Reference
Complete reference documentation for Asgard grammars, operations, and compilation.
Equation Grammar
Complete LEAN-style syntax specification for equations including BNF notation and examples.
Circuit Grammar
Full circuit syntax specification with combinators, atomic operations, and type checking.
Operations
Detailed reference for all atomic operations and combinators with signatures and behaviors.
Quick Reference
Equation Syntax
| Operation | Syntax | Example |
|---|---|---|
| Integration | int(term, var) |
int(f, x) |
| Differentiation | diff(term, var) |
diff(f, x) |
| Lambda | abstraction var. body |
abstraction x. x * x |
| Application | apply(fn, arg) |
apply(f, 5) |
| Arithmetic | +, -, *, /, ^ |
x + y * 2 |
Circuit Syntax
| Combinator | Signature | Description |
|---|---|---|
composition(f, g) |
A→B, B→C = A→C |
Sequential execution |
monoidal(f, g) |
A→B, C→D = A+C→B+D |
Parallel execution |
trace(f) |
A+X→B+X = A→B |
Feedback loop |
Atomic Operations
| Operation | Signature | Description |
|---|---|---|
register(dim) |
1→1 |
Integration |
deregister(dim) |
1→1 |
Differentiation |
add |
2→1 |
Addition |
multiplication |
2→1 |
Multiplication |
scalar(c) |
1→1 |
Constant scaling |
id |
1→1 |
Identity |
split |
1→2 |
Duplicate |
const(c) |
0→1 |
Constant |
var(name) |
1→1 |
Variable |
Next Steps
- Equation Grammar - Complete equation syntax
- Circuit Grammar - Complete circuit syntax
- Operations - Detailed operation reference