ret: Box<Type<'a>>,
+}
+
+impl<'a> FunctionType<'a> {
+    pub fn to_owned(&self) -> FunctionType<'static> {
+        FunctionType {
+            args: self.args.iter().map(|a| a.to_owned()).collect(),
+            ret: Box::new((*self.ret).to_owned()),
+        }
+    }
+}
+
+impl<'a> Display for FunctionType<'a> {
+    fn fmt(&self, f: &mut Formatter<'_>) -> fmt::Result {
+        write!(f, "fn {} -> {}", self.args.iter().join(", "), self.ret)
+    }
+}
+
+#[derive(Debug, PartialEq, Eq, Clone)]
+pub enum Type<'a> {
+    Int,
+    Float,
+    Bool,
+    CString,
+    Unit,
+    Tuple(Vec<Type<'a>>),
+    Var(Ident<'a>),
+    Function(FunctionType<'a>),
+}
+
+impl<'a> Type<'a> {
+    pub fn to_owned(&self) -> Type<'static> {
+        match self {
+            Type::Int => Type::Int,
+            Type::Float => Type::Float,
+            Type::Bool => Type::Bool,
+            Type::CString => Type::CString,
+            Type::Unit => Type::Unit,
+            Type::Var(v) => Type::Var(v.to_owned()),
+            Type::Function(f) => Type::Function(f.to_owned()),
+            Type::Tuple(members) => Type::Tuple(members.iter().map(Type::to_owned).collect()),
+        }
+    }
+
+    pub fn alpha_equiv(&self, other: &Self) -> bool {
+        fn do_alpha_equiv<'a>(
+            substs: &mut HashMap<&'a Ident<'a>, &'a Ident<'a>>,
+            lhs: &'a Type,
+            rhs: &'a Type,
+        ) -> bool {
+            match (lhs, rhs) {
+                (Type::Var(v1), Type::Var(v2)) => substs.entry(v1).or_insert(v2) == &v2,
+                (
+                    Type::Function(FunctionType {
+                        args: args1,
+                        ret: ret1,
+                    }),
+                    Type::Function(FunctionType {
+                        args: args2,
+                        ret: ret2,
+                    }),
+                ) => {
+                    args1.len() == args2.len()
+                        && args1
+                            .iter()
+                            .zip(args2)
+                            .all(|(a1, a2)| do_alpha_equiv(substs, a1, a2))
+                        && do_alpha_equiv(substs, ret1, ret2)
+                }
+                _ => lhs == rhs,
+            }
+        }
+
+        let mut substs = HashMap::new();
+        do_alpha_equiv(&mut substs, self, other)
+    }
+
+    pub fn traverse_type_vars<'b, F>(self, mut f: F) -> Type<'b>
+    where
+        F: FnMut(Ident<'a>) -> Type<'b> + Clone,
+    {
+        match self {
+            Type::Var(tv) => f(tv),
+            Type::Function(FunctionType { args, ret }) => Type::Function(FunctionType {
+                args: args
+                    .into_iter()
+                    .map(|t| t.traverse_type_vars(f.clone()))
+                    .collect(),
+                ret: Box::new(ret.traverse_type_vars(f)),
+            }),
+            Type::Int => Type::Int,
+            Type::Float => Type::Float,
+            Type::Bool => Type::Bool,
+            Type::CString => Type::CString,
+            Type::Tuple(members) => Type::Tuple(
+                members
+                    .into_iter()
+                    .map(|t| t.traverse_type_vars(f.clone()))
+                    .collect(),
+            ),
+            Type::Unit => Type::Unit,
+        }
+    }
+
+    pub fn as_tuple(&self) -> Option<&Vec<Type<'a>>> {
+        if let Self::Tuple(v) = self {
+            Some(v)
+        } else {
+            None
+        }
+    }
+}
+
+impl<'a> Display for Type<'a> {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        match self {
+            Type::Int => f.write_str("int"),
+            Type::Float => f.write_str("float"),
+            Type::Bool => f.write_str("bool"),
+            Type::CString => f.write_str("cstring"),
+            Type::Unit => f.write_str("()"),
+            Type::Var(v) => v.fmt(f),
+            Type::Function(ft) => ft.fmt(f),
+            Type::Tuple(ms) => write!(f, "({})", ms.iter().join(", ")),
+        }
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    fn type_var(n: &str) -> Type<'static> {
+        Type::Var(Ident::try_from(n.to_owned()).unwrap())
+    }
+
+    mod alpha_equiv {
+        use super::*;
+
+        #[test]
+        fn trivial() {
+            assert!(Type::Int.alpha_equiv(&Type::Int));
+            assert!(!Type::Int.alpha_equiv(&Type::Bool));
+        }
+
+        #[test]
+        fn simple_type_var() {
+            assert!(type_var("a").alpha_equiv(&type_var("b")));
+        }
+
+        #[test]
+        fn function_with_type_vars_equiv() {
+            assert!(Type::Function(FunctionType {
+                args: vec![type_var("a")],
+                ret: Box::new(type_var("b")),
+            })
+            .alpha_equiv(&Type::Function(FunctionType {
+                args: vec![type_var("b")],
+                ret: Box::new(type_var("a")),
+            })))
+        }
+
+        #[test]
+        fn function_with_type_vars_non_equiv() {
+            assert!(!Type::Function(FunctionType {
+                args: vec![type_var("a")],
+                ret: Box::new(type_var("a")),
+            })
+            .alpha_equiv(&Type::Function(FunctionType {
+                args: vec![type_var("b")],
+                ret: Box::new(type_var("a")),
+            })))
+        }
+    }
+}