This tutorial runs through the implementation of a basic toy language on top of MLIR. The goal of this tutorial is to introduce the concepts of MLIR, and especially how dialects can help easily support language specific constructs and transformations, while still offering an easy path to lower to LLVM or other codegen infrastructure. This tutorial is based on the model of the LLVM Kaleidoscope Tutorial.
This tutorial is divided in the following chapters:
- Chapter #1: Introduction to the Toy language, and the definition of its AST.
- Chapter #2: Traversing the AST to emit custom MLIR, introducing base MLIR concepts.
- Chapter #3: Defining and registering a dialect in MLIR, showing how we can start attaching semantics to our custom operations in MLIR.
- Chapter #4: High-level language-specific analysis and transformation, showcasing shape inference, generic function specialization, and basic optimizations.
- Chapter #5: Lowering to lower-level dialects. We'll convert our high level language specific semantics towards a generic linear-algebra oriented dialect for optimizations. Ultimately we will emit LLVM IR for code generation.
- Chapter #5: A REPL?
- Chapter #6: Custom backends? GPU using LLVM? TPU? XLA
This tutorial will be illustrated with a toy language that we’ll call “Toy” (naming is hard...). Toy is an array-based language that allows you to define functions, some math computation, and print results.
Because we want to keep things simple, the codegen will be limited to arrays of rank <= 2 and the only datatype in Toy is a 64-bit floating point type (aka ‘double’ in C parlance). As such, all values are implicitly double precision, Values are immutable: every operation returns a newly allocated value, and deallocation is automatically managed. But enough with the long description, nothing is better than walking through an example to get a better understanding:
FIXME: update/modify matrix multiplication to use @ instead of *
def main() {
# Define a variable `a` with shape <2, 3>, initialized with the literal value.
# The shape is inferred from the supplied literal.
var a = [[1, 2, 3], [4, 5, 6]];
# b is identical to a, the literal array is implicitely reshaped: defining new
# variables is the way to reshape arrays (element count must match).
var b<2, 3> = [1, 2, 3, 4, 5, 6];
# transpose() and print() are the only builtin, the following will transpose
# b and perform a matrix multiplication before printing the result.
print(a * transpose(b));
}
Type checking is statically performed through type inference, the language only requires type declarations to specify array shapes when needed. Function are generic: their parameters are unranked (in other word we know these are arrays but we don't know how many dimensions or the size of the dimensions). They are specialized for every newly discovered signature at call sites. Let's revisit the previous example by adding a user-defined function:
# User defined generic function that operates on unknown shaped arguments
def multiply_transpose(a, b) {
return a * transpose(b);
}
def main() {
# Define a variable `a` with shape <2, 3>, initialized with the literal value.
var a = [[1, 2, 3], [4, 5, 6]];
var b<2, 3> = [1, 2, 3, 4, 5, 6];
# This call will specialize `multiply_transpose` with <2, 3> for both
# arguments and deduce a return type of <2, 2> in initialization of `c`.
var c = multiply_transpose(a, b);
# A second call to `multiply_transpose` with <2, 3> for both arguments will
# reuse the previously specialized and inferred version and return `<2, 2>`
var d = multiply_transpose(b, a);
# A new call with `<2, 2>` for both dimension will trigger another
# specialization of `multiply_transpose`.
var e = multiply_transpose(c, d);
# Finally, calling into `multiply_transpose` with incompatible shape will
# trigger a shape inference error.
var e = multiply_transpose(transpose(a), c);
}
The AST is fairly straightforward from the above code, here is a dump of it:
Module:
Function
Proto 'multiply_transpose' @test/ast.toy:5:1'
Args: [a, b]
Block {
Return
BinOp: * @test/ast.toy:6:12
var: a @test/ast.toy:6:10
Call 'transpose' [ @test/ast.toy:6:14
var: b @test/ast.toy:6:24
]
} // Block
Function
Proto 'main' @test/ast.toy:9:1'
Args: []
Block {
VarDecl a<2, 3> @test/ast.toy:11:3
Literal: <2, 3>[<3>[1.000000e+00, 2.000000e+00, 3.000000e+00], <3>[4.000000e+00, 5.000000e+00, 6.000000e+00]] @test/ast.toy:11:17
VarDecl b<2, 3> @test/ast.toy:12:3
Literal: <6>[1.000000e+00, 2.000000e+00, 3.000000e+00, 4.000000e+00, 5.000000e+00, 6.000000e+00] @test/ast.toy:12:17
VarDecl c<> @test/ast.toy:15:3
Call 'multiply_transpose' [ @test/ast.toy:15:11
var: a @test/ast.toy:15:30
var: b @test/ast.toy:15:33
]
VarDecl d<> @test/ast.toy:18:3
Call 'multiply_transpose' [ @test/ast.toy:18:11
var: b @test/ast.toy:18:30
var: a @test/ast.toy:18:33
]
VarDecl e<> @test/ast.toy:21:3
Call 'multiply_transpose' [ @test/ast.toy:21:11
var: b @test/ast.toy:21:30
var: c @test/ast.toy:21:33
]
VarDecl e<> @test/ast.toy:24:3
Call 'multiply_transpose' [ @test/ast.toy:24:11
Call 'transpose' [ @test/ast.toy:24:30
var: a @test/ast.toy:24:40
]
var: c @test/ast.toy:24:44
]
} // Block
You can reproduce this result and play with the example in the examples/toy/Ch1/
directory, try running path/to/BUILD/bin/toyc-ch1 test/ast.toy -emit=ast.
The code for the lexer is fairly straighforward, it is all in a single header:
examples/toy/Ch1/include/toy/Lexer.h. The parser can be found in
examples/toy/Ch1/include/toy/Parser.h, it is a recursive descent parser. If
you are not familiar with such Lexer/Parser, these are very similar to the LLVM
Kaleidoscope equivalent that are detailed in the first two chapters of the
Kaleidoscope Tutorial.
The next chapter will demonstrate how to convert this AST into MLIR.