All: added new obsidian notes for autumn term 4th year

.github/CONTRIBUTING.md

@@ -15,3 +15,6 @@ See the provided [container](../.devcontainer).
 ### Locally
 Please use the dockerfile and vscode features from the [container setup](../.devcontainer) as a guide.
 - @oliverkillane is using MikTex + vscode + wsl on Windows
+
+## On Obsidian...
+Make sure to add new directories for latex notes as ignored from [obsidian's userIgnoreFilters](../.obsidian/app.json)

.obsidian/app.json

@@ -0,0 +1,20 @@
+{
+  "userIgnoreFilters": [
+    "50001 - Algorithm Analysis and Design/",
+    "50003 - Models of Computation/",
+    "50005 - Networks and Communications/",
+    "50006 - Compilers/",
+    "50008 - Probability and Statistics/",
+    "60001 - Advanced Computer Architecture/",
+    "60007 - Theory and Practice of Concurrent Programming/",
+    "60008 - Custom Computing/",
+    "60009 - Distributed Algorithms/",
+    "60017 - System Performance Engineering/",
+    "60023 - Type Systems for Programming Languages/",
+    "60029 - Data Processing Systems/",
+    "common/",
+    "tools/",
+    "README",
+    "LICENCE"
+  ]
+}

.obsidian/appearance.json

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+{
+  "accentColor": ""
+}

.obsidian/community-plugins.json

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+[]

.obsidian/core-plugins-migration.json

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+{
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+  "global-search": true,
+  "switcher": true,
+  "graph": true,
+  "backlink": true,
+  "canvas": true,
+  "outgoing-link": true,
+  "tag-pane": true,
+  "properties": false,
+  "page-preview": true,
+  "daily-notes": true,
+  "templates": true,
+  "note-composer": true,
+  "command-palette": true,
+  "slash-command": false,
+  "editor-status": true,
+  "bookmarks": true,
+  "markdown-importer": false,
+  "zk-prefixer": false,
+  "random-note": false,
+  "outline": true,
+  "word-count": true,
+  "slides": false,
+  "audio-recorder": false,
+  "workspaces": false,
+  "file-recovery": true,
+  "publish": false,
+  "sync": false
+}

.obsidian/core-plugins.json

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+[
+  "file-explorer",
+  "global-search",
+  "switcher",
+  "graph",
+  "backlink",
+  "canvas",
+  "outgoing-link",
+  "tag-pane",
+  "page-preview",
+  "daily-notes",
+  "templates",
+  "note-composer",
+  "command-palette",
+  "editor-status",
+  "bookmarks",
+  "outline",
+  "word-count",
+  "file-recovery"
+]

.obsidian/graph.json

@@ -0,0 +1,22 @@
+{
+  "collapse-filter": true,
+  "search": "",
+  "showTags": false,
+  "showAttachments": false,
+  "hideUnresolved": false,
+  "showOrphans": true,
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+  "colorGroups": [],
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+  "linkStrength": 1,
+  "linkDistance": 250,
+  "scale": 0.1846232622585825,
+  "close": false
+}

.obsidian/hotkeys.json

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+{}

.obsidian/workspace.json

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+{
+  "main": {
+    "id": "c4b3f9b423457a3e",
+    "type": "split",
+    "children": [
+      {
+        "id": "b31f72987442726a",
+        "type": "tabs",
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+            "type": "leaf",
+            "state": {
+              "type": "markdown",
+              "state": {
+                "file": "README.md",
+                "mode": "source",
+                "source": false
+              }
+            }
+          }
+        ]
+      }
+    ],
+    "direction": "vertical"
+  },
+  "left": {
+    "id": "349c566ccce2bac3",
+    "type": "split",
+    "children": [
+      {
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+        "type": "tabs",
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+            "type": "leaf",
+            "state": {
+              "type": "file-explorer",
+              "state": {
+                "sortOrder": "alphabetical"
+              }
+            }
+          },
+          {
+            "id": "487ae844bcec21a3",
+            "type": "leaf",
+            "state": {
+              "type": "search",
+              "state": {
+                "query": "",
+                "matchingCase": false,
+                "explainSearch": false,
+                "collapseAll": false,
+                "extraContext": false,
+                "sortOrder": "alphabetical"
+              }
+            }
+          },
+          {
+            "id": "5a1ef71029dce8b4",
+            "type": "leaf",
+            "state": {
+              "type": "bookmarks",
+              "state": {}
+            }
+          }
+        ]
+      }
+    ],
+    "direction": "horizontal",
+    "width": 300
+  },
+  "right": {
+    "id": "f80d2a15938ae6ce",
+    "type": "split",
+    "children": [
+      {
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+        "type": "tabs",
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+                "extraContext": false,
+                "sortOrder": "alphabetical",
+                "showSearch": false,
+                "searchQuery": "",
+                "backlinkCollapsed": false,
+                "unlinkedCollapsed": true
+              }
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+            "type": "leaf",
+            "state": {
+              "type": "outgoing-link",
+              "state": {
+                "file": "README.md",
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+                "unlinkedCollapsed": true
+              }
+            }
+          },
+          {
+            "id": "9c2c08320c062b9b",
+            "type": "leaf",
+            "state": {
+              "type": "tag",
+              "state": {
+                "sortOrder": "frequency",
+                "useHierarchy": true
+              }
+            }
+          },
+          {
+            "id": "cdc0190c6adf150b",
+            "type": "leaf",
+            "state": {
+              "type": "outline",
+              "state": {
+                "file": "README.md"
+              }
+            }
+          }
+        ]
+      }
+    ],
+    "direction": "horizontal",
+    "width": 300,
+    "collapsed": true
+  },
+  "left-ribbon": {
+    "hiddenItems": {
+      "switcher:Open quick switcher": false,
+      "graph:Open graph view": false,
+      "canvas:Create new canvas": false,
+      "daily-notes:Open today's daily note": false,
+      "templates:Insert template": false,
+      "command-palette:Open command palette": false
+    }
+  },
+  "active": "ae21474f075e159a",
+  "lastOpenFiles": [
+    "60029 - Data Processing Systems/advanced_topics/code/partition_comparison/build/_deps/googletest-src/docs/quickstart-bazel.md",
+    "70020 - Program Analysis/Extraction Function.md",
+    "70020 - Program Analysis/Power Set.md",
+    "70020 - Program Analysis/Orthogonal Projections.md",
+    "70020 - Program Analysis/Partial Order.md",
+    "70020 - Program Analysis/Partial Function.md",
+    "70020 - Program Analysis/Normed Vector Spaces.md",
+    "70020 - Program Analysis/Must Analysis.md",
+    "70020 - Program Analysis/MOP.md",
+    "70020 - Program Analysis/Live Variable Analysis.md",
+    "70020 - Program Analysis/Moore-Penrose Generalised Inverse.md",
+    "70020 - Program Analysis/Monte Carlo Algorithms.md",
+    "70020 - Program Analysis/Monotone Framework.md",
+    "70020 - Program Analysis/MFP.md",
+    "70020 - Program Analysis/May Analysis.md",
+    "70020 - Program Analysis/LV Constraints.md",
+    "70020 - Program Analysis/Linear Operator Semantics.md",
+    "70020 - Program Analysis/Lattice Equations.md",
+    "70020 - Program Analysis/Las Vegas Algorithm.md",
+    "70020 - Program Analysis/Isolated Entries & Exits.md",
+    "70020 - Program Analysis/Label Consistency.md",
+    "70020 - Program Analysis/Isomorphism.md",
+    "70020 - Program Analysis/Fixed Point.md",
+    "70020 - Program Analysis/Inner Product.md",
+    "70020 - Program Analysis/Fun Language for Program Analysis.md",
+    "70020 - Program Analysis/Halting Problem.md",
+    "70020 - Program Analysis/abstract interpretation.drawio.svg",
+    "70020 - Program Analysis/abstract interpretation general construction.drawio.svg",
+    "70020 - Program Analysis",
+    "70025 - Software Engineering for Industry"
+  ]
+}

70020 - Program Analysis/0-CFA Analysis.md

@@ -0,0 +1,43 @@
+## Definition
+Requires [[Abstract Domains]] and a specification of the analysis to produce $(\widehat{C}, \widehat{\rho})$
+- $\widehat{C}$ is an [[Abstract Domains#Abstract Cache]] (*shape* of the label)
+- $\widehat{\rho}$ is the [[Abstract Domains#Abstract Environment]] that associates values with each variable (*shape* of the variables)
+We have the entails relation:
+$$\vDash \ : (\widehat{\mathbf{Cache}} \times \widehat{\mathbf{Env}} \times \mathbf{Exp}) \to \{true, false\}
+ \qquad \qquad (\widehat{C}, \widehat{\rho}) \vDash e$$ Which means we have an acceptable [[Control Flow Analysis]]for expression $e$.
+- If a subexpression $t^\ell$ evaluates to a closure, then the closure must be predicted by $\widehat{C}(\ell)$
+
+This analysis is not [[Context Sensitive]] and in [[Control Flow Analysis]] terminology is [[Monovariant]].
+## Rules
+### Constants
+$$(\widehat{C}, \widehat{\rho}) \vDash_s c^\ell \quad \text{always}$$
+Since we care about closures only, constants are irrelevant.
+### Terms
+$$(\widehat{C}, \widehat{\rho}) \vDash_s x^\ell \Longleftrightarrow \widehat{\rho}(x) \subseteq \widehat{C}(\ell)$$
+The variable contains the same value as is predicted by the [[Abstract Domains#Abstract Cache|cache]].
+### if-else
+$$(\widehat{C}, \widehat{\rho}) \vDash_s \left[\mathbf{if} \ t_0^{\ell_0} \ \mathbf{then} \ t_1^{\ell_1} \ \mathbf{else} \ t_2^{\ell_2}\right]^\ell \ \Longleftrightarrow \begin{split} 
+& (\widehat{C}, \widehat{\rho}) \vDash_s t_0^{\ell_0} \land (\widehat{C}, \widehat{\rho}) \vDash_s t_1^{\ell_1} \land (\widehat{C}, \widehat{\rho}) \vDash_s t_2^{\ell_2} \\
+\land & \ \widehat{C}(\ell_1) \subseteq \widehat{C}(\ell) \\
+\land & \ \widehat{C}(\ell_2) \subseteq \widehat{C}(\ell)
+\end{split}$$
+The [[Abstract Domains#Abstract Cache|cache]] must contain the terms for both branches (& whence what this label could be).
+### Let
+$$(\widehat{C}, \widehat{\rho}) \vDash_s \left[ \mathbf{let} \ x = t_1^{\ell_1} \ \mathbf{in} \ t_2^{\ell_2} \right]^\ell \Longleftrightarrow \begin{split} 
+& (\widehat{C}, \widehat{\rho}) \vDash_s t_1^{\ell_1} \land (\widehat{C}, \widehat{\rho}) \vDash_s t_2^{\ell_2}\\
+\land & \ \widehat{C}(\ell_1) \subseteq \widehat{\rho}(x) \\
+\land & \ \widehat{C}(\ell_2) \subseteq \widehat{C}(\ell) \\
+\end{split}$$
+Like with [[0-CFA Analysis#if-else|if-else]] we need the [[Abstract Domains#Abstract Cache|cache]] to have the *shape* of $\ell$, but now we need to ensure that $\widehat{\rho}$ also has the shape of $x$.
+### Operator
+$$(\widehat{C}, \widehat{\rho}) \vDash_x \left[ t_1^{\ell_1} \ op \ t_2^{\ell_2} \right]^\ell \Longleftrightarrow (\widehat{C}, \widehat{\rho}) \vDash_s t_1^{\ell_1} \land (\widehat{C}, \widehat{\rho}) \vDash_s t_2^{\ell_2}$$
+$\widehat{C}$ must have the shape of both sides, as $op$ is assumed to be $+,-,\times, \div$ we assume its shape is not a closure.
+### Closure
+$$(\widehat{C}, \widehat{\rho}) \vDash_x \left[\mathbf{fn} \ x \Rightarrow e_0 \right]^\ell \Longleftrightarrow \{\mathbf{fn} \ x \Rightarrow e_0\} \subseteq \widehat{C}(\ell) \land (\widehat{C}, \widehat{\rho}) \vDash_s e_0$$
+We can include $\ell$ in $\widehat{C}$ because we assume [[Label Consistency]].
+### Application
+$$(\widehat{C}, \widehat{\rho}) \vDash_x \left[ t_1^{\ell_1} \ t_2^{\ell_2}\right]^\ell \Longleftrightarrow \begin{split} 
+& (\widehat{C}, \widehat{\rho}) \vDash_s t_1^{\ell_1} \land (\widehat{C}, \widehat{\rho}) \vDash_s t_2^{\ell_2} \\
+\land & \left( \forall (\mathbf{fn} \ x \Rightarrow t_0^{\ell_0}) \in \widehat{C}(\ell_1) : \widehat{C}(\ell_2) \subseteq \widehat{\rho}(x) \land \widehat{C}(\ell_0) \subseteq \widehat{C}(\ell) \right) \\
+\end{split}$$
+

70020 - Program Analysis/Abelian Additive Group.md

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+## Definition
+An *Abelian Group* is a commutative [[Group]]. An *Additive Group* is a [[Group]] with a $\bullet$ that is analogous/should be thought of as additive in some way. 
+- (*Abelian Group*) For a group $G$ $\forall a, b \in G : a \bullet b = b \bullet a$
+- (*Additive Group*) We can write $\bullet$ as $+$ instead
+
+## Examples
+### Integer Sets
+$$\text{For some } X \ \text{ we can have }(\mathcal{P}(X), \emptyset, \cup)$$
+
+

70020 - Program Analysis/Abstract Domains.md

@@ -0,0 +1,10 @@
+## Definition
+- Can be compared with the [[Fun Language for Program Analysis#Concrete Domain]].
+### Abstract Environment
+$$\widehat{\rho} \in \widehat{\mathbf{Env}} = \mathbf{Var} \to \widehat{\mathbf{Val}}$$
+- Maps variables to an abstract value
+### Abstract Cache
+$$\widehat{C} \in \widehat{\mathbf{Cache}} = \mathbf{Lab} \to \widehat{\mathbf{Val}}$$
+### Abstract Value
+$$\widehat{v} \in \widehat{\mathbf{Val}} = \mathcal{P}(\mathbf{Term})$$
+- A set of terms of the form $\mathbf{fn} \ x \Rightarrow e_0$