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sav08:syntax_and_shorthands_of_hol [2008/05/29 17:00] vkuncak |
sav08:syntax_and_shorthands_of_hol [2008/05/29 17:02] vkuncak |
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To obtain a logic based on such lambda calculus, we add two family of constants: | To obtain a logic based on such lambda calculus, we add two family of constants: | ||
* equality $=_{t \Rightarrow t \Rightarrow o}$ for each type $t$, denoting equality on elements of type $t$ | * equality $=_{t \Rightarrow t \Rightarrow o}$ for each type $t$, denoting equality on elements of type $t$ | ||
- | * selection operator $\iota_{(i \Rightarrow o) \Rightarrow o}$, denoting 'choice function' that takes a predicate and returns one element satisfying the predicate (if such element exists) | + | * selection operator $\iota_{(i \Rightarrow o) \Rightarrow i}$, denoting 'choice function' that takes a predicate and returns one element satisfying the predicate (if exactly one such element exists) |
Everything else (most of mathematics) can be defined in this logic, and to a large extent has been done in systems such as Isabelle and HOL. | Everything else (most of mathematics) can be defined in this logic, and to a large extent has been done in systems such as Isabelle and HOL. |