How to summarize an expression

Question

Is there a similar command as str in R in Mathematica?

> str(iris)
'data.frame':   150 obs. of  5 variables:
 $ Sepal.Length: num  5.1 4.9 4.7 4.6 5 5.4 4.6 5 4.4 4.9 ...
	 $ Sepal.Width : num  3.5 3 3.2 3.1 3.6 3.9 3.4 3.4 2.9 3.1 ...
 $ Petal.Length: num  1.4 1.4 1.3 1.5 1.4 1.7 1.4 1.5 1.4 1.5 ...
	 $ Petal.Width : num  0.2 0.2 0.2 0.2 0.2 0.4 0.3 0.2 0.2 0.1 ...
 $ Species     : Factor w/ 3 levels "setosa","versicolor",..: 1 1 1 1 1 1 1 1 1 1 ...

For ggplot plot in R, str also return a reasonable small output

 $ layers     :List of 1
	  ..$ :Classes 'proto', 'environment' <environment: 0x10b6168e0> 
 $ scales     :Reference class 'Scales' [package "ggplot2"] with 1 field
	  ..$ scales: list()
  ..and 21 methods, of which 9 are  possibly relevant:
  ..  add, clone, find, get_scales, has_scale, initialize, input, n,
  ..  non_position_scales
 $ mapping    :List of 3
	  ..$ x     : symbol x
  ..$ y     : symbol price
	  ..$ colour: symbol color
 $ theme      : list()
	 $ coordinates:List of 1
  ..$ limits:List of 2
	  .. ..$ x: NULL
  .. ..$ y: NULL
	  ..- attr(*, "class")= chr [1:2] "cartesian" "coord"
	 $ facet      :List of 1
  ..$ shrink: logi TRUE
	  ..- attr(*, "class")= chr [1:2] "null" "facet"
	 $ plot_env   :<environment: R_GlobalEnv> 
 $ labels     :List of 3
	  ..$ x     : chr "x"
  ..$ y     : chr "price"
	  ..$ colour: chr "color"
 - attr(*, "class")= chr [1:2] "gg" "ggplot"

I find it is pretty painful to open large figure output in FullForm or TreeForm. It is very useful to have a function that let you know the structure of the expression and the size of each element without knowing what is actually in the expression.

Update

Here is a rough example of what is looking for:

p = ContourPlot[x^2 + y^2 == 4, {x, -3, 3}, {y, -3, 3}];
p[[1]]

Output is something like following:

GraphicsComplex[{{-0.6991341991341999, 
 -1.872294372294372}, {-0.6428571428571431, 
 -1.8921568627450978}, {-0.6159420289855072, 
 -1.901656314699793}, {-0.5190476190476178, 
 -1.9285714285714288}, {-0.44824016563146996, 
 ...
 -1.872294372294372}}, 
 {{{}, {}, Tooltip[{Directive[RGBColor[0.368417, 
       0.506779, 0.709798], AbsoluteThickness[1.6]], 
     Line[{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 
      14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 
      26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 
...
      189, 190, 191, 192, 193}]}, x^2 + y^2 == 4]}}]

What I am asking is a function which can shrink the output down to a reasonable size. For large objects, only a few elements is shown as representatives, but the shape of the object is printed for reference.

SomeFunction[p]
GraphicsComplex[
List: Shape 192*2 {{-0.6991341991341999,  -1.872294372294372}, {-0.6428571428571431,  -1.8921568627450978}, ...
{{{}, {}, Tooltip[{Directive[RGBColor[0.368417, 
       0.506779, 0.709798], AbsoluteThickness[1.6]], 
     Line[ List: Shape 192*1  {1, 2, 3...}]
}, x^2 + y^2 == 4]}}]
]

here is the document of str funtion: http://www.inside-r.org/r-doc/utils/str . It claims

Ideally, only one line for each ‘basic’ structure is displayed. It is especially well suited to compactly display the (abbreviated) contents of (possibly nested) lists. The idea is to give reasonable output for any R object.

The document online keeping the examples unevaluated, I attach the output of the examples as below. It is clearly, str output plenty of information in a very compact form.

str> ## The following examples show some of 'str' capabilities
str> str(1:12)
 int [1:12] 1 2 3 4 5 6 7 8 9 10 ...

str> str(ls)
function (name, pos = -1L, envir = as.environment(pos), all.names = FALSE, 
    pattern, sorted = TRUE)  

str> str(args) #- more useful than  args(args) !
function (name)  

str> str(freeny)
'data.frame':   39 obs. of  5 variables:
 $ y                    : Time-Series  from 1962 to 1972: 8.79 8.79 8.81 8.81 8.91 ...
	 $ lag.quarterly.revenue: num  8.8 8.79 8.79 8.81 8.81 ...
 $ price.index          : num  4.71 4.7 4.69 4.69 4.64 ...
	 $ income.level         : num  5.82 5.83 5.83 5.84 5.85 ...
 $ market.potential     : num  13 13 13 13 13 ...

str> str(str)
function (object, ...)  

str> str(.Machine, digits.d = 20) # extra digits for identification of binary numbers
List of 18
 $ double.eps           : num 2.2204460492503130808e-16
	 $ double.neg.eps       : num 1.1102230246251565404e-16
 $ double.xmin          : num 2.2250738585072013831e-308
	 $ double.xmax          : num 1.7976931348623157081e+308
 $ double.base          : int 2
	 $ double.digits        : int 53
 $ double.rounding      : int 5
	 $ double.guard         : int 0
 $ double.ulp.digits    : int -52
	 $ double.neg.ulp.digits: int -53
 $ double.exponent      : int 11
	 $ double.min.exp       : int -1022
 $ double.max.exp       : int 1024
	 $ integer.max          : int 2147483647
 $ sizeof.long          : int 8
	 $ sizeof.longlong      : int 8
 $ sizeof.longdouble    : int 16
	 $ sizeof.pointer       : int 8

str> str( lsfit(1:9, 1:9))
List of 4
 $ coefficients: Named num [1:2] 1.18e-15 1.00
	  ..- attr(*, "names")= chr [1:2] "Intercept" "X"
	 $ residuals   : num [1:9] -9.01e-16 1.72e-15 -2.47e-16 -2.25e-16 -2.03e-16 ...
 $ intercept   : logi TRUE
	 $ qr          :List of 6
  ..$ qt   : num [1:9] -1.50e+01 7.75 -2.22e-16 0.00 2.22e-16 ...
	  ..$ qr   : num [1:9, 1:2] -3 0.333 0.333 0.333 0.333 ...
  .. ..- attr(*, "dimnames")=List of 2
  .. .. ..$ : NULL
	  .. .. ..$ : chr [1:2] "Intercept" "X"
  ..$ qraux: num [1:2] 1.33 1.26
	  ..$ rank : int 2
  ..$ pivot: int [1:2] 1 2
	  ..$ tol  : num 1e-07
  ..- attr(*, "class")= chr "qr"

str> str( lsfit(1:9, 1:9), max.level = 1)
List of 4
 $ coefficients: Named num [1:2] 1.18e-15 1.00
	  ..- attr(*, "names")= chr [1:2] "Intercept" "X"
	 $ residuals   : num [1:9] -9.01e-16 1.72e-15 -2.47e-16 -2.25e-16 -2.03e-16 ...
 $ intercept   : logi TRUE
	 $ qr          :List of 6
  ..- attr(*, "class")= chr "qr"

str> str( lsfit(1:9, 1:9), width = 60, strict.width = "cut")
List of 4
 $ coefficients: Named num [1:2] 1.18e-15 1.00
	  ..- attr(*, "names")= chr [1:2] "Intercept" "X"
	 $ residuals   : num [1:9] -9.01e-16 1.72e-15 -2.47e-16 -2..
 $ intercept   : logi TRUE
	 $ qr          :List of 6
  ..$ qt   : num [1:9] -1.50e+01 7.75 -2.22e-16 0.00 2.22e..
	  ..$ qr   : num [1:9, 1:2] -3 0.333 0.333 0.333 0.333 ...
  .. ..- attr(*, "dimnames")=List of 2
  .. .. ..$ : NULL
	  .. .. ..$ : chr [1:2] "Intercept" "X"
  ..$ qraux: num [1:2] 1.33 1.26
	  ..$ rank : int 2
  ..$ pivot: int [1:2] 1 2
	  ..$ tol  : num 1e-07
  ..- attr(*, "class")= chr "qr"

str> str( lsfit(1:9, 1:9), width = 60, strict.width = "wrap")
List of 4
$ coefficients: Named num [1:2] 1.18e-15 1.00
	..- attr(*, "names")= chr [1:2] "Intercept" "X"
	$ residuals : num [1:9] -9.01e-16 1.72e-15 -2.47e-16
   -2.25e-16 -2.03e-16 ...
$ intercept : logi TRUE
	$ qr :List of 6
..$ qt : num [1:9] -1.50e+01 7.75 -2.22e-16 0.00 2.22e-16
	   ...
	..$ qr : num [1:9, 1:2] -3 0.333 0.333 0.333 0.333 ...
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : NULL
	.. .. ..$ : chr [1:2] "Intercept" "X"
..$ qraux: num [1:2] 1.33 1.26
	..$ rank : int 2
..$ pivot: int [1:2] 1 2
	..$ tol : num 1e-07
..- attr(*, "class")= chr "qr"

str> op <- options(); str(op)   # save first;
List of 71
 $ CBoundsCheck                        : logi FALSE
	 $ HTTPUserAgent                       : chr "R (3.2.0 x86_64-apple-darwin13.4.0 x86_64 darwin13.4.0)"
 $ OutDec                              : chr "."
	 $ add.smooth                          : logi TRUE
 $ bitmapType                          : chr "quartz"
	 $ browser                             :function (url)  
 $ browserNLdisabled                   : logi FALSE
	 $ buildtools.check                    :function (action)  
 $ buildtools.with                     :function (code)  
	 $ check.bounds                        : logi FALSE
 $ citation.bibtex.max                 : int 1
	 $ continue                            : chr "+ "
 $ contrasts                           : Named chr [1:2] "contr.treatment" "contr.poly"
	  ..- attr(*, "names")= chr [1:2] "unordered" "ordered"
	 $ defaultPackages                     : chr [1:6] "datasets" "utils" "grDevices" "graphics" ...
 $ demo.ask                            : chr "default"
	 $ deparse.cutoff                      : int 60
 $ device                              : chr "RStudioGD"
	 $ device.ask.default                  : logi TRUE
 $ digits                              : int 7
	 $ dplyr.print_max                     : int 20
 $ dplyr.print_min                     : int 10
	 $ dplyr.strict_sql                    : logi FALSE
 $ dvipscmd                            : chr "dvips"
	 $ echo                                : logi TRUE
 $ editor                              : chr "vi"
	 $ encoding                            : chr "native.enc"
 $ error                               : language (structure(function ()  { ...
	 $ example.ask                         : chr "default"
	 $ expressions                         : int 5000
	 $ ggvis.renderer                      : chr "svg"
	 $ help.search.types                   : chr [1:3] "vignette" "demo" "help"
	 $ help.try.all.packages               : logi FALSE
	 $ help_type                           : chr "html"
	 $ install.packages.compile.from.source: chr "interactive"
	 $ internet.info                       : int 2
	 $ keep.source                         : logi TRUE
	 $ keep.source.pkgs                    : logi FALSE
	 $ locatorBell                         : logi TRUE
	 $ mailer                              : chr "mailto"
	 $ max.print                           : int 10000
	 $ menu.graphics                       : logi FALSE
	 $ na.action                           : chr "na.omit"
	 $ nwarnings                           : int 50
	 $ pager                               :function (files, header, title, delete.file)  
	 $ papersize                           : chr "a4"
	 $ pdfviewer                           : chr "/usr/bin/open"
	 $ pkgType                             : chr "both"
	 $ printcmd                            : chr "lpr"
	 $ prompt                              : chr "> "
	 $ repos                               : atomic [1:1] http://cran.stat.nus.edu.sg/
	  ..- attr(*, "RStudio")= logi TRUE
	 $ restart                             :function (afterRestartCommand = "")  
	 $ rl_word_breaks                      : chr " \t\n\"\\'`><=%;,|&{()}"
	 $ scipen                              : num 0
	 $ shiny.launch.browser                :function (url)  
	  ..- attr(*, "shinyViewerType")= num 3
	 $ show.coef.Pvalues                   : logi TRUE
	 $ show.error.messages                 : logi TRUE
	 $ show.signif.stars                   : logi TRUE
	 $ str                                 :List of 3
	  ..$ strict.width: chr "no"
	  ..$ digits.d    : int 3
	  ..$ vec.len     : int 4
	 $ str.dendrogram.last                 : chr "`"
	 $ stringsAsFactors                    : logi TRUE
	 $ texi2dvi                            : chr "/usr/local/bin/texi2dvi"
	 $ timeout                             : num 60
	 $ ts.S.compat                         : logi FALSE
	 $ ts.eps                              : num 1e-05
	 $ unzip                               : chr "/usr/bin/unzip"
	 $ useFancyQuotes                      : logi TRUE
	 $ verbose                             : logi FALSE
	 $ viewer                              :function (url, height = NULL)  
	 $ warn                                : num 0
	 $ warning.length                      : int 1000
	 $ width                               : int 75

str>                            # otherwise internal options() is used.
str> need.dev <-
str+   !exists(".Device") || is.null(.Device) || .Device == "null device"

str> { if(need.dev) postscript()
str+   str(par())
str+   if(need.dev) graphics.off()
str+ }
List of 72
 $ xlog     : logi FALSE
	 $ ylog     : logi FALSE
 $ adj      : num 0.5
	 $ ann      : logi TRUE
 $ ask      : logi TRUE
	 $ bg       : chr "white"
 $ bty      : chr "o"
	 $ cex      : num 1
 $ cex.axis : num 1
	 $ cex.lab  : num 1
 $ cex.main : num 1.2
	 $ cex.sub  : num 1
 $ cin      : num [1:2] 0.2 0.267
	 $ col      : chr "black"
 $ col.axis : chr "black"
	 $ col.lab  : chr "black"
 $ col.main : chr "black"
	 $ col.sub  : chr "black"
 $ cra      : num [1:2] 14.4 19.2
	 $ crt      : num 0
 $ csi      : num 0.267
	 $ cxy      : num [1:2] 0.029 0.0879
 $ din      : num [1:2] 8.56 5.49
	 $ err      : int 0
 $ family   : chr ""
	 $ fg       : chr "black"
 $ fig      : num [1:4] 0 1 0 1
	 $ fin      : num [1:2] 8.56 5.49
 $ font     : int 1
	 $ font.axis: int 1
 $ font.lab : int 1
	 $ font.main: int 2
 $ font.sub : int 1
	 $ lab      : int [1:3] 5 5 7
 $ las      : int 0
	 $ lend     : chr "round"
 $ lheight  : num 1
	 $ ljoin    : chr "round"
 $ lmitre   : num 10
	 $ lty      : chr "solid"
 $ lwd      : num 1
	 $ mai      : num [1:4] 1.36 1.09 1.09 0.56
 $ mar      : num [1:4] 5.1 4.1 4.1 2.1
	 $ mex      : num 1
 $ mfcol    : int [1:2] 1 1
	 $ mfg      : int [1:4] 1 1 1 1
 $ mfrow    : int [1:2] 1 1
	 $ mgp      : num [1:3] 3 1 0
 $ mkh      : num 0.001
	 $ new      : logi FALSE
 $ oma      : num [1:4] 0 0 0 0
	 $ omd      : num [1:4] 0 1 0 1
 $ omi      : num [1:4] 0 0 0 0
	 $ page     : logi TRUE
 $ pch      : int 1
	 $ pin      : num [1:2] 6.9 3.03
 $ plt      : num [1:4] 0.128 0.935 0.248 0.801
	 $ ps       : int 16
 $ pty      : chr "m"
	 $ smo      : num 1
 $ srt      : num 0
	 $ tck      : num NA
 $ tcl      : num -0.5
	 $ usr      : num [1:4] 0 1 0 1
 $ xaxp     : num [1:3] 0 1 5
	 $ xaxs     : chr "r"
 $ xaxt     : chr "s"
	 $ xpd      : logi FALSE
 $ yaxp     : num [1:3] 0 1 5
	 $ yaxs     : chr "r"
 $ yaxt     : chr "s"
	 $ ylbias   : num 0.2

str> ch <- letters[1:12]; is.na(ch) <- 3:5

str> str(ch) # character NA's
 chr [1:12] "a" "b" NA NA NA "f" "g" "h" "i" "j" ...

str> str(list(a = "A", L = as.list(1:100)), list.len = 9)
List of 2
 $ a: chr "A"
	 $ L:List of 100
  ..$ : int 1
	  ..$ : int 2
  ..$ : int 3
	  ..$ : int 4
  ..$ : int 5
	  ..$ : int 6
  ..$ : int 7
	  ..$ : int 8
  ..$ : int 9
  .. [list output truncated]

str> nchar(longch <- paste(rep(letters,100), collapse = ""))
[1] 2600

str> str(longch)
 chr "abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvw"| __truncated__

str> str(longch, nchar.max = 52)
 chr "abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxy"| __truncated__

str> str(longch, strict.width = "wrap")
chr
   "abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnop"..
   __truncated__

str> ## Settings for narrow transcript :
str> op <- options(width = 60,
str+               str = strOptions(strict.width = "wrap"))

str> str(lsfit(1:9,1:9))
List of 4
$ coefficients: Named num [1:2] 1.18e-15 1.00
	..- attr(*, "names")= chr [1:2] "Intercept" "X"
	$ residuals : num [1:9] -9.01e-16 1.72e-15 -2.47e-16
   -2.25e-16 -2.03e-16 ...
$ intercept : logi TRUE
	$ qr :List of 6
..$ qt : num [1:9] -1.50e+01 7.75 -2.22e-16 0.00 2.22e-16
	   ...
	..$ qr : num [1:9, 1:2] -3 0.333 0.333 0.333 0.333 ...
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : NULL
	.. .. ..$ : chr [1:2] "Intercept" "X"
..$ qraux: num [1:2] 1.33 1.26
	..$ rank : int 2
..$ pivot: int [1:2] 1 2
	..$ tol : num 1e-07
..- attr(*, "class")= chr "qr"

str> str(options())
List of 71
$ CBoundsCheck : logi FALSE
	$ HTTPUserAgent : chr "R (3.2.0 x86_64-apple-darwin13.4.0
   x86_64 darwin13.4.0)"
$ OutDec : chr "."
	$ add.smooth : logi TRUE
$ bitmapType : chr "quartz"
	$ browser :function (url)
$ browserNLdisabled : logi FALSE
	$ buildtools.check :function (action)
$ buildtools.with :function (code)
	$ check.bounds : logi FALSE
$ citation.bibtex.max : int 1
	$ continue : chr "+ "
$ contrasts : Named chr [1:2] "contr.treatment"
	   "contr.poly"
	..- attr(*, "names")= chr [1:2] "unordered" "ordered"
	$ defaultPackages : chr [1:6] "datasets" "utils"
   "grDevices" "graphics" ...
$ demo.ask : chr "default"
	$ deparse.cutoff : int 60
$ device : chr "RStudioGD"
	$ device.ask.default : logi TRUE
$ digits : int 7
	$ dplyr.print_max : int 20
$ dplyr.print_min : int 10
	$ dplyr.strict_sql : logi FALSE
$ dvipscmd : chr "dvips"
	$ echo : logi TRUE
$ editor : chr "vi"
	$ encoding : chr "native.enc"
$ error : language (structure(function () { ...
	$ example.ask : chr "default"
	$ expressions : int 5000
	$ ggvis.renderer : chr "svg"
	$ help.search.types : chr [1:3] "vignette" "demo" "help"
	$ help.try.all.packages : logi FALSE
	$ help_type : chr "html"
	$ install.packages.compile.from.source: chr "interactive"
	$ internet.info : int 2
	$ keep.source : logi TRUE
	$ keep.source.pkgs : logi FALSE
	$ locatorBell : logi TRUE
	$ mailer : chr "mailto"
	$ max.print : int 10000
	$ menu.graphics : logi FALSE
	$ na.action : chr "na.omit"
	$ nwarnings : int 50
	$ pager :function (files, header, title, delete.file)
	$ papersize : chr "a4"
	$ pdfviewer : chr "/usr/bin/open"
	$ pkgType : chr "both"
	$ printcmd : chr "lpr"
	$ prompt : chr "> "
	$ repos : atomic [1:1] http://cran.stat.nus.edu.sg/
	..- attr(*, "RStudio")= logi TRUE
	$ restart :function (afterRestartCommand = "")
	$ rl_word_breaks : chr " \t\n\"\\'`><=%;,|&{()}"
	$ scipen : num 0
	$ shiny.launch.browser :function (url)
	..- attr(*, "shinyViewerType")= num 3
	$ show.coef.Pvalues : logi TRUE
	$ show.error.messages : logi TRUE
	$ show.signif.stars : logi TRUE
	$ str :List of 4
	..$ strict.width: chr "wrap"
	..$ digits.d : num 3
	..$ vec.len : num 4
	..$ formatNum :function (x, ...)
	$ str.dendrogram.last : chr "`"
	$ stringsAsFactors : logi TRUE
	$ texi2dvi : chr "/usr/local/bin/texi2dvi"
	$ timeout : num 60
	$ ts.S.compat : logi FALSE
	$ ts.eps : num 1e-05
	$ unzip : chr "/usr/bin/unzip"
	$ useFancyQuotes : logi TRUE
	$ verbose : logi FALSE
	$ viewer :function (url, height = NULL)
	$ warn : num 0
	$ warning.length : int 1000
	$ width : int 60

str> ## reset to previous:
str> options(op)

str> ## Don't show: 
str>  ##-- Some "crazy" objects
str>  str(array(1:5, dim = 20))
 int [1:20(1d)] 1 2 3 4 5 1 2 3 4 5 ...

str>  str(factor(character(0)))
 Factor w/ 0 levels: 

str>  str(as.data.frame(NULL))
'data.frame':   0 obs. of  0 variables

str> ## End(Don't show)
str> str(quote( { A+B; list(C, D) } ))
length 3 {  A + B; list(C, D) }
 - attr(*, "srcref")=List of 3
  ..$ :Class 'srcref'  atomic [1:8] 53 12 53 12 12 12 53 53
	  .. .. ..- attr(*, "srcfile")=Classes 'srcfilecopy', 'srcfile' <environment: 0x10aa7f8d8> 
	  ..$ :Class 'srcref'  atomic [1:8] 53 14 53 16 14 16 53 53
  .. .. ..- attr(*, "srcfile")=Classes 'srcfilecopy', 'srcfile' <environment: 0x10aa7f8d8> 
  ..$ :Class 'srcref'  atomic [1:8] 53 19 53 28 19 28 53 53
  .. .. ..- attr(*, "srcfile")=Classes 'srcfilecopy', 'srcfile' <environment: 0x10aa7f8d8> 
 - attr(*, "srcfile")=Classes 'srcfilecopy', 'srcfile' <environment: 0x10aa7f8d8> 
 - attr(*, "wholeSrcref")=Class 'srcref'  atomic [1:8] 1 0 53 30 0 30 1 53
  .. ..- attr(*, "srcfile")=Classes 'srcfilecopy', 'srcfile' <environment: 0x10aa7f8d8> 

str> ## Don't show: 
str> had.stats4 <- "package:stats4" %in% search()

str> if(!had.stats4)
str+    rs <- 
str+ ## End(Don't show)
str+ ## S4 classes :
str+ require(stats4)
Loading required package: stats4

str> x <- 0:10; y <- c(26, 17, 13, 12, 20, 5, 9, 8, 5, 4, 8)

str> ll <- function(ymax = 15, xh = 6)
str+       -sum(dpois(y, lambda=ymax/(1+x/xh), log=TRUE))

str> fit <- mle(ll)

str> str(fit)
Formal class 'mle' [package "stats4"] with 9 slots
  ..@ call     : language mle(minuslogl = ll)
  ..@ coef     : Named num [1:2] 24.99 3.06
  .. ..- attr(*, "names")= chr [1:2] "ymax" "xh"
  ..@ fullcoef : Named num [1:2] 24.99 3.06
  .. ..- attr(*, "names")= chr [1:2] "ymax" "xh"
  ..@ vcov     : num [1:2, 1:2] 17.85 -3.72 -3.72 1.07
  .. ..- attr(*, "dimnames")=List of 2
  .. .. ..$ : chr [1:2] "ymax" "xh"
	  .. .. ..$ : chr [1:2] "ymax" "xh"
  ..@ min      : num 28.6
  ..@ details  :List of 6
  .. ..$ par        : Named num [1:2] 24.99 3.06
	  .. .. ..- attr(*, "names")= chr [1:2] "ymax" "xh"
	  .. ..$ value      : num 28.6
  .. ..$ counts     : Named int [1:2] 25 18
	  .. .. ..- attr(*, "names")= chr [1:2] "function" "gradient"
	  .. ..$ convergence: int 0
  .. ..$ message    : NULL
	  .. ..$ hessian    : num [1:2, 1:2] 0.203 0.706 0.706 3.388
  .. .. ..- attr(*, "dimnames")=List of 2
  .. .. .. ..$ : chr [1:2] "ymax" "xh"
	  .. .. .. ..$ : chr [1:2] "ymax" "xh"
  ..@ minuslogl:function (ymax = 15, xh = 6)  
  .. ..- attr(*, "srcref")=Class 'srcref'  atomic [1:8] 63 7 64 52 7 52 63 64
  .. .. .. ..- attr(*, "srcfile")=Classes 'srcfilecopy', 'srcfile' <environment: 0x10aa7f8d8> 
  ..@ nobs     : int NA
  ..@ method   : chr "BFGS"

Answer 1

I am not familiar with this function but based on your example there is some relation to SpokenString, e.g.

gr = Graphics[{Thick, Green, Rectangle[{0, -1}, {2, 1}], Red, Disk[], Blue, Circle[{2, 0}], 
   Yellow, Polygon[{{2, 0}, {4, 1}, {4, -1}}], Purple, Arrowheads[Large], 
   Arrow[{{4, 3/2}, {0, 3/2}, {0, 0}}], Black, Dashed, 
   Line[{{-1, 0}, {4, 0}}]}
];

gr // SpokenString

"a graphic consisting of a rectangle, a disk, a circle, a polygon with 3 vertices, an arrow and a line connecting 2 points"

For not displaying an entire expression you should look at Shallow and Short.

Short @ InputForm @ gr

Graphics[{Thickness[Large], <<14>>}]

I realize this is not equivalent to the functionality you show but I hope it helps nevertheless.

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Update

In your update one difference I see between your example and the existing output of Short is that you have a "Shape 192*2" tag while Short returns a Skeleton which provides only length. An alternative is to create whatever replacement you desire to represent these, e.g.:

p = ContourPlot[x^2 + y^2 == 4, {x, -3, 3}, {y, -3, 3}];

p[[1]] /. m_List /; ArrayQ[m, _, NumericQ] :> 
   "List of shape " <> ToString@Dimensions@m // InputForm

GraphicsComplex["List of shape {193, 2}", 
 {{"List of shape {0}", "List of shape {0}", 
   Tooltip[{Directive[RGBColor[0.368417, 0.506779, 0.709798], 
      AbsoluteThickness[1.6]], Line["List of shape {193}"]}, 
    x^2 + y^2 == 4]}}]

I am not aware of any built-in functions with summary rules of this specific kind, but the flexibility of Mathematica makes them easy to implement yourself. See the first link below for one example of this.

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Related questions featuring some more advanced methods:

• Making customized InputForm and ShortInputForm (additional example)

• The clearest way to represent Mathematica's evaluation sequence

• How to examine the structure of Graphics objects