Trying out ena

src/interpret.rs

@@ -51,7 +51,7 @@ pub fn literal_to_string<'a>(literal: &'a Literal<'a>) -> String {
                 elem_strings.push(literal_to_string(eval(elem_expr)));
             }
 
-            format!("[ {} ]", elem_strings.join(", "))
+            format!("[{}]", elem_strings.join(", "))
         },
     }
 }

src/lib.rs

@@ -1,6 +1,9 @@
 #![feature(box_patterns)]
 
-pub mod unify;
-pub mod interpret;
-pub mod repl;
+// pub mod unify;
+// pub mod interpret;
+// pub mod repl;
 
+pub mod solve;
+
+extern crate ena;

src/solve.rs

@@ -1,9 +1,19 @@
-use self::Type::*;
+use std::collections::BTreeSet;
+use self::VarContent::*;
+use self::Operator::*;
+use ena::unify::UnificationTable;
+use ena::unify::UnifyValue;
+use ena::unify::InPlace;
 
 pub type Name<'a> = &'a str;
 
 pub type ModuleName<'a> = &'a str;
 
+type UTable<'a> = UnificationTable<InPlace<Variable<'a>>>;
+
+type TypeUnion<'a> = BTreeSet<Type<'a>>;
+type VarUnion<'a> = BTreeSet<VarContent<'a>>;
+
 #[derive(Debug, PartialEq, Eq, PartialOrd, Ord)]
 pub enum Type<'a> {
     Symbol(&'a str),
@@ -11,6 +21,7 @@ pub enum Type<'a> {
     Float,
     Number,
     Function(Box<Type<'a>>, Box<Type<'a>>),
+    CallOperator(Operator, Box<&'a Type<'a>>, Box<&'a Type<'a>>),
 }
 
 
@@ -34,6 +45,267 @@ pub enum Problem {
     Mismatch
 }
 
+#[derive(Debug, PartialEq, Clone)]
+pub struct Variable<'a> {
+    content: VarContent<'a>,
+    rank: u8
+}
+
+#[derive(Debug, PartialEq)]
+enum VarContent<'a> {
+    Wildcard,
+    RigidVar(&'a Name<'a>),
+    FlexUnion(TypeUnion<'a>),
+    RigidUnion(TypeUnion<'a>),
+    Structure(FlatType<'a>),
+    Mismatch
+}
+
+fn unify_rigid<'a>(named: &'a VarContent<'a>, other: &'a VarContent<'a>) -> &'a VarContent<'a> {
+    match other {
+        Wildcard => named,
+        RigidVar(_) => Mismatch,
+        FlexUnion(_) => Mismatch,
+        RigidUnion(_) => Mismatch,
+        Mismatch => other
+    }
+}
+
+fn unify_rigid_union<'a>(rigid_union: &'a VarUnion<'a>, var: &'a VarContent<'a>, other: &'a VarContent<'a>) -> &'a VarContent<'a> {
+    match other {
+        Wildcard => var,
+        RigidVar(_) => Mismatch,
+        FlexUnion(flex_union) => {
+            // a flex union can conform to a rigid one, as long as
+            // as the rigid union contains all the flex union's options
+            if rigid_union.is_subset(flex_union) {
+                var
+            } else {
+                Mismatch
+            }
+        },
+        RigidUnion(_) => Mismatch,
+        Mismatch => other
+    }
+}
+
+fn unify_flex_union<'a>(flex_union: &'a VarUnion<'a>, var: &'a VarContent<'a>, other: &'a VarContent<'a>) -> &'a VarContent<'a> {
+    match other {
+        Wildcard => var,
+        RigidVar(_) => Mismatch,
+        RigidUnion(rigid_union) => {
+            // a flex union can conform to a rigid one, as long as
+            // as the rigid union contains all the flex union's options
+            if rigid_union.is_subset(flex_union) {
+                other
+            } else {
+                Mismatch
+            }
+        },
+        FlexUnion(other_union) => unify_flex_unions(flex_union, var, other_union, other),
+        Structure(flat_type) => unify_flex_union_with_flat_type(flex_union, flat_type),
+        Mismatch => other
+    }
+}
+
+fn unify_flex_unions<'a>(my_union: &'a VarUnion<'a>, my_var: &'a VarContent<'a>, other_union: &'a VarUnion<'a>, other_var: &'a VarContent<'a>) -> &'a VarContent<'a> {
+    // Prioritize not allocating a new BTreeSet if possible.
+    if my_union == other_union {
+        return my_var;
+    }
+
+    let types_in_common = my_union.intersection(other_union);
+
+    if types_in_common.is_empty() {
+        Mismatch
+    } else {
+        let unified_union: VarUnion<'a> = types_in_common.into_iter().collect();
+
+        FlexUnion(unified_union)
+    }
+}
+
+fn actually_unify<'a>(first: &'a VarContent<'a>, second: &'a VarContent<'a>) -> &'a VarContent<'a> {
+    match first {
+        // wildcard types defer to whatever the other type happens to be.
+        Wildcard => second,
+        FlexUnion(union) => unify_flex_union(union, first, second),
+        RigidVar(Name) => unify_rigid(first, second),
+        RigidUnion(union) => unify_rigid_union(union, first, second),
+        Structure(flat_type) => unify_structure(flat_type, first, second),
+        // Mismatches propagate.
+        Mismatch => first
+    }
+}
+
+type CanonicalModuleName = String;
+
+enum FlatType<'a> {
+    Function(Variable<'a>, Variable<'a>),
+    // Apply a higher-kinded type constructor by name
+    // e.g. apply `Array` to the variable `Int` to form `Array Int`
+    // ApplyTypeConstructor(CanonicalModuleName, Name, &'a Variable<'a>)
+    Tuple2(Variable<'a>, Variable<'a>),
+    // Tuple3(Variable<'a>, Variable<'a>, Variable<'a>),
+    // TupleN(Vec<Variable<'a>>), // Last resort - allocates
+    // Record1 (Map.Map N.Name Variable) Variable,
+}
+
+fn unify_args<'a>(arg1: &'a Variable<'a>, arg2: Variable) -> Result<Vec<Variable<'a>>, Vec<Variable<'a>>> {
+    guarded_unify(arg1, arg2)
+    // case subUnify arg1 arg2 of
+    // Unify k ->
+    //     k vars
+    //     (\vs () -> unifyArgs vs context others1 others2 ok err)
+    //     (\vs () -> unifyArgs vs context others1 others2 err err)
+}
+
+fn guarded_unify<'a>(utable: UTable<'a>, left: Variable<'a>, right: Variable<'a>) -> Result<(), ()> {
+    if utable.unioned(left, right) {
+        Ok(())
+    } else {
+        let left_descriptor = utable.probe_key(left);
+        let right_descriptor = utable.probe_key(right);
+
+        actually_unify(left, left_descriptor, right, right_descriptor)
+    }
+}
+
+pub fn unify_structure<'a>(utable: &'a mut UTable<'a>, flat_type: &'a FlatType<'a>, var: &'a VarContent<'a>, other: &'a VarContent<'a>) -> &'a VarContent<'a> {
+    match other {
+        Wildcard => var,
+        RigidVar(_) => Mismatch,
+        FlexUnion(union) => unify_flex_union_with_flat_type(flex_union, flat_type),
+        RigidUnion(_) => Mismatch,
+        Structure(other_flat_type) =>
+            match (flat_type, other) {
+                (FlatType::Function(my_arg, my_return),
+                 FlatType::Function(other_arg, other_return)) => {
+                    guarded_unify(utable, my_arg, other_arg);
+                    guarded_unify(utable, my_returned, other_returned);
+                },
+                (FlatType::Tuple2(my_first, my_second),
+                 FlatType::Tuple2(other_first, other_second)) => {
+                    guarded_unify(utable, my_first, other_first);
+                    guarded_unify(utable, my_second, other_second);
+                }
+            }
+
+        Mismatch =>
+            other
+    }
+}
+
+fn unify_flex_union_with_flat_type<'a>(utable: &'a mut UTable<'a>, flex_union: &'a VarUnion<'a>, flat_type: &'a FlatType<'a>) -> &'a VarContent<'a> {
+    if var_union_contains(flex_union, flat_type) {
+        // This will use the UnifyValue trait to unify the values.
+        utable.union(var1, var2);
+    } else {
+        Mismatch
+    }
+}
+
+
+type ExpectedType<'a> = Type<'a>;
+
+pub enum Constraint<'a> {
+    True,
+    Equal(Type<'a>, ExpectedType<'a>),
+    Batch(Vec<Constraint<'a>>),
+}
+
 pub fn infer_type<'a>(expr: Expr<'a>) -> Result<Type<'a>, Problem> {
     Err(Problem::Mismatch)
 }
+
+struct State {
+    errors: Vec<String>
+}
+
+
+impl<'a> UnifyValue for Variable<'a> {
+    // We return our own Mismatch variant to track errors.
+    type Error = ena::unify::NoError;
+
+    fn unify_values(value1: &'a Variable<'a>, value2: &'a Variable<'a>) -> Result<Variable<'a>, ena::unify::NoError> {
+        // TODO unify 'em
+        
+        // TODO problem: Elm's unification mutates and looks things up as it goes.
+        // I can see these possible ways to proceed:
+        // (1) Try to have the table's values contain a mutable reference to the table itself.
+        //     This sounds like a mistake.
+        // (2) Implement unification without mutating as we go.
+        //     Might be too slow, and might not even work.
+        //     Like, what if I need to look something up in the middle?
+        // (3) Make a custom fork of ena that supports Elm's way.
+        //      (3a) Change the unify_values function to accept the table itself, so it can be
+        //      passed in and used during unification
+        //      (3b) Change the unify_values function to accept the table itself, so it can be
+        //      passed in and used during unification. I'm not super confident this would work.
+        //
+        // Possibly before doing any of this, I should look at ena's examples/tests
+        
+        // TODO also I'm pretty sure in this implementation,
+        // I'm supposed to let them take care of the rank.
+        Ok(Variable {content, rank: min(rank1, rank2)})
+    }
+}
+
+fn type_to_var(rank: u8, typ: Type) -> Variable {
+    match typ {
+        Type::CallOperator(op, left_type, right_type) => {
+            let left_var = type_to_var(left_type);
+            let right_var = type_to_var(right_type);
+
+            // TODO should we match on op to hardcode the types we expect?
+            let flat_type = FlatType::Function(left_var, right_var);
+            let content = Structure(flat_type);
+
+            utable.new_key(Variable {rank, content})
+        }
+    }
+}
+
+
+pub fn unify(utable: Table, left_var: Variable, right_var: Variable) -> Result<(), ()>{
+    let left_content = utable.probe_value(left_var);
+    let right_content = utable.probe_value(right_var);
+
+    if left_content == right_content {
+        Ok(())
+    } else {
+        Ok(actually_unify(left, left_desc, right, right_desc))
+    }
+}
+
+pub fn solve(rank: u8, state: State, constraint: Constraint) {
+    match constraint {
+        True =>
+            state
+
+        Equal(actual_type, expectation) => {
+            let actual_var = type_to_var(rank, actual_type)
+            let expected_var = type_to_var(rank, expectation)
+            let answer = unify(actual_var, expected_var)
+
+            match answer {
+                Ok vars ->
+                    panic!("TODO abc");
+                    // do  introduce rank pools vars
+                    //     return state
+
+                    // UF.modify var $ \(Descriptor content _ mark copy) ->
+                    // Descriptor content rank mark copy
+
+                // Unify.Err vars actualType expectedType ->
+
+                //     panic!("TODO xyz");
+                // do  introduce rank pools vars
+                //     return $ addError state $
+                //         Error.BadExpr region category actualType $
+                //         Error.typeReplace expectation expectedType
+            }
+        }
+    }
+}
+

src/unify.rs

@@ -1,8 +1,10 @@
 use std::collections::BTreeSet;
+use std::collections::BTreeMap;
+use self::Type::*;
 
-pub type Ident<'a> = &'a str;
+pub type Name<'a> = &'a str;
 
-pub type Field<'a> = &'a str;
+pub type ModuleName<'a> = &'a str;
 
 #[derive(Debug, PartialEq, Eq, PartialOrd, Ord)]
 pub enum Type<'a> {
@@ -14,9 +16,9 @@ pub enum Type<'a> {
     Number,
     Symbol(&'a str),
     Array(Box<Type<'a>>),
-    Record(Vec<(Field<'a>, Type<'a>)>),
+    Function(Box<Type<'a>>, Box<Type<'a>>),
+    Record(BTreeMap<Name<'a>, Type<'a>>),
     Tuple(Vec<Type<'a>>),
-    Assignment(Ident<'a>, Box<Type<'a>>),
     Union(BTreeSet<Type<'a>>),
 }
 
@@ -25,39 +27,73 @@ pub enum Type<'a> {
 
 #[derive(Debug, PartialEq)]
 pub enum Expr<'a> {
-    Literal(&'a Literal<'a>),
-    Assignment(Ident<'a>, Box<&'a Expr<'a>>),
-    If(Box<&'a Expr<'a>> /* Conditional */, Box<&'a Expr<'a>> /* True branch */, Box<&'a Expr<'a>> /* False branch */),
+    // Variables
+    Declaration(&'a Pattern<'a>, Box<&'a Expr<'a>>, Box<Expr<'a>>),
+    LookupLocal(&'a Name<'a>),
+    LookupGlobal(&'a ModuleName<'a>, &'a Name<'a>),
+
+    // Scalars
+    Symbol(&'a str),
+    String(&'a str),
+    Char(char),
+    HexOctalBinary(i64),   // : Int
+    FractionalNumber(f64), // : Float
+    WholeNumber(i64),      // : Int | Float
+
+    // Collections
+    Array(Vec<Expr<'a>>),
+    Record(Vec<(&'a Name<'a>, &'a Expr<'a>)>),
+    Tuple(Vec<&'a Expr<'a>>),
+    LookupName(Name<'a>, Box<&'a Expr<'a>>),
     // TODO add record update
-    // TODO add conditional
-    // TODO add function
+
+    // Functions
+    Function(&'a Pattern<'a>, &'a Expr<'a>),
+    Call(Box<&'a Expr<'a>>, Box<&'a Expr<'a>>),
+    CallOperator(&'a Operator, Box<&'a Expr<'a>>, Box<&'a Expr<'a>>),
+
+    // Conditionals
+    If(Box<&'a Expr<'a>> /* Conditional */, Box<&'a Expr<'a>> /* True branch */, Box<&'a Expr<'a>> /* False branch */),
+    Case(Box<&'a Expr<'a>>, Vec<(&'a Pattern<'a>, &'a Expr<'a>)>),
 }
 
 #[derive(Debug, PartialEq)]
-pub enum Literal<'a> {
+pub enum Operator {
+    Plus, Minus, Star, Caret, Percent, FloatDivision, IntDivision,
+    GT, GTE, LT, LTE,
+    EQ, NE, And, Or,
+    QuestionMark, Or
+}
+
+#[derive(Debug, PartialEq)]
+pub enum Pattern<'a> {
+    Name(&'a Name<'a>),                // `foo =`
+    As(&'a Name<'a>, &'a Pattern<'a>), // `<pattern> as foo`
+    Type(&'a Type<'a>),
+    Symbol(&'a str),
     String(&'a str),
     Char(char),
-    Number(&'a str),
+    WholeNumber(&'a str),
+    FractionalNumber(&'a str),
     HexOctalBinary(&'a str),
-    Symbol(&'a str),
-    Array(Vec<Expr<'a>>),
-    Record(Vec<(Field<'a>, &'a Expr<'a>)>),
-    Tuple(Vec<&'a Expr<'a>>)
+    Tuple(Vec<Pattern<'a>>),
+    Record(Vec<(Name<'a>, Option<Pattern<'a>>)>), // { a = 5, b : Int as x, c }
 }
 
 
 pub fn infer<'a>(expr: &Expr<'a>) -> Result<Type<'a>, UnificationProblem> {
     match expr {
-        Expr::Literal(Literal::String(_)) => Ok(Type::String),
-        Expr::Literal(Literal::HexOctalBinary(_)) => Ok(Type::Int),
-        Expr::Literal(Literal::Char(_)) => Ok(Type::Char),
-        Expr::Literal(Literal::Number(_)) => Ok(Type::Number),
-        Expr::Literal(Literal::Symbol(sym)) => Ok(Type::Symbol(sym)),
-        Expr::Literal(Literal::Array(elem_exprs)) => {
+        Expr::String(_) => Ok(String),
+        Expr::Char(_) => Ok(Char),
+        Expr::HexOctalBinary(_) => Ok(Int),
+        Expr::FractionalNumber(_) => Ok(Float),
+        Expr::WholeNumber(_) => Ok(Number),
+        Expr::Symbol(sym) => Ok(Symbol(sym)),
+        Expr::Array(elem_exprs) => {
             let elem_type;
 
             if elem_exprs.is_empty() {
-                elem_type = Type::Unbound;
+                elem_type = Unbound;
             } else {
                 let mut unified_type = BTreeSet::new();
 
@@ -70,24 +106,24 @@ pub fn infer<'a>(expr: &Expr<'a>) -> Result<Type<'a>, UnificationProblem> {
                     // No point in storing a union of 1.
                     elem_type = unified_type.into_iter().next().unwrap()
                 } else {
-                    elem_type = Type::Union(unified_type)
+                    elem_type = Union(unified_type)
                 }
             }
 
-            Ok(Type::Array(Box::new(elem_type)))
+            Ok(Array(Box::new(elem_type)))
         },
-        Expr::Literal(Literal::Record(fields)) => {
-            let mut rec_type: Vec<(&'a str, Type<'a>)> = Vec::new();
+        Expr::Record(fields) => {
+            let mut rec_type: BTreeMap<&'a Name<'a>, Type<'a>> = BTreeMap::new();
 
             for (field, subexpr) in fields {
                 let field_type = infer(subexpr)?;
 
-                rec_type.push((&field, field_type));
+                rec_type.insert(&field, field_type);
             }
 
-            Ok(Type::Record(rec_type))
+            Ok(Record(rec_type))
         },
-        Expr::Literal(Literal::Tuple(exprs)) => {
+        Expr::Tuple(exprs) => {
             let mut tuple_type: Vec<Type<'a>> = Vec::new();
 
             for subexpr in exprs {
@@ -96,7 +132,7 @@ pub fn infer<'a>(expr: &Expr<'a>) -> Result<Type<'a>, UnificationProblem> {
                 tuple_type.push(field_type);
             }
 
-            Ok(Type::Tuple(tuple_type))
+            Ok(Tuple(tuple_type))
         },
         Expr::If(box cond, expr_if_true, expr_if_false) => {
             let cond_type = infer(&cond)?;
@@ -122,29 +158,197 @@ pub fn infer<'a>(expr: &Expr<'a>) -> Result<Type<'a>, UnificationProblem> {
                 // but we can pull it back out of the set
                 Ok(unified_type.into_iter().next().unwrap())
             } else {
-                Ok(Type::Union(unified_type))
+                Ok(Union(unified_type))
             }
         },
-        Expr::Assignment(ident, subexpr) => {
-            Ok(Type::Assignment(ident, Box::new(infer(subexpr)?)))
+        Call(func, arg) => {
+            
+        },
+        CallOperator(op, left_expr, right_expr) => {
+            let left = &(infer(left_expr)?);
+            let right = &(infer(right_expr)?);
+
+            match op {
+                Operator::EQ | Operator::NE | Operator::And | Operator::Or => {
+                    if types_match(left, right) {
+                        conform_to_bool(left)
+                    } else {
+                        Err(UnificationProblem::TypeMismatch)
+                    }
+                },
+                Operator::Plus | Operator::Minus | Operator::Star 
+                    | Operator::GT | Operator::LT | Operator::GTE | Operator::LTE 
+                    | Operator::Caret | Operator::Percent => {
+                    if types_match(left, right) {
+                        conform_to_number(left)
+                    } else {
+                        Err(UnificationProblem::TypeMismatch)
+                    }
+                },
+                Operator::FloatDivision => {
+                    if matches_float_type(left) && matches_float_type(right) {
+                        Ok(&Float)
+                    } else {
+                        Err(UnificationProblem::TypeMismatch)
+                    }
+                },
+                Operator::IntDivision => {
+                    if matches_int_type(left) && matches_int_type(right) {
+                        Ok(&Int)
+                    } else {
+                        Err(UnificationProblem::TypeMismatch)
+                    }
+                },
+                Operator::CombineStrings => {
+                    if matches_string_type(left) && matches_string_type(right) {
+                        Ok(&String)
+                    } else {
+                        Err(UnificationProblem::TypeMismatch)
+                    }
+                },
+                Operator::QuestionMark => {
+                    if types_match(left, right) {
+                        conform_to_optional(left)
+                    } else {
+                        Err(UnificationProblem::TypeMismatch)
                     }
                 }
+            }
+        },
+        Expr::Declaration(pattern, let_expr, in_expr) => {
+            // Think of this as a let..in even though syntactically it's not.
+            // We need to type-check the let-binding, but the type of the 
+            // *expression* we're expaning is only affected by the in-block.
+            check_pattern(&pattern, &let_expr)?;
+
+            infer(in_expr)
+        }
+    }
+}
+
+fn types_match<'a>(first: &'a Type<'a>, second: &'a Type<'a>) -> bool {
+    match (first, second) {
+        (Type::Union(first_types), Type::Union(second_types)) => {
+            // If any type is not directly present in the other union,
+            // it must at least match *some* type in the other union
+            first_types.difference(second_types).into_iter().all(|not_in_second_type| {
+                second_types.iter().any(|second_type| types_match(second_type, not_in_second_type))
+            }) &&
+            second_types.difference(first_types).into_iter().all(|not_in_first_type| {
+                first_types.iter().any(|first_type| types_match(first_type, not_in_first_type))
+            })
+        },
+
+        // Happy path: try these first, since we expect them to succeed.
+        // These are sorted based on a vague guess of how often they will be used in practice.
+        (Type::Symbol(sym_one), Type::Symbol(sym_two)) => sym_one == sym_two,
+        (Type::String, Type::String) => true,
+        (Type::Unbound, _) | (_, Type::Unbound)=> true,
+        (Type::Array(box elem_type_one), Type::Array(box elem_type_two)) => {
+            types_match(elem_type_one, elem_type_two)
+        },
+        (Type::Number, Type::Number) => true,
+        (Type::Number, other) => matches_number_type(other),
+        (other, Type::Number) => matches_number_type(other),
+        (Type::Int, Type::Int) => true,
+        (Type::Float, Type::Float) => true,
+        (Type::Tuple(first_elems), Type::Tuple(second_elems)) => {
+            // TODO verify that the elems and their types match up
+            // TODO write some scenarios to understand these better -
+            // like, what happens if you have a function that takes 
+            // a lambda whose argument takes an open record,
+            // and you pass a lamba whose argument takes *fewer* fields?
+            // that should work! the function is gonna pass it a lambda that
+            // has more fields than it needs.
+            // I think there's an element of directionality here that I'm
+            // disregarding. Maybe this function shouldn't commute.
+        },
+        (Type::Function(first_arg), Type::Function(second_arg)) => {
+            // TODO verify that the elems and their types match up
+        },
+        (Type::Record(first_fields), Type::Record(second_fields)) => {
+            // TODO verify that the fields and their types match up
+            // TODO what should happen if one is a superset of the other? fail?
+        },
+        (Type::Char, Type::Char) => true,
+
+        // Unhappy path - expect these to fail, so check them last
+        (Type::Union(first_types), _)  => {
+            first_types.iter().all(|typ| types_match(typ, second))
+        },
+        (_, Type::Union(second_types))  => {
+            second_types.iter().all(|typ| types_match(first, typ))
+        },
+        (Type::String, _) | (_, Type::String) => false,
+        (Type::Char, _) | (_, Type::Char) => false,
+        (Type::Int, _) | (_, Type::Int) => false,
+        (Type::Float, _) | (_, Type::Float) => false,
+        (Type::Symbol(_), _) | (_, Type::Symbol(_)) => false,
+        (Type::Array(_), _) | (_, Type::Array(_)) => false,
+        (Type::Record(_), _) | (_, Type::Record(_)) => false,
+        (Type::Tuple(_), _) | (_, Type::Tuple(_)) => false,
+        (Type::Function(_, _), _) | (_, Type::Function(_, _)) => false,
+    }
+}
+
+
+fn check_pattern<'a>(pattern: &'a Pattern<'a>, expr: &'a Expr<'a>) -> Result<(), UnificationProblem> {
+    let expr_type = infer(expr)?;
+
+    panic!("TODO check the pattern's type against expr_type, then write some tests for funky record pattern cases - this is our first real unification! Next one will be field access, ooooo - gonna want lots of tests for that")
 }
 
 const TRUE_SYMBOL_STR: &'static str = "True";
 const FALSE_SYMBOL_STR: &'static str = "False";
 
+pub fn matches_string_type<'a>(candidate: &Type<'a>) -> bool {
+    match candidate {
+        Unbound | String => true,
+        Type::Union(types) => {
+            types.iter().all(|typ| matches_string_type(typ))
+        },
+        _ => Err(UnificationProblem::TypeMismatch)
+    }
+}
+
 pub fn matches_bool_type<'a>(candidate: &Type<'a>) -> bool {
     match candidate {
-        Type::Symbol(str) => {
-            str == &TRUE_SYMBOL_STR || str == &FALSE_SYMBOL_STR
-        }
+        Type::Unbound => true,
+        Type::Symbol(str) => str == &TRUE_SYMBOL_STR || str == &FALSE_SYMBOL_STR,
         Type::Union(types) => {
-            types.len() <= 2 && types.iter().all(|typ| matches_bool_type(typ))
+            types.iter().all(|typ| matches_bool_type(typ))
         }
-        _ => {
-            false
+        _ => false
     }
+}
+
+pub fn matches_number_type<'a>(candidate: &Type<'a>) -> bool {
+    match candidate {
+        Type::Unbound | Type::Int | Type::Float | Type::Number => true,
+        Type::Union(types) => {
+            types.iter().all(|typ| matches_number_type(typ))
+        }
+        _ => false
+    }
+}
+
+pub fn matches_int_type<'a>(candidate: &Type<'a>) -> bool {
+    match candidate {
+        Type::Unbound | Type::Int => true,
+        Type::Union(types) => {
+            types.iter().all(|typ| matches_int_type(typ))
+        }
+        _ => false
+    }
+}
+
+pub fn matches_float_type<'a>(candidate: &Type<'a>) -> bool {
+    match candidate {
+        Type::Unbound | Type::Float => true,
+        Type::Union(types) => {
+            types.iter().all(|typ| matches_float_type(typ))
+        }
+        _ => false
     }
 }
 

tests/test_solve.rs

@@ -71,4 +71,16 @@ mod tests {
     fn int<'a>() -> Box<&'a Expr<'a>> { Box::new(&HexOctalBinary(0x12)) }
     fn float<'a>() -> Box<&'a Expr<'a>> { Box::new(&FractionalNumber(3.1)) }
     fn num<'a>() -> Box<&'a Expr<'a>> { Box::new(&WholeNumber(5)) }
+
+    // TODO test unions that ought to be equivalent, but only after
+    // a reduction of some sort, e.g.
+    //
+    // ((a|b)|c) vs (a|(b|c))
+    //
+    // ((a|z)|(b|z)) vs (a|b|z)
+    //
+    // ideally, we fix these when constructing unions
+    // e.g. if a user puts this in as an annotation, reduce it immediately
+    // and when we're inferring unions, always infer them flat.
+    // This way we can avoid checking recursively.
 }