# Core Constructs

lambdagent maps 11 agent constructs to Lambda calculus:

| # | Lambda Calculus | DSL | Example |
|---|---|---|---|
| 1 | λx.body | `Lam(name, prompt)` | `Lam("writer", "Write clearly.")` |
| 2 | (f x) | `agent(input)` | `agent("hello")` |
| 3 | λx.g(f(x)) | `f >> g` | `extract >> analyze >> report` |
| 4 | IF c t e | `If(cond, then_, else_)` | `If(lambda x: len(x)>100, long_handler, short_handler)` |
| 5 | Y combinator | `Loop(body, cond, N)` | `Loop(step, lambda r,s: "DONE" in r, 10)` |
| 6 | PAIR | `Pair(f, g)` | `Pair(researcher, critic)` |
| 7 | FST / SND | `Fst() / Snd()` | `Fst()(("a","b"))  # → "a"` |
| 8 | Oracle | `Tool(name, fn)` | `Tool("calc", lambda x: eval(x))` |
| 9 | CASE | `Route(cls, routes)` | `Route(classifier, {"code": coder, "math": solver})` |
| 10 | {x:T\|P(x)} | `Guard(agent, P)` | `Guard(writer, lambda x: len(x)>200, retry=2)` |
| 11 | Γ'=Γ∪s | `Memory(agent, store)` | `Memory(assistant, {"user": "Alice"})` |

All constructs are subclasses of `Term` and support:
- `>>` for composition
- `|` for parallel execution
- `()` for application (β-reduction)