feat: sem7

.gitignore

@@ -632,3 +632,13 @@ cs2109s/labs/ps6/MNIST/raw
 cs2109s/labs/ps7/MNIST/raw
 cs2109s/labs/.idea
 cs2109s/labs/ps7/cifar-10-batches-py
+
+# Devenv
+.devenv*
+devenv.local.nix
+
+# direnv
+.direnv
+
+# pre-commit
+.pre-commit-config.yaml

.gitmodules

@@ -0,0 +1,3 @@
+[submodule "cs4212/week-01-simple-2025"]
+	path = cs4212/week-01-simple-2025
+	url = https://github.com/cs4212/week-01-simple-2025

cs3234/labs/midterm-project.v

@@ -1510,19 +1510,150 @@ Qed.
 (*
    g. Implement the copy function either as an instance of list_fold_right or as an instance of list_fold_left, and justify your choice.
 *)
+Definition list_copy_as_list_fold_right (V : Type) (vs : list V) :=
+  list_fold_right V (list V) nil (fun v acc => v :: acc) vs.
+
+Compute test_list_copy list_copy_as_list_fold_right.
+
+Theorem list_copy_as_list_fold_right_satisfies_the_specification_of_list_copy :
+  specification_of_list_copy list_copy_as_list_fold_right.
+Proof.
+  unfold specification_of_list_copy, list_copy_as_list_fold_right.
+  split.
+  - intros V.
+    remember (fun v acc => v :: acc) as f eqn:H_f.
+    exact (fold_unfold_list_fold_right_nil V (list V) nil f).
+  - intros V v vs'.
+    remember (fun v acc => v :: acc) as f eqn:H_f.
+    rewrite -> (fold_unfold_list_fold_right_cons V (list V) nil f v vs').
+    rewrite -> H_f.
+    reflexivity.
+Qed.
+
+Definition list_copy_as_list_fold_left (V : Type) (vs : list V) :=
+  list_fold_left V (list V) nil (fun v acc => list_append V acc (v :: nil)) vs.
+
+Lemma about_list_copy_and_list_fold_left :
+  forall (V : Type)
+    (v : V)
+    (vs acc : list V)
+    (f : V -> list V -> list V),
+  (f = (fun (v : V) (acc : list V) => list_append V acc (v :: nil))) ->
+  list_fold_left V (list V) (v :: acc) f vs = v :: list_fold_left V (list V) acc f vs.
+Proof.
+  intros V v vs acc f H_f.
+  revert acc.
+  induction vs as [ | v' vs' IHvs' ];intros acc.
+  - rewrite -> (fold_unfold_list_fold_left_nil V (list V) (v :: acc) f).
+    rewrite -> (fold_unfold_list_fold_left_nil V (list V) acc f).
+    reflexivity.
+  - rewrite -> (fold_unfold_list_fold_left_cons V (list V) (v :: acc) f v' vs').
+    rewrite -> H_f.
+    rewrite <- H_f.
+    rewrite -> (fold_unfold_list_append_cons V v acc (v' :: nil)).
+    rewrite -> (IHvs' (list_append V acc (v' :: nil))).
+    rewrite -> (fold_unfold_list_fold_left_cons V (list V) acc f v' vs').
+    rewrite -> H_f.
+    rewrite <- H_f.
+    reflexivity.
+Qed.
+
+Theorem list_copy_as_list_fold_left_satisfies_the_specification_of_list_copy :
+  specification_of_list_copy list_copy_as_list_fold_left.
+Proof.
+  unfold specification_of_list_copy, list_copy_as_list_fold_left.
+  split.
+  - intros V.
+    remember (fun v acc => list_append V acc (v :: nil)) as f eqn:H_f.
+    exact (fold_unfold_list_fold_left_nil V (list V) nil f).
+  - intros V v vs'.
+    remember (fun v acc => list_append V acc (v :: nil)) as f eqn:H_f.
+    rewrite -> (fold_unfold_list_fold_left_cons V (list V) nil f v vs').
+    rewrite -> H_f.
+    rewrite <- H_f.
+    rewrite -> (fold_unfold_list_append_nil V (v :: nil)).
+    exact (about_list_copy_and_list_fold_left V v vs' nil f H_f).
+Qed.
+
+Compute test_list_copy list_copy_as_list_fold_left.
 
 (*
    h. Implement the append function either as an instance of list_fold_right or as an instance of list_fold_left, and justify your choice.
 *)
 
+(* Fixpoint list_append (V : Type) (v1s v2s : list V) : list V := *)
+(*   match v1s with *)
+
+(*   | nil => *)
+(*       v2s *)
+(*   | v1 :: v1s' => *)
+(*       v1 :: list_append V v1s' v2s *)
+(*   end. *)
+
+Definition list_append_as_list_fold_right (V : Type) (v1s v2s : list V) : list V :=
+  list_fold_right V (list V) v2s (fun v ih => v :: ih) v1s.
+
+Compute test_list_append list_append_as_list_fold_right.
+
+Theorem list_append_as_list_fold_right_satsifies_the_specification_of_list_append :
+  specification_of_list_append list_append_as_list_fold_right.
+Proof.
+  unfold specification_of_list_append, list_append_as_list_fold_right.
+  split.
+  - intros V v2s.
+    remember (fun v ih => v :: ih) as f eqn:H_f.
+    exact (fold_unfold_list_fold_right_nil V (list V) v2s f).
+  - intros V v1 v1s' v2s.
+    remember (fun v ih => v :: ih) as f eqn:H_f.
+    rewrite -> (fold_unfold_list_fold_right_cons V (list V) v2s f v1 v1s').
+    rewrite -> H_f.
+    reflexivity.
+Qed.
+
+(* This is very very wrong, but I'm giving up for now *)
+Definition list_append_as_list_fold_left (V : Type) (v1s v2s : list V) : list V :=
+  list_fold_left V (list V) v1s (fun v acc => v::acc) v2s.
+
+Compute list_append_as_list_fold_left nat (1 :: 2 :: nil) (3 :: 4 :: nil).
+
+Compute test_list_append list_append_as_list_fold_left.
+
+
+
+
 (*
    i. Implement the reverse function either as an instance of list_fold_right or as an instance of list_fold_left, and justify your choice.
 *)
 
+Definition list_reverse_as_list_fold_left (V: Type) (vs : list V) : list V :=
+  list_fold_left V (list V) nil (fun v acc => v :: acc) vs.
+
+Compute list_reverse_as_list_fold_left nat (1 :: 2 :: nil).
+
+Compute test_list_reverse list_reverse_as_list_fold_left.
+
+Theorem list_reverse_as_list_fold_left_satsifies_the_specification_of_list_reverse:
+  specification_of_list_reverse list_reverse_as_list_fold_left.
+Proof.
+  unfold specification_of_list_reverse, list_reverse_as_list_fold_left.
+  intros append S_append.
+  split.
+  - intros V.
+  remember (fun v acc => v :: acc) as f eqn:H_f.
+  exact (fold_unfold_list_fold_left_nil V (list V) nil f).
+  - intros V v vs'.
+    remember (fun v acc => v :: acc) as f eqn:H_f.
+    rewrite -> (fold_unfold_list_fold_left_cons V (list V) nil f v vs').
+
+  split.
+
+  Qed.
+
 (*
    j. Implement the map function either as an instance of list_fold_right or as an instance of list_fold_left, and justify your choice.
 *)
 
+
 (*
    k. Implement eqb_list either as an instance of list_fold_right or as an instance of list_fold_left, and justify your choice.
 *)

cs3234/labs/week-11_induction-principles.v

@@ -247,6 +247,28 @@ Proof.
   induction n as [ | [ | n''] IHn'].
 Abort.
 
+Lemma nat_ind2 :
+  forall P : nat -> Prop,
+    P 0 ->
+    P 1 ->
+    (forall k : nat, P k -> P (S k) -> P (S (S k))) ->
+    forall n : nat, P n.
+Proof.
+  intros P H_P0 H_P1 H_PSS [ | [ | n'' ] ].
+  - exact H_P0.
+  - exact H_P1.
+  - assert (both : forall m : nat, P m /\ P(S m)).
+    { intro m.
+      induction m as [ | m' [ IHm'  IHSm' ] ].
+      - exact (conj H_P0 H_P1).
+      - split.
+        + exact IHSm'.
+        + exact (H_PSS m' IHm' IHSm' ).
+    }
+    destruct (both n'') as [Pn'' PSn''].
+    exact (H_PSS n'' Pn'' PSn'').
+Qed.
+
 (* Thus equipped, the following theorem is proved pretty directly: *)
 
 Theorem there_is_at_most_one_fibonacci_function :
@@ -262,7 +284,18 @@ Proof.
          [H_fib2_0 [H_fib2_1 H_fib2_SS]]
          n.
   induction n as [ | | n'' IHn'' IHSn''] using nat_ind2.
-Abort.
+   - rewrite -> H_fib1_0.
+     rewrite -> H_fib2_0.
+     reflexivity.
+   - rewrite -> H_fib1_1.
+     rewrite -> H_fib2_1.
+     reflexivity.
+  - rewrite -> (H_fib1_SS n'').
+    rewrite -> (H_fib2_SS n'').
+    rewrite -> IHn''.
+    rewrite -> IHSn''.
+    reflexivity.
+Qed.
 
 (* ***** *)
 

cs4212/week-01-simple-2025

@@ -0,0 +1 @@
+Subproject commit 9ef6c4412425b9b537139ba7a5b1aada9a307896

devenv.lock

@@ -0,0 +1,103 @@
+{
+  "nodes": {
+    "devenv": {
+      "locked": {
+        "dir": "src/modules",
+        "lastModified": 1754141078,
+        "owner": "cachix",
+        "repo": "devenv",
+        "rev": "a21413b7977726581d26951da25d4c31235c3253",
+        "type": "github"
+      },
+      "original": {
+        "dir": "src/modules",
+        "owner": "cachix",
+        "repo": "devenv",
+        "type": "github"
+      }
+    },
+    "flake-compat": {
+      "flake": false,
+      "locked": {
+        "lastModified": 1747046372,
+        "owner": "edolstra",
+        "repo": "flake-compat",
+        "rev": "9100a0f413b0c601e0533d1d94ffd501ce2e7885",
+        "type": "github"
+      },
+      "original": {
+        "owner": "edolstra",
+        "repo": "flake-compat",
+        "type": "github"
+      }
+    },
+    "git-hooks": {
+      "inputs": {
+        "flake-compat": "flake-compat",
+        "gitignore": "gitignore",
+        "nixpkgs": [
+          "nixpkgs"
+        ]
+      },
+      "locked": {
+        "lastModified": 1750779888,
+        "owner": "cachix",
+        "repo": "git-hooks.nix",
+        "rev": "16ec914f6fb6f599ce988427d9d94efddf25fe6d",
+        "type": "github"
+      },
+      "original": {
+        "owner": "cachix",
+        "repo": "git-hooks.nix",
+        "type": "github"
+      }
+    },
+    "gitignore": {
+      "inputs": {
+        "nixpkgs": [
+          "git-hooks",
+          "nixpkgs"
+        ]
+      },
+      "locked": {
+        "lastModified": 1709087332,
+        "owner": "hercules-ci",
+        "repo": "gitignore.nix",
+        "rev": "637db329424fd7e46cf4185293b9cc8c88c95394",
+        "type": "github"
+      },
+      "original": {
+        "owner": "hercules-ci",
+        "repo": "gitignore.nix",
+        "type": "github"
+      }
+    },
+    "nixpkgs": {
+      "locked": {
+        "lastModified": 1753719760,
+        "owner": "cachix",
+        "repo": "devenv-nixpkgs",
+        "rev": "0f871fffdc0e5852ec25af99ea5f09ca7be9b632",
+        "type": "github"
+      },
+      "original": {
+        "owner": "cachix",
+        "ref": "rolling",
+        "repo": "devenv-nixpkgs",
+        "type": "github"
+      }
+    },
+    "root": {
+      "inputs": {
+        "devenv": "devenv",
+        "git-hooks": "git-hooks",
+        "nixpkgs": "nixpkgs",
+        "pre-commit-hooks": [
+          "git-hooks"
+        ]
+      }
+    }
+  },
+  "root": "root",
+  "version": 7
+}

devenv.nix

@@ -0,0 +1,5 @@
+{ pkgs, lib, config, inputs, ... }:
+
+{
+  packages = [ pkgs.git pkgs.opam pkgs.typst ];
+}

devenv.yaml

@@ -0,0 +1,15 @@
+# yaml-language-server: $schema=https://devenv.sh/devenv.schema.json
+inputs:
+  nixpkgs:
+    url: github:cachix/devenv-nixpkgs/rolling
+
+# If you're using non-OSS software, you can set allowUnfree to true.
+# allowUnfree: true
+
+# If you're willing to use a package that's vulnerable
+# permittedInsecurePackages:
+#  - "openssl-1.1.1w"
+
+# If you have more than one devenv you can merge them
+#imports:
+# - ./backend