From 1b3b6f7cf189f843da3e1e5d5c7c280d6a2f397e Mon Sep 17 00:00:00 2001 From: wadler <wadler@inf.ed.ac.uk> Date: Sun, 15 Sep 2019 17:36:16 +0100 Subject: [PATCH] minor fixes to assignments --- courses/tspl/2018/Assignment1.lagda.md | 4 ++-- courses/tspl/2019/Assignment1.lagda.md | 31 ++++++++++++-------------- src/plfa/part1/Induction.lagda.md | 4 ++-- 3 files changed, 18 insertions(+), 21 deletions(-) diff --git a/courses/tspl/2018/Assignment1.lagda.md b/courses/tspl/2018/Assignment1.lagda.md index 2b48c6a5..0252aff1 100644 --- a/courses/tspl/2018/Assignment1.lagda.md +++ b/courses/tspl/2018/Assignment1.lagda.md @@ -125,7 +125,7 @@ Give an example of an operator that has an identity and is associative but is not commutative. -#### Exercise `finite-|-assoc` (stretch) {#finite-plus-assoc} +#### Exercise `finite-+-assoc` (stretch) {#finite-plus-assoc} Write out what is known about associativity of addition on each of the first four days using a finite story of creation, as @@ -179,7 +179,7 @@ Show for all naturals `n`. Did your proof require induction? -#### Exercise `∸-|-assoc` {#monus-plus-assoc} +#### Exercise `∸-+-assoc` {#monus-plus-assoc} Show that monus associates with addition, that is, diff --git a/courses/tspl/2019/Assignment1.lagda.md b/courses/tspl/2019/Assignment1.lagda.md index 2b48c6a5..56888514 100644 --- a/courses/tspl/2019/Assignment1.lagda.md +++ b/courses/tspl/2019/Assignment1.lagda.md @@ -1,7 +1,7 @@ --- title : "Assignment1: TSPL Assignment 1" layout : page -permalink : /TSPL/2018/Assignment1/ +permalink : /TSPL/2019/Assignment1/ --- ``` @@ -12,15 +12,12 @@ module Assignment1 where ## Introduction -<!-- This assignment is due **1pm Friday 26 April**. --> - You must do _all_ the exercises labelled "(recommended)". Exercises labelled "(stretch)" are there to provide an extra challenge. You don't need to do all of these, but should attempt at least a few. -Exercises without a label are optional, and may be done if you want -some extra practice. +Exercises labelled "(practice)" are included for those who want extra practice. <!-- Submit your homework using the "submit" command. --> Please ensure your files execute correctly under Agda! @@ -39,17 +36,17 @@ open import plfa.part1.Relations using (_<_; z<s; s<s; zero; suc; even; odd) ## Naturals -#### Exercise `seven` {#seven} +#### Exercise `seven` (practice) {#seven} Write out `7` in longhand. -#### Exercise `+-example` {#plus-example} +#### Exercise `+-example` (practice) {#plus-example} Compute `3 + 4`, writing out your reasoning as a chain of equations. -#### Exercise `*-example` {#times-example} +#### Exercise `*-example` (practice) {#times-example} Compute `3 * 4`, writing out your reasoning as a chain of equations. @@ -116,7 +113,7 @@ Confirm that these both give the correct answer for zero through four. ## Induction -#### Exercise `operators` {#operators} +#### Exercise `operators` (practice) {#operators} Give another example of a pair of operators that have an identity and are associative, commutative, and distribute over one another. @@ -125,7 +122,7 @@ Give an example of an operator that has an identity and is associative but is not commutative. -#### Exercise `finite-|-assoc` (stretch) {#finite-plus-assoc} +#### Exercise `finite-+-assoc` (stretch) {#finite-plus-assoc} Write out what is known about associativity of addition on each of the first four days using a finite story of creation, as @@ -162,7 +159,7 @@ Show multiplication is associative, that is, for all naturals `m`, `n`, and `p`. -#### Exercise `*-comm` {#times-comm} +#### Exercise `*-comm` (practice) {#times-comm} Show multiplication is commutative, that is, @@ -171,7 +168,7 @@ Show multiplication is commutative, that is, for all naturals `m` and `n`. As with commutativity of addition, you will need to formulate and prove suitable lemmas. -#### Exercise `0∸n≡0` {#zero-monus} +#### Exercise `0∸n≡0` (practice) {#zero-monus} Show @@ -179,7 +176,7 @@ Show for all naturals `n`. Did your proof require induction? -#### Exercise `∸-|-assoc` {#monus-plus-assoc} +#### Exercise `∸-+-assoc` (practice) {#monus-plus-assoc} Show that monus associates with addition, that is, @@ -211,14 +208,14 @@ For each law: if it holds, prove; if not, give a counterexample. ## Relations -#### Exercise `orderings` {#orderings} +#### Exercise `orderings` (practice) {#orderings} Give an example of a preorder that is not a partial order. Give an example of a partial order that is not a preorder. -#### Exercise `≤-antisym-cases` {#leq-antisym-cases} +#### Exercise `≤-antisym-cases` (practice) {#leq-antisym-cases} The above proof omits cases where one argument is `z≤n` and one argument is `s≤s`. Why is it ok to omit them? @@ -233,7 +230,7 @@ Show that multiplication is monotonic with regard to inequality. Show that strict inequality is transitive. -#### Exercise `trichotomy` {#trichotomy} +#### Exercise `trichotomy` (practice) {#trichotomy} Show that strict inequality satisfies a weak version of trichotomy, in the sense that for any `m` and `n` that one of the following holds: @@ -255,7 +252,7 @@ As with inequality, some additional definitions may be required. Show that `suc m ≤ n` implies `m < n`, and conversely. -#### Exercise `<-trans-revisited` {#less-trans-revisited} +#### Exercise `<-trans-revisited` (practice) {#less-trans-revisited} Give an alternative proof that strict inequality is transitive, using the relating between strict inequality and inequality and diff --git a/src/plfa/part1/Induction.lagda.md b/src/plfa/part1/Induction.lagda.md index 565ec395..e7b96f88 100644 --- a/src/plfa/part1/Induction.lagda.md +++ b/src/plfa/part1/Induction.lagda.md @@ -697,7 +697,7 @@ judgments where the first number is less than _m_. There is also a completely finite approach to generating the same equations, which is left as an exercise for the reader. -#### Exercise `finite-|-assoc` (stretch) {#finite-plus-assoc} +#### Exercise `finite-+-assoc` (stretch) {#finite-plus-assoc} Write out what is known about associativity of addition on each of the first four days using a finite story of creation, as @@ -927,7 +927,7 @@ for all naturals `n`. Did your proof require induction? ``` -#### Exercise `∸-|-assoc` (practice) {#monus-plus-assoc} +#### Exercise `∸-+-assoc` (practice) {#monus-plus-assoc} Show that monus associates with addition, that is,