# Checkers.@test_forall — Macro.

@test_forall argument_data, prop

Checks prop on each tuples of values specified in argument_data. Returns Pass if prop holds for all values tested, Fail if prop does not hold for some tested value, and Error if a part of code could not be evaluated.

Arguments

• argument_data: a sequence of at least one comma-separated expression(s), specifying the sets of values for individual variables. Expressions must have the form x in iter, where x is any symbol that will be treated as a dummy variable, and iter is any iterable expression, i.e. one valid in constructing a for loop: "for x in iter". In particular, iter can be a:b, where a & b are integer-valued expressions; an array; or a set.
• prop is boolean-valued expression of the proposition to be checked for arguments in specified ranges, with reference to the dummy variables named in argument_data.

Details

@test_forall constructs a nested sequence of for-loops, and checks that prop evaluates to true for all combinations of values of variables specified by the loops. In set-theoretic terms, @test_forall tests prop on the Cartesian product of the sets of variables specified in argument_data.

Loops are generated from argument_data inductively, starting with the outermost loop as the leftmost expression, to the innermost loop as the rightmost. Variable ranges may depend on the values of previously referenced variables (see third example).

Examples

julia> @test_forall x in -1:1, x*(x-1)*(x+1) == 0
Test Passed
  Expression: (x in -1:1,x * (x - 1) * (x + 1) == 0)

julia> @test_forall x in -1:1, x*(x-2)*(x+1) == 0
Test Failed
  Expression: (x in -1:1,x * (x - 2) * (x + 1) == 0)

julia> @test_forall x in [0,1,2], y in x:4, y+4 > 2*x 
Test Passed
  Expression: (x in [0,1,2],y in x:4,(y + 4 > 2x) == true)

julia> @test_forall x in (1-1, 0+1, sqrt(4)), y in x:4, y+4 > 2*x
Test Passed
  Expression: (x in (1 - 1,0 + 1,sqrt(4)),y in x:4,(y + 4 > 2x) == true)

julia> @test_forall x in ["a","b"], y in ["z","w"], x*y in Set(["az","aw","bz","bw"])
Test Passed
  Expression: (x in ["a","b"],y in ["z","w"],x * y in Set(["az","aw","bz","bw"]))

# Bad design: throws UndefVarError: x not defined
# The outer loop for `y` refers to `x`, which comes later in `argument_data`.
julia> @test_forall y in x:4, x in 0:2, y+4 > 2*x
Error During Test
  Test threw an exception of type UndefVarError
  Expression: (y in x:4,x in 0:2,(y + 4 > 2x) == true)
  UndefVarError: x not defined

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