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use proptest::{
arbitrary::{any, any_with, arbitrary_with},
strategy::{Strategy, ValueTree},
test_runner::TestRunner,
};
use rand::{rngs::SmallRng, Rng, RngCore, SeedableRng};
use serde::{Deserialize, Serialize};
use std::collections::HashMap;
use crate::ast::*;
#[derive(Debug, PartialEq)]
pub struct Environment<'a> {
parent: Box<Option<&'a Environment<'a>>>,
bindings: HashMap<String, Value>,
}
impl<'a> Environment<'a> {
pub fn new() -> Self {
Environment {
parent: Box::new(None),
bindings: HashMap::new(),
}
}
fn bind(&mut self, var: &str, value: &Value) {
self.bindings.insert(var.to_string(), value.clone());
}
fn extends(&'a self) -> Self {
Environment {
parent: Box::new(Some(self)),
bindings: HashMap::new(),
}
}
fn lookup(&self, var: &str) -> Option<&Value> {
self.bindings.get(var).or_else(|| match *self.parent {
Some(parent) => parent.lookup(var),
None => None,
})
}
}
impl<'a> Default for Environment<'a> {
fn default() -> Self {
Self::new()
}
}
pub fn eval_all(values: &[Value]) -> Vec<Value> {
let mut env = Environment::new();
values.iter().map(|v| eval_whnf(v, &mut env)).collect()
}
/// Reduce the given value to weak head normal form using call-by-name
/// evaluation strategy.
///
/// call-by-name reduces the leftmost outermost redex first, which is
/// not under a lambda abstraction.
pub fn eval_whnf(arg: &Value, env: &mut Environment) -> Value {
match arg {
Value::Def(var, value) => {
env.bind(var, value);
Value::Bool(true) // TODO: return a more meaningful value?
}
Value::Let(var, value, expr) => {
let mut newenv = env.extends();
newenv.bind(var, value);
eval_whnf(expr, &mut newenv)
}
Value::App(l, r) => match eval_whnf(l, env) {
Value::Lam(v, body) => eval_whnf(&subst(&v, &body, r), env),
Value::Sym(var) => match env.lookup(&var) {
Some(val) => eval_whnf(&Value::App(Box::new(val.clone()), r.clone()), env),
None => arg.clone(),
},
other => Value::App(Box::new(other), r.clone()),
},
Value::Sym(var) => env.lookup(var).unwrap_or(arg).clone(),
other => other.clone(),
}
}
fn subst(var: &str, body: &Value, e: &Value) -> Value {
match body {
Value::Sym(x) if x == var => e.clone(),
Value::Lam(x, b) if x == var => {
let y = gensym();
let bd = subst(x, b, &Value::Sym(y.clone()));
Value::Lam(y, Box::new(bd))
}
Value::Lam(x, b) => Value::Lam(x.to_string(), Box::new(subst(var, b, e))),
Value::App(l, r) => Value::App(Box::new(subst(var, l, e)), Box::new(subst(var, r, e))),
other => other.clone(),
}
}
fn gensym() -> String {
let mut rng = rand::thread_rng();
let n1: u8 = rng.gen();
format!("x_{}", n1)
}
pub fn generate_expr(size: u32, runner: &mut TestRunner) -> Value {
match size {
0 | 1 => {
let n = any::<u16>().new_tree(runner).unwrap().current();
Value::Num(n.into())
}
2 => Value::Sym(identifier().new_tree(runner).unwrap().current()),
_ => todo!(),
}
}
#[cfg(test)]
mod lambda_test {
use crate::parser::parse;
use super::{eval_all, eval_whnf, Environment, Value};
fn parse1(string: &str) -> Value {
parse(string).pop().unwrap()
}
fn eval1(value: &Value) -> Value {
eval_whnf(value, &mut Environment::new())
}
#[test]
fn evaluating_a_non_reducible_value_yields_itself() {
let value = parse1("(foo 12)");
assert_eq!(value, eval1(&value));
}
#[test]
fn evaluating_application_on_an_abstraction_reduces_it() {
let value = parse1("((lam x x) 12)");
assert_eq!(Value::Num(12), eval1(&value));
}
#[test]
fn substitution_occurs_within_abstraction_body() {
let value = parse1("(((lam x (lam y x)) 13) 12)");
assert_eq!(Value::Num(13), eval1(&value));
}
#[test]
fn substitution_occurs_within_application_body() {
let value = parse1("(((lam x (lam y (y x))) 13) 12)");
assert_eq!(
Value::App(Box::new(Value::Num(12)), Box::new(Value::Num(13))),
eval1(&value)
);
}
#[test]
fn substitution_does_not_capture_free_variables() {
let value = parse1("(((lam x (lam x x)) 13) 12)");
assert_eq!(Value::Num(12), eval1(&value));
}
#[test]
fn interpretation_applies_to_both_sides_of_application() {
let value = parse1("((lam x x) ((lam x x) 12))");
assert_eq!(Value::Num(12), eval1(&value));
}
#[test]
fn reduction_is_applied_until_normal_form_is_reached() {
let value = parse1("((((lam y (lam x (lam y (x y)))) 13) (lam x x)) 11)");
assert_eq!(Value::Num(11), eval1(&value));
}
#[test]
fn reduction_always_select_leftmost_outermost_redex() {
// this should not terminate if we evaluate the rightmost redex first, eg.
// applicative order reduction
let value = parse1("((lam x 1) ((lam x (x x)) (lam x (x x))))");
assert_eq!(Value::Num(1), eval1(&value));
}
#[test]
fn defined_symbols_are_evaluated_to_their_definition() {
let values = parse("(def foo 12) foo");
assert_eq!(vec![Value::Bool(true), Value::Num(12)], eval_all(&values));
}
#[test]
fn let_expressions_bind_symbol_to_expression_in_environment() {
let values = parse("(let (foo (lam x x)) (foo 12))");
assert_eq!(vec![Value::Num(12)], eval_all(&values));
}
#[test]
fn let_expressions_introduce_new_scope_for_bindings() {
let values = parse("(let (foo (lam x x)) ((let (foo foo) foo) 13))");
assert_eq!(vec![Value::Num(13)], eval_all(&values));
}
#[test]
fn bound_symbol_in_higher_scope_are_resolved() {
let values = parse("(let (id (lam x x)) (let (foo 12) (id foo)))");
assert_eq!(vec![Value::Num(12)], eval_all(&values));
}
}
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