Math in manhattan

Question

I define the following operators:

Manhattan Addition a +_M b, for single-digit numbers, is the result of concatenating b onto a. So, a +_M b = 10a + b. Therefore, the general operator +_M is defined as thus:

a +M b = 10a + b

Manhattan Subtraction a –_M b, for single-digit numbers, is the result of removing the last b from a. Therefore, the operator –_M is defined as thus in pseudocode:

a –M b = a remove last b

Manhattan Multiplication a ×_M b is the result of replacing all instances of b in a with b instances of b. Ergo, ×_M is defined in pseudocode as:

a ×M b = a -> s/b/<b copies of b>/g

Manhattan Division a ÷_M b is defined in terms of ×_M:

1 ÷M b = the first character of b
a ÷M b = a ×M (1 ÷M b)

With all this in mind, create an interpreter that will evaluate infix expressions that use the following operators (i.e., a + b, not a b + or + a b)

+    Addition
-    Subtraction
/    Division
*    Multiplication
*M   Manhattan Multiplication
/M   Manhattan Division
+M   Manhattan Addition
-M   Manhattan Subtraction

Each Manhattan operator has a higher order precedence than their normal counterpart.

Test cases:

> 5 +M 10 + 3
63      // 5*10 + 10 + 3 => 60 + 3
> 10 *M 2
10      // no 2s in 10
> 10 *M 1
10      // one 1 in 10 replaced once
> 23 *M 3
2333    // 23 has one 3, which is replaced with three 3s
> 23 *M 2
223     // 23 has one 2, which is replaced with two 2s
> 232 *M 2
22322   // 232 has two 2s, which are replaced with two 2s
> 232 *M 23
23...(23 times)...232   // ...
> 123 *M 2 * 3
3669    // 1223 * 3 => 3669
> 5 + 3 +M 2
37      // 5 + (3 +M 2) => 5 + 32 => 37
> 150 /M 3
150     // 150 ÷M 3 => 150 ×M 3 => 150
> 150 /M 53
1555550 // 150 ÷M 53 => 150 ×M 5 => 1555550
> 50 -M 0
5
> 500 -M 0
50
> 5234 -M 5
234
> 12 +M 633 *M 3
6333453 // = 12 +M 6333333 = 120 + 6333333 = 6333453

This is a code-golf, so the shortest program in bytes wins.

Leaderboards

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# Language Name, N bytes

where N is the size of your submission. If you improve your score, you can keep old scores in the headline, by striking them through. For instance:

# Ruby, <s>104</s> <s>101</s> 96 bytes

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# Perl, 43 + 2 (-p flag) = 45 bytes

You can also make the language name a link which will then show up in the leaderboard snippet:

# [><>](http://esolangs.org/wiki/Fish), 121 bytes

var QUESTION_ID=59299,OVERRIDE_USER=8478;function answersUrl(e){return"http://api.stackexchange.com/2.2/questions/"+QUESTION_ID+"/answers?page="+e+"&pagesize=100&order=desc&sort=creation&site=codegolf&filter="+ANSWER_FILTER}function commentUrl(e,s){return"http://api.stackexchange.com/2.2/answers/"+s.join(";")+"/comments?page="+e+"&pagesize=100&order=desc&sort=creation&site=codegolf&filter="+COMMENT_FILTER}function getAnswers(){jQuery.ajax({url:answersUrl(answer_page++),method:"get",dataType:"jsonp",crossDomain:!0,success:function(e){answers.push.apply(answers,e.items),answers_hash=[],answer_ids=[],e.items.forEach(function(e){e.comments=[];var s=+e.share_link.match(/\d+/);answer_ids.push(s),answers_hash[s]=e}),e.has_more||(more_answers=!1),comment_page=1,getComments()}})}function getComments(){jQuery.ajax({url:commentUrl(comment_page++,answer_ids),method:"get",dataType:"jsonp",crossDomain:!0,success:function(e){e.items.forEach(function(e){e.owner.user_id===OVERRIDE_USER&&answers_hash[e.post_id].comments.push(e)}),e.has_more?getComments():more_answers?getAnswers():process()}})}function getAuthorName(e){return e.owner.display_name}function process(){var e=[];answers.forEach(function(s){var r=s.body;s.comments.forEach(function(e){OVERRIDE_REG.test(e.body)&&(r="<h1>"+e.body.replace(OVERRIDE_REG,"")+"</h1>")});var a=r.match(SCORE_REG);a&&e.push({user:getAuthorName(s),size:+a[2],language:a[1],link:s.share_link})}),e.sort(function(e,s){var r=e.size,a=s.size;return r-a});var s={},r=1,a=null,n=1;e.forEach(function(e){e.size!=a&&(n=r),a=e.size,++r;var t=jQuery("#answer-template").html();t=t.replace("{{PLACE}}",n+".").replace("{{NAME}}",e.user).replace("{{LANGUAGE}}",e.language).replace("{{SIZE}}",e.size).replace("{{LINK}}",e.link),t=jQuery(t),jQuery("#answers").append(t);var o=e.language;/<a/.test(o)&&(o=jQuery(o).text()),s[o]=s[o]||{lang:e.language,user:e.user,size:e.size,link:e.link}});var t=[];for(var o in s)s.hasOwnProperty(o)&&t.push(s[o]);t.sort(function(e,s){return e.lang>s.lang?1:e.lang<s.lang?-1:0});for(var c=0;c<t.length;++c){var i=jQuery("#language-template").html(),o=t[c];i=i.replace("{{LANGUAGE}}",o.lang).replace("{{NAME}}",o.user).replace("{{SIZE}}",o.size).replace("{{LINK}}",o.link),i=jQuery(i),jQuery("#languages").append(i)}}var ANSWER_FILTER="!t)IWYnsLAZle2tQ3KqrVveCRJfxcRLe",COMMENT_FILTER="!)Q2B_A2kjfAiU78X(md6BoYk",answers=[],answers_hash,answer_ids,answer_page=1,more_answers=!0,comment_page;getAnswers();var SCORE_REG=/<h\d>\s*([^\n,]*[^\s,]),.*?(\d+)(?=[^\n\d<>]*(?:<(?:s>[^\n<>]*<\/s>|[^\n<>]+>)[^\n\d<>]*)*<\/h\d>)/,OVERRIDE_REG=/^Override\s*header:\s*/i;

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Answer 1

Dyalog APL, 104 81 79 93 75 bytes

Edit: Now handles 4342343 -M 34 → 43423 correctly.

M←{⍎(5|⌊⍺⍺2)⊃'⍺×M⍣(⍺≠1)⍎⊃b'(b⎕R(⍵⍴'&')⊢a)'10⊥⍺⍵'(('(.*)',b←⍕⍵)⎕R'\1'⊢a←⍕⍺)}

Background

This extends APL to include the Manhattan operator. An operator in APL terminology is a modifier of functions (e.g. ÷). An example of an operator is ⍨ which modifies functions to swap their arguments so 3 = 2 ÷⍨ 6. So too, M modifies the basic arithmetic functions to be their Manhattan relatives. Note that since the resulting language is an extension of APL, APL's strict right-to-left precedence remains.

Explanation

The overarching structure is M←{⍎(5|⌊⍺⍺2)⊃…} which applies the function (+ or - or × or ÷) to 2 and uses the result to chose which string to evaluate. The strings are:

3 for -M: (('(.*)',b←⍕⍵)⎕R'\1'⊢a←⍕⍺)
 regex remove the last occurrence of b (string rep. of right arg.) in a (string rep. of left arg.)

2 for +M: '10⊥⍺⍵'
 evaluate the arguments as base-10 digits

1 for ×M: (b⎕R(⍵⍴'&')⊢a)
 replace occurrences of b with b ampersands (i.e. regex for the

0 for ÷M: '⍺×M⍣(⍺≠1)⍎⊃b'
 ⍎⊃b first digit of b
 ⍺×M⍣(⍺≠1) apply ⍺ ×M if ⍺ ≠ 1

⊃ out of of the above four strings, pick number:

(5|⌊⍺⍺2) mod-5 of the floor of the function applied to 2, namely:
 3 = 5 | ⌊-2
 2 = 5 | ⌊+2
 1 = 5 | ⌊×2 because ×2 ⇔ sgn(2) ⇔ 1
 0 = 5 | ⌊÷2 because ÷2 ⇔ 1 ÷ 2 ⇔ 0.5

Lots of thanks to my dear friend ngn for amazing shavings.

Answer 2

Perl, 100 99 98 bytes

97 bytes code + 1 byte command line

s/ |.*\K(\d)(\d*)-M\1|\+M/\2/g+s/(\d+)\*M(.)/$1=~s@$2@$&x$&@erg/e+s#/(M.)\d+#*\1#&&redo,$\=eval}{

Usage example:

echo "123 *M 2 * 3 + 150 /M 53" | perl -p entry.pl

Answer 3

Python, 644 bytes

import operator as o,re
x,q,t,r,w='*/+-M';mm,md,ma,ms='*M /M +M -M'.split()
n=lambda x:x
a=lambda a,b:str(10*int(a)+int(b))
v=lambda a,b:a[::-1].replace(b,'',1)[::-1]
m=lambda a,b:a.replace(b,b*int(b))
d=lambda a,b:m(a,b[0])if a>0 else b[0]
def p(s):s=s.group();ss=s.split();l=s.split(ss[1]);h={mm:m,md:d,ma:a,ms:v,x:o.mul,q:o.div,t:o.add,r:o.sub}.get(ss[1],n);return str(h(*map(int if h in[o.mul,o.div,o.add,o.sub]else n,map(u,map(str.strip,l)))))
def u(s):z=r'\d+ (?:\{0}{2}|\{1}{2}) \d+';return re.sub(z.format(t,r,''),p,re.sub(z.format(t,r,w),p,re.sub(z.format(x,q,''),p,re.sub(z.format(x,q,w),p,re.sub(r'\((.*)\)',u,s)))))
print u(input())

Accepts input on STDIN (wrapped in quotes). Uses regex to match and parse operations. All work is done on strings, and casting to and from ints is only used when doing normal mathematical operations.

I'm pretty sure this could be golfed further, so I'll be working on that over the next few days.