| | Who Cites trace consistent rel? |
|
| trace_consistent_rel |
Def trace_consistent_rel(rho;da;R;r)
==  i: ||r.args||. trace_consistent(rho;da;R;r.args[i]) |
| | | Thm* rho:Decl, r:rel(), da:Collection(dec()), R:(Label  Label ).
trace_consistent_rel(rho;da;R;r)  Prop |
|
| trace_consistent |
Def trace_consistent(rho;da;R;t)
== g:Label.
 term_mentions_guard(g;t)  
subtype_rel(({a:( [[da]] rho)| (R(g,kind(a))) } List); (rho(lbl_pr( < Trace, g > )))) |
| | |
Thm* rho:Decl, t:Term, da:Collection(dec()), R:(LabelLabel).
trace_consistent(rho;da;R;t) Prop |
|
| decls_mng |
Def [[ds]] rho == [[d]] rho for d {d:dec()| d ds } |
| | | Thm* ds:Collection(dec()), rho:Decl. [[ds]] rho Decl |
|
| dec |
Def dec() == Label SimpleType |
| | | Thm* dec() Type |
|
| decl |
Def Decl == LabelType |
| | | Thm* Decl{i} Type{i'} |
|
| rel |
Def rel() == relname()(Term List) |
| | | Thm* rel() Type |
|
| relname |
Def relname() == SimpleType+Label |
| | | Thm* relname() Type |
|
| st |
Def SimpleType == Tree(Label+Unit) |
| | | Thm* SimpleType Type |
|
| term |
Def Term == Tree(ts()) |
| | | Thm* Term Type |
|
| ts |
Def ts() == Label+Label+Label+Label+Label |
| | | Thm* ts() Type |
|
| sigma |
Def (d) == l:Labeldecl_type(d;l) |
| | | Thm* d:Decl. (d) Type |
|
| lbl |
Def Label == {p:Pattern| ground_ptn(p) } |
| | | Thm* Label Type |
|
| assert |
Def b == if b True else False fi |
| | | Thm* b:. b Prop |
|
| col |
Def Collection(T) == TProp |
| | | Thm* T:Type{i'}. Collection{i}(T) Type{i'} |
|
| int_seg |
Def {i..j } == {k: | i  k < j } |
| | | Thm* m,n:. {m..n} Type |
|
| length |
Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive) |
| | |
Thm* A:Type, l:A List. ||l|| |
| | |
Thm* ||nil|| |
|
| 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 |
|
| rel_mentions_trace |
Def rel_mentions_trace(r)
== reduce( x,y. mentions_trace(x)   y;false;r.args) |
| | | Thm* r:rel(). rel_mentions_trace(r) |
|
| rel_args |
Def t.args == 2of(t) |
| | |
Thm* t:rel(). t.args Term List |
|
| select |
Def l[i] == hd(nth_tl(i;l)) |
| | |
Thm* A:Type, l:A List, n:. 0n n < ||l|| l[n] A |
|
| term_mentions_guard |
Def term_mentions_guard(g;t)
== term_iterate(x.false;
x.false;
x.false;
x.false;
x.x = g;
x,y. x y;
t) |
| | | Thm* t:Term, g:Label. term_mentions_guard(g;t) |
|
| 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) |
|
| ptn |
Def Pattern == rec(T.ptn_con(T)) |
| | |
Thm* Pattern Type |
|
| pi2 |
Def 2of(t) == t.2 |
| | |
Thm* A:Type, B:(AType), p:(a:AB(a)). 2of(p) B(1of(p)) |
|
| mentions_trace |
Def mentions_trace(t)
== iterate(statevar x- > false
statevar x'- > false
funsymbol x- > false
freevar x- > false
trace(P)- > true
x(y)- > x y
over t) |
| | | Thm* t:Term. mentions_trace(t) |
|
| bor |
Def p q == if p true else q fi |
| | | Thm* p,q:. (p q) |
|
| reduce |
Def reduce(f;k;as) == Case of as; nil k ; a.as' f(a,reduce(f;k;as')) (recursive) |
| | |
Thm* A,B:Type, f:(ABB), k:B, as:A List. reduce(f;k;as) B |
|
| 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 |
|
| dec_mng |
Def [[d]] rho == Case(d) Case x : s = > x:[[s]] rho |
| | |
Thm* rho:Decl, d:dec(). [[d]] rho Decl |
|
| dbase |
Def x:y(a) == if a = x y else Top fi |
| | | Thm* x:Label, y:Type. x:y Decl |
|
| eq_lbl |
Def l1 = l2
== Case(l1)
Case ptn_atom(x) = >
Case(l2)
Case ptn_atom(y) = >
x=yAtom
Default = > false
Case ptn_int(x) = >
Case(l2)
Case ptn_int(y) = >
x=y
Default = > false
Case ptn_var(x) = >
Case(l2)
Case ptn_var(y) = >
x=yAtom
Default = > false
Case ptn_pr( < x, y > ) = >
Case(l2)
Case ptn_pr( < u, v > ) = >
x = uy = v
Default = > false
Default = > false
(recursive) |
| | |
Thm* l1,l2:Pattern. l1 = l2 |
|
| term_iter |
Def iterate(statevar x- > v(x)
statevar x''- > v'(x')
funsymbol op- > opr(op)
freevar f- > fvar(f)
trace(tr)- > trace(tr)
a(b)- > comb(a;b)
over t)
== term_iterate(x.v(x);
x'.v'(x');
op.opr(op);
f.fvar(f);
tr.trace(tr);
a,b. comb(a;b);
t) |
| | | Thm* A:Type, v,v',opr,fvar,trace:(LabelA), comb:(AAA), t:Term.
iterate(statevar x- > v(x)
statevar x''- > v'(x')
funsymbol op- > opr(op)
freevar f- > fvar(f)
trace(tr)- > trace(tr)
a(b)- > comb(a,b)
over t)
A |
|
| term_iterate |
Def term_iterate(v;
p;
op;
f;
tr;
a;
t)
== t_iterate(x.ts_case(x)
var(a)= > v(a)
var'(b)= > p(b)
opr(c)= > op(c)
fvar(d)= > f(d)
trace(P)= > tr(P)
end_ts_case ;a;t) |
| | | Thm* A:Type, v,op,f,p,tr:(LabelA), a:(AAA), t:Term. term_iterate(v;p;op;f;tr;a;t) A |
|
| 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_ptn_int |
Def Case ptn_int(x) = > body(x) cont(x1,z)
== (x1.inr(x2) = >
(x1.inl(x2) = > body(hd([x2 / tl(x1)])) cont(hd(x1),z))([x2 / tl(x1)])
cont
(hd(x1)
,z))
([x1]) |
|
| ts_case |
Def ts_case(x)
var(a)= > v(a)
var'(b)= > p(b)
opr(f)= > op(f)
fvar(x)= > f(x)
trace(P)= > t(P)
end_ts_case
== Case(x)
Case ts_var(a) = >
v(a)
Case ts_pvar(b) = >
p(b)
Case ts_op(f) = >
op(f)
Case ts_fvar(x) = >
f(x)
Case ts_trace(P) = >
t(P)
Default = >  |
| | |
Thm* A:Type, v,op,f,p,t:(LabelA), x:ts().
ts_case(x)var(a)= > v(a)var'(b)= > p(b)opr(f)= > op(f)fvar(y)= > f(y)trace(P)= > t(P)end_ts_case A |
|
| case_ts_trace |
Def Case ts_trace(x) = > body(x) cont(x1,z)
== (x1.inr(x2) = >
(x1.inr(x2) = >
(x1.inr(x2) = >
(x1.inr(x2) = > body(hd([x2 / tl(x1)])) cont(hd(x1),z))([x2 / tl(x1)])
cont
(hd(x1)
,z))
([x2 / tl(x1)])
cont
(hd(x1)
,z))
([x2 / tl(x1)])
cont
(hd(x1)
,z))
([x1]) |
|
| case_ts_fvar |
Def Case ts_fvar(x) = > body(x) cont(x1,z)
== (x1.inr(x2) = >
(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))
([x2 / tl(x1)])
cont
(hd(x1)
,z))
([x1]) |
|
| case_ts_op |
Def Case ts_op(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_ts_pvar |
Def Case ts_pvar(x) = > body(x) cont(x1,z)
== (x1.inr(x2) = >
(x1.inl(x2) = > body(hd([x2 / tl(x1)])) cont(hd(x1),z))([x2 / tl(x1)])
cont
(hd(x1)
,z))
([x1]) |
|
| 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 |
|
| tree |
Def Tree(E) == rec(T.tree_con(E;T)) |
| | |
Thm* E:Type. Tree(E) Type |
|
| st_mng |
Def [[s]] rho == t_iterate(st_lift(rho);x,y. xy;s) |
| | | Thm* rho:Decl, s:SimpleType. [[s]] rho Type |
|
| t_iterate |
Def t_iterate(l;n;t)
== Case(t)
Case x;y = >
n(t_iterate(l;n;x),t_iterate(l;n;y))
Case tree_leaf(x) = >
l(x)
Default = > True
(recursive) |
| | |
Thm* E,A:Type, l:(EA), n:(AAA), t:Tree(E). t_iterate(l;n;t) A |
|
| 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 |
Def Case(value) body == body(value,value) |
|
| ptn_con |
Def ptn_con(T) == Atom++Atom+(TT) |
| | | Thm* T:Type. ptn_con(T) Type |
|
| tl |
Def tl(l) == Case of l; nil nil ; h.t t |
| | |
Thm* A:Type, l:A List. tl(l) A List |
|
| le_int |
Def ij == j < i |
| | | Thm* i,j:. (ij) |
|
| eq_atom |
Def x=yAtom == if x=yAtomtrue; false fi |
| | | Thm* x,y:Atom. x=yAtom |
|
| eq_int |
Def i=j == if i=j true ; false fi |
| | | Thm* i,j:. (i=j) |
|
| case_ptn_atom |
Def Case ptn_atom(x) = > body(x) cont(x1,z)
== InjCase(x1; x2. body(x2); _. cont(z,z)) |
|
| clbl |
Def $x == ptn_atom("$x") |
|
| lbl_pair |
Def lbl_pr( < x, y > ) == ptn_pr( < x,y > ) |
| | | Thm* x,y:Pattern. lbl_pr( < x, y > ) Pattern |
| | |
Thm* x,y:Label. lbl_pr( < x, y > ) Label |
|
| kind |
Def kind(a) == 1of(a) |
| | | Thm* d:Decl, a:(d). kind(a) Label |
| | |
Thm* M:sm{i:l}(), a:M.action. kind(a) Label & kind(a) Pattern |
|
| tree_con |
Def tree_con(E;T) == E+(TT) |
| | | Thm* E,T:Type. tree_con(E;T) Type |
|
| 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)) |
|
| 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 |
|
| case_ts_var |
Def Case ts_var(x) = > body(x) cont(x1,z)
== InjCase(x1; x2. body(x2); _. cont(z,z)) |
|
| case_tree_leaf |
Def Case tree_leaf(x) = > body(x) cont(x1,z)
== InjCase(x1; x2. body(x2); _. cont(z,z)) |
|
| case_node |
Def Case x;y = > body(x;y) cont(x1,z)
== InjCase(x1; _. cont(z,z); x2. x2/x3,x2@0. body(x3;x2@0)) |
|
| ptn_atom |
Def ptn_atom(x) == inl(x) |
| | | Thm* T:Type, x:Atom. ptn_atom(x) ptn_con(T) |
| | |
Thm* x:Atom. ptn_atom(x) Pattern |
| | |
Thm* x:Atom. ptn_atom(x) Label |
|
| ptn_pr |
Def ptn_pr(x) == inr(inr(inr(x))) |
| | | Thm* T:Type, x:(TT). ptn_pr(x) ptn_con(T) |
| | |
Thm* x,y:Pattern. ptn_pr( < x,y > ) Pattern |
|
| pi1 |
Def 1of(t) == t.1 |
| | | Thm* A:Type, B:(AType), p:(a:AB(a)). 1of(p) A |
|
| col_member |
Def x c == c(x) |
| | | Thm* T:Type, x:T, c:Collection(T). x c Prop |
|
| dall |
Def D(i) for i I(x) ==  i:I. D(i)(x) |
| | | Thm* I:Type, D:(IDecl). D(i) for i I Decl |
|
| decl_type |
Def decl_type(d;x) == d(x) |
| | | Thm* dec:Decl, x:Label. decl_type(dec;x) Type |
|
| case_mk_dec |
Def Case lbl : typ = > body(lbl;typ)(x,z) == x/x2,x1. body(x2;x1) |
|
| st_lift |
Def st_lift(rho)(x) == InjCase(x; x'. rho(x'); a. Top) |
| | | Thm* rho:(LabelType). st_lift(rho) (Label+Unit)Type |
|
| top |
Def Top == Void given Void |
| | |
Thm* Top Type |
