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sav08:axioms_of_hol [2008/05/28 02:44] vkuncak |
sav08:axioms_of_hol [2015/04/21 17:30] (current) |
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| - | ====== Axioms of Classical HOL ====== | + | ====== Axioms and Inference Rules of Classical HOL ====== |
| Axiom system that is sound (but necessarily incomplete with respect to standard semantics) is the following: | Axiom system that is sound (but necessarily incomplete with respect to standard semantics) is the following: | ||
| Line 7: | Line 7: | ||
| - $\iota(\lambda y.(x=y)) = x$ (selecting element from $\{x\}$ gives $x$) | - $\iota(\lambda y.(x=y)) = x$ (selecting element from $\{x\}$ gives $x$) | ||
| + | Inference rule: | ||
| + | \begin{equation*} | ||
| + | \frac{C\ \ ; \ \ A=B} | ||
| + | {C[A:=B]} | ||
| + | \end{equation*} | ||
| + | which replaces one occurrence of $A$ in $C$ with $B$ (we cannot replace variables under $\lambda$) | ||