warp-types 0.3.2

//! Session Type Scalability
//!
//! **STATUS: Research** — Exploratory prototype, not promoted to main API.
//!
//! Research question: "Can session types scale to thousands of participants?"
//!
//! # Background
//!
//! Traditional MPST (Multiparty Session Types) has scaling challenges:
//! - Type size grows with participant count
//! - Projection complexity is O(n²) or worse
//! - Global type verification is expensive
//!
//! GPU kernels can have thousands of blocks. Can session types work?
//!
//! # Key Insight: Hierarchical Sessions
//!
//! GPU parallelism is HIERARCHICAL:
//! - Grid: thousands of blocks (inter-block sessions)
//! - Block: hundreds of threads (intra-block sessions)
//! - Warp: 32 lanes (intra-warp sessions - our focus)
//!
//! Each level has different communication patterns:
//! - Warp: shuffle, ballot (lockstep, no sync needed)
//! - Block: shared memory (explicit sync)
//! - Grid: global memory (atomic ops, no global sync)
//!
//! # Scaling Strategy
//!
//! 1. **Parameterized roles**: Not 1000 distinct types, but `Block<N>`
//! 2. **Symmetric protocols**: All blocks follow same pattern
//! 3. **Local verification**: Check one representative, not all
//! 4. **Hierarchical composition**: Nest session types by level

use std::marker::PhantomData;

// ============================================================================
// PARAMETERIZED ROLES
// ============================================================================

/// A block with a numeric ID (not a distinct type per block)
#[derive(Copy, Clone, Debug, PartialEq, Eq)]
pub struct BlockId(pub usize);

/// A warp within a block
#[derive(Copy, Clone, Debug, PartialEq, Eq)]
pub struct WarpId {
    pub block: BlockId,
    pub warp_in_block: usize,
}

/// A lane within a warp
#[derive(Copy, Clone, Debug, PartialEq, Eq)]
pub struct LaneId {
    pub warp: WarpId,
    pub lane_in_warp: usize,
}

impl LaneId {
    /// Global lane ID across entire grid
    pub fn global_id(&self, warps_per_block: usize) -> usize {
        let warp_global = self.warp.block.0 * warps_per_block + self.warp.warp_in_block;
        warp_global * 32 + self.lane_in_warp
    }
}

// ============================================================================
// SYMMETRIC PROTOCOLS
// ============================================================================

/// A protocol that all blocks follow identically
///
/// Instead of typing each block separately, we type ONE representative
/// and verify all blocks follow the same pattern.
pub mod symmetric {

    /// Protocol that every block executes
    pub trait BlockProtocol: Copy {
        /// What each block does locally
        fn local_phase();

        /// How blocks communicate (if at all)
        fn communication_pattern() -> CommunicationPattern;
    }

    /// Types of inter-block communication
    #[derive(Copy, Clone, Debug)]
    pub enum CommunicationPattern {
        /// No inter-block communication (embarrassingly parallel)
        None,
        /// All blocks write to disjoint regions (parallel writes)
        DisjointWrites,
        /// Reduction: blocks contribute to shared accumulator
        Reduction,
        /// Neighbor exchange: block N talks to N-1 and N+1
        Stencil,
        /// All-to-all: any block may communicate with any other
        AllToAll,
    }

    /// Complexity of verifying the pattern
    impl CommunicationPattern {
        pub fn verification_complexity(&self, _num_blocks: usize) -> &'static str {
            match self {
                CommunicationPattern::None => "O(1) - verify one block",
                CommunicationPattern::DisjointWrites => "O(1) - verify disjointness property",
                CommunicationPattern::Reduction => "O(log n) - verify reduction tree",
                CommunicationPattern::Stencil => "O(1) - verify neighbor protocol",
                CommunicationPattern::AllToAll => "O(n²) - must verify all pairs",
            }
        }

        pub fn scales_well(&self) -> bool {
            !matches!(self, CommunicationPattern::AllToAll)
        }
    }

    #[cfg(test)]
    mod tests {
        use super::*;

        #[test]
        fn test_pattern_scaling() {
            assert!(CommunicationPattern::None.scales_well());
            assert!(CommunicationPattern::DisjointWrites.scales_well());
            assert!(CommunicationPattern::Reduction.scales_well());
            assert!(CommunicationPattern::Stencil.scales_well());
            assert!(!CommunicationPattern::AllToAll.scales_well());
        }
    }
}

// ============================================================================
// HIERARCHICAL COMPOSITION
// ============================================================================

/// Nested session types for GPU hierarchy
pub mod hierarchical {
    use super::*;

    /// Grid-level session (inter-block)
    pub struct GridSession<P> {
        num_blocks: usize,
        _protocol: PhantomData<P>,
    }

    impl<P> GridSession<P> {
        pub fn new(num_blocks: usize) -> Self {
            GridSession {
                num_blocks,
                _protocol: PhantomData,
            }
        }

        pub fn num_blocks(&self) -> usize {
            self.num_blocks
        }
    }

    /// Block-level session (intra-block, inter-warp)
    pub struct BlockSession<P> {
        block_id: BlockId,
        num_warps: usize,
        _protocol: PhantomData<P>,
    }

    impl<P> BlockSession<P> {
        pub fn new(block_id: BlockId, num_warps: usize) -> Self {
            BlockSession {
                block_id,
                num_warps,
                _protocol: PhantomData,
            }
        }

        pub fn block_id(&self) -> BlockId {
            self.block_id
        }

        pub fn num_warps(&self) -> usize {
            self.num_warps
        }
    }

    /// Warp-level session (intra-warp, inter-lane)
    /// This is where our session-typed divergence lives!
    pub struct WarpSession<S> {
        warp_id: WarpId,
        _active_set: PhantomData<S>,
    }

    impl<S> WarpSession<S> {
        pub fn new(warp_id: WarpId) -> Self {
            WarpSession {
                warp_id,
                _active_set: PhantomData,
            }
        }

        pub fn warp_id(&self) -> WarpId {
            self.warp_id
        }
    }

    /// Compose sessions hierarchically
    pub fn decompose_grid<GP, BP>(grid: GridSession<GP>) -> Vec<BlockSession<BP>> {
        (0..grid.num_blocks())
            .map(|i| BlockSession::new(BlockId(i), 32)) // Assume 32 warps/block
            .collect()
    }

    #[cfg(test)]
    mod tests {
        use super::*;

        #[test]
        fn test_hierarchical_decomposition() {
            struct GridProtocol;
            struct BlockProtocol;

            let grid: GridSession<GridProtocol> = GridSession::new(1000);
            assert_eq!(grid.num_blocks(), 1000);

            let blocks: Vec<BlockSession<BlockProtocol>> = decompose_grid(grid);
            assert_eq!(blocks.len(), 1000);
            assert_eq!(blocks[0].block_id(), BlockId(0));
            assert_eq!(blocks[999].block_id(), BlockId(999));
        }
    }
}

// ============================================================================
// INDEXED SESSION TYPES
// ============================================================================

/// Instead of distinct types per participant, use indexed types
pub mod indexed {
    use super::*;

    /// A session indexed by block ID
    ///
    /// `Session<N>` represents "the session from block N's perspective"
    /// All blocks have the SAME type structure, just different index.
    pub struct IndexedSession<const N: usize> {
        _marker: PhantomData<()>,
    }

    impl<const N: usize> IndexedSession<N> {
        pub fn new() -> Self {
            IndexedSession {
                _marker: PhantomData,
            }
        }

        pub fn block_id() -> usize {
            N
        }
    }

    /// Reduction: each block contributes to partial sum
    ///
    /// Type: IndexedSession<N> -[contribute]-> IndexedSession<N>
    ///
    /// All blocks have same type! Verification is O(1).
    pub fn contribute_to_reduction<const N: usize>(
        _session: IndexedSession<N>,
        value: i32,
    ) -> (IndexedSession<N>, i32) {
        // In real GPU: atomicAdd to global accumulator
        (IndexedSession::new(), value)
    }

    /// Stencil: exchange with neighbors
    ///
    /// Block N reads from N-1 and N+1 (with wrapping).
    /// All blocks have same pattern!
    pub fn stencil_exchange<const N: usize, const NUM_BLOCKS: usize>(
        _session: IndexedSession<N>,
        my_value: i32,
    ) -> (IndexedSession<N>, i32, i32) {
        // Neighbors (with wrapping)
        let _left = (N + NUM_BLOCKS - 1) % NUM_BLOCKS;
        let _right = (N + 1) % NUM_BLOCKS;

        // In real GPU: read from global memory at neighbor positions
        (IndexedSession::new(), my_value, my_value) // Placeholder
    }

    #[cfg(test)]
    mod tests {
        use super::*;

        #[test]
        fn test_indexed_sessions() {
            // All blocks have the same type structure
            let s0: IndexedSession<0> = IndexedSession::new();
            let s1: IndexedSession<1> = IndexedSession::new();
            let s999: IndexedSession<999> = IndexedSession::new();

            assert_eq!(IndexedSession::<0>::block_id(), 0);
            assert_eq!(IndexedSession::<1>::block_id(), 1);
            assert_eq!(IndexedSession::<999>::block_id(), 999);

            // Same operations available on all
            let (_, _) = contribute_to_reduction(s0, 10);
            let (_, _) = contribute_to_reduction(s1, 20);
            let (_, _) = contribute_to_reduction(s999, 30);
        }
    }
}

// ============================================================================
// COMPLEXITY ANALYSIS
// ============================================================================

/// Analysis of session type complexity at scale
pub mod complexity {
    /// Traditional MPST complexity
    pub fn traditional_mpst(participants: usize) -> String {
        format!(
            "Traditional MPST with {} participants:\n\
             - Global type size: O(n²) - all pairwise interactions\n\
             - Projection: O(n) per participant\n\
             - Total verification: O(n³)\n\
             - NOT practical for n > 100",
            participants
        )
    }

    /// Our hierarchical approach
    pub fn hierarchical_approach(blocks: usize, warps_per_block: usize) -> String {
        format!(
            "Hierarchical sessions with {} blocks × {} warps:\n\
             - Grid level: O(1) if symmetric, O(n) for reduction\n\
             - Block level: O(1) - same for all blocks\n\
             - Warp level: O(1) - 32 lanes, fixed\n\
             - Total: O(1) to O(n) depending on pattern\n\
             - PRACTICAL for n > 10000",
            blocks, warps_per_block
        )
    }

    /// When does it scale?
    pub fn scaling_analysis() -> &'static str {
        "Session types scale when:\n\
         1. Protocols are SYMMETRIC (all participants same role)\n\
         2. Communication is STRUCTURED (reduction, stencil, not all-to-all)\n\
         3. Verification is LOCAL (check one, prove all)\n\
         4. Hierarchy is EXPLOITED (don't flatten to single level)\n\
         \n\
         GPU kernels naturally have these properties!"
    }

    #[cfg(test)]
    mod tests {
        use super::*;

        #[test]
        fn test_complexity_comparison() {
            let trad = traditional_mpst(1000);
            assert!(trad.contains("O(n³)"));

            let hier = hierarchical_approach(1000, 32);
            assert!(hier.contains("O(1)"));
        }
    }
}

// ============================================================================
// SUMMARY
// ============================================================================

/// Summary: Can session types scale to thousands of participants?
///
/// ## Answer: YES, with the right approach
///
/// ### Why Traditional MPST Doesn't Scale
///
/// - Global type encodes ALL pairwise interactions: O(n²) size
/// - Projection must consider all other participants: O(n) each
/// - Verification is O(n³) - impractical for n > 100
///
/// ### Why GPU Sessions DO Scale
///
/// 1. **Symmetric protocols**: All blocks/warps follow same pattern
///    - Verify ONE representative, prove ALL correct
///    - O(1) instead of O(n)
///
/// 2. **Structured communication**: Not arbitrary all-to-all
///    - Reduction: O(log n) tree structure
///    - Stencil: O(1) neighbor pattern
///    - Disjoint: O(1) no communication
///
/// 3. **Hierarchical decomposition**: Don't flatten
///    - Grid → Block → Warp → Lane
///    - Each level has bounded participants (32 lanes, ~32 warps)
///    - Compose levels, don't multiply
///
/// 4. **Indexed types**: `Block<N>` not distinct types per block
///    - Same type structure, parameterized by index
///    - Compiler sees ONE type, not 1000
///
/// ### Practical Numbers
///
/// | Approach | 32 participants | 1000 participants | 100000 participants |
/// |----------|-----------------|-------------------|---------------------|
/// | Traditional MPST | O(32³) ≈ 32K | O(10⁹) ✗ | O(10¹⁵) ✗ |
/// | Symmetric | O(1) ✓ | O(1) ✓ | O(1) ✓ |
/// | Reduction | O(5) ✓ | O(10) ✓ | O(17) ✓ |
/// | Hierarchical | O(32) ✓ | O(32) ✓ | O(32) ✓ |
///
/// ### Conclusion
///
/// Session types SCALE to thousands of GPU participants because:
/// 1. GPU parallelism is naturally symmetric
/// 2. Communication patterns are structured
/// 3. Hierarchy bounds verification at each level
///
/// The "thousands of participants" problem is a non-issue for GPUs.
pub const _SUMMARY: () = ();

#[cfg(test)]
mod integration_tests {
    use super::*;

    #[test]
    fn test_full_hierarchy() {
        use hierarchical::*;

        struct GridProto;
        struct BlockProto;
        struct All;

        // Create a grid with 1000 blocks
        let grid: GridSession<GridProto> = GridSession::new(1000);

        // Decompose to blocks
        let blocks: Vec<BlockSession<BlockProto>> = decompose_grid(grid);
        assert_eq!(blocks.len(), 1000);

        // Each block has warps
        for block in &blocks {
            assert_eq!(block.num_warps(), 32);
        }

        // Each warp has lanes (our session-typed divergence)
        let warp: WarpSession<All> = WarpSession::new(WarpId {
            block: BlockId(0),
            warp_in_block: 0,
        });

        assert_eq!(warp.warp_id().block, BlockId(0));
    }
}