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doc-src/Logics/syntax.tex

changeset 14209 | 180cd69a5dbb |

parent 9695 | ec7d7f877712 |

child 42637 | 381fdcab0f36 |

--- a/doc-src/Logics/syntax.tex Fri Sep 26 10:34:57 2003 +0200 +++ b/doc-src/Logics/syntax.tex Fri Sep 26 11:04:21 2003 +0200 @@ -36,9 +36,9 @@ syntax $\forall x.t$ to mean $All(\lambda x.t)$. We can also write $\forall x@1\ldots x@m.t$ to abbreviate $\forall x@1. \ldots \forall x@m.t$; this is possible for any constant provided that $\tau$ and $\tau'$ are the same type. -HOL's description operator $\varepsilon x.P\,x$ has type $(\alpha\To -bool)\To\alpha$ and can bind only one variable, except when $\alpha$ is -$bool$. ZF's bounded quantifier $\forall x\in A.P(x)$ cannot be declared as a +The Hilbert description operator $\varepsilon x.P\,x$ has type $(\alpha\To +bool)\To\alpha$ and normally binds only one variable. +ZF's bounded quantifier $\forall x\in A.P(x)$ cannot be declared as a binder because it has type $[i, i\To o]\To o$. The syntax for binders allows type constraints on bound variables, as in \[ \forall (x{::}\alpha) \; (y{::}\beta) \; z{::}\gamma. Q(x,y,z) \]