Author: Brodie Gaslam

# alike

#### Brodie Gaslam

## What is Alikeness?

`alike` is similar to `all.equal` from base R except it only compares object structure. As with `all.equal`, the first argument (`target`) must be matched by the second (`current`).

    library(vetr)
    alike(integer(5), 1:5)      # different values, but same structure

    [1] TRUE

    alike(integer(5), 1:4)      # wrong size

    [1] "`length(1:4)` should be 5 (is 4)"

    alike(integer(26), letters) # same size, but different types

    [1] "`letters` should be type \"integer-like\" (is \"character\")"

`alike` only compares structural elements that are defined in `target` (a.k.a. the template). This allows “wildcard” templates. For example, we consider length zero vectors to have undefined length so those match vectors of any length:

    alike(integer(), 1:5)

    [1] TRUE

    alike(integer(), 1:4)

    [1] TRUE

    alike(integer(), letters)  # type is still defined and must match

    [1] "`letters` should be type \"integer-like\" (is \"character\")"

Similarly, if a template does not specify an attribute, objects with any value for that attribute will match:

    alike(list(), data.frame())  # a data frame is a list with a attributes

    [1] TRUE

    alike(data.frame(), list())  # but a list does not have the data.frame attributes

    [1] "`list()` should be class \"data.frame\" (is \"list\")"

As an extension to the wildcard concept, we interpret partially specified core R attributes. Here we allow any three column integer matrix to match:

    mx.tpl <- matrix(integer(), ncol=3)          # partially specified matrix
    alike(mx.tpl, matrix(sample(1:12), nrow=4))  # any number of rows match

    [1] TRUE

    alike(mx.tpl, matrix(sample(1:12), nrow=3))  # but column count must match

    [1] "`matrix(sample(1:12), nrow = 3)` should have 3 columns (has 4)"

or a data frame of arbitrary number of rows, but same column structure as `iris`:

    iris.tpl <- iris[0, ]                        # no rows, but structure is defined
    alike(iris.tpl, iris[1:10, ])                # any number of rows match

    [1] TRUE

    alike(iris.tpl, CO2)                         # but column structure must match

    [1] "`names(CO2)[1]` should be \"Sepal.Length\" (is \"Plant\")"

“alikeness” is complex to describe, but should be intuitive to grasp. We recommend you look `example(alike)` to get a sense of “alikeness”. If you want to understand the specifics, read on.

## Declarative Comparison

`alike`’s template based comparison is declarative. You declare what structure an object is expected to implement, and `vetr` infers all the computations required to verify that is so. This makes is particularly well suited for enforcing structural requirements for S3 objects. The S4 system does this and more, but S3 objects are still used extensively in R code, and sometimes S4 classes are not appropriate.

There are several advantages to template based comparisons:

- Often times it is simpler to define a template than to write out all the checks to confirm an object conforms to a particular structure.
- We can generate the template from a known correct instance of an object and abstract away the elements that are not specific to the prototype (this is particularly valuable for otherwise complex objects).
- We can produce plainish-english interpretations of structural mismatches since we are dealing with a known limited set of comparisons.

The template concept was inspired by `vapply`.

## Object Comparison

### Overview

`alike` compares objects on type, length, and attributes. Recursive structures are compared element by element. Language objects and functions are compared specially because the concept of a value within those is more complex (e.g., is the `+` in `x + y` just a value?).

We will defer discussion of attribute comparison to the attributes section.

### Length Comparison

Objects must be the same length to be `alike`, unless the template (`target`) is zero length, in which case the object may be any length. Environments are an exception: we only require that all the elements present in `target` be present in `current`. Also, note that calls to `(` are ignored in language objects, which may affect length computation.

### Type Comparison

Type comparison is done on type (i.e. the `typeof`) with some adjustments to better align comparisons to “percieved” types as opposed to internal storage types.

#### Numerics and Integers

We allow integer vectors to be considered numeric, and short integer-like numerics to be treated as integers:

    alike(1L, 1)     # `1` is not technically integer, but we treat it as such

    [1] TRUE

    alike(1L, 1.1)   # 1.1 is not integer-like

    [1] "`1.1` should be type \"integer-like\" (is \"double\")"

    alike(1.1, 1L)   # integers can match numerics

    [1] TRUE

This feature is designed to simplify checks for integer-like numbers. The following two expressions are roughly equivalent:

    stopifnot(length(x) == 1L && (is.integer(x) || is.numeric(x) && floor(x) == x))
    stopifnot(alike(integer(1L), x))

See `?type_alike` for additional details.

Note that we only check numerics of length <= 100 for integerness to avoid full scans on large vectors. We expect that the primary source of these integer-like numerics is hand input vectors (e.g. `c(1, 2, 3)`), so hopefully this compromise is not too limiting. You can modify the threshold length for this treatment via the `fuzzy.int.max.len` parameter to the `settings` objects (see `?vetr_settings`).

#### Functions

Closures, builtins, and specials are all treated as a single type, even though internally they are stored as different types.

### Recursive Objects

`alike` will recurse through lists (and by extension data frames), pairlists, expressions, and environments and will check pairwise alikeness between the corresponding elements of the `target` and `current` objects.

Environments have slightly different comparison rules in two respects:

- only the elements present in the template are checked, so `current` may have additional items
- if the template is the global environment, then `current` must be too (this is because the global environment is often littered with many objects, and explicitly comparing it to another environment could be computationally expensive)

`NULL` elements within templates in recursive objects are considered undefined and as such act like wildcards:

    ## two NULLs match two length list
    alike(list(NULL, NULL), list(1:10, letters))

    [1] TRUE

    ## but not three length list
    alike(list(NULL, NULL), list(1:10, letters, iris))

    [1] "`length(list(1:10, letters, iris))` should be 2 (is 3)"

Note that top level `NULL`s do not act as wildcards:

    alike(NULL, 1:10)                   # NULL only matches NULL

    [1] "`1:10` should be `NULL` (is \"integer\")"

Treating `NULL` inconsistently depending on whether it is nested or not is a compromise designed to make `alike` a better fit for argument validation because arguments that are `NULL` by default are fairly common.

`alike` will check for self-referential loops in nested environments and prevent infinite recursion. If you somehow introduce a self-referential structure in a template without using environments then `alike` will get stuck in an infinite recursion loop.

We are currently considering adding new comparison modes for lists that would allow for checks more similar to environments (see #29).

### Language Objects, Formulas, and Functions

Alikeness for these types of objects is a little harder to define. We have settled on somewhat arbitrary semantics, though hopefully they are intuitive. These may change in the future as we gain experience using `alike` with these types of objects. This is particularly true of functions.

Language objects are also compared recursively, but alikeness has a slightly different meaning for them:

#### Language Objects

    alike(quote(sum(a, b)), quote(sum(x, y)))   # calls are consistent

    [1] TRUE

    alike(quote(sum(a, b)), quote(sum(x, x)))   # calls are inconsistent

    [1] "`quote(sum(x, x))[[3]]` should not be `x`"

    alike(quote(mean(a, b)), quote(sum(x, y)))  # functions are different

    [1] "`quote(sum(x, y))[[1]]` should be a call to `mean` (is a call to `sum`)"

Since variables can contain anything we do not require them to match directly across calls. In the examples above the second call fails because the template defines different variables for each argument, but the `current` object uses the same variable twice. The third call fails because the functions are different and as such the calls are fundamentally different.

If a function is defined in the calling frame, `alike` will `match.call` it prior to testing alikeness:

    fun <- function(a, b, c) NULL
    alike(quote(fun(p, q, p)), quote(fun(y, x, x)))

    [1] "`quote(fun(y, x, x))[[4]]` should be `y` (is `x`)"

    # `match.call` re-orders arguments
    alike(quote(fun(p, q, p)), quote(fun(b=y, x, x)))

    [1] TRUE

Constants match any constants, but keep in mind that expressions like `1:10` or `c(1, 2, 3)` are calls to `:` and `c` respectively, not constants in the context of language objects.

`NULL` is a wild card in calls as well:

    str(one.arg.tpl <- as.call(list(NULL, NULL)))

     language NULL(NULL)

    alike(one.arg.tpl, quote(log(10)))

    [1] TRUE

    alike(one.arg.tpl, quote(sd(runif(20))))

    [1] TRUE

    alike(one.arg.tpl, quote(log(10, 10)))

    [1] "`quote(log(10, 10))` should have 1 arguments (has 2)"

Calls to `(` are ignored when comparing calls since parentheses are redundant in call trees because the tree structure encodes operation precedence independent of operator precedence.

We concede that the rules for “alikeness” of language objects are arbitrary, but hope the outcomes of those rules is generally intuitive. Unfortunately value and structure are somewhat intertwined for language objects so we must impose our own view of what is value and what is structure.

#### Formulas

Formulas are treated like calls, except that constants must match:

    alike(y ~ x ^ 2, a ~ b ^ 2)

    [1] TRUE

    alike(y ~ x ^ 2, a ~ b ^ 3)

    [1] "`(a ~ b^3)[[3]][[3]]` should have identical constant values"

#### Functions

Functions are `alike` if the signature of the `current` function can reasonably be interpreted as a valid method for the `target` function.

    alike(print, print.default)   # print can be the generic for print.default

    [1] TRUE

    alike(print.default, print)   # but not vice versa

    [1] "`print` should have argument `digits` after argument `x`"

A method of a generic must have all arguments present in the generic, with the same default values if those are defined. If the generic contains `...` then the method may have additional arguments, but must also contain `...`.

Potential changes / improvements for function comparison are being considered in #35.

### S4 and R5 (RC Objects)

S4 and RC objects are considered alike if `current` inherits from `class(target)`. Since these objects embed structural information in their definitions `alike` relies on class alone to establish alikeness.

### Pointer Objects

Objects of the following types are actually references to specific memory locations:

- External Pointers
- Weak References
- Byte codes

These are typically attached as attributes to other objects that contain the information required to establish alikeness (e.g. `data.table`, byte-compiled functions), so we only check their type.

## Attribute Comparison

### Normal Attributes

Much of the structure of an object is determined by attributes. `alike` recursively compares object attributes and requires them to be `alike`, unless the attribute is a special attribute or an environment. Environments within attributes in the template must be matched by an environment, but nothing is checked about the environments to avoid expensive computations on objects that commonly include environments in their attributes (e.g. formulas); note this is different than the treatment of environments as actual objects.

Only attributes present in the template object are checked:

    alike(structure(logical(1L), a=integer(3L)), structure(TRUE, a=1:3, b=letters))

    [1] TRUE

    alike(structure(TRUE, a=1:3, b=letters), structure(logical(1L), a=integer(3L)))

    [1] "`structure(logical(1L), a = integer(3L))` should have attribute \"b\""

Attributes present in `current` but missing in `target` may be anything at all.

### Special Attributes

#### Overview

The special attributes are `names`, `row.names`, `dim`, `dimnames`, `class`, `tsp`, and `levels`. These attributes are discussed in sections 2.2 and 2.3 of the R Language Definition, and have well defined and consistently applied semantics in R. Since the semantics of these attributes are well known, we are able to define “alikeness” for them in a more granular way than we can for arbitrary attributes.

We also consider `srcref` to be a special attribute. This attribute is not checked.

#### row.names and names

If present in `target`, then must be matched exactly by the corresponding attribute in `current`, except that:

- zero length `target` `names`/`row.names` (i.e. `character(0L)`) will match any character `names`/`row.names`
- a zero character element (i.e. `""`) in a `target` `names`/`row.names` character vector will allow any value to match at the corresponding position of the `current` `names`/`row.names` vector

    alike(setNames(integer(), character()), 1:3)

    [1] "`1:3` should have attribute \"names\""

    alike(setNames(integer(), character()), c(a=1, b=2, c=3))

    [1] TRUE

    alike(setNames(integer(3), c("", "", "Z")), c(a=1, b=2, c=3))

    [1] "`names(c(a = 1, b = 2, c = 3))[3]` should be \"Z\" (is \"c\")"

    alike(setNames(integer(3), c("", "", "Z")), c(a=1, b=2, Z=3))

    [1] TRUE

#### dim

`dim` attributes must be identical between `target` and `current`, except that if a value of the `dim` vector is zero in `target` then the corresponding value in `current` can be any value. This is how comparisons like the following succeed:

    mx.tpl <- matrix(integer(), ncol=3)                # partially specified matrix
    alike(mx.tpl, matrix(sample(1:12), nrow=4))

    [1] TRUE

    alike(mx.tpl, matrix(sample(1:12), nrow=3))        # wrong number of columns

    [1] "`matrix(sample(1:12), nrow = 3)` should have 3 columns (has 4)"

    str(mx.tpl)    # notice 0 for 1st dimension

     int[0 , 1:3]

#### dimnames

Must also be identical, except that if the `target` value of the `dimnames` list for a particular dimension is `NULL`, then the corresponding `dimnames` value in `current` may be anything. As with `names`, zero character `dimname` element elements match any name.

    mx.tpl <- matrix(integer(), ncol=3, dimnames=list(row.id=NULL, c("R", "G", "")))
    mx.cur <- matrix(sample(0:255, 12), ncol=3, dimnames=list(row.id=1:4, rgb=c("R", "G", "Blue")))
    mx.cur2 <- matrix(sample(0:255, 12), ncol=3, dimnames=list(1:4, c("R", "G", "b")))

    alike(mx.tpl, mx.cur)

    [1] TRUE

    alike(mx.tpl, mx.cur2)

    [1] "`dimnames(mx.cur2)` should have attribute \"names\""

Note that `dimnames` can have a `names` attribute. This `names` attributed is treated as described in row.names and names.

    names(dimnames(mx.tpl))

    [1] "row.id" ""

#### class

S3 objects are considered alike if the `current` class inherits from the `target` class. Note that “inheritance” here is used in a stricter context than in the typical S3 application:

- Every class present in `target` must be present in `current`
- The overlapping classes must be in the same order
- The last class in `current` must be the same as the last class in `target`

To illustrate:

    tpl <- structure(TRUE, class=c("a", "b", "c"))
    cur <- structure(TRUE, class=c("x", "a", "b", "c"))
    cur2 <- structure(TRUE, class=c("a", "b", "c", "x"))

    alike(tpl, cur)

    [1] TRUE

    alike(tpl, cur2)

    [1] "`class(cur2)[2]` should be \"a\" (is \"b\")"

#### tsp

The `tsp` attribute of `ts` objects behaves similarly to the `dim` attribute. Any component (i.e. start, end, frequency) that is set to zero will act as a wild card. Other components must be identical. It is illegal to set `tsp` components to zero throught the standard R interface, but you may use `abstract` as a work-around.

#### levels

Levels are compared like row.names and names.

#### srcref

This attribute is completely ignored.

#### Normal Attributes that Happen To Have Special Names

If an object contains one of the special attributes, but the attribute value is inconsistent with the standard definition of the attribute, `alike` will silently treat that attribute as any other normal attribute.

## Modifying Comparison Behavior

You can use the `settings` parameter to `alike` to modify comparison behavior. See `?vetr_settings` for details.

## Creating Templates

### From The Ground Up

You can always create your own templates by manually building R structures:

    int.scalar <- integer(1L)
    int.mat.2.by.4 <- matrix(integer(), 2, 4)
    # A df without column names
    df.chr.num.num <- structure(
      list(character(), numeric(), numeric()), class="data.frame"
    )

### Abstracting Existing Structures

Alternatively, you can start with a known structure, and abstract away the instance-specific details. For example, suppose we are sending sample collectors out on the field to record information about iris flowers:

    iris.tpl <- iris[0, ]
    alike(iris.tpl, iris.sample.1)  # make sure they submit data correctly

Or equivalently:

    iris.tpl <- abstract(iris)

`abstract` is an S3 generic defined by `alike` along with methods for common objects. `abstract` primarily sets the `length` of atomic vectors to zero:

    abstract(list(c(a=1, b=2, c=3), letters))

    [[1]]
    named numeric(0)

    [[2]]
    character(0)

and also abstracts the `dim`, `dimnames`, and `tsp` attributes if present. Other attributes are left untouched unless a specific `abstract` method exists for a particular object that also modifies attributes. One example of such a method is `abstract.lm`, and it does some minor tweaking to the base abstractions to allow us to match models produced by `lm`:

    df.dummy <- data.frame(x=runif(3), y=runif(3), z=runif(3))
    mdl.tpl <- abstract(lm(y ~ x + z, df.dummy))
    # TRUE, expecting bi-variate model
    alike(mdl.tpl, lm(Sepal.Length ~ Sepal.Width + Petal.Width, iris))

    [1] TRUE

    alike(mdl.tpl, lm(Sepal.Length ~ Sepal.Width, iris))

    [1] "`lm(Sepal.Length ~ Sepal.Width, iris)$terms[[3]]` should be a call to `+` (is \"symbol\")"

The error message is telling us that at index `"terms"` (i.e. `lm(Sepal.Length ~ Sepal.Width, iris)$terms`) `alike` was expecting a call to `+` instead of a symbol (i.e `Sepal.Width + <somevar>` instead of `Sepal.Width`). The message could certainly be more eloquent, but with a little context it should provide enough information to figure out the problem.

## Performance Considerations

### Sample Timings

We have gone to great lengths to make `alike` fast so that it can be included in other functions without concerns for what overhead:

    type_and_len <- function(a, b)
      typeof(a) == typeof(b) && length(a) == length(b)  # for reference

    bench_mark(times=1e4,
      identical(rivers, rivers),
      alike(rivers, rivers),
      type_and_len(rivers, rivers)
    )

    Mean eval time from 10000 iterations, in microseconds:
      identical(rivers, rivers)     ~  0.2
      alike(rivers, rivers)         ~  1.0
      type_and_len(rivers, rivers)  ~  0.6

While `alike` is slower than `identical` and the comparable bare bones R function, it is competitive with a bare bones R function that checks types and length. As objects grow more complex, `identical` will obviously pull ahead, though `alike` should be sufficiently fast for most applications:

    bench_mark(times=1e4,
      identical(mtcars, mtcars),
      alike(mtcars, mtcars)
    )

    Mean eval time from 10000 iterations, in microseconds:
      identical(mtcars, mtcars)  ~  0.3
      alike(mtcars, mtcars)      ~  4.7

In the above example, we are comparing the data frames, their attributes, and the 11 columns individually.

Keep in mind that the complexity of the `alike` comparison is driven by the complexity of the template, not the object we are checking, so we can always manage the expense of the `alike` evaluation.

Comparisons that succeed will be substantially faster than comparisons that fail as the construction of error messages is non-trivial and we have prioritized optimization in the success case.

Language object comparison is relatively slow. We intend to optimize this some day.

Templates with large numbers of attributes (e.g. > 25) may scale non-linearly. We intend to optimize this some day, though in our experience objects with that many attributes are rare (note having multiple objects each with a handful attributes nested in recursive structures is not a problem).

Large objects will be slower to evaluate. Let us revisit the `lm` example, though this time we compare our template to itself to ensure that the comparisons succeed for `alike`, `all.equal`, and `identical`:

    mdl.tpl <- abstract(lm(y ~ x + z, data.frame(x=runif(3), y=runif(3), z=runif(3))))
    # compare mdl.tpl to itself to ensure success in all three scenarios
    bench_mark(
      alike(mdl.tpl, mdl.tpl),
      all.equal(mdl.tpl, mdl.tpl),   # for reference
      identical(mdl.tpl, mdl.tpl)
    )

    Mean eval time from 1000 iterations, in microseconds:
      alike(mdl.tpl, mdl.tpl)      ~   60
      all.equal(mdl.tpl, mdl.tpl)  ~  515
      identical(mdl.tpl, mdl.tpl)  ~    1

Even with template as large as `lm` results (check `str(mdl.tpl)`) we can evaluate `alike` thousands of times before the overhead becomes noticeable.

### Pre-defining Templates

Some fairly innocuous R expressions carry substantial overhead. Consider:

    df.tpl <- data.frame(a=integer(), b=numeric())
    df.cur <- data.frame(a=1:10, b=1:10 + .1)

    bench_mark(
      alike(df.tpl, df.cur),
      alike(data.frame(integer(), numeric()), df.cur)
    )

    Mean eval time from 1000 iterations, in microseconds:
      alike(df.tpl, df.cur)                     ~   3
      alike(data.frame(integer(), numeric())..  ~  88

`data.frame` is a particularly slow constructor, but in general you are best served by defining your templates (including calls to `abstract`) outside of your function so they are created on package load rather than every time your function is called.

## Miscellaneous

### `alike` as an S3 generic

`alike` is not currently an S3 generic, but will likely one in the future provided we can create an implementation with and acceptable performance profile.