***Testbed for Little_Math_Language V2 and TCL demo examples calculations, numerical analysis ***
 
This page is under development. Comments are welcome, but please load any comments in the comments section at the bottom of the page. Please include your wiki MONIKER and date in your comment with the same courtesy that I will give you. Aside from your courtesy, your wiki MONIKER and date as a signature and minimal good faith of any internet post are the rules of this TCL-WIKI. Its very hard to reply reasonably without some background of the correspondent on his WIKI bio page. Thanks, [gold] 15Oct2020

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Title:  Little_Math_Language V2
<<TOC>>

***Preface***
[gold] 15Oct2020  Here is extension of programs  [A little math language] by [RS] and [A little math language revisited] written by [AM] in 2004.  
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***Introduction***
Wrote some code for charts supporting [A little math language] by Richard Suchenwirth 2002-01-02 and  [A little math language revisited] written by [AM] in 2004. Called  Little_Math_Language V2  in TCL as partial math language interpreter. Learning experience, Added some easy eye console displays for my bad eyes. And trying some new features as a testbed. Math calculation forms seem to be working.  
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***Discussion*** 
 
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The analogy of using  Little_Math_Language V2 to control the large TCL language is like sticking an Apple computer for the human operator  in front of a Cray computer.  The human mind probably can only understand and use a limited set of instructions, an interface in hardware or TCL? language as a limited set of instructions might be useful. After all, the human mind was designed to chase rabbits.
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***Screenshots***      
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***figure 1.   as vaporware*** 
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***Figure 1. A little math language revisited screenshot one***
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[A little math language revisited screenshot]
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***Figure 2. A little math language revisited screenshot two***
[A little math language revisited screenshot two]

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***figure 3. screenshot 3***
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[Testbed for Little_Math_Language screenshot] 
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***figure 4.   computer geeks***
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*** References ***
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   * [A little math language revisited]
   * [Playing with Recursion] by [RS]
   * [Functional Programming]
   * [recursion]
   * [Salt and Sugar]
   * [Math sugar]
   * [Radical Language Modification]
   * [func]
   * John McCarthy: A basis for a mathematical theory of computation, in: 
   * Computer Programming and Formal Systems.
   * P.Braffort, D.Hirschberg (ed.), Amsterdam:North Holland 1963,
   * several versions, archived pdf [http://www-formal.stanford.edu/jmc/basis1.pdf]
   * McCarthy’s LISP and Basis for Theory of Computation, archived pdf[https://hapoc2015.sciencesconf.org/conference/hapoc2015/pages/Dai.pdf]
   * en.wikipedia.org search on <John McCarthy computer> [https://en.wikipedia.org/wiki/John_McCarthy_(computer_scientist)]
   * John McCarthy at Stanford web site, archived [https://web.archive.org/web/20131011125002/http://www-formal.stanford.edu/jmc/]
   * Towards a Mathematical Science of Computation, J. McCarthy,
   * Computer Science Department,Stanford University, archived pdf [https://web.archive.org/web/20130319040125/http://www-formal.stanford.edu/jmc/towards.pdf]
   * Elephant 2000: A Programming Language Based on Speech Acts
   * John McCarthy, Stanford University, archived [https://web.archive.org/web/20130319040119/http://www-formal.stanford.edu/jmc/elephant.pdf]
   * Elephant input and output statements are characterized
   * as speech acts and programs, which 
   * can refer directly to the past.
   * Elephant proposal contains summary
   * on  McCarthy mathematical theory of computation  
   * King that learns? [A Program That Learns]
   * [upvar sugar]
   * [Salt and Sugar]
   * [Math sugar]
   * [A little math language]
   * [args]
   * [RS]
   * [LV]     
   * [Radical Language Modification]
   * [Functional Programming]
   * [Custom curry] 
   * [Playing with recursion]
   * [Modeling COND with expr]
   * [Sample Math Programs]
   * Professor Frisby's Mostly Adequate Guide to Functional Programming [https://github.com/MostlyAdequate/mostly-adequate-guide]
   * [expr shorthand for Tcl9]
   * [Steps towards functional programming]
   * [Tacit programming]
   * The fortran call statement appeared in Fortran2 (1958).  example of call exit, fortran 4     
   * Thocp code, http://www.thocp.net/software/languages/fortran.htm
   * [Natural User Interface]
   * [Natural Languages] category
   * [Game kingdom of strategy]
   * wikipedia.org wiki The_Sumerian_Game
   * [Find all words]
   * [Things German]
   * [How to synthesize a query]
   * [Writing Tk programs so that the user can extend or interact with them without modifying the application]
   * [Ruslish]
   * [Accumulator Generators]
   * [Accumulator Generator]
   * [Whadjasay]
   * disassemble byte code [https://www.magicsplat.com/blog/disassemble/]
   *  One Liners Programs Compendium [https://wiki.tcllang.org/page/One+Liners+Programs+Compendium++and+TCL+demo+examples+calculations%2C+numerical+analysis]
   * [One Liners]
   * [Oneliner's Pie in the Sky]
   * Ref. WIKI BOOKS, Tcl_Programming_Introduction, [https://en.wikibooks.org/wiki/Tcl_Programming/Introduction]
   * Book Section  contrasts one liners programs
   * versus  traditional procedural  approach, 
   * Multiple  Wiki Books on TCL programming  [https://en.wikibooks.org/wiki/Category:Book:Tcl_Programming]
   * [if]
   * [New Control Structures]
   * Kernighan and Pike: The practice of programming  
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****Appendix TCL programs and scripts ****

**** Pretty Print Version*** 

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        ;# Title: Little_Math_Language_AM V2 in TCL
        ;# console extension to little_math_language
        ;# proc mathlang.tcl from AM, (original on tcl wiki 05-21-2004)
        ;# proc test code from RS
        ;# ref A little math language revisited, page on TCL Wiki
        ;# A little math language, page on TCL Wiki
        ;# Richard Suchenwirth 2002-01-02
        ;# Original program  by Arjen Markus on TCL Wiki
        ;# Reorganized code
        ;# for print and self_help
        ;# to tcl console.
        ;# written on Windows 10 on TCL
        ;# working under TCL version 8.6
        ;# on TCL WIKI , 20Oct2020
        ;# added statements for TCLLIB library
        package require math::numtheory
        package require math::constants
        package require math::trig
        package require math
        namespace path {::tcl::mathop ::tcl::mathfunc math::numtheory math::trig math::constants }
        ;# Tried to keep clean AM  code in upper section
        ;# added extension to console below. -gold
        ;# mathlang.tcl --
        ;#    Provide commands that allow a more usual mathematical syntax:
        ;#
        ;#    mathfunc {x} {
        ;#       sinc = sin(x)/x if x != 0
        ;#       sinc = 0        otherwise
        ;#    }
        ;#    math {
        ;#       a = x*x + y*y
        ;#    }
        ;#
        ;#    Still to do: mathfunc
        ;#
        ;# (7 july 2004) Small improvement:
        ;#               recognise array elements
        ;#
        namespace eval ::mathsyntax {
            namespace export math
            variable cached_calcs {}
            variable func_names \
                    {abs acos asin atan atan2 ceil cos cosh double
                        exp floor fmod hypot int log log10 pow rand round
                        sin sinh sqrt srand tan tanh wide}
        }
        ;# ToExpr --
        ;#    Transform an expression to the form expr wants
        ;# Arguments:
        ;#    expression     A right-hand side of an assignment
        ;# Result:
        ;#    Valid Tcl expression
        ;#
        proc ::mathsyntax::ToExpr { expression } {
            variable func_names
            set rhs [string map {" " ""} $expression]
            set indices [regexp -inline -all -indices {[a-zA-Z][a-zA-Z0-9_]*} $rhs]
            set offset 0
            foreach idx $indices {
                foreach {start stop} $idx {break}
                set start [expr {$start+$offset}]
                set stop  [expr {$stop+$offset}]
                set next  [expr {$stop+1}]
                if { [string index $rhs $next] != "(" } {
                    set char [string index $rhs $start]
                    set rhs  [string replace $rhs $start $start "\$$char" ]
                    incr offset
                } else {
                    set char [string index $rhs $start]
                    set name [string range $rhs $start $stop]
                    if { [lsearch $func_names $name] < 0 } {
                        set rhs  [string replace $rhs $start $start "\$$char" ]
                    }
                }
            }
            return $rhs
        }
        ;# Transform --
        ;#    Transform a series of mathematical expressions into Tcl code
        ;# Arguments:
        ;#    id         ID to use
        ;#    calc       One or more mathematical assignments
        ;# Result:
        ;#    None
        ;# Side effects:
        ;#    A private procedure is created
        ;# Note:
        ;#    No conditions yet
        ;#
        proc ::mathsyntax::Transform { id calc } {
            set calc [split $calc "\n"]
            set body {"uplevel 2 \{"}
            foreach assign $calc {
                set assign [string trim $assign]
                if { $assign != "" } {
                    regexp {([a-zA-Z][a-zA-Z0-9_()]*) *= *(.*)} $assign ==> lhs rhsfull
                    ;#
                    ;# Is there a condition?
                    ;#
                    set cond1 [string first " if"        $rhsfull]
                    ;# PM: set cond2 [string first " otherwise" $rhsfull]
                    set cond  ""
                    if { $cond1 > 0 } {
                        set rhs  [string range $rhsfull 0 [expr {$cond1-1}]]
                        set cond [string range $rhsfull [expr {$cond1+3}] end]
                        lappend body "if { [ToExpr $cond] } \{"
                    } else {
                        set rhs $rhsfull
                    }
                    ;# If the left-hand side refers to an array element,
                    ;# we need to add a dollar-sign
                    ;#
                    set lhs [string map {"(" "($"} $lhs]
                    ;#
                    ;# Prepare the assignment
                    ;#
                    set rhs [ToExpr $rhs]
                    lappend body "set $lhs \[expr {$rhs}\]"
                    if { $cond != "" } {
                        lappend body "\}"
                    }
                }
            }
            lappend body "\}"
            proc Cached$id {} [join $body "\n"]
        }
        ;# math --
        ;#    Allow mathematical expressions inside Tcl code
        ;# Arguments:
        ;#    calc       One or more mathematical assignments
        ;# Result:
        ;#    None
        ;# Side effects:
        ;#    As the code is executed in the caller's scope, variables
        ;#    in the calling procedure are set
        ;#    The code is transformed into a procedure that is cached
        ;#
        proc ::mathsyntax::math { calc } {
            variable cached_calcs
            set id [lsearch $cached_calcs $calc]
            if { $id < 0 } {
                lappend cached_calcs $calc
                set id [expr {[llength $cached_calcs]-1}]
                Transform $id $calc
            }
            ::mathsyntax::Cached$id
        }
        ;#
        ;# Simple test
        ;#
        if {0} {
            namespace import ::mathsyntax::math
            set a 1
            set b 1
            set c ""
            set d ""
            set sinc ""
            math {
                c = a + b
                d = a + cos(b+c)
            }
            puts "$c $d"
            for {set i 0} {$i < 20} {incr i} {
                math {
                    x = 0.1*i
                    sinc = 1 if x == 0
                    sinc = sin(x)/x if x != 0
                    y(i) = sinc*sinc
                }
                puts "$i $x $sinc $y($i)"
            }
            ;#
            ;# Just to check
            ;#
            parray y  }
        ;# end of AM deck
        ;# add cosmetics below to bottom of file
        ;#  or source Little_Math_Language_AM
        ;# added statements above for TCLLIB library
        proc test args {
            foreach {case expected}  $args  {
                catch {uplevel 1 $case} res  ;# RS
                if {$res != $expected} {error "$case->$res, expected $expected"}
                puts "example >>  $case -> $res, & expected was $expected"
                ;# res ,  expected, variables  were not recycling ???
                ;# proc test is RS code from TCL Wiki
            }
        }
        console show
        console eval {.console config -bg palegreen}
        console eval {.console config -font {fixed 20 bold}}
        console eval {wm geometry . 40x20}
        console eval {wm title . "Little_Math_Language_AM in TCL , screen grab and paste from console  to texteditor"}
        console eval {. configure -background orange -highlightcolor brown -relief raised -border 30}
        console eval { proc self_helpx {} {
                set msg "Little_Math_Language_AM,
                large black type on green
                from TCL,
                self help listing
                ;# Conventional text editor formulas grabbed
                ;# from internet screens can be pasted
                ;# into green screen console
                ;# colon is statement end
                ;# proc test code from RS
                ;# ref A little math language revisited, page on TCL Wiki
                ;# Original program  by Arjen Markus on TCL Wiki
                ;# Reorganized code from
                ;# for print and self_help
                ;# to tcl console.
                ;# mathlang.tcl from AM, (original on tcl wiki 05-21-2004) "
                tk_messageBox -title "self_helpxx" -message $msg } }
        console eval {.menubar.help add command -label Self_help -command self_helpx }
        proc basic_alphabet_variables {} {
            global a b c d e f g h i j k l m n o p q r s t u v w x y z
            global A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
            foreach i {a b c d e f g h i j k l m n o p q r s t u v w x y z} {
                set $i 1
            }
            foreach i {A B C D E F G H I J K L M N O P Q R S T U V W X Y Z} {
                set $i 1
            } }
        proc demo {} {
            puts " demo "
            namespace import ::mathsyntax::math
            ;# set lower & upper case global alphabet_variables to 1
            basic_alphabet_variables
            set a 1
            set b 1
            set c ""
            set d ""
            set sinc ""
            math {
                c = a + b
                d = a + cos(b+c)
            }
            puts "$c $d"
            for {set i 0} {$i < 20} {incr i} {
                math {
                    x = 0.1*i
                    sinc = 1 if x == 0
                    sinc = sin(x)/x if x != 0
                    y(i) = sinc*sinc
                }
                puts "$i $x $sinc $y($i)"
            }
            ;#
            ;#
            parray y
            puts " returns to TCL 8.6  for check   = [exp 5 ]"
            puts "  set a 1 , set b 1 , set c 1 & <c d sinc strings nulled> "
            puts "math c = a + b ; d = a + cos(b+c), puts c d "
            puts "$c $d"
            test { isprime 7 } 1
            test { + 1 1     } 2
            test { - 10 1    } 9
            test { * 10 1    } 10
            test { / 10 2    } 5
            test { math { a = 10 / 2 } } 5
            test { math { b = 10. / 2 } } 5.
            test { math { c = 10. / 2. } } 5.
            test { math { d = 1 + 1  } } 2
            test { math { e = 10 - 1 } } 9
            test { math { f = 10 * 1 } } 10
            test { math { g = 10 / 2 } } 5
            test { math { h = 10 ** 2 } } 100
            test { math { i = 10 % 2 } }   0
            test { math { i = 3 * 4 / 2 } }   6
            test { math { i = (3>2) } }  1
            test { math { i = (3<2) } }  0
        }
        demo
        # end of file     
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***Extension  Code   ***
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**Hidden Comments Section**

<<discussion>>
Please include your wiki MONIKER and date in your comment with the same courtesy that I will give you. Thanks, [gold] 15Oct2020 
 
                              
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<<categories>> Numerical Analysis | Toys | Calculator | Mathematics| Example| Toys and Games | Games | Application | GUI
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