1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
|
#![warn(missing_docs)]
//! This crate implements some recursion schemes in Rust.
//!
//! The name "receme" is a mix of "Recursion Scheme".
//!
//! See [this series of five blog
//! articles](https://blog.sumtypeofway.com/posts/introduction-to-recursion-schemes.html)
//! for an introduction to recursion schemes, and see [this series of
//! three articles](https://recursion.wtf/posts/rust_schemes/) for
//! where I got inspired to write this library.
//!
//! Note that, since Rust does not have higher-kinded polymorphism, it
//! is sometimes cumbersome to implement some notions, though.
//!
//! # Another crate
//!
//! The author of the above-mentionned three-article series has
//! already implemented the recursion schemes in Rust, in [this
//! repository](https://github.com/inanna-malick/recursion), so why do
//! it myself?
//!
//! One reason is that I want my package to not depend on anything
//! other than the default Rust toolchains. This is perhaps not a
//! very convincing reason, but I just want to do so.
//!
//! Another reason is that I want the design to be modular: if there
//! is another crate that provides a similar functionality, I can
//! quickly switch the underlying mechanism to adopt to the new crate
//! instead.
//!
//! Consequently I decided to write this library, and provide a
//! default implementation. This way by default the package does not
//! depend on external crates, and if so demanded, can switch to use
//! an external crate instantaneously, at least hopefully.
// The following modules are for traits.
pub mod algebra;
pub mod catana;
pub mod coalgebra;
pub mod coralgebra;
pub mod functor;
pub mod hylo;
pub mod parapo;
pub mod ralgebra;
// pub mod futhis;
// The following modules are for default implementations.
pub mod tree;
// TODO: benchmarks
#[cfg(test)]
mod test_expr_tree {
use super::{
catana::{Ana, Cata},
functor::Functor,
hylo::Hylo,
tree::{DFTree, TEStrategy, Tree, TreeIndex},
};
// Just for testing const generics and fixed size arrays, that is
// to say, just for fun.
// fn demo<T, const N: usize>(v: Vec<T>) -> Result<[T; N], String> {
// v.try_into()
// .map_err(|v: Vec<T>| format!("expected a vector of length {N}, but got {}", v.len()))
// }
// #[test]
// fn test_demo() -> Result<(), String> {
// let v: Vec<usize> = vec![1, 2, 3];
// let w: Vec<usize> = vec![1, 2];
// assert_eq!(demo::<_, 2>(w)?, [1, 2]);
// assert_eq!(demo::<_, 3>(v)?, [1, 2, 3]);
// Ok(())
// }
#[derive(Debug, Clone)]
enum Expr<T> {
Add(T, T),
Lit(isize),
}
impl<T> Functor<T> for Expr<T> {
type Target<S> = Expr<S>;
fn fmap<S>(self, mut f: impl FnMut(T) -> S) -> Self::Target<S> {
match self {
Expr::Add(a, b) => Expr::Add(f(a), f(b)),
Expr::Lit(value) => Expr::Lit(value),
}
}
}
#[test]
fn test_cata() {
/// This is an Expr-algebra, but only for a specific type,
/// `isize`.
fn eval(expr: Expr<isize>) -> isize {
match expr {
Expr::Add(a, b) => a + b,
Expr::Lit(value) => value,
}
}
/// Use a temporary function to construct a tree.
///
/// Should use an anamorphism for this purpose, later.
fn construct_tree() -> Tree<Expr<TreeIndex>> {
use Expr::{Add, Lit};
let strategy: TEStrategy = TEStrategy::UnsafeArena;
// This represents the following expression
//
// Add(1, Add(3, Add(10, -1))).
let elements = vec![
Add(1, 2).fmap(TreeIndex::new),
Lit(1),
Add(3, 4).fmap(TreeIndex::new),
Lit(3),
Add(5, 6).fmap(TreeIndex::new),
Lit(10),
Lit(-1),
];
Tree::new(elements, strategy)
}
let tree = construct_tree();
let result = tree.cata(eval);
assert_eq!(result, 13isize);
}
#[test]
fn test_ana() {
// Just a ugly hack, haha.
let mut vector: Vec<Expr<TreeIndex>> = vec![
Expr::Add(1, 2).fmap(TreeIndex::new),
Expr::Lit(1),
Expr::Add(3, 4).fmap(TreeIndex::new),
Expr::Lit(3),
Expr::Add(5, 6).fmap(TreeIndex::new),
Expr::Lit(10),
Expr::Lit(-14),
];
let mut vector1: Vec<Expr<TreeIndex>> = vec![
Expr::Add(1, 2).fmap(TreeIndex::new),
Expr::Lit(1),
Expr::Add(3, 4).fmap(TreeIndex::new),
Expr::Lit(3),
Expr::Add(5, 6).fmap(TreeIndex::new),
Expr::Lit(10),
Expr::Lit(-14),
];
let mut tree = Tree::ana(TreeIndex::new(0), |value: TreeIndex| {
// This is safe since we visit each valid node exactly
// once.
std::mem::replace(&mut vector[*value], Expr::Lit(0))
});
tree.set_strategy(TEStrategy::UnsafeArena);
let tree = tree;
println!("tree is {tree:#?}");
let result = tree.cata(|expr| match expr {
Expr::Add(a, b) => a + b,
Expr::Lit(v) => v,
});
assert_eq!(result, 0);
// test df_tree
let dftree = DFTree::ana(TreeIndex::new(0), |value: TreeIndex| {
// This is safe since we visit each valid node exactly
// once.
std::mem::replace(&mut vector1[*value], Expr::Lit(0))
});
let tree = dftree.to_tree();
println!("dftree = {tree:#?}");
let result = tree.cata(|expr| match expr {
Expr::Add(a, b) => a + b,
Expr::Lit(v) => v,
});
assert_eq!(result, 0);
}
#[test]
fn test_hylo() {
// Again using the ugly hack
let vector: Vec<Expr<TreeIndex>> = vec![
Expr::Add(1, 2).fmap(TreeIndex::new),
Expr::Lit(1),
Expr::Add(3, 4).fmap(TreeIndex::new),
Expr::Lit(3),
Expr::Add(5, 6).fmap(TreeIndex::new),
Expr::Lit(10),
Expr::Lit(14),
];
fn eval_expr(mut v: Vec<Expr<TreeIndex>>) -> isize {
Tree::hylo(
TreeIndex::new(0),
|expr| match expr {
Expr::Add(a, b) => a + b,
Expr::Lit(v) => v,
},
|value: TreeIndex| std::mem::replace(&mut v[*value], Expr::Lit(0)),
)
}
assert_eq!(eval_expr(vector), 28);
}
}
|
