# Golf a FRACTRAN interpreter

# Description

From the Esolangs wiki,

In Fractran,

- a program consists of a finite list of positive, rational numbers.
- The input to a program is a positive integer n.
- The list is then searched in order, for a rational number $p/q$ such that $n×p/q$ is an integer.
- Then n is replaced by $n×p/q$ and the search is restarted from the beginning of the list.
- The program halts when no such number $p/q$ can be found, and the final n becomes the output from the program.
- Output the final value of $n$.

Your task is to implement an interpreter for this language.

# Input

You are to take two inputs:

- $n$, an integer
- $A$, an array of fractions, which may be taken as a list of pairs, or in the rational datatype of your language.

# Output

A single integer, the final value of $n$.

# Test Cases

Formatted as

```
program
input
output
```

```
78/55, 5/3, 1/5, 11/2, 5/7
1096135733
328842888196762472689573703
3/2
1296
6561
455/33, 11/13, 1/11, 3/7, 11/2, 1/3
72
15625
```

[APL (Dyalog Unicode)], 33 byt …

over 1 year ago

[Brachylog], 16 bytes g …

1y ago

[Python 3], 76 71 bytes Sav …

1y ago

JavaScript, 44 bytes …

over 1 year ago

Japt v2.0a0, 18 bytes The ` …

1y ago

[Ruby], 51 50 bytes -1 from R …

1y ago

J, 36 char ``` {.2{(}.,(=< …

4mo ago

Ruby, 44 bytes ->p,n{n=I …

8mo ago

## 8 answers

# APL (Dyalog Unicode), 33 bytes

```
{×x←⊃(2⌷⍵)(÷⍨(/⍨)0=|)⍺×1⌷⍵:x∇⍵⋄⍺}
```

The first case doesn't work because it gets really big, but the other two do. The input is taken on the left and the fractions are taken as a table on the right.

```
{×x←⊃(2⌷⍵)(÷⍨(/⍨)0=|)⍺×1⌷⍵:x∇⍵⋄⍺}
⍺× ⍝ n multiplied by
1⌷⍵ ⍝ The first row of the right argument (every p)
(2⌷⍵) ⍝ Second row of right arg (all q's)
| ⍝ All n×p modulo q
0= ⍝ Check which ones are 0 (rational)
÷⍨ ⍝ Make another vector of 'n×p÷q's
/⍨ ⍝ And keep the ones that were rational
⊃ ⍝ Pick the first (0 if empty)
x← ⍝ Assign to x
× ⍝ Sign of x
⍺ ⍝ If sign is 0, return n
x∇⍵ ⍝ Otherwise, call again with x as new n
```

# Brachylog, 16 bytes

```
g₂;.z∋zbᵗ×ᵐ/ℤ↰|w
```

This is a function submission, which inputs *n* from the left and *A* from the right (as a list of two-element lists). Output is to standard output.

## Explanation

```
g₂;.z∋zbᵗ×ᵐ/ℤ↰|w
g₂ place two list wrappers around the left input
;. append the right input
z cycling zip; because the left input is length 1,
this pairs it with each element of the right input
∋ find {the first} element for which no assertions fail
[at this point, the element looks like [[n], [num, denom]]
for some pair [num, denom] in A]
z rearrange to [[n, num], [n, denom]]
bᵗ remove first of last pair ([[n, num], [denom]])
×ᵐ take product of each inner list ([n×num, denom])
/ℤ divide; assert result (n×num÷denom) is an integer
↰ recurse (loop back to start of program)
| if all else fails (i.e. ∋ found no elements)
w output the current value to standard output
```

#### 0 comment threads

# JavaScript, 44 bytes

```
a=>g=n=>a.every(([p,q])=>(x=n*p/q)%1)?n:g(x)
```

#### 0 comment threads

# Japt v2.0a0, 18 bytes

The `r÷`

can be removed if we can take an array of floats instead.

```
T=V£*Xr÷Ãæv1)?ßT:U
```

```
T=V£*Xr÷Ãæv1)?ßT:U :Implicit input of integer U and 2D-array V
T= :Assign to variable T
V£ : Map each X in V
* : Multiply U by
Xr÷ : X reduced by division
Ã : End map
æ : Get the first element that
v1 : Is divisible by 1
) :End assignment
? :If truthy (not undefined)
ßT :Recursive call with arguments U=T and V unchanged
:U :Else return U
```

#### 0 comment threads

# J, 36 char

```
{._2{(}.,~(=<.)@v{.@#v=.}.*{.)^:(<_)
```

**Sample runs:**

```
{._2{(}.,~(=<.)@v{.@#v=.}.*{.)^:(<_) 1096135733 78r55 5r3 1r5 11r2 5r7
328842888196762472689573703
{._2{(}.,~(=<.)@v{.@#v=.}.*{.)^:(<_) 1296 3r2
6561
{._2{(}.,~(=<.)@v{.@#v=.}.*{.)^:(<_) 72 455r33 11r13 1r11 3r7 11r2 1r3
15625
```

## 1 comment thread