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The meaning of $S$ and $\Sigma$ is defined on slide 6. $S$ is a set of base types (for example, natural numbers $\mathbb N$, Booleans $\mathbb N$, etc.): these are just formal symbols. $\Sigma$ is a set of operators, which included constants and functions (for example, $0 : \mathbb N$, $\text{true} : \mathbb B$, $\text{not} : \mathbb B \to \mathbb B$, etc.): ...


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It's not clear exactly what your confusion is, so I'll try to explain the example more clearly, and you reply in the comments if something's still not apparent. In the interpretation of the simply-typed $\lambda$-calculus in a cartesian-closed category, contexts $\Gamma$ and types $A$ are interpreted as objects $⟦\Gamma⟧$ and $⟦A⟧$ (types being equivalent ...


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