Module symbolic_diff 

Symbolic differentiation of TLExpr.

This module implements formal symbolic differentiation of TensorLogic expressions with respect to named variables. It supports:

• Standard arithmetic differentiation rules (sum, product, quotient, power, chain)
• Unary transcendental functions (sin, cos, exp, log, sqrt, abs)
• Logical differentiation (AND, OR, NOT, implication)
• Quantifiers treated as scoped operators (bound variable treated as independent)
• Let-bindings via substitution
• Jacobian computation for multiple variables
• Post-differentiation algebraic simplification

Design Notes

In TLExpr, a scalar variable named "x" is represented as a zero-arity predicate: TLExpr::Pred { name: "x".to_string(), args: vec![] }. This convention is used throughout the codebase and is the basis for variable detection in this module.

Arithmetic negation (unary minus) does not have its own TLExpr variant. It is represented as TLExpr::Sub(Constant(0.0), inner) or TLExpr::Mul(Constant(-1.0), inner). The simplification pass recognises the Sub(0, e) form and folds it to a negated constant where possible.

Example

use tensorlogic_compiler::symbolic_diff::{differentiate, DiffConfig};
use tensorlogic_ir::TLExpr;

// d(x * x)/dx  →  x * 1 + x * 1  →  (after simplification) x + x
let x = TLExpr::pred("x", vec![]);
let expr = TLExpr::mul(x.clone(), x.clone());
let config = DiffConfig::default();
let result = differentiate(&expr, "x", &config).expect("differentiate");
// result.derivative is the symbolic derivative (x + x)

Structs

DiffConfig

Configuration for symbolic differentiation.

DiffResult

The result of differentiating a single expression.

Enums

DiffError

Error type for symbolic differentiation.

Functions

differentiate

Symbolically differentiate expr with respect to the variable named var.

jacobian

Compute the Jacobian: differentiate expr with respect to each variable in vars.

simplify_derivative

Basic algebraic simplification applied to derivative expressions.