/
up_downvalue_test.sj
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/
up_downvalue_test.sj
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ClearAll(fib)
fib(1) := 1
fib(2) := 1
fib(n_) := fib(n-1) + fib(n-2)
T fib(10) == 55
Clear(fib) # removes definition
T Head(fib(11)) == fib
fib(1) := 1
fib(2) := 1
fib(n_) := fib(n-1) + fib(n-2)
ClearAll(fib) # removes definition
T Head(fib(11)) == fib # does not evaluate to number
# Test sorting of downvalues
# Enter downvalues in wrong order.
fib(n_) := fib(n-1) + fib(n-2)
fib(1) := 1
fib(2) := 1
T fib(10) == 55
ClearAll(fib)
## Condition on pattern
# Careful, I am mixing '=' and ':=' here
g(1) := "cat"
g(x_Integer) = "int"
g(x_Float64) = "float"
T g(1) == "cat"
T g(2) == "int"
T g(2.0) == "float"
ClearAll(g,h,a,b)
h(x_^2) := x
T h((a+b)^2) == a + b
ClearAll(h)
h(x_,x_) := x
h(x_,y_) := 2
T h(a,a) == a
T h(a,b) == 2
ClearAll(h,a,b)
## Restrictions on patterns. Match head and/or "pattern test"
ClearAll(stringgt4, g, gt5, h)
stringgt4(x_) := StringLength(x) > 4
gt5(x_) := x > 5
g(x_Integer`EvenQ`) := x
g(x_AbstractString`stringgt4`) = "Greater than 4"
g(x_AbstractFloat`gt5`) = 1
T Head(g(3)) == g
T g(4) == 4
T Head(g(5)) == g
T Head(g("cat")) == g
T g("zebra") == "Greater than 4"
T Head(g(4.0)) == g
T g(6.0) == 1
h(x_AbstractFloat`J( y -> y < 3)`) = 1
T Head(h(2)) == h
T Head(h(4)) == h
T Head(h(2)) == h
T Head(h(4.0)) == h
T h(2.0) == 1
ClearAll(a,b,stringgt4,g,gt5)
#### UpValues
ClearAll(m1,m2)
rate(m1) ^= 1/2
rate(m2) ^= 3/4
T rate(m1)/rate(m2) == 2/3
# All subtypes of Integer match. All subtypes of FloatingPoint match.
ClearAll(a,p)
a^3 ^= p
T a^3 == p
T Apply(List,a^2) == [a,2]
T a^BI(3) == p
ClearAll(a,p)
ClearAll(a,p)
a^4.0 ^= p
## We will follow Mma and not do this:
#T (a^4 == p) != True
## rather do this
T Head(a^4 == p) == Equal
T a^BF(4) == p
T a^4.0 == p
ClearAll(a,p)
z(a(y_)) ^= y^2
T z(a(3)) == 9
y = 100
h([x_,y_]) := x^y
y = 101
T h([3,4]) == 81
T y == 101
#### UpSetDelayed
UpSetDelayed( f(g(x_)) , fg(x) )
T [f(g(2)), f(h(2))] == [fg(2),f(h(2))]
UpSetDelayed( rand(int) , Random(Integer))
tabsum = Apply(Plus,Table(rand(int), [100]))
T tabsum != 0
T tabsum != 100
f(h(0)) ^= h0
UpSetDelayed( f(h(x_)) , 2 * f(h(x - 1)))
T f(h(10)) == 1024 * h0
# FIXME. We cannot yet handle more than one arg on the lhs
# @ UpSetDelayed( area(sq, s_) , s^2)
UpSetDelayed( area(sq(s_)), s^2)
T area(sq(3)) == 9
ClearAll(g,h)
# The rule is associated with all symbols occuring on level one in lhs
UpSetDelayed( meth(g(x_), h(y_)) , fgh(x, y) )
T UpValues(h) == UpValues(g) == [HoldPattern(meth(g(x_),h(y_))) :> (fgh(x,y))]
ClearAll(f,h)
UpSetDelayed( f(h(x_)) , f1(x))
T UpValues(h) == [HoldPattern(f(h(x_))) :> f1(x)]
UpSetDelayed( f(h(x_)) , f2(x))
T UpValues(h) == [HoldPattern(f(h(x_))) :> f2(x)]
ClearAll(f1,f2,g,h)
# FIXME Need to implement tags, which should be compared to upsetdelayed here.
UpSetDelayed( f2( g(x_), h(y_) ) , gh(x * y))
T UpValues(g) == [HoldPattern(f2(g(x_),h(y_))) :> gh(x * y)]
T UpValues(h) == [HoldPattern(f2(g(x_),h(y_))) :> gh(x * y)]
T f2(g(3),h(4)) == gh(12)
ClearAll(f2,g,h,gh)
# FIXME: WARNING: Symbol 'Pattern' is protected
# UpSetDelayed( a_mod + b_mod , modPlus(a, b))
# Alternatives in DownValue rules
h(x_Integer | x_Float) := x^2
T h(3) == 9
T h(3.0) == 9
T Head(h(1/2)) == h
ClearAll(f,g,fg,h,a,z,y,x,rate,m1,m2, rand, int, tabsum, h0, s, area, sq, fgh, meth)
# Use Set, rather than SetDelayed.
f(x_) = x^2
T f(3) == 9 # 9, rather than 3^2
ClearAll(f,sd)
## The following triggered recursion limit reached in infseval() in evaluation.jl at 3 iterations.
## So, we have increased it to 10. We will have to increase agian because user code may call
## rule functions at greater depth... but, I want to know when this happens
sd(n_) := sd(1,n)
sd(xmax_, n_) := sd(0,xmax,n)
sd(xmin_, xmax_, n_) := xmin + (xmax-xmin)*Range(0,n)/n
T Length(sd(10)) == 11
ClearAll(sd)