Differences
This shows you the differences between two versions of the page.
Both sides previous revision Previous revision | Next revision Both sides next revision | ||
sav08:simply_typed_lambda_calculus [2008/05/27 23:14] vkuncak |
sav08:simply_typed_lambda_calculus [2008/10/13 08:27] vkuncak |
||
---|---|---|---|
Line 4: | Line 4: | ||
* 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 | ||
+ | |||
===== Simple Types ===== | ===== Simple Types ===== | ||
Line 11: | Line 12: | ||
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). |