From d94ceeab2e57f24da01289d433ef5ef944be105c Mon Sep 17 00:00:00 2001 From: Danila Fedorin Date: Sat, 31 Aug 2024 11:37:28 -0700 Subject: [PATCH] Make minor edits to part 5 of SPA Signed-off-by: Danila Fedorin --- content/blog/05_spa_agda_semantics.md | 18 +++++++++--------- 1 file changed, 9 insertions(+), 9 deletions(-) diff --git a/content/blog/05_spa_agda_semantics.md b/content/blog/05_spa_agda_semantics.md index 33aa7ad..b1514ee 100644 --- a/content/blog/05_spa_agda_semantics.md +++ b/content/blog/05_spa_agda_semantics.md @@ -9,7 +9,7 @@ draft: true In the previous several posts, I've formalized the notion of lattices, which are an essential ingredient to formalizing the analyses in Anders Møller's -lecutre notes. However, there can be no program analysis without a program +lecture notes. However, there can be no program analysis without a program to analyze! In this post, I will define the (very simple) language that we will be analyzing. An essential aspect of the language is its [semantics](https://en.wikipedia.org/wiki/Semantics_(computer_science), which @@ -40,9 +40,9 @@ This time, the English interpretation of the rule is as follows: > then to evaluate the statement, you evaluate its `then` branch. These rules are certainly not equivalent. For instance, the former allows -the "then" branch to be executed when the condition is `2` two; however, in +the "then" branch to be executed when the condition is `2`; however, in the latter, the value of the conditional must be `1`. If our analysis were -_flow-sensitive_ (our first few will not be), then this difference would change +intelligent (our first few will not be), then this difference would change its output when determining the signs of the following program: ``` @@ -58,7 +58,7 @@ Using the first, more "relaxed" rule, the condition would be considered "true", and the sign of `y` would be `-`. On the other hand, using the second, "stricter" rule, the sign of `y` would be `+`. I stress that in this case, I am showing a flow-sensitive analysis (one that can understand control flow -and make more speciifc predictions); for our simplest analyses, we will not +and make more specific predictions); for our simplest analyses, we will not be aiming for flow-sensitivity. There is plenty of work to do even then. The point of showing these two distinct rules is that we need to be very precise @@ -137,7 +137,7 @@ it prints its argument to the console! For the formalization, it turns out to be convenient to separate "simple" statements from "complex" ones. Pragmatically speaking, the difference is that between the "simple" and the "complex" is control flow; simple statements -will be guaranteed to always execute one-by-one, without any decisions or jumps. +will be guaranteed to always execute without any decisions or jumps. The reason for this will become clearer in subsequent posts; I will foreshadow a bit by saying that consecutive simple statements can be placed into a single [basic block](https://en.wikipedia.org/wiki/Basic_block). @@ -151,7 +151,7 @@ noop ``` These will always be executed in the same order, exactly once. Here, `noop` -is a conveneint type of statement that simply does nothing. +is a convenient type of statement that simply does nothing. On the other hand, the following statement is not simple: @@ -161,7 +161,7 @@ while x { } ``` -it's not simple because it makes decisions about how the code should be executed; +It's not simple because it makes decisions about how the code should be executed; if `x` is nonzero, it will try executing the statement in the body of the loop (`x = x - 1`). Otherwise, it would skip evaluating that statement, and carry on with subsequent code. @@ -171,12 +171,12 @@ I first define simple statements using the `BasicStmt` type: {{< codelines "Agda" "agda-spa/Language/Base.agda" 18 20 >}} Complex statements are just called `Stmt`; they include loops, conditionals and -sequences ( +sequences --- {{< sidenote "right" "then-note" "\(s_1\ \text{then}\ s_2\)" >}} The standard notation for sequencing in imperative languages is \(s_1; s_2\). However, Agda gives special meaning to the semicolon, and I couldn't find any passable symbolic alternatives. -{{< /sidenote >}} is a sequence where \(s_2\) is evaluated after \(s_1\)). +{{< /sidenote >}} is a sequence where \(s_2\) is evaluated after \(s_1\). Complex statements subsume simple statements, which I model using the constructor `⟨_⟩`.