[analysis] Implement an array lattice (#6057)

The elements of `Array<L, N>` lattice are arrays of length `N` of elements of
`L`, compared pairwise with each other. This lattice is a concrete
implementation of what would be written L^N with pen and paper.

1 files changed, 122 insertions, 0 deletions

diff --git a/src/analysis/lattices/array.h b/src/analysis/lattices/array.h
new file mode 100644
index 000000000..3426a3a77
--- /dev/null
+++ b/src/analysis/lattices/array.h
@@ -0,0 +1,122 @@
+/*
+ * Copyright 2023 WebAssembly Community Group participants
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#ifndef wasm_analysis_lattices_array_h
+#define wasm_analysis_lattices_array_h
+
+#include <array>
+#include <utility>
+
+#include "../lattice.h"
+#include "bool.h"
+#include "flat.h"
+
+namespace wasm::analysis {
+
+// A lattice whose elements are N-tuples of elements of L. Also written as L^N.
+template<Lattice L, size_t N> struct Array {
+  using Element = std::array<typename L::Element, N>;
+
+  L lattice;
+
+  Array(L&& lattice) : lattice(std::move(lattice)) {}
+
+private:
+  // Use a template parameter pack to generate N copies of
+  // `lattice.getBottom()`. TODO: Use C++20 lambda template parameters instead
+  // of a separate helper function.
+  template<size_t... I>
+  Element getBottomImpl(std::index_sequence<I...>) const noexcept {
+    return {((void)I, lattice.getBottom())...};
+  }
+  template<size_t... I>
+  Element getTopImpl(std::index_sequence<I...>) const noexcept {
+    return {((void)I, lattice.getTop())...};
+  }
+
+public:
+  Element getBottom() const noexcept {
+    return getBottomImpl(std::make_index_sequence<N>());
+  }
+
+  Element getTop() const noexcept
+#if __cplusplus >= 202002L
+    requires FullLattice<L>
+#endif
+  {
+    return getTopImpl(std::make_index_sequence<N>());
+  }
+
+  // `a` <= `b` if all their elements are pairwise <=, etc. Unless we determine
+  // that there is no relation, we must check all the elements.
+  LatticeComparison compare(const Element& a, const Element& b) const noexcept {
+    auto result = EQUAL;
+    for (size_t i = 0; i < N; ++i) {
+      switch (lattice.compare(a[i], b[i])) {
+        case NO_RELATION:
+          return NO_RELATION;
+        case EQUAL:
+          continue;
+        case LESS:
+          if (result == GREATER) {
+            // Cannot be both less and greater.
+            return NO_RELATION;
+          }
+          result = LESS;
+          continue;
+        case GREATER:
+          if (result == LESS) {
+            // Cannot be both greater and less.
+            return NO_RELATION;
+          }
+          result = GREATER;
+          continue;
+      }
+    }
+    return result;
+  }
+
+  // Pairwise join on the elements.
+  bool join(Element& joinee, const Element& joiner) const noexcept {
+    bool result = false;
+    for (size_t i = 0; i < N; ++i) {
+      result |= lattice.join(joinee[i], joiner[i]);
+    }
+    return result;
+  }
+
+  // Pairwise meet on the elements.
+  bool meet(Element& meetee, const Element& meeter) const noexcept
+#if __cplusplus >= 202002L
+    requires FullLattice<L>
+#endif
+  {
+    bool result = false;
+    for (size_t i = 0; i < N; ++i) {
+      result |= lattice.meet(meetee[i], meeter[i]);
+    }
+    return result;
+  }
+};
+
+#if __cplusplus >= 202002L
+static_assert(FullLattice<Array<Bool, 1>>);
+static_assert(Lattice<Array<Flat<bool>, 1>>);
+#endif
+
+} // namespace wasm::analysis
+
+#endif // wasm_analysis_lattices_array_h