roc/compiler/builtins/src/std.rs

use roc_collections::all::{default_hasher, MutMap, MutSet};
use roc_module::ident::TagName;
use roc_module::symbol::Symbol;
use roc_region::all::Region;
use roc_types::builtin_aliases::{
    bool_type, dict_type, float_type, int_type, list_type, nat_type, num_type, ordering_type,
    result_type, set_type, str_type, u64_type,
};
use roc_types::solved_types::SolvedType;
use roc_types::subs::VarId;
use std::collections::HashMap;

#[derive(Clone, Copy, Debug)]
pub enum Mode {
    Standard,
    Uniqueness,
}

#[derive(Debug, Clone)]
pub struct StdLib {
    pub mode: Mode,
    pub types: MutMap<Symbol, (SolvedType, Region)>,
    pub applies: MutSet<Symbol>,
}

pub fn standard_stdlib() -> StdLib {
    StdLib {
        mode: Mode::Standard,
        types: types(),
        applies: vec![
            Symbol::LIST_LIST,
            Symbol::SET_SET,
            Symbol::DICT_DICT,
            Symbol::STR_STR,
        ]
        .into_iter()
        .collect(),
    }
}

/// Keep this up to date by hand! It's the number of builtin aliases that are imported by default.
const NUM_BUILTIN_IMPORTS: usize = 7;

/// These can be shared between definitions, they will get instantiated when converted to Type
const TVAR1: VarId = VarId::from_u32(1);
const TVAR2: VarId = VarId::from_u32(2);
const TVAR3: VarId = VarId::from_u32(3);
const TVAR4: VarId = VarId::from_u32(4);
const TOP_LEVEL_CLOSURE_VAR: VarId = VarId::from_u32(5);

pub fn types() -> MutMap<Symbol, (SolvedType, Region)> {
    let mut types = HashMap::with_capacity_and_hasher(NUM_BUILTIN_IMPORTS, default_hasher());

    let mut add_type = |symbol, typ| {
        debug_assert!(
            !types.contains_key(&symbol),
            "Duplicate type definition for {:?}",
            symbol
        );

        // TODO instead of using Region::zero for all of these,
        // instead use the Region where they were defined in their
        // source .roc files! This can give nicer error messages.
        types.insert(symbol, (typ, Region::zero()));
    };

    // Num module

    // add or (+) : Num a, Num a -> Num a
    add_type(
        Symbol::NUM_ADD,
        top_level_function(
            vec![num_type(flex(TVAR1)), num_type(flex(TVAR1))],
            Box::new(num_type(flex(TVAR1))),
        ),
    );

    fn overflow() -> SolvedType {
        SolvedType::TagUnion(
            vec![(TagName::Global("Overflow".into()), vec![])],
            Box::new(SolvedType::Wildcard),
        )
    }

    // addChecked : Num a, Num a -> Result (Num a) [ Overflow ]*
    add_type(
        Symbol::NUM_ADD_CHECKED,
        top_level_function(
            vec![num_type(flex(TVAR1)), num_type(flex(TVAR1))],
            Box::new(result_type(num_type(flex(TVAR1)), overflow())),
        ),
    );

    // addWrap : Int range, Int range -> Int range
    add_type(
        Symbol::NUM_ADD_WRAP,
        top_level_function(
            vec![int_type(flex(TVAR1)), int_type(flex(TVAR1))],
            Box::new(int_type(flex(TVAR1))),
        ),
    );

    // sub or (-) : Num a, Num a -> Num a
    add_type(
        Symbol::NUM_SUB,
        top_level_function(
            vec![num_type(flex(TVAR1)), num_type(flex(TVAR1))],
            Box::new(num_type(flex(TVAR1))),
        ),
    );

    // subWrap : Int range, Int range -> Int range
    add_type(
        Symbol::NUM_SUB_WRAP,
        top_level_function(
            vec![int_type(flex(TVAR1)), int_type(flex(TVAR1))],
            Box::new(int_type(flex(TVAR1))),
        ),
    );

    // subChecked : Num a, Num a -> Result (Num a) [ Overflow ]*
    add_type(
        Symbol::NUM_SUB_CHECKED,
        top_level_function(
            vec![num_type(flex(TVAR1)), num_type(flex(TVAR1))],
            Box::new(result_type(num_type(flex(TVAR1)), overflow())),
        ),
    );

    // mul or (*) : Num a, Num a -> Num a
    add_type(
        Symbol::NUM_MUL,
        top_level_function(
            vec![num_type(flex(TVAR1)), num_type(flex(TVAR1))],
            Box::new(num_type(flex(TVAR1))),
        ),
    );

    // mulWrap : Int range, Int range -> Int range
    add_type(
        Symbol::NUM_MUL_WRAP,
        top_level_function(
            vec![int_type(flex(TVAR1)), int_type(flex(TVAR1))],
            Box::new(int_type(flex(TVAR1))),
        ),
    );

    // mulChecked : Num a, Num a -> Result (Num a) [ Overflow ]*
    add_type(
        Symbol::NUM_MUL_CHECKED,
        top_level_function(
            vec![num_type(flex(TVAR1)), num_type(flex(TVAR1))],
            Box::new(result_type(num_type(flex(TVAR1)), overflow())),
        ),
    );

    // abs : Num a -> Num a
    add_type(
        Symbol::NUM_ABS,
        top_level_function(vec![num_type(flex(TVAR1))], Box::new(num_type(flex(TVAR1)))),
    );

    // neg : Num a -> Num a
    add_type(
        Symbol::NUM_NEG,
        top_level_function(vec![num_type(flex(TVAR1))], Box::new(num_type(flex(TVAR1)))),
    );

    // isEq or (==) : a, a -> Bool
    add_type(
        Symbol::BOOL_EQ,
        top_level_function(vec![flex(TVAR1), flex(TVAR1)], Box::new(bool_type())),
    );

    // isNeq or (!=) : a, a -> Bool
    add_type(
        Symbol::BOOL_NEQ,
        top_level_function(vec![flex(TVAR1), flex(TVAR1)], Box::new(bool_type())),
    );

    // isLt or (<) : Num a, Num a -> Bool
    add_type(
        Symbol::NUM_LT,
        top_level_function(
            vec![num_type(flex(TVAR1)), num_type(flex(TVAR1))],
            Box::new(bool_type()),
        ),
    );

    // isLte or (<=) : Num a, Num a -> Bool
    add_type(
        Symbol::NUM_LTE,
        top_level_function(
            vec![num_type(flex(TVAR1)), num_type(flex(TVAR1))],
            Box::new(bool_type()),
        ),
    );

    // isGt or (>) : Num a, Num a -> Bool
    add_type(
        Symbol::NUM_GT,
        top_level_function(
            vec![num_type(flex(TVAR1)), num_type(flex(TVAR1))],
            Box::new(bool_type()),
        ),
    );

    // isGte or (>=) : Num a, Num a -> Bool
    add_type(
        Symbol::NUM_GTE,
        top_level_function(
            vec![num_type(flex(TVAR1)), num_type(flex(TVAR1))],
            Box::new(bool_type()),
        ),
    );

    // compare : Num a, Num a -> [ LT, EQ, GT ]
    add_type(
        Symbol::NUM_COMPARE,
        top_level_function(
            vec![num_type(flex(TVAR1)), num_type(flex(TVAR1))],
            Box::new(ordering_type()),
        ),
    );

    // toFloat : Num * -> Float *
    add_type(
        Symbol::NUM_TO_FLOAT,
        top_level_function(
            vec![num_type(flex(TVAR1))],
            Box::new(float_type(flex(TVAR2))),
        ),
    );

    // isNegative : Num a -> Bool
    add_type(
        Symbol::NUM_IS_NEGATIVE,
        top_level_function(vec![num_type(flex(TVAR1))], Box::new(bool_type())),
    );

    // isPositive : Num a -> Bool
    add_type(
        Symbol::NUM_IS_POSITIVE,
        top_level_function(vec![num_type(flex(TVAR1))], Box::new(bool_type())),
    );

    // isZero : Num a -> Bool
    add_type(
        Symbol::NUM_IS_ZERO,
        top_level_function(vec![num_type(flex(TVAR1))], Box::new(bool_type())),
    );

    // isEven : Num a -> Bool
    add_type(
        Symbol::NUM_IS_EVEN,
        top_level_function(vec![num_type(flex(TVAR1))], Box::new(bool_type())),
    );

    // isOdd : Num a -> Bool
    add_type(
        Symbol::NUM_IS_ODD,
        top_level_function(vec![num_type(flex(TVAR1))], Box::new(bool_type())),
    );

    // maxInt : Int range
    add_type(Symbol::NUM_MAX_INT, int_type(flex(TVAR1)));

    // minInt : Int range
    add_type(Symbol::NUM_MIN_INT, int_type(flex(TVAR1)));

    // div : Int, Int -> Result Int [ DivByZero ]*
    let div_by_zero = SolvedType::TagUnion(
        vec![(TagName::Global("DivByZero".into()), vec![])],
        Box::new(SolvedType::Wildcard),
    );

    add_type(
        Symbol::NUM_DIV_INT,
        top_level_function(
            vec![int_type(flex(TVAR1)), int_type(flex(TVAR1))],
            Box::new(result_type(int_type(flex(TVAR1)), div_by_zero.clone())),
        ),
    );

    // bitwiseAnd : Int a, Int a -> Int a
    add_type(
        Symbol::NUM_BITWISE_AND,
        top_level_function(
            vec![int_type(flex(TVAR1)), int_type(flex(TVAR1))],
            Box::new(int_type(flex(TVAR1))),
        ),
    );

    // bitwiseXor : Int a, Int a -> Int a
    add_type(
        Symbol::NUM_BITWISE_XOR,
        top_level_function(
            vec![int_type(flex(TVAR1)), int_type(flex(TVAR1))],
            Box::new(int_type(flex(TVAR1))),
        ),
    );

    // rem : Int a, Int a -> Result (Int a) [ DivByZero ]*
    add_type(
        Symbol::NUM_REM,
        top_level_function(
            vec![int_type(flex(TVAR1)), int_type(flex(TVAR1))],
            Box::new(result_type(int_type(flex(TVAR1)), div_by_zero.clone())),
        ),
    );

    // mod : Int a, Int a -> Result (Int a) [ DivByZero ]*
    add_type(
        Symbol::NUM_MOD_INT,
        top_level_function(
            vec![int_type(flex(TVAR1)), int_type(flex(TVAR1))],
            Box::new(result_type(int_type(flex(TVAR1)), div_by_zero.clone())),
        ),
    );

    // Float module

    // div : Float a, Float a -> Float a
    add_type(
        Symbol::NUM_DIV_FLOAT,
        top_level_function(
            vec![float_type(flex(TVAR1)), float_type(flex(TVAR1))],
            Box::new(result_type(float_type(flex(TVAR1)), div_by_zero.clone())),
        ),
    );

    // mod : Float a, Float a -> Result (Float a) [ DivByZero ]*
    add_type(
        Symbol::NUM_MOD_FLOAT,
        top_level_function(
            vec![float_type(flex(TVAR1)), float_type(flex(TVAR1))],
            Box::new(result_type(float_type(flex(TVAR1)), div_by_zero)),
        ),
    );

    // sqrt : Float a -> Float a
    let sqrt_of_negative = SolvedType::TagUnion(
        vec![(TagName::Global("SqrtOfNegative".into()), vec![])],
        Box::new(SolvedType::Wildcard),
    );

    add_type(
        Symbol::NUM_SQRT,
        top_level_function(
            vec![float_type(flex(TVAR1))],
            Box::new(result_type(float_type(flex(TVAR1)), sqrt_of_negative)),
        ),
    );

    // round : Float a -> Int b
    add_type(
        Symbol::NUM_ROUND,
        top_level_function(
            vec![float_type(flex(TVAR1))],
            Box::new(int_type(flex(TVAR2))),
        ),
    );

    // sin : Float a -> Float a
    add_type(
        Symbol::NUM_SIN,
        top_level_function(
            vec![float_type(flex(TVAR1))],
            Box::new(float_type(flex(TVAR1))),
        ),
    );

    // cos : Float a -> Float a
    add_type(
        Symbol::NUM_COS,
        top_level_function(
            vec![float_type(flex(TVAR1))],
            Box::new(float_type(flex(TVAR1))),
        ),
    );

    // tan : Float a -> Float a
    add_type(
        Symbol::NUM_TAN,
        top_level_function(
            vec![float_type(flex(TVAR1))],
            Box::new(float_type(flex(TVAR1))),
        ),
    );

    // maxFloat : Float a
    add_type(Symbol::NUM_MAX_FLOAT, float_type(flex(TVAR1)));

    // minFloat : Float a
    add_type(Symbol::NUM_MIN_FLOAT, float_type(flex(TVAR1)));

    // pow : Float a, Float a -> Float a
    add_type(
        Symbol::NUM_POW,
        top_level_function(
            vec![float_type(flex(TVAR1)), float_type(flex(TVAR1))],
            Box::new(float_type(flex(TVAR1))),
        ),
    );

    // ceiling : Float a -> Int b
    add_type(
        Symbol::NUM_CEILING,
        top_level_function(
            vec![float_type(flex(TVAR1))],
            Box::new(int_type(flex(TVAR2))),
        ),
    );

    // powInt : Int a, Int a -> Int a
    add_type(
        Symbol::NUM_POW_INT,
        top_level_function(
            vec![int_type(flex(TVAR1)), int_type(flex(TVAR1))],
            Box::new(int_type(flex(TVAR1))),
        ),
    );

    // floor : Float a -> Int b
    add_type(
        Symbol::NUM_FLOOR,
        top_level_function(
            vec![float_type(flex(TVAR1))],
            Box::new(int_type(flex(TVAR2))),
        ),
    );

    // atan : Float a -> Float a
    add_type(
        Symbol::NUM_ATAN,
        top_level_function(
            vec![float_type(flex(TVAR1))],
            Box::new(float_type(flex(TVAR1))),
        ),
    );

    // acos : Float a -> Float a
    add_type(
        Symbol::NUM_ACOS,
        top_level_function(
            vec![float_type(flex(TVAR1))],
            Box::new(float_type(flex(TVAR1))),
        ),
    );

    // asin : Float a -> Float a
    add_type(
        Symbol::NUM_ASIN,
        top_level_function(
            vec![float_type(flex(TVAR1))],
            Box::new(float_type(flex(TVAR1))),
        ),
    );

    // Bool module

    // and : Bool, Bool -> Bool
    add_type(
        Symbol::BOOL_AND,
        top_level_function(vec![bool_type(), bool_type()], Box::new(bool_type())),
    );

    // or : Bool, Bool -> Bool
    add_type(
        Symbol::BOOL_OR,
        top_level_function(vec![bool_type(), bool_type()], Box::new(bool_type())),
    );

    // xor : Bool, Bool -> Bool
    add_type(
        Symbol::BOOL_XOR,
        top_level_function(vec![bool_type(), bool_type()], Box::new(bool_type())),
    );

    // not : Bool -> Bool
    add_type(
        Symbol::BOOL_NOT,
        top_level_function(vec![bool_type()], Box::new(bool_type())),
    );

    // Str module

    // Str.split : Str, Str -> List Str
    add_type(
        Symbol::STR_SPLIT,
        top_level_function(
            vec![str_type(), str_type()],
            Box::new(list_type(str_type())),
        ),
    );

    // Str.concat : Str, Str -> Str
    add_type(
        Symbol::STR_CONCAT,
        top_level_function(vec![str_type(), str_type()], Box::new(str_type())),
    );

    // Str.joinWith : List Str, Str -> Str
    add_type(
        Symbol::STR_JOIN_WITH,
        top_level_function(
            vec![list_type(str_type()), str_type()],
            Box::new(str_type()),
        ),
    );

    // isEmpty : Str -> Bool
    add_type(
        Symbol::STR_IS_EMPTY,
        top_level_function(vec![str_type()], Box::new(bool_type())),
    );

    // startsWith : Str, Str -> Bool
    add_type(
        Symbol::STR_STARTS_WITH,
        top_level_function(vec![str_type(), str_type()], Box::new(bool_type())),
    );

    // endsWith : Str, Str -> Bool
    add_type(
        Symbol::STR_ENDS_WITH,
        top_level_function(vec![str_type(), str_type()], Box::new(bool_type())),
    );

    // countGraphemes : Str -> Nat
    add_type(
        Symbol::STR_COUNT_GRAPHEMES,
        top_level_function(vec![str_type()], Box::new(nat_type())),
    );

    // fromInt : Int a -> Str
    add_type(
        Symbol::STR_FROM_INT,
        top_level_function(vec![int_type(flex(TVAR1))], Box::new(str_type())),
    );

    // fromFloat : Float a -> Str
    add_type(
        Symbol::STR_FROM_FLOAT,
        top_level_function(vec![float_type(flex(TVAR1))], Box::new(str_type())),
    );

    // List module

    // get : List elem, Nat -> Result elem [ OutOfBounds ]*
    let index_out_of_bounds = SolvedType::TagUnion(
        vec![(TagName::Global("OutOfBounds".into()), vec![])],
        Box::new(SolvedType::Wildcard),
    );

    add_type(
        Symbol::LIST_GET,
        top_level_function(
            vec![list_type(flex(TVAR1)), nat_type()],
            Box::new(result_type(flex(TVAR1), index_out_of_bounds)),
        ),
    );

    // first : List elem -> Result elem [ ListWasEmpty ]*
    let list_was_empty = SolvedType::TagUnion(
        vec![(TagName::Global("ListWasEmpty".into()), vec![])],
        Box::new(SolvedType::Wildcard),
    );

    add_type(
        Symbol::LIST_FIRST,
        top_level_function(
            vec![list_type(flex(TVAR1))],
            Box::new(result_type(flex(TVAR1), list_was_empty.clone())),
        ),
    );

    // last : List elem -> Result elem [ ListWasEmpty ]*
    add_type(
        Symbol::LIST_LAST,
        top_level_function(
            vec![list_type(flex(TVAR1))],
            Box::new(result_type(flex(TVAR1), list_was_empty)),
        ),
    );

    // set : List elem, Nat, elem -> List elem
    add_type(
        Symbol::LIST_SET,
        top_level_function(
            vec![list_type(flex(TVAR1)), nat_type(), flex(TVAR1)],
            Box::new(list_type(flex(TVAR1))),
        ),
    );

    // concat : List elem, List elem -> List elem
    add_type(
        Symbol::LIST_CONCAT,
        top_level_function(
            vec![list_type(flex(TVAR1)), list_type(flex(TVAR1))],
            Box::new(list_type(flex(TVAR1))),
        ),
    );

    // contains : List elem, elem -> Bool
    add_type(
        Symbol::LIST_CONTAINS,
        top_level_function(
            vec![list_type(flex(TVAR1)), flex(TVAR1)],
            Box::new(bool_type()),
        ),
    );

    // sum :  List (Num a) -> Num a
    add_type(
        Symbol::LIST_SUM,
        top_level_function(
            vec![list_type(num_type(flex(TVAR1)))],
            Box::new(num_type(flex(TVAR1))),
        ),
    );

    // walk : List elem, (elem -> accum -> accum), accum -> accum
    add_type(
        Symbol::LIST_WALK,
        top_level_function(
            vec![
                list_type(flex(TVAR1)),
                closure(vec![flex(TVAR1), flex(TVAR2)], TVAR3, Box::new(flex(TVAR2))),
                flex(TVAR2),
            ],
            Box::new(flex(TVAR2)),
        ),
    );

    // walkBackwards : List elem, (elem -> accum -> accum), accum -> accum
    add_type(
        Symbol::LIST_WALK_BACKWARDS,
        top_level_function(
            vec![
                list_type(flex(TVAR1)),
                closure(vec![flex(TVAR1), flex(TVAR2)], TVAR3, Box::new(flex(TVAR2))),
                flex(TVAR2),
            ],
            Box::new(flex(TVAR2)),
        ),
    );

    // keepIf : List elem, (elem -> Bool) -> List elem
    add_type(
        Symbol::LIST_KEEP_IF,
        top_level_function(
            vec![
                list_type(flex(TVAR1)),
                closure(vec![flex(TVAR1)], TVAR2, Box::new(bool_type())),
            ],
            Box::new(list_type(flex(TVAR1))),
        ),
    );

    // map : List before, (before -> after) -> List after
    add_type(
        Symbol::LIST_MAP,
        top_level_function(
            vec![
                list_type(flex(TVAR1)),
                closure(vec![flex(TVAR1)], TVAR3, Box::new(flex(TVAR2))),
            ],
            Box::new(list_type(flex(TVAR2))),
        ),
    );

    // append : List elem, elem -> List elem
    add_type(
        Symbol::LIST_APPEND,
        top_level_function(
            vec![list_type(flex(TVAR1)), flex(TVAR1)],
            Box::new(list_type(flex(TVAR1))),
        ),
    );

    // prepend : List elem, elem -> List elem
    add_type(
        Symbol::LIST_PREPEND,
        top_level_function(
            vec![list_type(flex(TVAR1)), flex(TVAR1)],
            Box::new(list_type(flex(TVAR1))),
        ),
    );

    // join : List (List elem) -> List elem
    add_type(
        Symbol::LIST_JOIN,
        top_level_function(
            vec![list_type(list_type(flex(TVAR1)))],
            Box::new(list_type(flex(TVAR1))),
        ),
    );

    // single : a -> List a
    add_type(
        Symbol::LIST_SINGLE,
        top_level_function(vec![flex(TVAR1)], Box::new(list_type(flex(TVAR1)))),
    );

    // repeat : Nat, elem -> List elem
    add_type(
        Symbol::LIST_REPEAT,
        top_level_function(
            vec![nat_type(), flex(TVAR1)],
            Box::new(list_type(flex(TVAR1))),
        ),
    );

    // reverse : List elem -> List elem
    add_type(
        Symbol::LIST_REVERSE,
        top_level_function(
            vec![list_type(flex(TVAR1))],
            Box::new(list_type(flex(TVAR1))),
        ),
    );

    // len : List * -> Nat
    add_type(
        Symbol::LIST_LEN,
        top_level_function(vec![list_type(flex(TVAR1))], Box::new(nat_type())),
    );

    // isEmpty : List * -> Bool
    add_type(
        Symbol::LIST_IS_EMPTY,
        top_level_function(vec![list_type(flex(TVAR1))], Box::new(bool_type())),
    );

    // Dict module

    // Dict.hashTestOnly : Nat, v -> Nat
    add_type(
        Symbol::DICT_TEST_HASH,
        top_level_function(vec![u64_type(), flex(TVAR2)], Box::new(nat_type())),
    );

    // len : Dict * * -> Nat
    add_type(
        Symbol::DICT_LEN,
        top_level_function(
            vec![dict_type(flex(TVAR1), flex(TVAR2))],
            Box::new(nat_type()),
        ),
    );

    // empty : Dict * *
    add_type(Symbol::DICT_EMPTY, dict_type(flex(TVAR1), flex(TVAR2)));

    // singleton : k, v -> Dict k v
    add_type(
        Symbol::DICT_SINGLETON,
        top_level_function(
            vec![flex(TVAR1), flex(TVAR2)],
            Box::new(dict_type(flex(TVAR1), flex(TVAR2))),
        ),
    );

    // get : Dict k v, k -> Result v [ KeyNotFound ]*
    let key_not_found = SolvedType::TagUnion(
        vec![(TagName::Global("KeyNotFound".into()), vec![])],
        Box::new(SolvedType::Wildcard),
    );

    add_type(
        Symbol::DICT_GET,
        top_level_function(
            vec![dict_type(flex(TVAR1), flex(TVAR2)), flex(TVAR1)],
            Box::new(result_type(flex(TVAR2), key_not_found)),
        ),
    );

    // Dict.insert : Dict k v, k, v -> Dict k v
    add_type(
        Symbol::DICT_INSERT,
        top_level_function(
            vec![
                dict_type(flex(TVAR1), flex(TVAR2)),
                flex(TVAR1),
                flex(TVAR2),
            ],
            Box::new(dict_type(flex(TVAR1), flex(TVAR2))),
        ),
    );

    // Dict.remove : Dict k v, k -> Dict k v
    add_type(
        Symbol::DICT_REMOVE,
        top_level_function(
            vec![dict_type(flex(TVAR1), flex(TVAR2)), flex(TVAR1)],
            Box::new(dict_type(flex(TVAR1), flex(TVAR2))),
        ),
    );

    // Dict.contains : Dict k v, k -> Bool
    add_type(
        Symbol::DICT_CONTAINS,
        top_level_function(
            vec![dict_type(flex(TVAR1), flex(TVAR2)), flex(TVAR1)],
            Box::new(bool_type()),
        ),
    );

    // Dict.keys : Dict k v -> List k
    add_type(
        Symbol::DICT_KEYS,
        top_level_function(
            vec![dict_type(flex(TVAR1), flex(TVAR2))],
            Box::new(list_type(flex(TVAR1))),
        ),
    );

    // Dict.values : Dict k v -> List v
    add_type(
        Symbol::DICT_VALUES,
        top_level_function(
            vec![dict_type(flex(TVAR1), flex(TVAR2))],
            Box::new(list_type(flex(TVAR2))),
        ),
    );

    // Dict.union : Dict k v, Dict k v -> Dict k v
    add_type(
        Symbol::DICT_UNION,
        top_level_function(
            vec![
                dict_type(flex(TVAR1), flex(TVAR2)),
                dict_type(flex(TVAR1), flex(TVAR2)),
            ],
            Box::new(dict_type(flex(TVAR1), flex(TVAR2))),
        ),
    );

    // Dict.intersection : Dict k v, Dict k v -> Dict k v
    add_type(
        Symbol::DICT_INTERSECTION,
        top_level_function(
            vec![
                dict_type(flex(TVAR1), flex(TVAR2)),
                dict_type(flex(TVAR1), flex(TVAR2)),
            ],
            Box::new(dict_type(flex(TVAR1), flex(TVAR2))),
        ),
    );

    // Dict.difference : Dict k v, Dict k v -> Dict k v
    add_type(
        Symbol::DICT_DIFFERENCE,
        top_level_function(
            vec![
                dict_type(flex(TVAR1), flex(TVAR2)),
                dict_type(flex(TVAR1), flex(TVAR2)),
            ],
            Box::new(dict_type(flex(TVAR1), flex(TVAR2))),
        ),
    );

    // Dict.walk : Dict k v, (k, v, accum -> accum), accum -> accum
    add_type(
        Symbol::DICT_WALK,
        top_level_function(
            vec![
                dict_type(flex(TVAR1), flex(TVAR2)),
                closure(
                    vec![flex(TVAR1), flex(TVAR2), flex(TVAR3)],
                    TVAR4,
                    Box::new(flex(TVAR3)),
                ),
                flex(TVAR3),
            ],
            Box::new(flex(TVAR3)),
        ),
    );

    // Set module

    // empty : Set a
    add_type(Symbol::SET_EMPTY, set_type(flex(TVAR1)));

    // singleton : a -> Set a
    add_type(
        Symbol::SET_SINGLETON,
        top_level_function(vec![flex(TVAR1)], Box::new(set_type(flex(TVAR1)))),
    );

    // len : Set * -> Nat
    add_type(
        Symbol::SET_LEN,
        top_level_function(vec![set_type(flex(TVAR1))], Box::new(nat_type())),
    );

    // toList : Set a -> List a
    add_type(
        Symbol::SET_TO_LIST,
        top_level_function(
            vec![set_type(flex(TVAR1))],
            Box::new(list_type(flex(TVAR1))),
        ),
    );

    // fromList : Set a -> List a
    add_type(
        Symbol::SET_FROM_LIST,
        top_level_function(
            vec![list_type(flex(TVAR1))],
            Box::new(set_type(flex(TVAR1))),
        ),
    );

    // union : Set a, Set a -> Set a
    add_type(
        Symbol::SET_UNION,
        top_level_function(
            vec![set_type(flex(TVAR1)), set_type(flex(TVAR1))],
            Box::new(set_type(flex(TVAR1))),
        ),
    );

    // difference : Set a, Set a -> Set a
    add_type(
        Symbol::SET_DIFFERENCE,
        top_level_function(
            vec![set_type(flex(TVAR1)), set_type(flex(TVAR1))],
            Box::new(set_type(flex(TVAR1))),
        ),
    );

    // intersection : Set a, Set a -> Set a
    add_type(
        Symbol::SET_INTERSECTION,
        top_level_function(
            vec![set_type(flex(TVAR1)), set_type(flex(TVAR1))],
            Box::new(set_type(flex(TVAR1))),
        ),
    );

    // Set.walk : Set a, (a, b -> b), b -> b
    add_type(
        Symbol::SET_WALK,
        top_level_function(
            vec![
                set_type(flex(TVAR1)),
                closure(vec![flex(TVAR1), flex(TVAR2)], TVAR3, Box::new(flex(TVAR2))),
                flex(TVAR2),
            ],
            Box::new(flex(TVAR2)),
        ),
    );

    add_type(
        Symbol::SET_INSERT,
        top_level_function(
            vec![set_type(flex(TVAR1)), flex(TVAR1)],
            Box::new(set_type(flex(TVAR1))),
        ),
    );

    add_type(
        Symbol::SET_REMOVE,
        top_level_function(
            vec![set_type(flex(TVAR1)), flex(TVAR1)],
            Box::new(set_type(flex(TVAR1))),
        ),
    );

    add_type(
        Symbol::SET_CONTAINS,
        top_level_function(
            vec![set_type(flex(TVAR1)), flex(TVAR1)],
            Box::new(bool_type()),
        ),
    );

    // Result module

    // map : Result a err, (a -> b) -> Result b err
    add_type(
        Symbol::RESULT_MAP,
        top_level_function(
            vec![
                result_type(flex(TVAR1), flex(TVAR3)),
                closure(vec![flex(TVAR1)], TVAR4, Box::new(flex(TVAR2))),
            ],
            Box::new(result_type(flex(TVAR2), flex(TVAR3))),
        ),
    );

    // mapErr : Result a x, (x -> y) -> Result a x
    add_type(
        Symbol::RESULT_MAP_ERR,
        top_level_function(
            vec![
                result_type(flex(TVAR1), flex(TVAR3)),
                closure(vec![flex(TVAR3)], TVAR4, Box::new(flex(TVAR2))),
            ],
            Box::new(result_type(flex(TVAR1), flex(TVAR2))),
        ),
    );

    // withDefault : Result a x, a -> a
    add_type(
        Symbol::RESULT_WITH_DEFAULT,
        top_level_function(
            vec![result_type(flex(TVAR1), flex(TVAR3)), flex(TVAR1)],
            Box::new(flex(TVAR1)),
        ),
    );

    types
}

#[inline(always)]
fn flex(tvar: VarId) -> SolvedType {
    SolvedType::Flex(tvar)
}

#[inline(always)]
fn top_level_function(arguments: Vec<SolvedType>, ret: Box<SolvedType>) -> SolvedType {
    SolvedType::Func(
        arguments,
        Box::new(SolvedType::Flex(TOP_LEVEL_CLOSURE_VAR)),
        ret,
    )
}

#[inline(always)]
fn closure(arguments: Vec<SolvedType>, closure_var: VarId, ret: Box<SolvedType>) -> SolvedType {
    SolvedType::Func(arguments, Box::new(SolvedType::Flex(closure_var)), ret)
}