statement stringlengths 4 1.37k | proof stringclasses 1
value | type stringclasses 6
values | symbolic_name stringlengths 1 27 | library stringclasses 4
values | filename stringclasses 35
values | imports listlengths 0 0 | deps listlengths 0 25 | docstring stringclasses 1
value | source_url stringclasses 1
value | commit stringclasses 1
value |
|---|---|---|---|---|---|---|---|---|---|---|
wp : (Statement × ℙ Sequent × Wp_Env) ß Result | ZAX | wp | daz | src/daz/dtd514.doc | [] | [
"Statement"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
FLAG ::= True | False | Z | FLAG | daz | src/daz/dtd514.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
[LABEL] | Z | LABEL | daz | src/daz/dtd514.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
mean : ¯ × ¯ → ¯
----
x, y:¯ • mean(x, y) = (x +R y) /R 2.0 | ZAX | mean | daz | src/daz/mdt530.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
sum_squares : ¯ × ¯ → ¯
----
x, y:¯ • sum_squares(x, y) = x ^Z 2 +R y ^Z 2 | ZAX | sum_squares | daz | src/daz/mdt530.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
Dom:('a ª 'b) → ('a) ℙ
----
(r : ('a ª 'b))
• Dom r = {x | y • (x, y) r} | HOLCONST | Dom | hol | src/hol/dtd071.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
Ran:('a ª 'b) → ('b) ℙ
----
(r : ('a ª 'b))
• Ran r = {y | x • (x, y) r} | HOLCONST | Ran | hol | src/hol/dtd071.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
Id:('a) ℙ → ('a ª 'a)
----
(s : ('a) ℙ )
• Id s = {(x, y) | x = y ∧ x s} | HOLCONST | Id | hol | src/hol/dtd071.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
Graph:('a → 'b) → ('a ª 'b)
----
f : 'a → 'b
• Graph f = {(x, y) | y = f x} | HOLCONST | Graph | hol | src/hol/dtd071.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
$R_»_R:('a ª 'b) → ('b ª 'c) → ('a ª 'c)
----
r s • r R_»_R s =
{(x,z)| y • (x,y) r ∧ (y,z) s} | HOLCONST | R_»_R | hol | src/hol/dtd071.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
$R_o_R:('b ª 'c) → ('a ª 'b) → ('a ª 'c)
----
r s • r R_o_R s = s R_»_R r | HOLCONST | R_o_R | hol | src/hol/dtd071.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
$InvRel:('a ª 'b) → ('b ª 'a)
----
r • InvRel r = {(x,y)| (y,x) r} | HOLCONST | InvRel | hol | src/hol/dtd071.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
$Image:('a ª 'b) → ('a) ℙ → ('b) ℙ
----
r s • r Image s = {y| x • x s ∧ (x, y) r} | HOLCONST | Image | hol | src/hol/dtd071.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
$Reflexive:('a ª 'a) ℙ
----
Reflexive = {r | x • (x, x) r} | HOLCONST | Reflexive | hol | src/hol/dtd071.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
$Symmetric:('a ª 'a) ℙ
----
Symmetric = {r | x y • (x, y) r ⇒ (y, x) r} | HOLCONST | Symmetric | hol | src/hol/dtd071.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
$Transitive:('a ª 'a) ℙ
----
Transitive = {r | x y z • (x, y) r ∧ (y, z) r ⇒ (x, z) r} | HOLCONST | Transitive | hol | src/hol/dtd071.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
$Injective:('a ª 'b) ℙ
----
Injective = {r | x y; z • (x, z) r ∧ (y, z) r ⇒ x = y} | HOLCONST | Injective | hol | src/hol/dtd071.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
$Surjective:'b SET → ('a ª 'b) ℙ
----
s • Surjective s = {r | s = Ran r} | HOLCONST | Surjective | hol | src/hol/dtd071.doc | [] | [
"Ran"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
$Total:'a SET → ('a ª 'b) ℙ
----
s • Total s = {r | s = Dom r} | HOLCONST | Total | hol | src/hol/dtd071.doc | [] | [
"Dom"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
$Functional:('a ª 'b) ℙ
----
Functional = {r | x; w z • (x, w) r ∧ (x, z) r ⇒ w = z} | HOLCONST | Functional | hol | src/hol/dtd071.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
$RelCombine:('a ª 'b) → ('a ª 'c) → ('a ª ('b × 'c))
----
f g • RelCombine f g
= {(x, (y,z)) | (x,y) f ∧ (x,z) g} | HOLCONST | RelCombine | hol | src/hol/dtd071.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
$At:('a ª 'b) → 'a → 'b
----
(f : ('a ª 'b)) (x : 'a) (y : 'b)
• (x, y) f ∧ (z • (x, z) f ⇒ z = y) ⇒ f At x = y | HOLCONST | At | hol | src/hol/dtd072.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
Finite:'a ℙ ℙ
----
Finite = ¥{u | {} u ∧ a x • a u ⇒ ({x} À a) u} | HOLCONST | Finite | hol | src/hol/dtd073.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
Min : î SET → î
----
m a • m a ∧ (i • i a ⇒ m ¼ i) ⇒ Min a = m | HOLCONST | Min | hol | src/hol/dtd073.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
$Max:î ℙ → î
----
m a • m a ∧ (i • i a ⇒ i ¼ m) ⇒ Max a = m | HOLCONST | Max | hol | src/hol/dtd073.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
Size : 'a SET → î
----
a • Size a = Min {i | list • Length list = i ∧ Elems list = a} | HOLCONST | Size | hol | src/hol/dtd073.doc | [] | [
"Elems",
"Min"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
$Iter:î → ('a ª 'a) → ('a ª 'a)
----
(r : 'a ª 'a)(n : î)
• Iter 0 r = Id Universe
∧ Iter (n+1) r = r » (Iter n r) | HOLCONST | Iter | hol | src/hol/dtd073.doc | [] | [
"Id"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
Elems : 'a LIST → 'a SET
----
Elems [] = {}
∧ x l •
Elems (Cons x l) = {x} À Elems l | HOLCONST | Elems | hol | src/hol/dtd074.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
Distinct : 'a LIST SET
----
[] Distinct
∧ x l • (Cons x l) Distinct ¤ ³x Elems l ∧ l Distinct | HOLCONST | Distinct | hol | src/hol/dtd074.doc | [] | [
"Elems"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
$Lists:'a ℙ → 'a LIST ℙ
----
(a : 'a ℙ ) • Lists a = {l | Elems l a} | HOLCONST | Lists | hol | src/hol/dtd074.doc | [] | [
"Elems"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
$Lists1: 'a ℙ → 'a LIST ℙ
----
(a : 'a ℙ ) • Lists1 a = Lists a \ {[]} | HOLCONST | Lists1 | hol | src/hol/dtd074.doc | [] | [
"Lists"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
InjLists:'a ℙ → 'a LIST ℙ
----
(a : 'a ℙ ) • InjLists a = Lists a ¬ Distinct | HOLCONST | InjLists | hol | src/hol/dtd074.doc | [] | [
"Distinct",
"Lists"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
Nth:'a LIST → î → 'a
----
(l : 'a LIST) (x : 'a) (n : î) •
Nth (Cons x l) n
= if n = 1
then x
else Nth l (n-1) | HOLCONST | Nth | hol | src/hol/dtd074.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
ListRel:'a LIST → (î ª 'a)
----
(l : 'a LIST) •
ListRel l = 1 .. Length l ò (Graph(Nth l)) | HOLCONST | ListRel | hol | src/hol/dtd074.doc | [] | [
"Graph",
"Nth"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
RelList:(î ª 'a) → 'a LIST
----
(l : 'a LIST) • RelList (ListRel l) = l | HOLCONST | RelList | hol | src/hol/dtd074.doc | [] | [
"ListRel"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
Last:'a LIST → 'a
----
x l • Last (Cons x l) =
if l = [] then x else Last l | HOLCONST | Last | hol | src/hol/dtd074.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
Front:'a LIST → 'a LIST
----
x l • Front (Cons x l) =
if l = [] then [] else (Cons x (Front l)) | HOLCONST | Front | hol | src/hol/dtd074.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
Enumerate: î ℙ → (î ª î)
----
a:î ℙ •
Enumerate a =
{ (i, j) | l • j a
∧ l Distinct
∧ Length l = i
∧ Elems l = a ¬ 0 .. j } | HOLCONST | Enumerate | hol | src/hol/dtd074.doc | [] | [
"Distinct",
"Elems"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
Squash:(î ª 'a) → (î ª 'a)
----
r:î ª 'a • Squash r = Enumerate (Dom r) » r | HOLCONST | Squash | hol | src/hol/dtd074.doc | [] | [
"Dom",
"Enumerate"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
Extract:î ℙ → 'a LIST → 'a LIST
----
a l •
Extract a l = RelList (Squash (a ò (ListRel l))) | HOLCONST | Extract | hol | src/hol/dtd074.doc | [] | [
"ListRel",
"RelList",
"Squash"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
$Prefix:'a LIST → 'a LIST → BOOL
----
s t • s Prefix t ¤ ( v • s ë v = t) | HOLCONST | Prefix | hol | src/hol/dtd074.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
$Suffix:'a LIST → 'a LIST → BOOL
----
s t • s Suffix t ¤ ( u • u ë s = t) | HOLCONST | Suffix | hol | src/hol/dtd074.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
$In:'a LIST → 'a LIST → BOOL
----
s t • s In t ¤ ( u v • u ë s ë v = t) | HOLCONST | In | hol | src/hol/dtd074.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
Flat:'a LIST LIST → 'a LIST
----
(e: 'a LIST) (l: 'a LIST LIST) • Flat [] = []
∧ Flat (Cons e l) = e ë (Flat l) | HOLCONST | Flat | hol | src/hol/dtd074.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
Irrefl : ('a SET × ('a → 'a → BOOL)) → BOOL
----
X $<< •
Irrefl(X, $<<)
¤ x • x X ⇒ ³x << x | HOLCONST | Irrefl | hol | src/hol/dtd115.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
Antisym : ('a SET × ('a → 'a → BOOL)) → BOOL
----
X $<< •
Antisym(X, $<<)
¤ x y • x X ∧ y X ∧ ³x = y ⇒ ³(x << y ∧ y << x) | HOLCONST | Antisym | hol | src/hol/dtd115.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
Trans : ('a SET × ('a → 'a → BOOL)) → BOOL
----
X $<< •
Trans(X, $<<)
¤ x y z • x X ∧ y X ∧ z X ∧ x << y ∧ y << z ⇒ x << z | HOLCONST | Trans | hol | src/hol/dtd115.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
StrictPartialOrder : ('a SET × ('a → 'a → BOOL)) → BOOL
----
X $<< •
StrictPartialOrder(X, $<<)
¤ Irrefl(X, $<<) ∧ Antisym(X, $<<) ∧ Trans(X, $<<) | HOLCONST | StrictPartialOrder | hol | src/hol/dtd115.doc | [] | [
"Antisym",
"Irrefl",
"Trans"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
Trich : ('a SET × ('a → 'a → BOOL)) → BOOL
----
X $<< •
Trich(X, $<<)
¤ x y • x X ∧ y X ∧ ³x = y ⇒ x << y ² y << x | HOLCONST | Trich | hol | src/hol/dtd115.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
StrictLinearOrder : ('a SET × ('a → 'a → BOOL)) → BOOL
----
X $<< • StrictLinearOrder(X, $<<) ¤ StrictPartialOrder(X, $<<) ∧ Trich(X, $<<) | HOLCONST | StrictLinearOrder | hol | src/hol/dtd115.doc | [] | [
"StrictPartialOrder",
"Trich"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
$DenseIn : 'a SET → ('a SET × ('a → 'a → BOOL)) → BOOL
----
A X $<< •
A DenseIn (X, $<<)
¤ x y • x X ∧ y X ∧ x << y ⇒ a • a A ∧ x << a ∧ a << y | HOLCONST | DenseIn | hol | src/hol/dtd115.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
Dense : ('a SET × ('a → 'a → BOOL)) → BOOL
----
X $<< • Dense (X, $<<) ¤ X DenseIn (X, $<<) | HOLCONST | Dense | hol | src/hol/dtd115.doc | [] | [
"DenseIn"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
UpperBound : ('a SET × ('a → 'a → BOOL) × 'a) → BOOL
----
A $<< x • UpperBound(A, $<<, x) ¤ a • a A ⇒ a << x | HOLCONST | UpperBound | hol | src/hol/dtd115.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
$HasSupremum : 'a SET → ('a × 'a SET × ('a → 'a → BOOL)) → BOOL
----
A $<< x X • A HasSupremum(x, X, $<<) ¤
UpperBound(A, $<<, x) ∧ y • y X ∧ UpperBound(A, $<<, y) ⇒ ³y << x | HOLCONST | HasSupremum | hol | src/hol/dtd115.doc | [] | [
"UpperBound"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
UnboundedAbove : ('a SET × ('a → 'a → BOOL)) → BOOL
----
A $<< • UnboundedAbove(A, $<<) ¤ b • b A ⇒ c • c A ∧ b << c | HOLCONST | UnboundedAbove | hol | src/hol/dtd115.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
UnboundedBelow : ('a SET × ('a → 'a → BOOL)) → BOOL
----
A $<< • UnboundedBelow(A, $<<) ¤ b • b A ⇒ c • c A ∧ c << b | HOLCONST | UnboundedBelow | hol | src/hol/dtd115.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
Complete : ('a SET × ('a → 'a → BOOL)) → BOOL
----
X $<< •
Complete(X, $<<)
¤ A x • ³A = {} ∧ A X
∧ UnboundedAbove(A, $<<)
∧ x X
∧ UpperBound(A, $<<, x)
⇒ y • y X ∧ A HasSupremum(y, X, $<<) | HOLCONST | Complete | hol | src/hol/dtd115.doc | [] | [
"HasSupremum",
"UnboundedAbove",
"UpperBound"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
Cuts : ('a SET × ('a → 'a → BOOL)) → 'a SET SET
----
X $<< A •
A Cuts(X, $<<)
¤ A X
∧ ³A = {}
∧ UnboundedAbove(A, $<<)
∧ ( x • x X ∧ UpperBound(A, $<<, x))
∧ (a b • a A ∧ b X ∧ b << a ⇒ b A) | HOLCONST | Cuts | hol | src/hol/dtd115.doc | [] | [
"UnboundedAbove",
"UpperBound"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
DownSet : ('a SET × ('a → 'a → BOOL) × 'a) → 'a SET
----
X $<< x •
DownSet(X, $<<, x) = { y | y X ∧ y << x } | HOLCONST | DownSet | hol | src/hol/dtd115.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
DownSets : ('a SET × ('a → 'a → BOOL) × 'a SET) → 'a SET SET
----
X $<< A s •
s DownSets(X, $<<, A)
¤ x • x A ∧ s = DownSet(X, $<<, x) | HOLCONST | DownSets | hol | src/hol/dtd115.doc | [] | [
"DownSet"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
Sup: ¯ SET → ¯
----
A • ³A = {} ∧ ( b • x • x A ⇒ x ¼ b)
⇒ (x • x A ⇒ x ¼ Sup A) ∧ (b • (x • x A ⇒ x ¼ b) ⇒ Sup A ¼ b) | HOLCONST | Sup | hol | src/hol/dtd116.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
AbsR: ¯ → ¯
----
x • AbsR x = if î¯ 0 ¼ x then x else ~ x | HOLCONST | AbsR | hol | src/hol/dtd116.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
Float : î → ú → ú → ¯
----
m p e • Float m p e = î¯ m * î¯ 10 ^ (e + ~p) | HOLCONST | Float | hol | src/hol/dtd116.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
MaxR : ¯ LIST → ¯
----
(x • MaxR [x] = x)
∧ (x y L •
MaxR (Cons x (Cons y L)) =
if x < MaxR (Cons y L)
then MaxR (Cons y L)
else x) | HOLCONST | MaxR | hol | src/hol/dtd116.doc | [] | [
"Max"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
MinR : ¯ LIST → ¯
----
(x • MinR [x] = x)
∧ (x y L •
MinR (Cons x (Cons y L)) =
if x > MinR (Cons y L)
then MinR (Cons y L)
else x) | HOLCONST | MinR | hol | src/hol/dtd116.doc | [] | [
"Min"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
Enter:('a → 'a → BOOL) → 'a → 'a LIST → 'a LIST
----
rel x y ys •
Enter rel x [] = [x]
∧ Enter rel x (Cons y ys) =
if rel x y
then Cons x (Cons y ys)
else Cons y (Enter rel x ys) | HOLCONST | Enter | hol | src/hol/int002.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
Sort:('a → 'a → BOOL) → 'a LIST → 'a LIST
----
rel x xs •
Sort rel [] = []
∧ Sort rel (Cons x xs) = Enter rel x (Sort rel xs) | HOLCONST | Sort | hol | src/hol/int002.doc | [] | [
"Enter"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
$C:î → î → î
----
n j •
0 C 0 = 1
∧ (n+1) C 0 = 1
∧ 0 C (j+1) = 0
∧ (n+1) C (j+1) = n C j + n C (j+1) | HOLCONST | C | hol | src/hol/int002.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
Reflexive: ('a → 'a → BOOL) → BOOL
----
rel • Reflexive rel ¤ x • rel x x | HOLCONST | Reflexive | hol | src/hol/int002.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
Transitive: ('a → 'a → BOOL) → BOOL
----
rel • Transitive rel ¤ x y z • rel x y ∧ rel y z ⇒ rel x z | HOLCONST | Transitive | hol | src/hol/int002.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
Symmetric: ('a → 'a → BOOL) → BOOL
----
rel • Symmetric rel ¤ x y • rel x y ⇒ rel y x | HOLCONST | Symmetric | hol | src/hol/int002.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
Euclidean: ('a → 'a → BOOL) → BOOL
----
rel • Euclidean rel ¤ x y z • rel x y ∧ rel x z ⇒ rel y z | HOLCONST | Euclidean | hol | src/hol/int002.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
Valid: ('W)VALUATION → BOOL
----
A • Valid A ¤ x • A x | HOLCONST | Valid | hol | src/hol/int002.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
NeSet : 'a LIST → 'a LIST;
Set : 'a LIST → 'a LIST
----
T | HOLCONST | NeSet | hol | src/hol/int008.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
C3 : î → î
----
x • C3 x = x + 42 | HOLCONST | C3 | hol | src/hol/mdt121.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
C4 : BOOL → BOOL → BOOL
----
x y • C4 x y = ³x ∧ ³y | HOLCONST | C4 | hol | src/hol/mdt121.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
encode : STRING → STRING
----
ch : CHAR; s : STRING •
encode "" = ""
∧ encode (Cons ch s) =
if ch {`$`; `(`; `)`; `,`; `:`; ` ⇔ `; ` • `}
then Cons `$` (Cons ch (encode s))
else Cons ch (encode s) | HOLCONST | encode | hol | src/hol/spc001.doc | [] | [
"STRING"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
comma_list : STRING LIST → STRING
----
comma_list [] = ""
∧ x t • comma_list (Cons x t)
= if t = []
then x
else x @ (Cons `,` (comma_list t)) | HOLCONST | comma_list | hol | src/hol/spc001.doc | [] | [
"STRING"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
mk_var_type_rep: STRING → STRING
----
s • mk_var_type_rep s = encode s | HOLCONST | mk_var_type_rep | hol | src/hol/spc001.doc | [] | [
"STRING",
"encode"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
mk_type_rep: STRING × STRING LIST → STRING
----
s tl • mk_type_rep(s, tl) = "(" @ comma_list tl @ ")" @ encode s | HOLCONST | mk_type_rep | hol | src/hol/spc001.doc | [] | [
"STRING",
"comma_list",
"encode"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
is_type : STRING SET
----
is_type = ¥{X:STRING SET |
(s • mk_var_type_rep s X)
∧ (pars tycon •
Elems pars X
⇒ mk_type_rep(tycon, pars) X)} | HOLCONST | is_type | hol | src/hol/spc001.doc | [] | [
"Elems",
"STRING",
"mk_type_rep",
"mk_var_type_rep"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
mk_var_type: STRING → TYPE
----
s • mk_var_type s = abs_type (mk_var_type_rep s) | HOLCONST | mk_var_type | hol | src/hol/spc001.doc | [] | [
"STRING",
"mk_var_type_rep"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
mk_type: STRING × TYPE LIST → TYPE
----
s tl • mk_type(s, tl) = abs_type(mk_type_rep(s, Map rep_type tl)) | HOLCONST | mk_type | hol | src/hol/spc001.doc | [] | [
"STRING",
"mk_type_rep"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
dest_type: TYPE → STRING × (TYPE LIST)
----
s tyl • dest_type(mk_type(s, tyl)) = (s, tyl) | HOLCONST | dest_type | hol | src/hol/spc001.doc | [] | [
"STRING",
"mk_type"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
Bool : TYPE
----
Bool = mk_type("BOOL", []) | HOLCONST | Bool | hol | src/hol/spc001.doc | [] | [
"mk_type"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
type_ty_vars: TYPE → STRING SET
----
(x s • x type_ty_vars (mk_var_type s) ¤ x = s)
∧ (x s tyl •
x type_ty_vars (mk_type (s, tyl))
¤ ty • ty Elems tyl ∧ x type_ty_vars ty) | HOLCONST | type_ty_vars | hol | src/hol/spc001.doc | [] | [
"Elems",
"STRING",
"mk_type",
"mk_var_type"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
mk_var_rep : STRING × TYPE → STRING
----
s ty • mk_var_rep (s, ty) = "V" @ encode s @ ":" @ rep_type ty | HOLCONST | mk_var_rep | hol | src/hol/spc001.doc | [] | [
"STRING",
"encode"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
mk_const_rep : STRING × TYPE → STRING
----
s ty • mk_const_rep (s, ty) = "C" @ encode s @ ":" @ rep_type ty | HOLCONST | mk_const_rep | hol | src/hol/spc001.doc | [] | [
"STRING",
"encode"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
mk_comb_rep : STRING × STRING → STRING
----
tm1 tm2 • mk_comb_rep (tm1, tm2) = "(" @ tm1 @ ")(" @ tm2 @ ")" | HOLCONST | mk_comb_rep | hol | src/hol/spc001.doc | [] | [
"STRING"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
mk_abs_rep : STRING × TYPE × STRING → STRING
----
s ty tm • mk_abs_rep (s, ty, tm) = " ⇔ V" @ s @ ":" @ rep_type ty @ " • " @ tm | HOLCONST | mk_abs_rep | hol | src/hol/spc001.doc | [] | [
"STRING"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
Fun : TYPE → TYPE → TYPE
----
ty1 ty2 • Fun ty1 ty2 = mk_type(" → ", [ty1; ty2]) | HOLCONST | Fun | hol | src/hol/spc001.doc | [] | [
"mk_type"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
is_wf_term : (STRING × TYPE) SET
----
is_wf_term = ¥{X:(STRING × TYPE) SET |
(s ty • (mk_var_rep(s, ty), ty) X)
∧ (s ty • (mk_const_rep(s, ty), ty) X)
∧ (f a tya ty • ((f, Fun tya ty) X ∧ (a, tya) X) ⇒ (mk_comb_rep(f, a), ty) X)
∧ (s b tys tyb • (b, tyb) X ⇒ (mk_abs_rep(s, tys, b), Fun tys ty... | HOLCONST | is_wf_term | hol | src/hol/spc001.doc | [] | [
"Fun",
"STRING",
"mk_abs_rep",
"mk_comb_rep",
"mk_const_rep",
"mk_var_rep"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
type_of_term : TERM → TYPE
----
tm • type_of_term tm = Snd(rep_term tm) | HOLCONST | type_of_term | hol | src/hol/spc001.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
mk_var : (STRING × TYPE) → TERM
----
s ty • mk_var (s, ty) = abs_term (mk_var_rep(s, ty), ty) | HOLCONST | mk_var | hol | src/hol/spc001.doc | [] | [
"STRING",
"mk_var_rep"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
mk_const : (STRING × TYPE) → TERM
----
s ty • mk_const (s, ty) = abs_term (mk_const_rep(s, ty), ty) | HOLCONST | mk_const | hol | src/hol/spc001.doc | [] | [
"STRING",
"mk_const_rep"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
has_mk_comb : (TERM × TERM) → TERM → BOOL
----
f a tm •
has_mk_comb (f, a) tm ¤
ty • rep_term tm = (mk_comb_rep(Fst(rep_term f), Fst(rep_term a)), ty)
∧ type_of_term f = Fun (type_of_term a) ty | HOLCONST | has_mk_comb | hol | src/hol/spc001.doc | [] | [
"Fun",
"mk_comb_rep",
"type_of_term"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
has_mk_abs : (TERM × TERM) → TERM → BOOL
----
v b tm • has_mk_abs (v, b) tm ¤
( s tys • mk_var(s, tys) = v
∧ rep_term tm =
(mk_abs_rep(s, tys, Fst(rep_term b)), Fun tys (type_of_term b))) | HOLCONST | has_mk_abs | hol | src/hol/spc001.doc | [] | [
"Fun",
"mk_abs_rep",
"mk_var",
"type_of_term"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
inst_type : (STRING → TYPE) → TYPE → TYPE
----
(f: STRING → TYPE) •
(s • inst_type f (mk_var_type s) = f s)
∧ (s tl • inst_type f (mk_type(s, tl)) =
mk_type(s, Map (inst_type f) tl)) | HOLCONST | inst_type | hol | src/hol/spc001.doc | [] | [
"STRING",
"mk_type",
"mk_var_type"
] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
concl : SEQ → TERM
----
concl = Snd | HOLCONST | concl | hol | src/hol/spc001.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f | ||
hyp : SEQ → (TERM SET)
----
hyp = Fst | HOLCONST | hyp | hol | src/hol/spc001.doc | [] | [] | https://github.com/RobArthan/pp | dabebf8fdbdede1a3ad6333500c6663ecd15c98f |
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