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Update 002-bounded-recursion.md

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minor fixups
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Eric McCarthy 2021-06-08 18:32:05 -07:00 committed by GitHub
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docs/rfc/002-bounded-recursion.md
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@ -51,7 +51,7 @@ unrolling loops, inlining functions, decomposing arrays, etc.
Of interest to this RFC is the inlining of functions,
in which a function call is replaced with the function body,
after binding the formal parameters to the the actual arguments,
and taking care to rename apart variables to avoid conflicts.
and taking care to rename variables if needed to avoid conflicts.
Since the `main` function is the entry point into a Leo program,
conceptually, for the purpose of this RFC,
@ -151,13 +151,13 @@ This is an example:
```js
function double(const count: u32, sum: u32) -> u32 {
if count > 1 {
return double(count - 1, sum + sum)
return double(count - 1, sum + sum);
} else {
return sum + sum;
}
}
function main(x: u32) -> u32 {
return double(3, x)
return double(3, x);
}
===> {inline call double(3, x)}
@ -165,7 +165,7 @@ function main(x: u32) -> u32 {
function main(x: u32) -> u32 {
let sum1 = x; // bind and rename parameter of function sum
if 3 > 1 {
return double(2, sum1 + sum1)
return double(2, sum1 + sum1);
} else {
return sum1 + sum1;
}
@ -175,7 +175,7 @@ function main(x: u32) -> u32 {
function main(x: u32) -> u32 {
let sum1 = x;
return double(2, sum1 + sum1)
return double(2, sum1 + sum1);
}
===> {inine call double(2, sum1 + sum1)}
@ -184,7 +184,7 @@ function main(x: u32) -> u32 {
let sum1 = x;
let sum2 = sum1 + sum1; // bind and rename parameter of function sum
if 2 > 1 {
return double(1, sum2 + sum2)
return double(1, sum2 + sum2);
} else {
return sum2 + sum2;
}
@ -205,7 +205,7 @@ function main(x: u32) -> u32 {
let sum2 = sum1 + sum1;
let sum3 = sum2 + sum2; // bind and rename parameter of function sum
if 1 > 1 {
return double(0, sum3 + sum3)
return double(0, sum3 + sum3);
} else {
return sum3 + sum3;
}
@ -225,13 +225,13 @@ This is a slightly more complex example
```js
function double(const count: u32, sum: u32) -> u32 {
if count > 1 && sum < 30 {
return double(count - 1, sum + sum)
return double(count - 1, sum + sum);
} else {
return sum + sum;
}
}
function main(x: u32) -> u32 {
return double(3, x)
return double(3, x);
}
===> {inline call double(3, x)}
@ -239,7 +239,7 @@ function main(x: u32) -> u32 {
function main(x: u32) -> u32 {
let sum1 = x; // bind and rename parameter of function sum
if 3 > 1 && sum1 < 30 {
return double(2, sum1 + sum1)
return double(2, sum1 + sum1);
} else {
return sum1 + sum1;
}
@ -250,7 +250,7 @@ function main(x: u32) -> u32 {
function main(x: u32) -> u32 {
let sum1 = x;
if sum1 < 30 {
return double(2, sum1 + sum1)
return double(2, sum1 + sum1);
} else {
return sum1 + sum1;
}
@ -263,7 +263,7 @@ function main(x: u32) -> u32 {
if sum1 < 30 {
let sum2 = sum1 + sum1; // bind and rename parameter of function sum
if 2 > 1 && sum2 < 30 {
return double(1, sum2 + sum2)
return double(1, sum2 + sum2);
} else {
return sum2 + sum2;
}
@ -279,7 +279,7 @@ function main(x: u32) -> u32 {
if sum1 < 30 {
let sum2 = sum1 + sum1;
if sum2 < 30 {
return double(1, sum2 + sum2)
return double(1, sum2 + sum2);
} else {
return sum2 + sum2;
}
@ -297,7 +297,7 @@ function main(x: u32) -> u32 {
if sum2 < 30 {
let sum3 = sum2 + sum2; // bind and rename parameter of function sum
if 1 > 1 && sum3 < 30 {
return double(0, sum3 + sum3)
return double(0, sum3 + sum3);
} else {
return sum3 + sum3;
}
@ -409,7 +409,7 @@ n! =def= [IF n = 0 THEN 1 ELSE n * (n-1)!]
```
terminates because, if `n` is not 0, we have that `n-1 < n`,
and `<` is well-founded on the natural numbers;
in this example, the measure of the (only) argument is the argument itself.
in this example, the measure of the argument is the argument itself.
(A relation is well-founded when
it has no infinite strictly decreasing sequence;
note that, in the factorial example,