Differences
This shows you the differences between two versions of the page.
Both sides previous revision Previous revision Next revision | Previous revision | ||
sav08:axioms_of_hol [2008/05/28 02:44] vkuncak |
sav08:axioms_of_hol [2015/04/21 17:30] (current) |
||
---|---|---|---|
Line 1: | Line 1: | ||
- | ====== 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 $\lambda$) |