| Some definitions of interest. |
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ma-valtype | Def ma-valtype(da; k) == da(k)?Top |
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Kind-deq | Def KindDeq == union-deq(IdLnk Id;Id;product-deq(IdLnk;Id;IdLnkDeq;IdDeq);IdDeq) |
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Knd | Def Knd == (IdLnk Id)+Id |
| | Thm* Knd Type |
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IdLnk | Def IdLnk == Id Id  |
| | Thm* IdLnk Type |
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idlnk-deq | Def IdLnkDeq == product-deq(Id;Id ;IdDeq;product-deq(Id; ;IdDeq;NatDeq)) |
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ma-state | Def State(ds) == x:Id ds(x)?Top |
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Id | Def Id == Atom  |
| | Thm* Id Type |
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deq | Def EqDecider(T) == eq:T T    x,y:T. x = y  (eq(x,y)) |
| | Thm* T:Type. EqDecider(T) Type |
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fpf-compatible | Def f || g == x:A. x dom(f) & x dom(g)  f(x) = g(x) B(x) |
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id-deq | Def IdDeq == product-deq(Atom; ;AtomDeq;NatDeq) |
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product-deq | Def product-deq(A;B;a;b) == <proddeq(a;b),prod-deq(A;B;a;b)> |
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assert | Def b == if b True else False fi |
| | Thm* b: . b Prop |
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fpf-join | Def f g == <1of(f) @ filter( a. a dom(f);1of(g)), a.f(a)?g(a)> |
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fpf-cap | Def f(x)?z == if x dom(f) f(x) else z fi |
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fpf-dom | Def x dom(f) == deq-member(eq;x;1of(f)) |
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deq-member | Def deq-member(eq;x;L) == reduce( a,b. eqof(eq)(a,x)  b;false ;L) |
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fpf | Def a:A fp-> B(a) == d:A List a:{a:A| (a d) } B(a) |
| | Thm* A:Type, B:(A Type). a:A fp-> B(a) Type |
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fpf-ap | Def f(x) == 2of(f)(x) |
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iff | Def P  Q == (P  Q) & (P  Q) |
| | Thm* A,B:Prop. (A  B) Prop |
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l_member | Def (x l) == i: . i<||l|| & x = l[i] T |
| | Thm* T:Type, x:T, l:T List. (x l) Prop |
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locl | Def locl(a) == inr(a) |
| | Thm* a:Id. locl(a) Knd |
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map | Def map(f;as) == Case of as; nil nil ; a.as' [(f(a)) / map(f;as')]
Def (recursive) |
| | Thm* A,B:Type, f:(A B), l:A List. map(f;l) B List |
| | Thm* A,B:Type, f:(A B), l:A List . map(f;l) B List |
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not | Def A == A  False |
| | Thm* A:Prop. ( A) Prop |
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pi1 | Def 1of(t) == t.1 |
| | Thm* A:Type, B:(A Type), p:(a:A B(a)). 1of(p) A |
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pi2 | Def 2of(t) == t.2 |
| | Thm* A:Type, B:(A Type), p:(a:A B(a)). 2of(p) B(1of(p)) |
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rcv | Def rcv(l; tg) == inl(<l,tg>) |
| | Thm* l:IdLnk, tg:Id. rcv(l; tg) Knd |
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top | Def Top == Void given Void |
| | Thm* Top Type |