coverage.md

Coverage of the APLT Compiler

This page documents the functionality of the APLT compiler.

Datatypes

Supported datatypes include booleans, integers, doubles, and characters. Strings are represented as character arrays. Nested arrays are currently not supported, except in a limited fashion for resembling tuples (see below).

Monadic Functions

Expression	Name	Meaning	Notes
⍴ A	Shape	Returns the shape of the array A as a vector of integers.
⍳ N	Iota	Returns a vector of length N with values [1,...,N].
, A	Ravel	Returns the vector of values appearing in A in row-major order.
+ A	Identity	Returns A.
- A	Negation	Returns the array A with all elements negated.
÷ A	Reciprocal	Returns the array A with elements being the reciprocal values of the values in A.
× A	Sign	Returns the array A with elements being -1 for negative values in A and 1 for positive values in A.
⌈ A	Ceil	Returns A with elements ceiled.	The function returns an integer array.
⌊ A	Floor	Returns A with elements floored.	The function returns an integer array.
⍉ A	Transpose	Returns the transposed version of A.
~ A	Logical negation	Returns A with boolean elements negated.	Assumes A to be of boolean type.
○ A	Pi times	Returns A with all elements multiplied by pi.
⍟ A	Log	Returns A with the natural logarithm applied to all elements.
? A	Random	Returns random values between 0 and 1 (if the argument is 0) and otherwise between 0 and the argument (whole number).
≢ A	Tally	Returns the size of the outer dimension of A.

Dyadic Functions

Expression	Name	Meaning	Notes
B ⍴ A	Reshape	Returns an array with shape B and values taken from ,A (rotated if there are not sufficiently many values in A).	The length of the vector B must be statically decided.
B ⍉ A	Dyadic transpose	Returns the generalized transposed version of A, according to the dimension index vector B.	B must be an integer vector of the same length as A.
B + A	Addition	Pair-wise addition of elements in B and A.	Scalar expansion supported: Arrays A and B must be of the same shape unless one of the arrays is a scalar value in which case the array is extended to match the shape of the other array.
B - A	Subtraction	Pair-wise subtraction of elements in B and A.	Scalar expansion supported.
B ÷ A	Division	Pair-wise division of elements in B and A.	Scalar expansion supported.
B × A	Multiplication	Pair-wise multiplication of elements in B and A.	Scalar expansion supported.
B ⌈ A	Maximum	Pair-wise maximum of elements in B and A.	Scalar expansion supported.
B ⌊ A	Minimum	Pair-wise minimum of elements in B and A.	Scalar expansion supported.
N ↑ A	Take	Returns the vector resulting from taking N elements from A (row-major order).	When N is negative, values are taken from the right.
N ↓ A	Drop	Returns the vector resulting from dropping N elements from A (row-major order).	When N is negative, values are dropped from the right.
N ⌽ A	Rotate	Returns the vector resulting from rotating values in A to the left N steps (row-major order).	When N is negative, values are right-rotated.
N ⊖ A	Rotate last	Returns the vector resulting from rotating values (in A) N steps along the last axis (column-major order).	When N is negative, values are rotated in the opposite directions.
B , A	Catenate	Returns the vector resulting from catenating elements in B with elements in A (row-major order).
B ⍪ A	Catenate last	Returns the vector resulting from catenating elements in B with elements in A (column-major order).
B ∨ A	Boolean or	Returns the logical disjunction of B and A.	Scalar expansion supported.
B ∧ A	Boolean and	Returns the logical conjunction of B and A.	Scalar expansion supported.
B ⍱ A	Boolean nor	Returns the negation of the logical disjunction of B and A.	Scalar expansion supported.
B ⍲ A	Boolean nand	Returns the negation of the logical conjunction of B and A.	Scalar expansion supported.
B = A	Equality	Pair-wise equality of elements in B and A.	Scalar expansion supported.
B ≠ A	Not equal	Pair-wise inequality of elements in B and A.	Scalar expansion supported.
B < A	Less than	Pair-wise less than comparison of elements in B and A.	Scalar expansion supported.
B ≤ A	Less than or equal	Pair-wise less than or equal comparison of elements in B and A.	Scalar expansion supported.
B > A	Greater than	Pair-wise greater than comparison of elements in B and A.	Scalar expansion supported.
B ≥ A	Greater than or equal	Pair-wise greater that or equal comparison of elements in B and A.	Scalar expansion supported.
B / A	Compress	Returns the elements in A (as a vector) for which the corresponding elements in the boolean vector B are true.	Assumes A to be a vector of the same length as the boolean vector B.
B / A	Replicate	Returns repeated elements from A (as a vector) with the repetition controlled by the corresponding elements in the integer vector B.	Assumes A to be a vector of the same length as the integer vector B.
B ○ A	Circ	Returns the trigonometric function on A dependent on the integer value B; 1:sin, 2:cos, 3:tan.	The value of B has to be statically determined.

Monadic Operators

Expression	Name	Meaning	Notes
f /	Reduce	Returns a monadic function that reduces (using f) its argument array along the first axis. The argument to the operator must be a dyadic function.	Certain limitations apply.
f ⌿	Reduce last axis	Returns a monadic function that reduces (using f) its argument array along the last axis. The argument to the operator must be a dyadic function.	Certain limitations apply.
f ¨	Each	Returns a monadic function that maps (using f) over its argument array. The argument to the operator must be a monadic function.
∘. f	Outer product	Returns a dyadic function that applies f to all elements (pairs) from the cartesian product of the array arguments.

Dyadic Operators

Expression	Name	Meaning	Notes
f . g	Inner product	Returns a dyadic function that performs the inner product of its arguments (using f and g). The arguments to the operator must be a dyadic function.	Certain limitations apply.
f ⍣ n	Power	Returns a monadic function that iteratively applies f to its argument n times.	Parentheses may be needed to separate n from the argument to the resulting function. The function f may take (and produce) a vector of arrays, which may be indexed in the body of f using array indexing.

Scalar extensions

Scalar extensions are supported.

Identity items

For certain built-in functions, identity items are supported:

Function	Left-identity	Right-identity
+	0	0
-		0
×	1	1
÷		1
`	`	0
=,≥,≤	1	1
≠,>,<	0	0
∨		0
∧		1
⌈	-inf	-inf
⌊	inf	inf

Quad Assignment (output)

Intermediate arrays may be printed using assignment to the quad-character:

⎕ ← A

Arrays of rank 2 are printed as matrices. Other arrays are printed using a flat representation, specifying both the shape vector and the underlying values.

Trains (points-free notation)

APLT supports writing expressions in points-free (also called tacit) notation. For instance, the APL code

mean ← +/÷≢
⎕ ← mean 2 37 4 1

results in the output 11. APLT support both monadic and dyadic Agh trains and monadic and dyadic fgh trains.

Tuples of arrays

APLT supports having tuples of arrays of different ranks and types. For instance, a tuple c of a vector, a pair (of two vectors), and a scalar, may be constructed as

a ← 1 2 4 3
b ← 'hello'
c ← a (b a) 4

Tuples, such as c, may be passed to functions and deconstructed using index notation:

f ← {
  a1 ← +/⍵[1]
  a2 ← ⊃⍴(⍵[2])[1]
  a1 + a2 + ⍵[3]
}
⎕ ← f c   ⍝ --> [](19)

A particular use of this feature is in conjunction with the power operator. See the powtup.apl test example.

System Functions

Expression	Name	Meaning	Notes
⎕ReadFile file	READ FILE	Takes a filepath as parameter and returns a vector of characters	Fails in case the file cannot be read.
⎕ReadIntVecFile file	READ INT VECTOR FROM FILE	Takes a filepath as parameter and returns a vector of integers	Fails in case the input file cannot be read or does not contain a sequence of integers separated by space characters.

Using APLT

Here is the output from executing aplt on the command-line:

bash-3.2$ aplt 
Usage: ../apltail/aplt [OPTIONS]... file.apl...
 -o file        : write TAIL program to file
 -oc file       : write LAILA program to file
 -c             : compile only (no evaluation)
 -noopt         : disable optimizations
 -materialize   : disable materialization of arrays
 -p_tail        : print TAIL program
 -p_types       : print types in TAIL code
 -p_laila       : print LAILA code
 -s_parse       : stop after parsing
 -s_tail        : stop after TAIL generation
 -silent        : evaluation output only (unless there are errors)
 -v             : verbose
 -O n           : optimisation level (n>0 optimises double operations aggresively)
 -comments      : write comments in generated C code
 -unsafe        : don't include assert code in generated C code for array indexing
 -stat_laila    : print statistics for LAILA code generation
 -opt_hoist     : enable hoist optimization in LAILA code generation
 -opt_loopsplit : enable loop split optimization in LAILA code generation