diff --git a/src/librustc_mir/dataflow/generic.rs b/src/librustc_mir/dataflow/generic.rs
new file mode 100644
index 0000000000000..886044c069282
--- /dev/null
+++ b/src/librustc_mir/dataflow/generic.rs
@@ -0,0 +1,512 @@
+//! Dataflow analysis with arbitrary transfer functions.
+//!
+//! This module is a work in progress. You should instead use `BitDenotation` in
+//! `librustc_mir/dataflow/mod.rs` and encode your transfer function as a [gen/kill set][gk]. In
+//! doing so, your analysis will run faster and you will be able to generate graphviz diagrams for
+//! debugging with no extra effort. The interface in this module is intended only for dataflow
+//! problems that cannot be expressed using gen/kill sets.
+//!
+//! FIXME(ecstaticmorse): In the long term, the plan is to preserve the existing `BitDenotation`
+//! interface, but make `Engine` and `ResultsCursor` the canonical way to perform and inspect a
+//! dataflow analysis. This requires porting the graphviz debugging logic to this module, deciding
+//! on a way to handle the `before` methods in `BitDenotation` and creating an adapter so that
+//! gen-kill problems can still be evaluated efficiently. See the discussion in [#64566][] for more
+//! information.
+//!
+//! [gk]: https://en.wikipedia.org/wiki/Data-flow_analysis#Bit_vector_problems
+//! [#64566]: https://github.com/rust-lang/rust/pull/64566
+
+use std::cmp::Ordering;
+use std::ops;
+
+use rustc::mir::{self, traversal, BasicBlock, Location};
+use rustc_data_structures::bit_set::BitSet;
+use rustc_data_structures::indexed_vec::{Idx, IndexVec};
+use rustc_data_structures::work_queue::WorkQueue;
+
+use crate::dataflow::BottomValue;
+
+/// A specific kind of dataflow analysis.
+///
+/// To run a dataflow analysis, one must set the initial state of the `START_BLOCK` via
+/// `initialize_start_block` and define a transfer function for each statement or terminator via
+/// the various `effect` methods. The entry set for all other basic blocks is initialized to
+/// `Self::BOTTOM_VALUE`. The dataflow `Engine` then iteratively updates the various entry sets for
+/// each block with the cumulative effects of the transfer functions of all preceding blocks.
+///
+/// You should use an `Engine` to actually run an analysis, and a `ResultsCursor` to inspect the
+/// results of that analysis like so:
+///
+/// ```ignore(cross-crate-imports)
+/// fn do_my_analysis(body: &mir::Body<'tcx>, dead_unwinds: &BitSet<BasicBlock>) {
+///     // `MyAnalysis` implements `Analysis`.
+///     let analysis = MyAnalysis::new();
+///
+///     let results = Engine::new(body, dead_unwinds, analysis).iterate_to_fixpoint();
+///     let mut cursor = ResultsCursor::new(body, results);
+///
+///     for (_, statement_index) in body.block_data[START_BLOCK].statements.iter_enumerated() {
+///         cursor.seek_after(Location { block: START_BLOCK, statement_index });
+///         let state = cursor.get();
+///         println!("{:?}", state);
+///     }
+/// }
+/// ```
+pub trait Analysis<'tcx>: BottomValue {
+    /// The index type used to access the dataflow state.
+    type Idx: Idx;
+
+    /// A name, used for debugging, that describes this dataflow analysis.
+    ///
+    /// The name should be suitable as part of a filename, so avoid whitespace, slashes or periods
+    /// and try to keep it short.
+    const NAME: &'static str;
+
+    /// The size of each bitvector allocated for each block.
+    fn bits_per_block(&self, body: &mir::Body<'tcx>) -> usize;
+
+    /// Mutates the entry set of the `START_BLOCK` to contain the initial state for dataflow
+    /// analysis.
+    fn initialize_start_block(&self, body: &mir::Body<'tcx>, state: &mut BitSet<Self::Idx>);
+
+    /// Updates the current dataflow state with the effect of evaluating a statement.
+    fn apply_statement_effect(
+        &self,
+        state: &mut BitSet<Self::Idx>,
+        statement: &mir::Statement<'tcx>,
+        location: Location,
+    );
+
+    /// Updates the current dataflow state with the effect of evaluating a statement.
+    ///
+    /// Note that the effect of a successful return from a `Call` terminator should **not** be
+    /// acounted for in this function. That should go in `apply_call_return_effect`. For example,
+    /// in the `InitializedPlaces` analyses, the return place is not marked as initialized here.
+    fn apply_terminator_effect(
+        &self,
+        state: &mut BitSet<Self::Idx>,
+        terminator: &mir::Terminator<'tcx>,
+        location: Location,
+    );
+
+    /// Updates the current dataflow state with the effect of a successful return from a `Call`
+    /// terminator.
+    ///
+    /// This is separated from `apply_terminator_effect` to properly track state across
+    /// unwind edges for `Call`s.
+    fn apply_call_return_effect(
+        &self,
+        state: &mut BitSet<Self::Idx>,
+        block: BasicBlock,
+        func: &mir::Operand<'tcx>,
+        args: &[mir::Operand<'tcx>],
+        return_place: &mir::Place<'tcx>,
+    );
+
+    /// Applies the cumulative effect of an entire basic block to the dataflow state (except for
+    /// `call_return_effect`, which is handled in the `Engine`).
+    ///
+    /// The default implementation calls `statement_effect` for every statement in the block before
+    /// finally calling `terminator_effect`. However, some dataflow analyses are able to coalesce
+    /// transfer functions for an entire block and apply them at once. Such analyses should
+    /// override `block_effect`.
+    fn apply_whole_block_effect(
+        &self,
+        state: &mut BitSet<Self::Idx>,
+        block: BasicBlock,
+        block_data: &mir::BasicBlockData<'tcx>,
+    ) {
+        for (statement_index, stmt) in block_data.statements.iter().enumerate() {
+            let location = Location { block, statement_index };
+            self.apply_statement_effect(state, stmt, location);
+        }
+
+        let location = Location { block, statement_index: block_data.statements.len() };
+        self.apply_terminator_effect(state, block_data.terminator(), location);
+    }
+
+    /// Applies the cumulative effect of a sequence of statements (and possibly a terminator)
+    /// within a single basic block.
+    ///
+    /// When called with `0..block_data.statements.len() + 1` as the statement range, this function
+    /// is equivalent to `apply_whole_block_effect`.
+    fn apply_partial_block_effect(
+        &self,
+        state: &mut BitSet<Self::Idx>,
+        block: BasicBlock,
+        block_data: &mir::BasicBlockData<'tcx>,
+        mut range: ops::Range<usize>,
+    ) {
+        if range.is_empty() {
+            return;
+        }
+
+        // The final location might be a terminator, so iterate through all statements until the
+        // final one, then check to see whether the final one is a statement or terminator.
+        //
+        // This can't cause the range to wrap-around since we check that the range contains at
+        // least one element above.
+        range.end -= 1;
+        let final_location = Location { block, statement_index: range.end };
+
+        for statement_index in range {
+            let location = Location { block, statement_index };
+            let stmt = &block_data.statements[statement_index];
+            self.apply_statement_effect(state, stmt, location);
+        }
+
+        if final_location.statement_index == block_data.statements.len() {
+            let terminator = block_data.terminator();
+            self.apply_terminator_effect(state, terminator, final_location);
+        } else {
+            let stmt = &block_data.statements[final_location.statement_index];
+            self.apply_statement_effect(state, stmt, final_location);
+        }
+    }
+}
+
+#[derive(Clone, Copy, Debug)]
+enum CursorPosition {
+    AtBlockStart(BasicBlock),
+    After(Location),
+}
+
+impl CursorPosition {
+    fn block(&self) -> BasicBlock {
+        match *self {
+            Self::AtBlockStart(block) => block,
+            Self::After(Location { block, .. }) => block,
+        }
+    }
+}
+
+/// Inspect the results of dataflow analysis.
+///
+/// This cursor has linear performance when visiting statements in a block in order. Visiting
+/// statements within a block in reverse order is `O(n^2)`, where `n` is the number of statements
+/// in that block.
+pub struct ResultsCursor<'mir, 'tcx, A>
+where
+    A: Analysis<'tcx>,
+{
+    body: &'mir mir::Body<'tcx>,
+    results: Results<'tcx, A>,
+    state: BitSet<A::Idx>,
+
+    pos: CursorPosition,
+
+    /// Whether the effects of `apply_call_return_effect` are currently stored in `state`.
+    ///
+    /// This flag ensures that multiple calls to `seek_after_assume_call_returns` with the same
+    /// target only result in one invocation of `apply_call_return_effect`.
+    is_call_return_effect_applied: bool,
+}
+
+impl<'mir, 'tcx, A> ResultsCursor<'mir, 'tcx, A>
+where
+    A: Analysis<'tcx>,
+{
+    /// Returns a new cursor for `results` that points to the start of the `START_BLOCK`.
+    pub fn new(body: &'mir mir::Body<'tcx>, results: Results<'tcx, A>) -> Self {
+        ResultsCursor {
+            body,
+            pos: CursorPosition::AtBlockStart(mir::START_BLOCK),
+            is_call_return_effect_applied: false,
+            state: results.entry_sets[mir::START_BLOCK].clone(),
+            results,
+        }
+    }
+
+    /// Resets the cursor to the start of the given `block`.
+    pub fn seek_to_block_start(&mut self, block: BasicBlock) {
+        self.state.overwrite(&self.results.entry_sets[block]);
+        self.pos = CursorPosition::AtBlockStart(block);
+        self.is_call_return_effect_applied = false;
+    }
+
+    /// Updates the cursor to hold the dataflow state immediately before `target`.
+    pub fn seek_before(&mut self, target: Location) {
+        assert!(target <= self.body.terminator_loc(target.block));
+
+        if target.statement_index == 0 {
+            self.seek_to_block_start(target.block);
+        } else {
+            self._seek_after(Location {
+                block: target.block,
+                statement_index: target.statement_index - 1,
+            });
+        }
+    }
+
+    /// Updates the cursor to hold the dataflow state at `target`.
+    ///
+    /// If `target` is a `Call` terminator, `apply_call_return_effect` will not be called. See
+    /// `seek_after_assume_call_returns` if you wish to observe the dataflow state upon a
+    /// successful return.
+    pub fn seek_after(&mut self, target: Location) {
+        assert!(target <= self.body.terminator_loc(target.block));
+
+        // This check ensures the correctness of a call to `seek_after_assume_call_returns`
+        // followed by one to `seek_after` with the same target.
+        if self.is_call_return_effect_applied {
+            self.seek_to_block_start(target.block);
+        }
+
+        self._seek_after(target);
+    }
+
+    /// Equivalent to `seek_after`, but also calls `apply_call_return_effect` if `target` is a
+    /// `Call` terminator whose callee is convergent.
+    pub fn seek_after_assume_call_returns(&mut self, target: Location) {
+        assert!(target <= self.body.terminator_loc(target.block));
+
+        self._seek_after(target);
+
+        if target != self.body.terminator_loc(target.block) {
+            return;
+        }
+
+        let term = self.body.basic_blocks()[target.block].terminator();
+        if let mir::TerminatorKind::Call {
+            destination: Some((return_place, _)),
+            func,
+            args,
+            ..
+        } = &term.kind {
+            if !self.is_call_return_effect_applied {
+                self.is_call_return_effect_applied = true;
+                self.results.analysis.apply_call_return_effect(
+                    &mut self.state,
+                    target.block,
+                    func,
+                    args,
+                    return_place,
+                );
+            }
+        }
+    }
+
+    fn _seek_after(&mut self, target: Location) {
+        let Location { block: target_block, statement_index: target_index } = target;
+
+        if self.pos.block() != target_block {
+            self.seek_to_block_start(target_block);
+        }
+
+        // If we're in the same block but after the target statement, we need to reset to the start
+        // of the block.
+        if let CursorPosition::After(Location { statement_index: curr_index, .. }) = self.pos {
+            match curr_index.cmp(&target_index) {
+                Ordering::Equal => return,
+                Ordering::Less => {},
+                Ordering::Greater => self.seek_to_block_start(target_block),
+            }
+        }
+
+        // The cursor is now in the same block as the target location pointing at an earlier
+        // statement.
+        debug_assert_eq!(self.pos.block(), target_block);
+        if let CursorPosition::After(Location { statement_index, .. }) = self.pos {
+            debug_assert!(statement_index < target_index);
+        }
+
+        let first_unapplied_statement = match self.pos {
+            CursorPosition::AtBlockStart(_) => 0,
+            CursorPosition::After(Location { statement_index, .. }) => statement_index + 1,
+        };
+
+        let block_data = &self.body.basic_blocks()[target_block];
+        self.results.analysis.apply_partial_block_effect(
+            &mut self.state,
+            target_block,
+            block_data,
+            first_unapplied_statement..target_index + 1,
+        );
+
+        self.pos = CursorPosition::After(target);
+        self.is_call_return_effect_applied = false;
+    }
+
+    /// Gets the dataflow state at the current location.
+    pub fn get(&self) -> &BitSet<A::Idx> {
+        &self.state
+    }
+}
+
+/// A completed dataflow analysis.
+pub struct Results<'tcx, A>
+where
+    A: Analysis<'tcx>,
+{
+    analysis: A,
+    entry_sets: IndexVec<BasicBlock, BitSet<A::Idx>>,
+}
+
+/// All information required to iterate a dataflow analysis to fixpoint.
+pub struct Engine<'a, 'tcx, A>
+where
+    A: Analysis<'tcx>,
+{
+    analysis: A,
+    bits_per_block: usize,
+    body: &'a mir::Body<'tcx>,
+    dead_unwinds: &'a BitSet<BasicBlock>,
+    entry_sets: IndexVec<BasicBlock, BitSet<A::Idx>>,
+}
+
+impl<A> Engine<'a, 'tcx, A>
+where
+    A: Analysis<'tcx>,
+{
+    pub fn new(
+        body: &'a mir::Body<'tcx>,
+        dead_unwinds: &'a BitSet<BasicBlock>,
+        analysis: A,
+    ) -> Self {
+        let bits_per_block = analysis.bits_per_block(body);
+
+        let bottom_value_set = if A::BOTTOM_VALUE == true {
+            BitSet::new_filled(bits_per_block)
+        } else {
+            BitSet::new_empty(bits_per_block)
+        };
+
+        let mut entry_sets = IndexVec::from_elem(bottom_value_set, body.basic_blocks());
+        analysis.initialize_start_block(body, &mut entry_sets[mir::START_BLOCK]);
+
+        Engine {
+            analysis,
+            bits_per_block,
+            body,
+            dead_unwinds,
+            entry_sets,
+        }
+    }
+
+    pub fn iterate_to_fixpoint(mut self) -> Results<'tcx, A> {
+        let mut temp_state = BitSet::new_empty(self.bits_per_block);
+
+        let mut dirty_queue: WorkQueue<BasicBlock> =
+            WorkQueue::with_none(self.body.basic_blocks().len());
+
+        for (bb, _) in traversal::reverse_postorder(self.body) {
+            dirty_queue.insert(bb);
+        }
+
+        // Add blocks that are not reachable from START_BLOCK to the work queue. These blocks will
+        // be processed after the ones added above.
+        for bb in self.body.basic_blocks().indices() {
+            dirty_queue.insert(bb);
+        }
+
+        while let Some(bb) = dirty_queue.pop() {
+            let bb_data = &self.body[bb];
+            let on_entry = &self.entry_sets[bb];
+
+            temp_state.overwrite(on_entry);
+            self.analysis.apply_whole_block_effect(&mut temp_state, bb, bb_data);
+
+            self.propagate_bits_into_graph_successors_of(
+                &mut temp_state,
+                (bb, bb_data),
+                &mut dirty_queue,
+            );
+        }
+
+        Results {
+            analysis: self.analysis,
+            entry_sets: self.entry_sets,
+        }
+    }
+
+    fn propagate_bits_into_graph_successors_of(
+        &mut self,
+        in_out: &mut BitSet<A::Idx>,
+        (bb, bb_data): (BasicBlock, &'a mir::BasicBlockData<'tcx>),
+        dirty_list: &mut WorkQueue<BasicBlock>,
+    ) {
+        match bb_data.terminator().kind {
+            mir::TerminatorKind::Return
+            | mir::TerminatorKind::Resume
+            | mir::TerminatorKind::Abort
+            | mir::TerminatorKind::GeneratorDrop
+            | mir::TerminatorKind::Unreachable => {}
+
+            mir::TerminatorKind::Goto { target }
+            | mir::TerminatorKind::Assert { target, cleanup: None, .. }
+            | mir::TerminatorKind::Yield { resume: target, drop: None, .. }
+            | mir::TerminatorKind::Drop { target, location: _, unwind: None }
+            | mir::TerminatorKind::DropAndReplace { target, value: _, location: _, unwind: None } =>
+            {
+                self.propagate_bits_into_entry_set_for(in_out, target, dirty_list);
+            }
+
+            mir::TerminatorKind::Yield { resume: target, drop: Some(drop), .. } => {
+                self.propagate_bits_into_entry_set_for(in_out, target, dirty_list);
+                self.propagate_bits_into_entry_set_for(in_out, drop, dirty_list);
+            }
+
+            mir::TerminatorKind::Assert { target, cleanup: Some(unwind), .. }
+            | mir::TerminatorKind::Drop { target, location: _, unwind: Some(unwind) }
+            | mir::TerminatorKind::DropAndReplace {
+                target,
+                value: _,
+                location: _,
+                unwind: Some(unwind),
+            } => {
+                self.propagate_bits_into_entry_set_for(in_out, target, dirty_list);
+                if !self.dead_unwinds.contains(bb) {
+                    self.propagate_bits_into_entry_set_for(in_out, unwind, dirty_list);
+                }
+            }
+
+            mir::TerminatorKind::SwitchInt { ref targets, .. } => {
+                for target in targets {
+                    self.propagate_bits_into_entry_set_for(in_out, *target, dirty_list);
+                }
+            }
+
+            mir::TerminatorKind::Call { cleanup, ref destination, ref func, ref args, .. } => {
+                if let Some(unwind) = cleanup {
+                    if !self.dead_unwinds.contains(bb) {
+                        self.propagate_bits_into_entry_set_for(in_out, unwind, dirty_list);
+                    }
+                }
+
+                if let Some((ref dest_place, dest_bb)) = *destination {
+                    // N.B.: This must be done *last*, after all other
+                    // propagation, as documented in comment above.
+                    self.analysis.apply_call_return_effect(in_out, bb, func, args, dest_place);
+                    self.propagate_bits_into_entry_set_for(in_out, dest_bb, dirty_list);
+                }
+            }
+
+            mir::TerminatorKind::FalseEdges { real_target, imaginary_target } => {
+                self.propagate_bits_into_entry_set_for(in_out, real_target, dirty_list);
+                self.propagate_bits_into_entry_set_for(in_out, imaginary_target, dirty_list);
+            }
+
+            mir::TerminatorKind::FalseUnwind { real_target, unwind } => {
+                self.propagate_bits_into_entry_set_for(in_out, real_target, dirty_list);
+                if let Some(unwind) = unwind {
+                    if !self.dead_unwinds.contains(bb) {
+                        self.propagate_bits_into_entry_set_for(in_out, unwind, dirty_list);
+                    }
+                }
+            }
+        }
+    }
+
+    fn propagate_bits_into_entry_set_for(
+        &mut self,
+        in_out: &BitSet<A::Idx>,
+        bb: BasicBlock,
+        dirty_queue: &mut WorkQueue<BasicBlock>,
+    ) {
+        let entry_set = &mut self.entry_sets[bb];
+        let set_changed = self.analysis.join(entry_set, &in_out);
+        if set_changed {
+            dirty_queue.insert(bb);
+        }
+    }
+}
diff --git a/src/librustc_mir/dataflow/mod.rs b/src/librustc_mir/dataflow/mod.rs
index 319abbbe7b643..5ab4e25b683cb 100644
--- a/src/librustc_mir/dataflow/mod.rs
+++ b/src/librustc_mir/dataflow/mod.rs
@@ -30,6 +30,7 @@ use self::move_paths::MoveData;
 
 mod at_location;
 pub mod drop_flag_effects;
+pub mod generic;
 mod graphviz;
 mod impls;
 pub mod move_paths;
diff --git a/src/librustc_mir/lib.rs b/src/librustc_mir/lib.rs
index 6a49ed6ed9fa1..9a03719ab61f5 100644
--- a/src/librustc_mir/lib.rs
+++ b/src/librustc_mir/lib.rs
@@ -23,6 +23,7 @@ Rust MIR: a lowered representation of Rust. Also: an experiment!
 #![feature(try_blocks)]
 #![feature(mem_take)]
 #![feature(associated_type_bounds)]
+#![feature(range_is_empty)]
 
 #![recursion_limit="256"]