Nuprl - Some Definitions

nd_auto_lang	`Def L(NDA)(l) == NDA(l)` `Thm* Alph,St:Type, NDA:NDA(Alph;St). L(NDA) LangOver(Alph)`
nd_accept_list	`Def NDA(l) == q:St. NDA(l)q & (F(NDA)(q))` `Thm* Alph,St:Type, NDA:NDA(Alph;St), l:Alph*. NDA(l) Prop`
NDA_fin	`Def F(n) == 2of(2of(n))` `Thm* Alph,States:Type, n:NDA(Alph;States). F(n) States`
assert	`Def b == if b True else False fi` `Thm* b:. b Prop`
nd_compute_list	`Def NDA(l)q == if null(l) q = I(NDA) St else t:St. NDA(tl(l))t & NDA(t,hd(l),q) fi (recursive)` `Thm* Alph,St:Type, NDA:NDA(Alph;St), l:Alph*, q:St. NDA(l)q Prop`
NDA_init	`Def I(n) == 1of(2of(n))` `Thm* Alph,States:Type, n:NDA(Alph;States). I(n) States`
pi2	`Def 2of(t) == t.2` `Thm* A:Type, B:(AType), p:a:AB(a). 2of(p) B(1of(p))`
hd	`Def hd(l) == Case of l; nil "?" ; h.t h` `Thm* A:Type, l:A*. \|\|l\|\|1 hd(l) A`
NDA_act	`Def n == 1of(n)` `Thm* Alph,States:Type, n:NDA(Alph;States). n StatesAlphStatesProp`
tl	`Def tl(l) == Case of l; nil nil ; h.t t` `Thm* A:Type, l:A. tl(l) A`
null	`Def null(as) == Case of as; nil true ; a.as' false Thm* T:Type, as:T. null(as)` `Thm null(nil)`
pi1	`Def 1of(t) == t.1` `Thm* A:Type, B:(AType), p:a:AB(a). 1of(p) A`

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