Binary_Integer_Tree Module Interface Specification

(0) CHARACTERISTICS

-type specified: tree

-features: deterministic, non-parameterized

-foreign types: path

(1) SYNTAX

ACCESS-PROGRAMS

Program Name	Arg#1	Arg#2	Arg#3	Arg#4	Result Type
SETNIL	tree:O
SETTREE	tree:O	int:V	tree:V	tree:V
ALTERNODE	tree:VO	path:V	int:V
ALTERTREE	tree:VO	path:V	tree:V
GETNODE	tree:V	path:V			int

(2) CANONICAL TRACES

canonical(T)

AUXILIARY FUNCTIONS

change: <tree> × <path> × <int> <tree>

change(R, P, j) (validpath(R, P)) =

Condition	Value
path::emptypath(P)	SETTREE(, j, U, V) where U,V:<tree>; i:<int> [R = SETTREE(, i, U, V) ]
path::goleft(P)	SETTREE(, i, change(U, path::subpath(P), j), V) where U,V:<tree>; i:<int> [R = SETTREE(, i, U, V) ]
path::goright(P)	SETTREE(, i, U, change(V, path::subpath(P), j)) where U,V:<tree>; i:<int> [R = SETTREE(, i, U, V) ]

getval: <tree> × <path> <int>

getval(R, P) (validpath(R, P)) =

Condition	Value
path::emptypath(P)	i where U,V:<tree>; i:<int> [R = SETTREE(*, i, U, V) ]
path::goleft(P)	getval(U, path::subpath(P)) where U,V:<tree>; i:<int> [R = SETTREE(*, i, U, V) ]
path::goright(P)	getval(V, path::subpath(P)) where U,V:<tree>; i:<int> [R = SETTREE(*, i, U, V) ]

update: <tree> × <path> × <tree> <tree>

update(R, P, X) (validpath(R, P)) =

Condition	Value
path::emptypath(P)	X
path::goleft(P)	SETTREE(, i, update(U, path::subpath(P), X), V) where U,V:<tree>; i:<int> [R = SETTREE(, i, U, V) ]
path::goright(P)	SETTREE(, i, U, update(V, path::subpath(P), X)) where U,V:<tree>; i:<int> [R = SETTREE(, i, U, V) ]

validpath: <tree> × <path> <bool>

validpath(R, P) = i:<int>; U,V:<tree> [R = SETTREE(*, i, U, V) (path::emptypath(P) path::goleft(P) validpath(U, path::subpath(P)) path::goright(P) validpath(V, path::subpath(P)))]

(3) SEMANTICS

ACCESS-PROGRAMS

Legality(SETNIL(n)) = %legal%

SETNIL(n ) = _

Legality(SETTREE(n, i, U, V)) = %legal%

SETTREE(n , i, U, V) = SETTREE(*, i, U, V)

Legality(ALTERNODE((n, T), P, i)) =

Condition	Value
Źvalidpath(T, P)	%invalidpath%
validpath(T, P)	%legal%

ALTERNODE((n, T) , P, i) = change(T, P, i)

Legality(ALTERTREE((n, T), P, X)) =

Condition	Value
Źvalidpath(T, P)	%invalidpath%
validpath(T, P)	%legal%

ALTERTREE((n, T) , P, X) = update(T, P, X)

Legality(GETNODE(T, P)) =

GETNODE(T, P) = getval(T, P)