Calc Everything Is a Function

Proposed sequence of labs about the calculator for course 23/24

The PL labs of this group:

while -> strings -> left-side -> array-maps-and-null

corresponds to the branches

while
strings
left-side
array-map

of the repo functions-solution (opens in a new tab)

➜  functions-solution git:(left-side) git remote -v
origin  git@github.com:ULL-ESIT-PL/functions-solution.git (fetch)
origin  git@github.com:ULL-ESIT-PL/functions-solution.git (push)
pcgull-solution https://github.com/ULL-ESIT-PL-2223/arith2js-parallel-computing-group-parallel.git (fetch)
pcgull-solution https://github.com/ULL-ESIT-PL-2223/arith2js-parallel-computing-group-parallel.git (push)
scope-intro-solution    git@github.com:ULL-ESIT-PL/calc2js-solution.git (fetch)
scope-intro-solution    git@github.com:ULL-ESIT-PL/calc2js-solution.git (push)
upstream        https://github.com/ULL-ESIT-PL/arith2js-solution.git (fetch)
upstream        https://github.com/ULL-ESIT-PL/arith2js-solution.git (push)

➜  functions-solution git:(left-side) pwd -P
/Users/casianorodriguezleon/campus-virtual/2223/pl2223/practicas/functions/functions-solution

Regrets

Don't know how to deal with this

Goal: Functions on the left side of an assignment

In the calculator language, the left side of an assignment only an ID is allowed. We want to extend the language to allow the modification of functions.

Introduction

We want to extend the language so that on the left side of an assignment you can have a function modification. For example, the following code should be valid:

test/data/input/fun.calc

f = fun(x) { x + 1 },
f(0+2) = 8, # Constant folding lab for the future 0+1, 1*8
f(1+3) = 1000,
write(f(0)), # 1
write(f(2)), # 8
write(f(4))  # 1000

Goal: Array notation for functions and otherwise

The notation

a = [4;7;9 ... 0]

defines a as a function such that a(0) returns 4, a(1) returns 7, and a(2) returns 9 and otherwise returns 0.

If the ... expression is not present, the function returns an special object called null for any argument not explicitly defined.

a = [4+2;5+3i;9-i],
print(a(0)), # { re: 6, im: 0 }
a(1) = 333,  
print(a(1)), # { re: 333, im: 0 }
print(a(9)), # null
print(a)     #  { re: 6, im: 0 }, { re: 333, im: 0 }, { re: 9, im: -1 } ]

The former code translates to

➜  functions-solution git:(array-map) ✗ bin/calc2js.mjs test/data/input/arr.calc | npx prettier --parser babel
#!/usr/bin/env node
const {
    arr,
    Complex,
    print,
    memoize
} = require('/Users/casianorodriguezleon/campus-virtual/2223/pl2223/practicas/functions/functions-solution/src/support-lib.js');
 
/* End of support code */
 
let $a;
 
((((($a = arr(
    Complex('4').add(Complex('2')),
    Complex('5').add(Complex('3i')),
    Complex('9').sub(Complex('i'))
)),
print($a(Complex('0')))),
($a = memoize($a, [Complex('1')], Complex('333'), 0))),
print($a(Complex('1')))),
print($a(Complex('9')))),
    print($a);

Hashes/Maps/Objects

Proposed syntax for hashes/maps:

a = { 4: 5; 7: 3i; "hello": 6 ... 0}

meaning a function that a(4) = 5, a(7) = 3i, a("hello") = 6 and otherwise a(x) = 0 for all x.

An alternative to explore/study is to consider the introduction of the meth keyword that will define a functions that usea the "object" as a context. For example, the following code:

b = { "x": 5;  "add": meth(z) { x + z} },
f("add")(3) # 8

null object

Introduce null as an extension of 0 and the empty string "" so that it holds the following properties:

null + 4 == 4,
null + "hello" == "hello", # this is not the JS behavior
null * 4 == 0,
4 - null == 4,
fun(x) { x + 1 } * null # is the same as fun(x) { 0 },
null && true == false,

Notice that if a is a function like in the former example a * null is the function a(x) = 0 for any x.

Array Operations Complex