apltail

An APL Compiler targeting a Typed Array Intermediate Language.

This software implements an APL compiler in Standard ML. The compiler targets a typed array intermediate language [1]. The executable also contains an interpreter for TAIL and a compiler from TAIL into C.

See the compilation scheme.

See also the coverage page.

An example

Consider the following program:

f ← {5+⍵}    ⍝ Function adding 5 to its argument (⍵)
+/ f ⍳ 30    ⍝ Apply f to the vector 1..30 and
             ⍝  sum up the elements in the resulting vector

Here is what happens when the program is compiled and executed:

bash-3.2$ ./aplt -p_tail lib/prelude.apl tests/test.apl
[Reading file: lib/prelude.apl]
[Reading file: tests/test.apl]
Resulting program:
let v0:<int>30 = iotaV(30) in
i2d(reduce(addi,0,eachV(fn v1:[int]0 => addi(5,v1),v0)))
Evaluating
Result is [](615.0)

Another example

Consider the program

diff ← {1↓⍵−¯1⌽⍵}
signal ← {¯50⌈50⌊50×(diff 0,⍵)÷0.01+⍵}
+/ signal ⍳ 100

Here is the result of compiling and evaluating it:

bash-3.2$ ./aplt -p_tail lib/prelude.apl tests/signal.apl
[Reading file: lib/prelude.apl]
[Reading file: tests/signal.apl]
Resulting program:
let v0:<int>100 = iotaV(100) in
let v3:<int>101 = consV(0,v0) in
reduce(addd,0.00,each(fn v11:[double]0 => maxd(~50.00,v11),each(fn v10:[double]0 => mind(50.00,v10),each(fn v9:[double]0 => muld(50.00,v9),zipWith(divd,each(i2d,drop(1,zipWith(subi,v3,rotateV(~1,v3)))),eachV(fn v2:[double]0 => addd(0.01,v2),eachV(i2d,v0)))))))
Evaluating
Result is [](258.557340366)

Example demonstrating transpose and a double-reduce

Consider the following APL program:

a ← 3 2 ⍴ ⍳ 5
a2 ← 3 2 ⍴ ⍳ 4
b ← ⍉ a
c ← b, ⍉ a2
×/ +/ c

⍝ 1 2    1 3 5  1 3 1  -+-> 14
⍝ 3 4    2 4 1  2 4 2  -+-> 15
⍝ 5 1
⍝                          ---
⍝                          210

Here is the result of compiling and evaluating it:

bash-3.2$ ./aplt -p_tail lib/prelude.apl tests/test15.apl
[Reading file: lib/prelude.apl]
[Reading file: tests/test15.apl]
Resulting program:
let v0:[int]2 = reshape([3,2],iotaV(5)) in
let v1:[int]2 = reshape([3,2],iotaV(4)) in
let v2:[int]2 = transp(v0) in
let v3:[int]2 = cat(v2,transp(v1)) in
i2d(reduce(muli,1,reduce(addi,0,v3)))
Evaluating
Result is [](210.0)

Example demonstrating matrix-multiplication

a ← 3 2 ⍴ ⍳ 5
b ← ⍉ a
c ← a +.× b
×/ +/ c

⍝       1  3  5
⍝       2  4  1
⍝
⍝ 1 2   5 11  7  -+->    23
⍝ 3 4  11 25 19  -+->    55
⍝ 5 1   7 19 26  -+->    52
⍝                     65780

Here is the result of compiling and evaluating the example using the prelude definition of inner product:

bash-3.2$ ./aplt -p_tail lib/prelude.apl tests/test13.apl
[Reading file: lib/prelude.apl]
[Reading file: tests/test13.apl]
Resulting program:
let v0:[int]2 = reshape([3,2],iotaV(5)) in
let v1:[int]2 = transp(v0) in
let v6:[int]3 = transp2([2,1,3],reshape([3,3,2],v0)) in
let v12:[int]3 = transp2([1,3,2],reshape([3,2,3],v1)) in
let v17:[int]2 = reduce(addi,0,zipWith(muli,v6,v12)) in
i2d(reduce(muli,1,reduce(addi,0,v17)))
Evaluating
Result is [](65780.0)

Without optimizations, the compilation results in a slightly larger output:

bash-3.2$ ./aplt -p_tail -noopt lib/prelude.apl tests/test13.apl
[Reading file: lib/prelude.apl]
[Reading file: tests/test13.apl]
Resulting program:
let v0:[int]2 = reshape([3,2],iotaV(5)) in
let v1:[int]2 = transp(v0) in
let v2:<int>3 = catV(dropV(b2iV(tt),shape(v1)),shape(v0)) in
let v3:[int]0 = subi(firstV(shapeV(shape(v0))),b2iV(tt)) in
let v4:<int>3 = iotaV(firstV(shapeV(v2))) in
let v5:<int>3 = catV(rotateV(v3,dropV(~1,v4)),takeV(~1,v4)) in
let v6:[int]3 = transp2(v5,reshape(v2,v0)) in
let v7:<int>3 = catV(dropV(~1,shape(v0)),shape(v1)) in
let v8:S(int,2) = firstV(shapeV(shape(v0))) in
let v9:<int>3 = iotaV(firstV(shapeV(v7))) in
let v10:<int>1 = dropV(negi(v8),rotateV(v8,iotaV(firstV(shapeV(v9))))) in
let v11:<int>3 = catV(dropV(~1,iotaV(v8)),snocV(v10,v8)) in
let v12:[int]3 = transp2(v11,reshape(v7,v1)) in
let v17:[int]2 = reduce(addi,0,zipWith(muli,v6,v12)) in
i2d(reduce(muli,1,reduce(addi,0,v17)))
Evaluating
Result is [](65780.0)

Try it!

The software makes use of the sml-unicode library for lexing and the sml-aplparse library for parsing. It also uses various other packages that can be installed with smlpkg, which itself needs to be available on the system for pulling down the library sources.

You also need a Standard ML compiler (e.g., Mlton or MLKit).

To pull down the dependent libraries and to compile the source, execute the following commands in a shell:

$ make prepare
$ make all

These commands will leave an executable aplt in the root directory of the repository.

To run a series of tests, execute make test in your shell.

To get aplt to output type instantiation list for the polymorphic functions, such as reduce, each, and take, you may pass the option -p_types to aplt.

See also the coverage page.

To compile with MLKit instead of with MLton, which takes quite some time, instead of typing make all above, type instead MLCOMP=mlkit make all.

License

This software is published under the MIT License.

References

[1] Martin Elsman and Martin Dybdal. Compiling a Subset of APL Into a Typed Intermediate Language. In ACM SIGPLAN International Workshop on Libraries, Languages and Compilers for Array Programming (ARRAY'14). Edinburgh, UK. June, 2014. pdf, bibtex.