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Revising for Wednesday's lecture

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Adam Chlipala 2022-03-06 14:47:05 -05:00
parent eb53c0d714
commit 955fd59327
2 changed files with 20 additions and 20 deletions
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6
ProofByReflection.v
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@ -50,7 +50,7 @@ Unset Printing All.
* theorem. This Ltac procedure always works (at least on machines with * theorem. This Ltac procedure always works (at least on machines with
* infinite resources), but it has a serious drawback, which we see when we * infinite resources), but it has a serious drawback, which we see when we
* print the proof it generates that 256 is even. The final proof term has * print the proof it generates that 256 is even. The final proof term has
* length super-linear in the input value, which we reveal with * length superlinear in the input value, which we reveal with
* [Set Printing All], to disable all syntactic niceties and show every node of * [Set Printing All], to disable all syntactic niceties and show every node of
* the internal proof AST. The problem is that each [Even_SS] application needs * the internal proof AST. The problem is that each [Even_SS] application needs
* a choice of [n], and we wind up giving every even number from 0 to 254 in * a choice of [n], and we wind up giving every even number from 0 to 254 in
@ -59,7 +59,7 @@ Unset Printing All.
* It is also unfortunate not to have static-typing guarantees that our tactic * It is also unfortunate not to have static-typing guarantees that our tactic
* always behaves appropriately. Other invocations of similar tactics might * always behaves appropriately. Other invocations of similar tactics might
* fail with dynamic type errors, and we would not know about the bugs behind * fail with dynamic type errors, and we would not know about the bugs behind
* these errors until we happened to attempt to prove complex enough goals. * these errors until we happened to attempt to prove complex-enough goals.
* *
* The techniques of proof by reflection address both complaints. We will be * The techniques of proof by reflection address both complaints. We will be
* able to write proofs like in the example above with constant size overhead * able to write proofs like in the example above with constant size overhead
@ -416,7 +416,7 @@ Proof.
apply multiStepClosure_ok. apply multiStepClosure_ok.
simplify. simplify.
(* Here we'll see that the Frap libary uses slightly different, optimized (* Here we'll see that the Frap library uses slightly different, optimized
* versions of the model-checking relations. For instance, [multiStepClosure] * versions of the model-checking relations. For instance, [multiStepClosure]
* takes an extra set argument, the _worklist_ recording newly discovered * takes an extra set argument, the _worklist_ recording newly discovered
* states. There is no point in following edges out of states that were * states. There is no point in following edges out of states that were

2
ProofByReflection_template.v
View file

@ -171,7 +171,7 @@ Proof.
apply multiStepClosure_ok. apply multiStepClosure_ok.
simplify. simplify.
(* Here we'll see that the Frap libary uses slightly different, optimized (* Here we'll see that the Frap library uses slightly different, optimized
* versions of the model-checking relations. For instance, [multiStepClosure] * versions of the model-checking relations. For instance, [multiStepClosure]
* takes an extra set argument, the _worklist_ recording newly discovered * takes an extra set argument, the _worklist_ recording newly discovered
* states. There is no point in following edges out of states that were * states. There is no point in following edges out of states that were