| | Who Cites tag rel? |
|
| tag_rel | Def R(tg) == swap adjacent[ tg(x) = tg(y)  Label]^* |
| | | Thm*  A:Type, tg:(A  Label). R(tg) (A List)(A List)Prop |
|
| lbl | Def Label == {p:Pattern|  ground_ptn(p) } |
| | | Thm* Label Type |
|
| 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 |
|
| rel_star | Def (R^*)(x,y) == n:. x R^n y |
| | | Thm* T:Type, R:(TTProp). (R^*) TTProp |
|
| int_seg | Def {i..j } == {k: | i  k < j } |
| | | Thm* m,n:. {m..n} Type |
|
| nat | Def == {i:| 0i } |
| | | Thm* Type |
|
| lelt | Def i j < k == ij & j < k |
|
| le | Def AB == B < A |
| | | Thm* i,j:. (ij) Prop |
|
| not | Def A == A   False |
| | | Thm* A:Prop. (A) Prop |
|
| 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)  |
|
| assert | Def b == if b True else False fi |
| | | Thm* b:. b Prop |
|
| ptn | Def Pattern == rec(T.ptn_con(T)) |
| | | Thm* Pattern Type |
|
| 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 |
|
| 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 |
|
| select | Def l[i] == hd(nth_tl(i;l)) |
| | | Thm* A:Type, l:A List, n:. 0n n < ||l|| l[n] A |
|
| length | Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive) |
| | | Thm* A:Type, l:A List. ||l|| |
| | | Thm* ||nil|| |
|
| rel_exp | Def R^n == if n=0 x,y. x = y T else x,y. z:T. (x R z) & (z R^n-1 y) fi (recursive) |
| | | Thm* n:, T:Type, R:(TTProp). R^n TTProp |
|
| case_default | Def Default = > body(value,value) == body |
|
| band | Def pq == if p q else false fi |
| | | Thm* p,q:. (pq) |
|
| 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)))) |
|
| 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]) |
|
| case | Def Case(value) body == body(value,value) |
|
| ptn_con | Def ptn_con(T) == Atom++Atom+(T T) |
| | | Thm* T:Type. ptn_con(T) Type |
|
| flip | Def (i, j)(x) == if x=ij ;x=ji else x fi |
| | | Thm* k:, i,j:k. (i, j) kk |
|
| 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 |
|
| 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 |
|
| mklist | Def mklist(n;f) == primrec(n;nil;i,l. l @ [(f(i))]) |
| | | Thm* T:Type, n:, f:(nT). mklist(n;f) T List |
|
| 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 |
|
| eq_int | Def i=j == if i=j true ; false fi |
| | | Thm* i,j:. (i=j) |
|
| tl | Def tl(l) == Case of l; nil nil ; h.t t |
| | | Thm* A:Type, l:A List. tl(l) A List |
|
| case_inl | Def inl(x) = > body(x) cont(value,contvalue) == InjCase(value; x. body(x); _. cont(contvalue,contvalue)) |
|
| case_inr | Def inr(x) = > body(x) cont(value,contvalue) == InjCase(value; _. cont(contvalue,contvalue); x. body(x)) |
|
| le_int | Def ij == j < i |
| | | Thm* i,j:. (ij) |
|
| 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 |
|
| lt_int | Def i < j == if i < j true ; false fi |
| | | Thm* i,j:. (i < j) |
|
| bnot | Def b == if b false else true fi |
| | | Thm* b:. b |
