| Some definitions of interest. |
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assert | Def b == if b True else False fi |
| | Thm* b:. b Prop |
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band | Def pq == if p q else false fi |
| | Thm* p,q:. (pq) |
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decidable | Def Dec(P) == P P |
| | Thm* A:Prop. Dec(A) Prop |
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iff | Def P Q == (P Q) & (P Q) |
| | Thm* A,B:Prop. (A B) Prop |
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sfa_doc_greater_list_bound | Def y greater-bounds x == i:||x||. x[i]<y |
| | Thm* x: List, y:. y greater-bounds x Prop |
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int_seg | Def {i..j} == {k:| i k < j } |
| | Thm* m,n:. {m..n} Type |
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kleene_minimize | Def mu(f) == if f(0) 0 else 1+mu(x.f(1+x)) fi (recursive) |
| | Thm* mu {f:()| x:. f(x) } |
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nat | Def == {i:| 0i } |
| | Thm* Type |
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le | Def AB == B<A |
| | Thm* i,j:. (ij) Prop |
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nequal | Def a b T == a = b T |
| | Thm* A:Type, x,y:A. (x y) Prop |
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sfa_doc_factorial | Def x! == if x=0 1 else x(x-1)! fi (recursive) |
| | Thm* x:. x! |
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sfa_doc_ntuple | Def A^n == if n=0 Unit ; n=1 A else A(A^(n-1)) fi (recursive) |
| | Thm* A:Type, n:. (A^n) Type |
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sfa_doc_sample_intmod | Def mod k == x,y://(m:. x-y = mk) |
| | Thm* k:. mod k Type |
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sfa_doc_sexpr | Def Sexpr(A) == rec(T.(TT)+A) |
| | Thm* A:Type. Sexpr(A) Type |
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sfa_doc_sexpr_reverse | Def Reverse(e)
Def == Case of e
Def == CaInj(x) Inj(x)
Def == CaCons(s1;s2) Cons(Reverse(s2);Reverse(s1))
Def (recursive) |
| | Thm* A:Type, e:Sexpr(A). Reverse(e) Sexpr(A) |
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sfa_doc_sexpr_cons | Def Cons(s1;s2) == inl(<s1,s2>) |
| | Thm* A:Type, s1,s2:Sexpr(A). Cons(s1;s2) Sexpr(A) |
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sfa_doc_sexpr_inj | Def Inj(a) == inr(a) |
| | Thm* A:Type, a:A. Inj(a) Sexpr(A) |
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subtype | Def S T == x:S. x T |
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top | Def Top == Void(given Void) |
| | Thm* Top Type |