| Who Cites append? |
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append |
Def as @ bs == Case of as; nil bs ; a.as' [a / (as' @ bs)] (recursive) |
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Thm* T:Type, as,bs:T List. (as @ bs) T List |
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decl |
Def Decl == Label Type |
| | Thm* decl{i:l} Type{i'} |
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sigma |
Def ( d) == l:Label decl_type(d;l) |
| | Thm* d:Decl. ( d) Type |
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lbl |
Def Label == {p:Pattern| ground_ptn(p) } |
| | Thm* Label Type |
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trace_projection |
Def tr | P == filter( x.P(kind(x));tr) |
| | Thm* d:Decl, tr:( d) List, P:(Label  ). tr | P ( d) List |
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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) |
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Thm* p:Pattern. ground_ptn(p)  |
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assert |
Def b == if b True else False fi |
| | Thm* b: . b Prop |
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ptn |
Def Pattern == rec(T.ptn_con(T)) |
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Thm* Pattern Type |
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decl_type |
Def decl_type(d;x) == d(x) |
| | Thm* dec:Decl, x:Label. decl_type(dec;x) Type |
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kind |
Def kind(a) == 1of(a) |
| | Thm* d:Decl, a:( d). kind(a) Label |
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filter |
Def filter(P;l) == reduce( a,v. if P(a) [a / v] else v fi;nil;l) |
| | Thm* T:Type, P:(T  ), l:T List. filter(P;l) T List |
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case_default |
Def Default = > body(value,value) == body |
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band |
Def p q == if p q else false fi |
| | Thm* p,q: . (p q)  |
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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+(T T) |
| | Thm* T:Type. ptn_con(T) Type |
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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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reduce |
Def reduce(f;k;as) == Case of as; nil k ; a.as' f(a,reduce(f;k;as')) (recursive) |
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Thm* A,B:Type, f:(A B B), k:B, as:A List. reduce(f;k;as) B |
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hd |
Def hd(l) == Case of l; nil "?" ; h.t h |
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Thm* A:Type, l:A List. ||l|| 1  hd(l) A |
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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 |
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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)) |