ddlog_std.dl

/*
Copyright (c) 2021 VMware, Inc.
SPDX-License-Identifier: MIT

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/

/* Description: DDlog "standard library" automatically imported into every module */

import ddlog_rt
import ddlog_bigint

#[alias]
typedef u8   = bit<8>
#[alias]
typedef u16  = bit<16>
#[alias]
typedef u32  = bit<32>
#[alias]
typedef u64  = bit<64>
#[alias]
typedef u128 = bit<128>

typedef s8   = signed<8>
typedef s16  = signed<16>
typedef s32  = signed<32>
typedef s64  = signed<64>
typedef s128 = signed<128>

#[alias]
typedef usize = bit<64>
#[alias]
typedef isize = signed<64>

/*
 * Weight of a record in a DDlog collection.  This type is internal to the
 * DDlog engine and is only visible to the programmer inside the `Inspect`
 * operator.  Positive weight indicates that the record is being added
 * to a collection; negative weight corresponds to a deletion.
 */
typedef DDWeight = s64

/*
 * DDEpoch, DDIteration, and DDNestedTS types model DDlog timestamps.
 */

/* DDlog epoch.  An epoch, associated with each event inside DDlog, is the
 * serial number of the transaction that triggered this event.  This type is
 * internal to the DDlog engine and is only visible to the programmer inside
 * the `Inspect` operator. */
typedef DDEpoch = u64

/* Internal iteration number.  Events that occur inside recursive rules
 * are timestamped with an epoch and iteration number of the fixed point
 * computation within the epoch. */
typedef DDIteration = u64

/* Full nested timestamp consisting of an epoch and iteration number. */
typedef DDNestedTS = DDNestedTS {
    epoch: DDEpoch,
    iter: DDIteration
}

function to_string(ts: DDNestedTS): string {
    "(${ts.epoch},${ts.iter})"
}

/*
 * Type-erased representation of any DDlog value.  Allows storing
 * instances of different types, unknown at compile time, in the same
 * relation.
 *
 * Any value can be converted to `Any`.  Conversely A `Any` can be
 * converted back to the strongly typed representation.
 *
 * Note: `Any` relies on Rust's TypeId mechanism to order instances
 * with different underlying types.  As a result, the ordering may
 * differ across Rust compiler releases.
 */
extern type Any

/* Convert arbitrary DDlog type to Any. */
extern function to_any(#[by_val] x: 'T): Any

/* Convert `Any` back to an instance of type `'T`.
 * Returns `None` if `value` stores an instance of a
 * different type. */
extern function from_any(#[by_val] value: Any): Option<'T>

/*
 * Ref
 */
#[size=8]
#[shared_ref]
extern type Ref<'A>

extern function ref_new(#[by_val] x: 'A): Ref<'A>

#[return_by_ref]
extern function deref(x: Ref<'A>): 'A

/*
 * max(), min()
 */
function min(x: 'A, y: 'A): 'A = if (x < y) x else y
function max(x: 'A, y: 'A): 'A = if (x > y) x else y

/*
 * Arithmetic functions
 */
extern function u8_pow32(base: u8, exp: bit<32>): u8
extern function u16_pow32(base: u16, exp: bit<32>): u16
extern function u32_pow32(base: u32, exp: bit<32>): u32
extern function u64_pow32(base: u64, exp: bit<32>): u64
extern function u128_pow32(base: u128, exp: bit<32>): u128
extern function s8_pow32(base: s8, exp: bit<32>): s8
extern function s16_pow32(base: s16, exp: bit<32>): s16
extern function s32_pow32(base: s32, exp: bit<32>): s32
extern function s64_pow32(base: s64, exp: bit<32>): s64
extern function s128_pow32(base: s128, exp: bit<32>): s128
extern function bigint_pow32(base: bigint, exp: bit<32>): bigint

function pow32(base: u8, exp: bit<32>): u8 {
    u8_pow32(base, exp)
}
function pow32(base: u16, exp: bit<32>): u16 {
    u16_pow32(base, exp)
}
function pow32(base: u32, exp: bit<32>): u32 {
    u32_pow32(base, exp)
}
function pow32(base: u64, exp: bit<32>): u64 {
    u64_pow32(base, exp)
}
function pow32(base: u128, exp: bit<32>): u128 {
    u128_pow32(base, exp)
}
function pow32(base: s8, exp: bit<32>): s8 {
    s8_pow32(base, exp)
}
function pow32(base: s16, exp: bit<32>): s16 {
    s16_pow32(base, exp)
}
function pow32(base: s32, exp: bit<32>): s32 {
    s32_pow32(base, exp)
}
function pow32(base: s64, exp: bit<32>): s64 {
    s64_pow32(base, exp)
}
function pow32(base: s128, exp: bit<32>): s128 {
    s128_pow32(base, exp)
}
function pow32(base: bigint, exp: bit<32>): bigint {
    bigint_pow32(base, exp)
}

/*
 * Option
 */

#[rust="serde(from=\"::std::option::Option<A>\", into=\"::std::option::Option<A>\", bound(serialize=\"A: Clone+Serialize\"))"]
// This type has a custrom FromRecord implementation in std.rs.
#[custom_from_record]
typedef Option<'A> = None
                   | Some{x: 'A}

function is_none(x: Option<'A>): bool = {
    match (x) {
        None -> true,
        _    -> false
    }
}

function is_some(x: Option<'A>): bool = {
    match (x) {
        Some{} -> true,
        _      -> false
    }
}

/* Applies transformation `f` to the value stored inside `Option`.
 */
function map(opt: Option<'A>, f: function('A): 'B): Option<'B> {
    match (opt) {
        None -> None,
        Some{x} -> Some{f(x)}
    }
}

/* Returns default value of a type.
 */
extern function default(): 'T

/* Returns the contained `Some` value or a provided default.
 */
function unwrap_or(x: Option<'A>, def: 'A): 'A = {
    match (x) {
        Some{v} -> v,
        None -> def
    }
}

/* Returns the default value for the given type if `opt` is
 * `None`.
 */
function unwrap_or_default(#[by_val] opt: Option<'A>): 'A {
    option_unwrap_or_default(opt)
}

function to_set(o: Option<'X>): Set<'X> {
    match (o) {
        Some{x} -> set_singleton(x),
        None -> set_empty()
    }
}
function to_vec(o: Option<'X>): Vec<'X> {
    match (o) {
        Some{x} -> vec_singleton(x),
        None -> vec_empty()
    }
}

/* Transforms the `Option<'T>` into a `Result<'T, 'E>`,
 * mapping `Some{x}` to `Ok{v}` and `None` to `Err{e}`. */
function ok_or(o: Option<'T>, e: 'E): Result<'T, 'E> {
    match (o) {
        Some{x} -> Ok{x},
        None    -> Err{e}
    }
}

/* Transforms `Option<'T>` into `Result<'T, 'E>`, mapping `Some{x}
 * to `Ok{v}` and `None` to `Err{e()}`.
 * Function `e` is only evaluated on error. */
function ok_or_else(o: Option<'T>, e: function(): 'E): Result<'T, 'E> {
    match (o) {
        Some{x} -> Ok{x},
        None    -> Err{e()}
    }
}

/* Returns `None` if the option is `None`, otherwise calls `f` with the
 * wrapped value and returns the result.
 */
function and_then(o: Option<'T>, f: function('T): Option<'U>): Option<'U> {
    match (o) {
        None -> None,
        Some{x} -> f(x)
    }
}

/*
 * Either
 */
typedef Either<'A,'B> = Left{l: 'A}
                      | Right{r: 'B}

/*
 * Result
 */
typedef Result<'V,'E> = Ok{res: 'V}
                      | Err{err: 'E}

function is_ok(res: Result<'V,'E>): bool = {
    match (res) {
        Ok{} -> true,
        Err{} -> false
    }
}

function is_err(res: Result<'V,'E>): bool = {
    match (res) {
        Ok{} -> false,
        Err{} -> true
    }
}

/* Returns the contained Ok value or a provided default.
 */
function unwrap_or(res: Result<'V,'E>, def: 'V): 'V = {
    match (res) {
        Ok{v} -> v,
        Err{} -> def
    }
}

/* Returns the default value for the given type if `res` is
 * an error.
 */
function unwrap_or_default(#[by_val] res: Result<'V,'E>): 'V {
    result_unwrap_or_default(res)
}

/* Maps a `Result<'V1, 'E>` to `Result<'V2, 'E>` by applying a function to a
 * contained `Ok` value, leaving an `Err` value untouched.
 */
function map(res: Result<'V1, 'E>, f: function('V1): 'V2): Result<'V2, 'E> {
    match (res) {
        Err{e} -> Err{e},
        Ok{x} -> Ok{f(x)}
    }
}

/* Maps a `Result<'V, 'E1>` to `Result<'V, 'E2>` by applying a function to a
 * contained `Err` value, leaving an `Ok` value untouched.
 */
function map_err(res: Result<'V, 'E1>, f: function('E1): 'E2): Result<'V, 'E2> {
    match (res) {
        Err{e} -> Err{f(e)},
        Ok{x} -> Ok{x}
    }
}

/*
 * This function is deprecated; please use range_vec.
 *
 * Range; all values starting at 'from' and ending at 'to'
 * inclusively, in steps of 'step'.  'step' must be positive.
 */
//extern function range(from: 'A, to: 'A, step: 'A): Vec<'A>

/*
 * Range function that produces a vector.  The vector contains
 * all values starting at 'from' (inclusive) up to 'to' (exclusive),
 * in increments of 'step'.  If 'step' is zero the returned vector
 * is always empty.
 */
extern function range_vec(from: 'A, to: 'A, step: 'A): Vec<'A>

/* Convert any DDlog type into a string in a programmer-facing,
 * debugging context.  Implemented by calling the `Debug::fmt()`
 * method of the underlying Rust type. */
extern function to_string_debug(x: 'T): string

/*
 * String conversion
 */
function to_string(x: bool): string {
    __builtin_2string(x)
}
function to_string(x: bigint): string {
    __builtin_2string(x)
}
function to_string(x: float): string {
    __builtin_2string(x)
}
function to_string(x: double): string {
    __builtin_2string(x)
}
function to_string(x: s8): string {
    __builtin_2string(x)
}
function to_string(x: s16): string {
    __builtin_2string(x)
}
function to_string(x: s32): string {
    __builtin_2string(x)
}
function to_string(x: s64): string {
    __builtin_2string(x)
}
function to_string(x: s128): string {
    __builtin_2string(x)
}
function to_string(x: u8): string {
    __builtin_2string(x)
}
function to_string(x: u16): string {
    __builtin_2string(x)
}
function to_string(x: u32): string {
    __builtin_2string(x)
}
function to_string(x: u64): string {
    __builtin_2string(x)
}
function to_string(x: u128): string {
    __builtin_2string(x)
}
function to_string(x: string): string {
    __builtin_2string(x)
}

extern function hex(x: 'X): string

extern function parse_dec_u64(s: string): Option<bit<64>>
extern function parse_dec_i64(s: string): Option<signed<64>>

function contains(s1: string, s2: string): bool {
    string_contains(s1, s2)
}

function join(strings: Vec<string>, sep: string): string {
    string_join(strings, sep)
}

function len(s: string): usize {
    string_len(s)
}

/* Replaces all matches of `from` with `to`.
 *
 * `replace` creates a new string, and copies the data from `s` into it. While
 * doing so, it attempts to find matches of a pattern. If it finds any, it
 * replaces them with `to`.
 */

function replace(s: string, from: string, to: string): string {
    string_replace(s, from, to)
}

function split(s: string, sep: string): Vec<string> {
    string_split(s, sep)
}

function starts_with(s: string, prefix: string): bool {
    string_starts_with(s, prefix)
}

function ends_with(s: string, suffix: string): bool {
    string_ends_with(s, suffix)
}

// Convert a byte array into a string, returning Err if v contains any invalid data.
extern function from_utf8(buffer: Vec<u8>): Result<string, string>
// Returns Vec<u16> of the string encoded as UTF-16.
extern function encode_utf16(s: string): Vec<u16>
// Decode a UTF-16–encoded vector v into a String, returning Err if v contains any invalid data.
extern function from_utf16(buffer: Vec<u16>): Result<string, string>

/* Substring of `s` that begins at `start` and continues up to, but not
 * including, `end`.*/
function substr(s: string, start: usize, end: usize): string {
    string_substr(s, start, end)
}

// bytes comprising the utf-8 representation of the string
function to_bytes(s: string): Vec<u8> {
    string_to_bytes(s)
}

/* Returns a string slice with leading and trailing whitespace removed.
 *
 * 'Whitespace' is defined according to the terms of the Unicode Derived
 * Core Property White_Space
 */
function trim(s: string): string {
    string_trim(s)
}

/* Returns the lowercase equivalent of `s` as a new string.
 *
 * 'Lowercase' is defined according to the terms of the Unicode Derived
 * Core Property Lowercase.
 */
function to_lowercase(s: string): string {
    string_to_lowercase(s)
}

/* Returns the uppercase equivalent of `s` as a new string.
 */
function to_uppercase(s: string): string {
    string_to_uppercase(s)
}

function reverse(s: string): string {
    string_reverse(s)
}

/*
 * hashing
 */
extern function hash32(x: 'X): bit<32>
extern function hash64(x: 'X): bit<64>
extern function hash128(x: 'X): bit<128>

/* The `Group` type is used exclusively in aggregation operations.  It
 * represents a non-empty list of objects.
 * `'K` is the type of group key, and `'V` is the type of value in the group.
 */
#[iterate_by_val=iter:('V, ddlog_std::DDWeight)]
extern type Group<'K,'V>

/* Extracts group key.
 */
extern function group_key(g: Group<'K, 'V>): 'K

/*
 * Standard aggregates
 */

/* Returns the number of distinct elements in the group, which is guaranteed
 * to be >0. */
extern function group_count_distinct(g: Group<'K, 'V>): usize

/* Returns the first element of the group.
 * It always exists, as aggregation cannot return an empty group. */
extern function group_first(g: Group<'K, 'V>): 'V

/* Returns `n`th element of the group if the group is large enough
 * or `None` otherwise.
 */
extern function group_nth(g: Group<'K,'V>, n: usize): Option<'V>

extern function group_to_set(g: Group<'K, 'V>): Set<'V>
extern function group_to_vec(g: Group<'K, 'V>): Vec<'V>
extern function group_to_map(g: Group<'K1, ('K2,'V)>): Map<'K2,'V>
extern function group_to_setmap(g: Group<'K1, ('K2,'V)>): Map<'K2,Set<'V>>

extern function group_set_unions(g: Group<'K, Set<'A>>): Set<'A>

/* Optimized version of group_set_unions that, when the group consits of
 * a single set, simply returns the reference to this set. */
extern function group_setref_unions(g: Group<'K, Ref<Set<'A>>>): Ref<Set<'A>>

/* Smallest and largest group elements. */
extern function group_min(g: Group<'K, 'V>): 'V
extern function group_max(g: Group<'K, 'V>): 'V

function key(g: Group<'K, 'V>): 'K {
    group_key(g)
}

function count_distinct(g: Group<'K, 'V>): usize {
    group_count_distinct(g)
}

/* The first element of the group.  This operation is well defined,
 * as a group returned by `group-by` cannot be empty.
 *
 * Note: DDlog does not guarantee any specific ordering of elements withing
 * the group, e.g., the first element is not necessarily the smallest one. */
function first(g: Group<'K, 'V>): 'V {
    group_first(g)
}

/* Nth element of the group. */
function nth(g: Group<'K,'V>, n: usize): Option<'V> {
    group_nth(g, n)
}

/* Extract the set of group elements.  Since the group may contain duplicates,
 * the size of the resulting set can be smaller than the size of the group. */
function to_set(g: Group<'K, 'V>): Set<'V> {
    group_to_set(g)
}

/* Convert group to a vector of its elements.  The resulting
 * vector has the same size and the same elements (and in the same
 * order) as the group. */
function to_vec(g: Group<'K, 'V>): Vec<'V> {
    group_to_vec(g)
}

/* Convert a group of key-value tuples into a map. */
function to_map(g: Group<'K1, ('K2,'V)>): Map<'K2,'V> {
    group_to_map(g)
}

function to_setmap(g: Group<'K1, ('K2,'V)>): Map<'K2,Set<'V>> {
    group_to_setmap(g)
}

function group_unzip(g: Group<'K, ('X,'Y)>): (Vec<'X>, Vec<'Y>) = {
    var xs: Vec<'X> = vec_with_capacity(g.count_distinct());
    var ys: Vec<'Y> = vec_with_capacity(g.count_distinct());
    for ((v, _) in g) {
        (var x, var y) = v;
        vec_push(xs, x);
        vec_push(ys, y)
    };
    (xs,ys)
}

function union(g: Group<'K, Set<'A>>): Set<'A> {
    group_set_unions(g)
}

/* Obsolete; use `union(Group<_, Ref<Set<>>>)` instead. */
function setref_unions(g: Group<'K, Ref<Set<'A>>>): Ref<Set<'A>> {
    group_setref_unions(g)
}

function union(g: Group<'K, Ref<Set<'A>>>): Ref<Set<'A>> {
    group_setref_unions(g)
}

function min(g: Group<'K, 'V>): 'V {
    group_min(g)
}

function max(g: Group<'K, 'V>): 'V {
    group_max(g)
}

/*
 * Vec
 */
#[dyn_alloc]
#[iterate_by_ref=iter:'A]
extern type Vec<'A>

extern function vec_empty(): Vec<'A>
extern function vec_with_length(len: usize, x: 'A): Vec<'A>
extern function vec_with_capacity(len: usize): Vec<'A>
extern function vec_singleton(#[by_val] x: 'X): Vec<'X>

function len(v: Vec<'X>): usize {
    vec_len(v)
}

function push(v: mut Vec<'X>, #[by_val] x: 'X) {
    vec_push(v, x)
}

function pop(v: mut Vec<'X>): Option<'X> {
    vec_pop(v)
}

function append(v: mut Vec<'X>, other: Vec<'X>) {
    vec_append(v, other)
}

function push_imm(v: Vec<'X>, #[by_val] x: 'X): Vec<'X> {
    vec_push_imm(v, x)
}

function contains(v: Vec<'X>, x: 'X): bool {
    vec_contains(v, x)
}

function is_empty(v: Vec<'X>): bool {
    vec_is_empty(v)
}

function nth(v: Vec<'X>, n: usize): Option<'X> {
    vec_nth(v, n)
}

function to_set(#[by_val] s: Vec<'A>): Set<'A> {
    vec_to_set(s)
}

function sort(v: mut Vec<'X>) {
    vec_sort(v)
}

function sort_imm(#[by_val] v: Vec<'X>): Vec<'X> {
    vec_sort_imm(v)
}

function zip(#[by_val] v1: Vec<'X>, #[by_val] v2: Vec<'Y>): Vec<('X, 'Y)> {
    vec_zip(v1, v2)
}

function unzip(#[by_val] v: Vec<('X, 'Y)>): (Vec<'X>, Vec<'Y>) {
    vec_unzip(v)
}

/* Reverse vector in-place. */
function reverse(v: mut Vec<'X>) {
    vec_reverse(v)
}

/* Reverse `v`.  Return reversed vector, leaving the input vector unmodified. */
function reverse_imm(v: Vec<'X>): Vec<'X> {
    var res = v;
    res.reverse();
    res
}


/* Convert vector of tuple into a map.  Key-value pairs are added in the
 * order they occur in the input vector; hence the resulting map will
 * contain the last value associated with each key. */
function to_map(v: Vec<('K, 'V)>): Map<'K, 'V> {
    var res = map_empty();
    for (kv in v) {
       res.insert(kv.0, kv.1);
    };
    res
}

/* Resize vector.  If `new_size` is greater than `v.len()`, then
 * all new slots are filled with `value`. */
function resize(v: mut Vec<'X>, new_len: usize, value: 'X) {
    vec_resize(v, new_len, value)
}

/*
 * Shortens the vector, keeping the first `len` elements and dropping the rest.
 * If `len` is greater than the vector's current length, this has no effect.
 */
function truncate(v: mut Vec<'X>, len: usize) {
    vec_truncate(v, len)
}

/* Swap value at index `idx` for `value`.
 * Stores the old value at this index in `value` unless `idx` exceeds
 * the size of the vector (in which case the vector remains unmodified).
 * Returns true if the swap happened and false otherwise. */
function swap_nth(v: mut Vec<'X>, idx: usize, value: mut 'X): bool {
    vec_swap_nth(v, idx, value)
}

/* Set value at index `idx` to `value`.
 * If `idx` exceeds the size of the vector (in which case the vector remains unmodified).
 * Returns true if update happened and false otherwise. */
function update_nth(v: mut Vec<'X>, idx: usize, #[by_val] value: 'X): bool {
    vec_update_nth(v, idx, value)
}

/*
 * Map
 */

#[dyn_alloc]
#[iterate_by_val=iter:('K,'V)]
extern type Map<'K,'V>

extern function map_empty(): Map<'K, 'V>
extern function map_singleton(#[by_val] k: 'K, #[by_val] v: 'V): Map<'K, 'V>

function size(m: Map<'K, 'V>): usize {
    map_size(m)
}

function insert(m: mut Map<'K,'V>, #[by_val] k: 'K, #[by_val] v: 'V) {
    map_insert(m, k, v)
}

function remove(m: mut Map<'K,'V>, k: 'K): Option<'V> {
    map_remove(m, k)
}

function insert_imm(#[by_val] m: Map<'K,'V>, #[by_val] k: 'K, #[by_val] v: 'V): Map<'K,'V> {
    map_insert_imm(m, k, v)
}

function get(m: Map<'K,'V>, k:'K): Option<'V> {
    map_get(m, k)
}

function contains_key(m: Map<'K,'V>, k: 'K): bool {
    map_contains_key(m, k)
}

function is_empty(m: Map<'K,'V>): bool {
    map_is_empty(m)
}

/// If a key is present in both maps keep the one from m2
function union(#[by_val] m1: Map<'K, 'V>, #[by_val] m2: Map<'K,'V>): Map<'K, 'V> {
    map_union(m1, m2)
}

function keys(m: Map<'K, 'V>): Vec<'K> {
    map_keys(m)
}

function values(m: Map<'K, 'V>): Vec<'V> {
    map_values(m)
}

function nth_key(m: Map<'K, 'V>, n: usize): Option<'K> {
    map_nth_key(m, n)
}

function nth_value(m: Map<'K, 'V>, n: usize): Option<'V> {
    map_nth_value(m, n)
}

/*
 * Set
 */

#[dyn_alloc]
#[iterate_by_ref=iter:'A]
extern type Set<'A>

extern function set_singleton(#[by_val] x: 'X): Set<'X>
extern function set_empty(): Set<'X>

function size(s: Set<'X>): usize {
    set_size(s)
}

function insert(s: mut Set<'X>, #[by_val] v: 'X) {
    set_insert(s, v)
}

function insert_imm(#[by_val] s: Set<'X>, #[by_val] v: 'X): Set<'X> {
    set_insert_imm(s, v)
}

function contains(s: Set<'X>, v: 'X): bool {
    set_contains(s, v)
}

function is_empty(s: Set<'X>): bool {
    set_is_empty(s)
}

function nth(s: Set<'X>, n: usize): Option<'X> {
    set_nth(s, n)
}

function to_vec(s: Set<'A>): Vec<'A> {
    set_to_vec(s)
}

function union(s1: Set<'X>, s2: Set<'X>): Set<'X> {
    set_union(s1, s2)
}

/* Obsolete; use `union(Vec<Set<>>)` instead. */
function unions(sets: Vec<Set<'X>>): Set<'X> {
    set_unions(sets)
}

function union(sets: Vec<Set<'X>>): Set<'X> {
    set_unions(sets)
}

function intersection(s1: Set<'X>, s2: Set<'X>): Set<'X> {
    set_intersection(s1, s2)
}

function difference(s1: Set<'X>, s2: Set<'X>): Set<'X> {
    set_difference(s1, s2)
}

/*
 * Endianness
 */
extern function ntohl(x: bit<32>): bit<32>
extern function ntohs(x: bit<16>): bit<16>

extern function htonl(x: bit<32>): bit<32>
extern function htons(x: bit<16>): bit<16>

/*
 * Internals
 *
 * We currently don't have a way to selectively export functions, but the use of
 * these functions outside of this module is discouraged.
 */

extern function option_unwrap_or_default(#[by_val] opt: Option<'A>): 'A
extern function result_unwrap_or_default(#[by_val] res: Result<'V,'E>): 'V

extern function string_contains(s1: string, s2: string): bool
extern function string_join(strings: Vec<string>, sep: string): string
extern function string_len(s: string): usize
extern function string_to_lowercase(s: string): string
extern function str_to_lower(s: string): string
extern function string_replace(s: string, from: string, to: string): string
extern function string_split(s: string, sep: string): Vec<string>
extern function string_starts_with(s: string, prefix: string): bool
extern function string_ends_with(s: string, suffix: string): bool
extern function string_substr(s: string, start: usize, end: usize): string
// bytes comprising the utf-8 representation of the string
extern function string_to_bytes(s: string): Vec<u8>
extern function string_trim(s: string): string
extern function string_to_uppercase(s: string): string
extern function string_reverse(s: string): string

extern function vec_len(v: Vec<'X>): usize
extern function vec_push(v: mut Vec<'X>, #[by_val] x: 'X)
extern function vec_pop(v: mut Vec<'X>): Option<'X>
extern function vec_append(v: mut Vec<'X>, other: Vec<'X>)
extern function vec_push_imm(v: Vec<'X>, #[by_val] x: 'X): Vec<'X>
extern function vec_contains(v: Vec<'X>, x: 'X): bool
extern function vec_is_empty(v: Vec<'X>): bool
extern function vec_nth(v: Vec<'X>, n: usize): Option<'X>
extern function vec_to_set(#[by_val] s: Vec<'A>): Set<'A>
extern function vec_sort(v: mut Vec<'X>)
extern function vec_sort_imm(#[by_val] v: Vec<'X>): Vec<'X>
extern function vec_resize(v: mut Vec<'X>, new_len: usize, value: 'X)
extern function vec_truncate(v: mut Vec<'X>, len: usize)
extern function vec_swap_nth(v: mut Vec<'X>, idx: usize, value: mut 'X): bool
extern function vec_update_nth(v: mut Vec<'X>, idx: usize, #[by_val] value: 'X): bool
extern function vec_zip(#[by_val] v1: Vec<'X>, #[by_val] v2: Vec<'Y>): Vec<('X, 'Y)>
extern function vec_unzip(#[by_val] v: Vec<('X, 'Y)>): (Vec<'X>, Vec<'Y>)
extern function vec_reverse(v: mut Vec<'X>)

extern function map_size(m: Map<'K, 'V>): usize
extern function map_insert(m: mut Map<'K,'V>, #[by_val] k: 'K, #[by_val] v: 'V)
extern function map_remove(m: mut Map<'K,'V>, k: 'K): Option<'V>
extern function map_insert_imm(#[by_val] m: Map<'K,'V>, #[by_val] k: 'K, #[by_val] v: 'V): Map<'K,'V>
extern function map_get(m: Map<'K,'V>, k:'K): Option<'V>
extern function map_contains_key(m: Map<'K,'V>, k: 'K): bool
extern function map_is_empty(m: Map<'K,'V>): bool
extern function map_nth_key(m: Map<'K, 'V>, n: usize): Option<'K>
extern function map_nth_value(m: Map<'K, 'V>, n: usize): Option<'V>
extern function map_union(#[by_val] m1: Map<'K, 'V>, #[by_val] m2: Map<'K,'V>): Map<'K, 'V>
extern function map_keys(m: Map<'K, 'V>): Vec<'K>
extern function map_values(m: Map<'K, 'V>): Vec<'V>

extern function set_size(s: Set<'X>): usize
extern function set_insert(s: mut Set<'X>, #[by_val] v: 'X)
extern function set_insert_imm(#[by_val] s: Set<'X>, #[by_val] v: 'X): Set<'X>
extern function set_contains(s: Set<'X>, v: 'X): bool
extern function set_is_empty(s: Set<'X>): bool
extern function set_nth(s: Set<'X>, n: usize): Option<'X>
extern function set_to_vec(#[by_val] s: Set<'A>): Vec<'A>
extern function set_union(#[by_val] s1: Set<'X>, #[by_val] s2: Set<'X>): Set<'X>
extern function set_unions(#[by_val] sets: Vec<Set<'X>>): Set<'X>
extern function set_intersection(s1: Set<'X>, s2: Set<'X>): Set<'X>
extern function set_difference(s1: Set<'X>, s2: Set<'X>): Set<'X>

extern function __builtin_2string(x: 'X): string

/* Representation of a group used for all I/O
 * (serialization, formatting, (Into/From)Record, Flatbuf).
 *
 * This is part of DDlog internals and should not be used in
 * application code. */
typedef DDlogGroup<'K, 'V> = DDlogGroup {
    key: 'K,
    vals: Vec<('V, DDWeight)>
}

/* Unique ID of a node or a sink in a distributed DDlog system. */
typedef D3logLocationId = u128

relation Singleton()
Singleton().