49 lines
1.2 KiB
Go
49 lines
1.2 KiB
Go
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package dfa
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import (
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"fmt"
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"strings"
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)
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// Dot returns a directed graph in [Graphviz] format that represents the finite
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// join-semilattice ⟨S, ≤⟩. Vertices represent elements in S and edges
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// represent the ≤ relation between elements. We map from ⟨S, ∨⟩ to ⟨S, ≤⟩ by
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// computing x ∨ y for all elements in [S]², where x ≤ y iff x ∨ y == y.
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//
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// The resulting graph can be filtered through [tred] to compute the transitive
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// reduction of the graph, the visualisation of which corresponds to the Hasse
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// diagram of the semilattice.
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//
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// [Graphviz]: https://graphviz.org/
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// [tred]: https://graphviz.org/docs/cli/tred/
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func Dot[L Semilattice[Elem], Elem any](states []Elem) string {
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var sb strings.Builder
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sb.WriteString("digraph{\n")
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sb.WriteString("rankdir=\"BT\"\n")
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for i, v := range states {
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if vs, ok := any(v).(fmt.Stringer); ok {
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fmt.Fprintf(&sb, "n%d [label=%q]\n", i, vs)
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} else {
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fmt.Fprintf(&sb, "n%d [label=%q]\n", i, fmt.Sprintf("%v", v))
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}
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}
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var l L
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for dx, x := range states {
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for dy, y := range states {
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if dx == dy {
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continue
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}
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if l.Equals(l.Merge(x, y), y) {
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fmt.Fprintf(&sb, "n%d -> n%d\n", dx, dy)
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}
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}
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}
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sb.WriteString("}")
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return sb.String()
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}
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