feat: define KLR representation

NKL/KLR.lean

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+/-
+Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Paul Govereau
+-/
+
+
+/-!
+# Abstract syntax of Core NKL language
+
+This language is the result of "tracing", and is used as the
+portable format, a.k.a. Kernel Language Representation (KLR).
+-/
+
+namespace NKL.KLR
+
+-- TODO
+inductive Ty where
+
+inductive Const where
+  | none
+  | bool (value : Bool)
+  | int (value : Int)
+  | float (value : Float)
+  | string (value : String)
+  deriving Repr, BEq
+
+namespace Const
+
+-- Python-like rules for conversion to boolean
+def isTrue : Const -> Bool
+  | .none     => false
+  | .bool b   => b
+  | .int i    => i != 0
+  | .float f  => f != 0.0
+  | .string s => s != ""
+
+-- Python-like rules for conversion to integer
+def toInt : Const -> Except String Int
+  | .none       => throw "none cannot be converted to an integer"
+  | .bool true  => return 1
+  | .bool false => return 0
+  | .int i      => return i
+  | .float f    =>
+      -- Python is a bit strange here, it truncates both
+      -- positive and negative numbers toward zero
+      if f < 0.0 then
+        return (Int.ofNat (Float.floor (-f)).toUInt64.toBitVec.toNat).neg
+      else
+        return Int.ofNat (Float.floor f).toUInt64.toBitVec.toNat
+  | .string s   =>
+      match s.toInt? with
+      | .none  => throw s!"string {s} cannot be converted to an integer"
+      | .some i => return i
+
+end Const
+
+inductive IndexExpr where
+  | var (name : String)
+  | int (i : Int)
+  | neg (expr : IndexExpr)
+  | add (left right : IndexExpr)
+  | mul (scalar : Int) (expr : IndexExpr)
+  | floor (expr : IndexExpr) (scalar : Int)
+  | ceil (expr : IndexExpr) (scalar : Int)
+  | mod (expr : IndexExpr) (scalar : Int)
+  deriving Repr, BEq
+
+inductive Index where
+  | ellipsis
+  | coord (e : Option IndexExpr)
+  | range (l u step : Option IndexExpr)
+  deriving Repr, BEq
+
+inductive Expr where
+  | var (x : String)
+  | const (c : Const)
+  | tensor (name : String) (shape : List Int)
+  | tuple (xs : List Expr)
+  | list (xs : List Expr)
+  | access (t : Expr) (ix : List Index)
+  | binop (op : String) (left right : Expr)
+  | unop (op : String) (e : Expr)
+  | call (f : Expr) (args : List Expr) (keywords : List (String × Expr))
+  deriving Repr, BEq
+
+namespace Expr
+
+-- TODO: Just a place-holder for now
+def toAffine : Expr -> Except String IndexExpr
+  | .var v => return .var v
+  | .const (.int i) => return .int i
+  | e => throw s!"toAffine unimp {repr e}"
+
+-- TODO: Just a place-holder for now
+def simplify : Expr -> Expr :=
+  fun x => x
+
+end Expr
+
+inductive Stmt where
+  | pass
+  | expr (v : Expr)
+  | ret (v : Expr)
+  | assign (x : String) (e : Expr)
+  | loop (x : String) (l u step : IndexExpr) (body : List Stmt)
+  deriving Repr, BEq