# types

## Basic idea

Static disciplines that classify program values and rule out classes of errors before execution. Type systems range from simple (Hindley-Milner) to dependent (Coq, Lean) — more expressive types catch more errors but cost more to check.

## Key formulas

* Typing judgement: $\Gamma \vdash e : \tau$
* Function type: $\tau\_1 \to \tau\_2$
* Universal type: $\forall \alpha.\ \tau$
* Curry-Howard: types ≅ propositions; programs ≅ proofs.


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