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A toy Wolfram Language interpreter in Haskell


Recently I wrote a toy Wolfram Language interpreter as a way to learn more about Wolfram Language. I have implemented some basic language structure and built-in functions. I have hosted it on github.

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A simple term rewriting system with Wolfram Language's syntax

Inspired by the book Write Yourself a Scheme in 48 Hours. I decide to write myself a simple Wolfram Language-like interpreter to learn more about Haskell as well as achieve a deeper understanding about Wolfram Language.

Running (Using Stack)

git clone
cd mmaclone/mmaclone
stack setup
stack build
stack exec mmaclone-exe

Prebulid binary files are available on the release page


This interpreter is intended to mimic every exact detail of Wolfram Language, including but not limited to its syntax, semantic, expression structure, evaluation details, etc. (All the scripts below were executed in the REPL session of the mmaclone program)

  1. The program support nearly all Wolfram Language's syntax sugar, infix operators as well as their precedence. Inequality expression chain is parsed in the same way with Wolfram Language.
    In[1]:= FullForm[a==b>=c<=d<e]
    Out[1]= Inequality[a,Equal,b,GreaterEqual,c,LessEqual,d]

Some more complicated examples.

    In[2]:= FullForm[P@1@2//3]
    Out[2]= 3[P[1[2]]]
    In[3]:= FullForm[P''''[x]]
    Out[3]= Derivative[4][P][x]
    In[4]:= FullForm[Hold[(1 ##&)[2]]]
    Out[4]= Hold[Function[Times[1,SlotSequence[1]]][2]]
  1. Wolfram Language's powerful pattern matching is also implemented with scrupulous.

    (*The famous bubble sort implementation*)
    In[1]:= sortRule := {x___,y_,z_,k___}/;y>z -> {x,z,y,k}
    In[2]:= {64, 44, 71, 48, 96, 47, 59, 71, 73, 51, 67, 50, 26, 49, 49}//.sortRule
    Out[2]= {26,44,47,48,49,49,50,51,59,64,67,71,71,73,96}
    (*Symbolic manipulation*)
    In[3]:= rules:={Log[x_ y_]:>Log[x]+Log[y],Log[x_^k_]:>k Log[x]}
    In[4]:= Log[a (b c^d)^e] //. rules
    Out[4]= Log[a]+e (Log[b]+d Log[c])

Currently, the derivative function D is not built-in supported, but you could easily implement one with the powerful pattern matching facilities.

      In[5]:= D[a_,x_]:=0
      In[6]:= D[x_,x_]:=1
      In[7]:= D[a_+b__,x_]:=D[a,x]+D[Plus[b],x]
      In[8]:= D[a_ b__,x_]:=D[a,x] b+a D[Times[b],x]
      In[9]:= D[a_^(b_), x_]:= a^b(D[b,x] Log[a]+D[a,x]/a b)
      In[10]:= D[Log[a_], x_]:= D[a, x]/a
      In[11]:= D[Sin[a_], x_]:= D[a,x] Cos[a]
      In[12]:= D[Cos[a_], x_]:=-D[a,x] Sin[a]
      (*performing derivative*)
      In[13]:= D[Sin[x]/x,x]
      Out[13]= -x^(-2) Sin[x]+Cos[x] x^(-1)
      In[14]:= D[%,x]
      Out[14]= -Cos[x] x^(-2)-(-2 x^(-3) Sin[x]+Cos[x] x^(-2))-x^(-1) Sin[x]

Pattern test facility is of the same semantic with `Wolfram Language`'s.

      In[15]:= {{1,1},{0,0},{0,2}}/.{x_,x_}/;x+x==2 -> a
      Out[15]= {a,{0,0},{0,2}}
      In[16]:= {a, b, c, d, a, b, b, b} /. a | b -> x
      Out[16]= {x,x,c,d,x,x,x,x}
      In[17]:= g[a_*b__]:=g[a]+g[Times[b]]
      In[18]:= g[x y z k l]
      Out[18]= g[k]+g[l]+g[x]+g[y]+g[z]
      In[19]:= q[i_,j_]:=q[i,j]=q[i-1,j]+q[i,j-1];q[i_,j_]/;i<0||j<0=0;q[0,0]=1;Null
      In[20]:= q[5,5]
      Out[20]= 252
  1. Some interesting scripts
      In[1]:= ((#+##&) @@#&) /@{{1,2},{2,2,2},{3,4}}
      Out[1]= {4,8,10}
      In[2]:= fib[n_]:=fib[n]=fib[n-1]+fib[n-2];fib[1]=fib[2]=1;Null
      In[3]:= fib[100]
      Out[3]= 354224848179261915075
      In[4]:= fib[1000000000000]
      Iteration Limit exceeded, try to increase $IterationLimit
      In[5]:= Print/@fib/@{10,100}
      Out[5]= {Null,Null}


For more information please refer to the project wiki (still under construction).

Features that are likely to be added in future versions:

(Some serious design errors are exposed during development, which I consider are inhibiting the project from scaling up. So currently my primary focus would be on refactor rather than adding new features/functions)

  1. More mathematical functions (Sin, Cos, Mod etc...)
  2. Arbitrary precision floating arithmetic using GMP(GNU Multiple Precision Arithmetic Library), currently arbitrary integer, double and rational number are supported.
  3. More built-in functions (Level, Import, Derivativeetc...)
  4. More sophisticated pattern matching
  • ~~head specification (of the form Blank[Head], currently it only support list type)~~(Implemented)
  • ~~Pattern Test~~(Implemented)
  • ~~BlankSequence, BlankNullSequence~~(Implemented)
  • Other pattern matching expression, like Verbatim, Longest
  1. ~~RecursionLimit~~(Implemented)
  2. Negative index e.g. in Part
  3. Negative level specification
  4. Curried function e.g. f[a][b] (currently it will throw an error if one is trying to attach value to the curried form through Set or SetDelayed)
  5. Use iPython as front end
  6. ~~Replace String implementation with more efficient Text~~(Implemented)
POSTED BY: Yonghao Jin
1 year ago

Well done! This is a rather major endeavour! is this just for fun? or do you have serious intensions to 'rebuild' Mathematica :o

POSTED BY: Sander Huisman
1 year ago

Thanks for your response! It is just for fun, a serious 'rebuild' requires farrrr more expertise and effort:).

POSTED BY: Yonghao Jin
1 year ago

You already implemented pattern matching which is one of the hardest parts I presume ;)

POSTED BY: Sander Huisman
1 year ago

enter image description here - you have earned "Featured Contributor" badge, congratulations !

This is a great post and it has been selected for the curated Staff Picks group. Your profile is now distinguished by a "Featured Contributor" badge and displayed on the "Featured Contributor" board.

POSTED BY: Moderation Team
1 year ago

That's cool, but I hope you do not run into legal troubles. According to the mathematica eula, under "ownership", they see their language as part of their product's IP and don't grant anyone to use its distinctive features outside of the product.

POSTED BY: Harald Schilly
1 year ago

Well, this project seems to live on: Mathics: A free, light-weight alternative to Mathematica

Mathics is a free, general-purpose online computer algebra system featuring Mathematica-compatible syntax and functions. It is backed by highly extensible Python code, relying on SymPy for most mathematical tasks.

POSTED BY: Sam Carrettie
1 year ago

Group Abstract Group Abstract