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sav08:simply_typed_lambda_calculus [2008/05/27 23:14] vkuncak |
sav08:simply_typed_lambda_calculus [2008/10/13 08:27] vkuncak |
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| * foundation of modern functional programming languages (when extended with recursion) | * foundation of modern functional programming languages (when extended with recursion) | ||
| * particularly suitable as a foundation of logic: due to termination properties | * particularly suitable as a foundation of logic: due to termination properties | ||
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| ===== Simple Types ===== | ===== Simple Types ===== | ||
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| The set of simple types are defined by grammar | The set of simple types are defined by grammar | ||
| \[ | \[ | ||
| - | \tau ::= \beta \mid (\tau \Rightarrow \tau) | + | \tau ::= B \mid (\tau \Rightarrow \tau) |
| \] | \] | ||
| The type $\tau_1 \doublerightarrow \tau_2$ is meant to denote functions from $\tau_1$ to $\tau_2$ (whether it denotes total or partial or computable functions, depends on particular semantics). | The type $\tau_1 \doublerightarrow \tau_2$ is meant to denote functions from $\tau_1$ to $\tau_2$ (whether it denotes total or partial or computable functions, depends on particular semantics). | ||