Intermediate Representation

The MIND IR is a typed, SSA-based intermediate representation designed for tensor operations and automatic differentiation.

IR Structure

MIND IR uses Static Single Assignment (SSA) form with explicit types:

// Example IR for: y = relu(x @ w)
%0 = mind.const : tensor<2x2xf32> = [[1.0, 2.0], [3.0, 4.0]]
%1 = mind.randn : tensor<2x2xf32>
%2 = mind.matmul(%0, %1) : tensor<2x2xf32>
%3 = mind.relu(%2) : tensor<2x2xf32>
mind.return %3

Core Operations

Category	Operations
Arithmetic	add, sub, mul, div, neg, pow
Linear Algebra	matmul, transpose, dot
Activations	relu, sigmoid, tanh, softmax, gelu
Reductions	sum, mean, max, min, prod
Shape	reshape, broadcast, squeeze, unsqueeze
Convolution	conv2d, maxpool2d, avgpool2d

Type Representation

IR types encode both dtype and shape information:

tensor<f32>           // Scalar
tensor<10xf32>        // 1D, static shape
tensor<2x3xf32>       // 2D, static shape
tensor<?x?xf32>       // 2D, dynamic shape
tensor<2x?xf32>       // Mixed static/dynamic

Canonicalization

The IR undergoes canonicalization passes to normalize operations:

Constant folding for compile-time-known values
Identity elimination (x + 0 → x, x * 1 → x)
Strength reduction (x * 2 → x + x for integers)
Dead code elimination

Lowering Pipeline

Source (.mind)
    ↓ Parse
AST
    ↓ Type check
Typed AST
    ↓ Lower
MIND IR (High-level)
    ↓ Canonicalize
MIND IR (Canonical)
    ↓ Autodiff (if needed)
MIND IR + Gradients
    ↓ Lower to MLIR
MLIR Dialects
    ↓ Lower to LLVM
LLVM IR
    ↓ Codegen
Machine Code

Learn More

See the full IR specification at mind-spec/ir.md.