| | Who Cites R async? |
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| R_async | Def asyncR(E) == swap adjacent[ loc(E)(x) = loc(E)(y) &  (is-send(E)(x)) & (is-send(E)(y))  (is-send(E)(x)) & (is-send(E)(y))] |
| | | Thm*  E:EventStruct. asyncR(E)  (|E| List)  (|E| List)Prop |
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| event_is_snd | Def is-send(E) == 1of(2of(2of(2of(2of(E))))) |
| | | Thm* E:EventStruct. is-send(E) |E| |
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| lbl | Def Label == {p:Pattern| ground_ptn(p) } |
| | | Thm* Label Type |
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| assert | Def b == if b True else False fi |
| | | Thm* b:. b Prop |
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| swap_adjacent | Def swap adjacent[P(x;y)](L1,L2) ==  i: (||L1||-1). P(L1[i];L1[(i+1)]) & L2 = swap(L1;i;i+1) A List |
| | | Thm* A:Type, P:(AAProp). swap adjacent[P(x,y)] (A List)(A List)Prop |
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| int_seg | Def {i..j } == {k: | i  k < j } |
| | | Thm* m,n:. {m..n} Type |
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| lelt | Def i j < k == ij & j < k |
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| le | Def AB == B < A |
| | | Thm* i,j:. (ij) Prop |
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| not | Def A == A   False |
| | | Thm* A:Prop. (A) Prop |
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| event_loc | Def loc(E) == 1of(2of(2of(2of(E)))) |
| | | Thm* E:EventStruct. loc(E) |E|Label |
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| carrier | Def |S| == 1of(S) |
| | | Thm* S:Structure. |S| Type |
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| pi2 | Def 2of(t) == t.2 |
| | | Thm* A:Type, B:(AType), p:(a:A B(a)). 2of(p) B(1of(p)) |
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| pi1 | Def 1of(t) == t.1 |
| | | Thm* A:Type, B:(AType), p:(a:AB(a)). 1of(p) A |
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| ground_ptn | Def ground_ptn(p) == Case(p) Case ptn_var(v) = > false Case ptn_pr( < x, y > ) = > ground_ptn(x) ground_ptn(y) Default = > true (recursive) |
| | | Thm* p:Pattern. ground_ptn(p) |
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| ptn | Def Pattern == rec(T.ptn_con(T)) |
| | | Thm* Pattern Type |
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| swap | Def swap(L;i;j) == (L o (i, j)) |
| | | Thm* T:Type, L:T List, i,j:||L||. swap(L;i;j) T List |
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| permute_list | Def (L o f) == mklist(||L||; i.L[(f(i))]) |
| | | Thm* T:Type, L:T List, f:(||L||||L||). (L o f) T List |
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| select | Def l[i] == hd(nth_tl(i;l)) |
| | | Thm* A:Type, l:A List, n:. 0n n < ||l|| l[n] A |
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| length | Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive) |
| | | Thm* A:Type, l:A List. ||l|| |
| | | Thm* ||nil|| |
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| case_default | Def Default = > body(value,value) == body |
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| band | Def pq == if p q else false fi |
| | | Thm* p,q:. (pq) |
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| case_lbl_pair | Def Case ptn_pr( < x, y > ) = > body(x;y) cont(x1,z) == InjCase(x1; _. cont(z,z); x2. InjCase(x2; _. cont(z,z); x2@0. InjCase(x2@0; _. cont(z,z); x2@1. x2@1/x3,x2@2. body(x3;x2@2)))) |
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| case_ptn_var | Def Case ptn_var(x) = > body(x) cont(x1,z) == (x1.inr(x2) = > (x1.inr(x2) = > (x1.inl(x2) = > body(hd([x2 / tl(x1)])) cont(hd(x1),z))([x2 / tl(x1)]) cont(hd(x1),z))([x2 / tl(x1)]) cont(hd(x1),z))([x1]) |
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| case | Def Case(value) body == body(value,value) |
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| ptn_con | Def ptn_con(T) == Atom++Atom+(TT) |
| | | Thm* T:Type. ptn_con(T) Type |
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| flip | Def (i, j)(x) == if x=ij ;x=ji else x fi |
| | | Thm* k:, i,j:k. (i, j) kk |
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| nth_tl | Def nth_tl(n;as) == if n0 as else nth_tl(n-1;tl(as)) fi (recursive) |
| | | Thm* A:Type, as:A List, i:. nth_tl(i;as) A List |
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| hd | Def hd(l) == Case of l; nil "?" ; h.t h |
| | | Thm* A:Type, l:A List. ||l|| 1 hd(l) A |
| | | Thm* A:Type, l:A List . hd(l) A |
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| tl | Def tl(l) == Case of l; nil nil ; h.t t |
| | | Thm* A:Type, l:A List. tl(l) A List |
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| case_inl | Def inl(x) = > body(x) cont(value,contvalue) == InjCase(value; x. body(x); _. cont(contvalue,contvalue)) |
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| case_inr | Def inr(x) = > body(x) cont(value,contvalue) == InjCase(value; _. cont(contvalue,contvalue); x. body(x)) |
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| mklist | Def mklist(n;f) == primrec(n;nil;i,l. l @ [(f(i))]) |
| | | Thm* T:Type, n:, f:(nT). mklist(n;f) T List |
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| primrec | Def primrec(n;b;c) == if n=0 b else c(n-1,primrec(n-1;b;c)) fi (recursive) |
| | | Thm* T:Type, n:, b:T, c:(nTT). primrec(n;b;c) T |
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| eq_int | Def i=j == if i=j true ; false fi |
| | | Thm* i,j:. (i=j) |
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| le_int | Def ij == j < i |
| | | Thm* i,j:. (ij) |
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| append | Def as @ bs == Case of as; nil bs ; a.as' [a / (as' @ bs)] (recursive) |
| | | Thm* T:Type, as,bs:T List. (as @ bs) T List |
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| lt_int | Def i < j == if i < j true ; false fi |
| | | Thm* i,j:. (i < j) |
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| bnot | Def b == if b false else true fi |
| | | Thm* b:. b |
