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
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
//! Quantification of type / length parameters.

use core::mem;

use crate::{
    alloc::{hash_map::Entry, vec, HashMap, HashSet, Vec},
    types::{FnParams, ParamConstraints},
    visit::{self, Visit, VisitMut},
    Function, Object, PrimitiveType, Tuple, Type, UnknownLen,
};

#[derive(Debug, Default)]
struct ParamStats {
    mentioning_fns: HashSet<usize>,
}

#[derive(Debug, Clone, Copy)]
struct FunctionInfo {
    parent: usize,
    depth: usize,
}

#[derive(Debug, Default)]
struct ParamQuantifierOutput {
    type_params: HashMap<usize, ParamStats>,
    len_params: HashMap<usize, ParamStats>,
    functions: Vec<FunctionInfo>,
}

impl ParamQuantifierOutput {
    fn place_params<Prim>(self, constraints: ParamConstraints<Prim>) -> ParamPlacement<Prim>
    where
        Prim: PrimitiveType,
    {
        let functions = &self.functions;
        ParamPlacement::new(
            Self::place_params_of_certain_kind(functions, self.type_params),
            Self::place_params_of_certain_kind(functions, self.len_params),
            constraints,
        )
    }

    fn place_param(functions: &[FunctionInfo], stats: ParamStats) -> usize {
        let depths = stats.mentioning_fns.iter().map(|&idx| functions[idx].depth);
        let max_depth = depths
            .clone()
            .max()
            .expect("A param must be mentioned at least once by construction");
        let min_depth = depths
            .min()
            .expect("A param must be mentioned at least once by construction");

        // Group mentions by function depth.
        let mut mentions_by_depth: Vec<HashSet<_>> =
            vec![HashSet::new(); max_depth + 1 - min_depth];
        for idx in stats.mentioning_fns {
            let depth = functions[idx].depth;
            mentions_by_depth[depth - min_depth].insert(idx);
        }

        // Map functions to parents until we have a single function on top.
        let mut depth = max_depth;
        while depth > min_depth {
            let indexes = mentions_by_depth.pop().unwrap();
            let prev_level = mentions_by_depth.last_mut().unwrap();
            prev_level.extend(indexes.into_iter().map(|idx| functions[idx].parent));
            depth -= 1;
        }

        let mut level = mentions_by_depth.pop().unwrap();
        debug_assert!(mentions_by_depth.is_empty());
        while level.len() > 1 {
            level = level.into_iter().map(|idx| functions[idx].parent).collect();
        }
        level.into_iter().next().unwrap()
    }

    fn place_params_of_certain_kind(
        functions: &[FunctionInfo],
        params: HashMap<usize, ParamStats>,
    ) -> HashMap<usize, Vec<usize>> {
        let placements = params
            .into_iter()
            .map(|(idx, stats)| (idx, Self::place_param(functions, stats)));
        let mut params: HashMap<_, Vec<_>> = HashMap::new();
        for (idx, fn_idx) in placements {
            params.entry(fn_idx).or_default().push(idx);
        }

        for function_params in params.values_mut() {
            function_params.sort_unstable();
        }

        params
    }
}

#[derive(Debug)]
pub(crate) struct ParamQuantifier<'a, Prim: PrimitiveType> {
    constraints: &'a ParamConstraints<Prim>,
    output: ParamQuantifierOutput,
    current_function_idx: usize,
    current_function_depth: usize,
}

impl<'a, Prim: PrimitiveType> ParamQuantifier<'a, Prim> {
    fn new(constraints: &'a ParamConstraints<Prim>) -> Self {
        Self {
            constraints,
            output: ParamQuantifierOutput::default(),
            current_function_idx: usize::MAX, // immediately overridden
            current_function_depth: 0,        // immediately overridden
        }
    }

    fn object_constraint(&self, var_idx: usize) -> Option<&'a Object<Prim>> {
        let constraints = self.constraints.type_params.get(&var_idx)?;
        constraints.object.as_ref()
    }

    pub fn fill_params(function: &mut Function<Prim>, constraints: ParamConstraints<Prim>) {
        let mut analyzer = ParamQuantifier::new(&constraints);
        analyzer.visit_function(function);
        let mut placement = analyzer.output.place_params(constraints);
        placement.visit_function_mut(function);
    }
}

impl<Prim: PrimitiveType> Visit<Prim> for ParamQuantifier<'_, Prim> {
    fn visit_type(&mut self, ty: &Type<Prim>) {
        match ty {
            Type::Var(var) if !var.is_free() => {
                let entry = self.output.type_params.entry(var.index());
                let is_new_var = matches!(entry, Entry::Vacant(_));
                let stats = entry.or_default();
                stats.mentioning_fns.insert(self.current_function_idx);

                if is_new_var {
                    // Visit object constraints only on the first var encounter, both to save time
                    // and to prevent infinite recursion for recursive constraints.
                    if let Some(object) = self.object_constraint(var.index()) {
                        self.visit_object(object);
                    }
                }
            }
            _ => visit::visit_type(self, ty),
        }
    }

    fn visit_tuple(&mut self, tuple: &Tuple<Prim>) {
        let (_, middle, _) = tuple.parts();
        let middle_len = middle.and_then(|middle| middle.len().components().0);
        let Some(middle_len) = middle_len else {
            visit::visit_tuple(self, tuple);
            return;
        };

        if let UnknownLen::Var(var) = middle_len {
            if !var.is_free() {
                let stats = self.output.len_params.entry(var.index()).or_default();
                stats.mentioning_fns.insert(self.current_function_idx);
            }
        }
        visit::visit_tuple(self, tuple);
    }

    fn visit_function(&mut self, function: &Function<Prim>) {
        let this_function_idx = self.output.functions.len();
        let old_function_idx = mem::replace(&mut self.current_function_idx, this_function_idx);

        self.output.functions.push(FunctionInfo {
            parent: old_function_idx,
            depth: self.current_function_depth,
        });
        self.current_function_depth += 1;

        visit::visit_function(self, function);

        self.current_function_idx = old_function_idx;
        self.current_function_depth -= 1;
    }
}

#[derive(Debug)]
struct ParamPlacement<Prim: PrimitiveType> {
    // Grouped by function index.
    type_params: HashMap<usize, Vec<usize>>,
    // Grouped by function index.
    len_params: HashMap<usize, Vec<usize>>,
    function_count: usize,
    current_function_idx: usize,
    constraints: ParamConstraints<Prim>,
}

impl<Prim: PrimitiveType> ParamPlacement<Prim> {
    fn new(
        type_params: HashMap<usize, Vec<usize>>,
        len_params: HashMap<usize, Vec<usize>>,
        constraints: ParamConstraints<Prim>,
    ) -> Self {
        Self {
            type_params,
            len_params,
            function_count: 0,
            current_function_idx: usize::MAX,
            constraints,
        }
    }
}

impl<Prim: PrimitiveType> VisitMut<Prim> for ParamPlacement<Prim> {
    // TODO: what if the params are already present on the `function`?
    fn visit_function_mut(&mut self, function: &mut Function<Prim>) {
        let this_function_idx = self.function_count;
        let old_function_idx = mem::replace(&mut self.current_function_idx, this_function_idx);
        self.function_count += 1;

        visit::visit_function_mut(self, function);

        let mut params = FnParams::default();
        if let Some(type_params) = self.type_params.remove(&self.current_function_idx) {
            params.type_params = type_params
                .into_iter()
                .map(|idx| {
                    let constraints = self
                        .constraints
                        .type_params
                        .get(&idx)
                        .cloned()
                        .unwrap_or_default();
                    (idx, constraints)
                })
                .collect();
        }
        if let Some(len_params) = self.len_params.remove(&self.current_function_idx) {
            params.len_params = len_params
                .into_iter()
                .map(|idx| {
                    let is_static = self.constraints.static_lengths.contains(&idx);
                    (idx, is_static)
                })
                .collect();
        }
        if this_function_idx == 0 {
            // Root function; set constraints.
            params.constraints = Some(mem::take(&mut self.constraints));
        }

        function.set_params(params);

        self.current_function_idx = old_function_idx;
    }
}

#[cfg(test)]
mod tests {
    use core::iter;

    use super::*;
    use crate::{
        alloc::ToString,
        arith::{CompleteConstraints, Num},
        Object,
    };

    #[test]
    fn analyzing_map_fn() {
        let map_arg = Function::builder()
            .with_arg(Type::param(0))
            .returning(Type::param(1));
        let mut map_fn = <Function>::builder()
            .with_arg(Type::param(0).repeat(UnknownLen::param(0)))
            .with_arg(map_arg)
            .returning(Type::param(1).repeat(UnknownLen::param(0)));

        let constraints = ParamConstraints::default();
        let mut analyzer = ParamQuantifier::new(&constraints);
        analyzer.visit_function(&map_fn);
        let analyzer = analyzer.output;

        assert_eq!(analyzer.functions.len(), 2);
        assert_eq!(analyzer.functions[0].parent, usize::MAX);
        assert_eq!(analyzer.functions[0].depth, 0);
        assert_eq!(analyzer.functions[1].parent, 0);
        assert_eq!(analyzer.functions[1].depth, 1);

        let mut both_fn_indexes = HashSet::new();
        both_fn_indexes.extend(vec![0_usize, 1]);
        assert_eq!(analyzer.type_params.len(), 2);
        assert_eq!(analyzer.type_params[&0].mentioning_fns, both_fn_indexes);
        assert_eq!(analyzer.type_params[&1].mentioning_fns, both_fn_indexes);

        assert_eq!(analyzer.len_params.len(), 1);
        let mut root_fn_index = HashSet::new();
        root_fn_index.insert(0);
        assert_eq!(analyzer.len_params[&0].mentioning_fns, root_fn_index);

        let mut placement = analyzer.place_params(constraints);
        let expected_type_params: HashMap<_, _> = iter::once((0, vec![0, 1])).collect();
        assert_eq!(placement.type_params, expected_type_params);
        let expected_len_params: HashMap<_, _> = iter::once((0, vec![0])).collect();
        assert_eq!(placement.len_params, expected_len_params);

        placement.visit_function_mut(&mut map_fn);
        assert_eq!(map_fn.to_string(), "(['T; N], ('T) -> 'U) -> ['U; N]");
    }

    #[test]
    fn params_are_added_from_object_constraints() {
        let obj: Object<Num> = Object::from([("x", Type::param(1))]);
        let constraints = CompleteConstraints {
            object: Some(obj),
            ..CompleteConstraints::default()
        };
        let constraints = ParamConstraints {
            type_params: iter::once((0, constraints)).collect(),
            static_lengths: HashSet::new(),
        };

        let identity_fn = Function::builder()
            .with_arg(Type::param(0))
            .returning(Type::param(0));

        let mut analyzer = ParamQuantifier::new(&constraints);
        analyzer.visit_function(&identity_fn);
        let analyzer = analyzer.output;

        assert_eq!(analyzer.functions.len(), 1);
        assert_eq!(analyzer.type_params.len(), 2);
        let expected_fns: HashSet<_> = iter::once(0).collect();
        assert_eq!(analyzer.type_params[&0].mentioning_fns, expected_fns);
        assert_eq!(analyzer.type_params[&1].mentioning_fns, expected_fns);
    }

    #[test]
    fn placing_params() {
        #[rustfmt::skip]
        let functions = vec![
            FunctionInfo { parent: usize::MAX, depth: 0 },
            FunctionInfo { parent: 0, depth: 1 },
            FunctionInfo { parent: 1, depth: 2 },
            FunctionInfo { parent: 1, depth: 2 },
            FunctionInfo { parent: 0, depth: 1 },
            FunctionInfo { parent: 4, depth: 2 },
            FunctionInfo { parent: 0, depth: 1 },
        ];
        // Corresponds to this tree:
        //      0
        //  1   4   6
        // 2 3  5

        let type_param_mentions: &[(&[usize], usize)] = &[
            (&[0_usize], 0),
            (&[1], 1),
            (&[2, 4, 5], 0),
            (&[2, 3], 1),
            (&[3], 3),
        ];
        let type_params = type_param_mentions
            .iter()
            .copied()
            .enumerate()
            .map(|(idx, (mentions, _))| {
                (
                    idx,
                    ParamStats {
                        mentioning_fns: mentions.iter().copied().collect(),
                    },
                )
            })
            .collect();

        let analyzer = ParamQuantifierOutput {
            type_params,
            len_params: HashMap::new(),
            functions,
        };
        let placements = analyzer
            .place_params::<Num>(ParamConstraints::default())
            .type_params;

        for (i, (_, expected_placement)) in type_param_mentions.iter().copied().enumerate() {
            assert!(
                placements[&expected_placement].contains(&i),
                "Unexpected placements: {placements:?}"
            );
        }
    }
}