Formal Reasoning About Programs
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Clément Pit-Claudel 1e81721268 Make the ht1 tactic a bit more robust in HoareLogic.v
(Without this change, the HtIf rule can fail to generalize and unify spuriously
with goals of the right shape)
2021-04-12 15:07:34 -04:00
.gitignore Separate out library code with its own license 2020-03-17 09:22:06 -04:00
_CoqProject EvaluationContexts_template 2021-03-30 16:12:37 -04:00
_CoqProject.fraplib Separate out library code with its own license 2020-03-17 09:22:06 -04:00
AbstractInterpret.v Prevent more warnings for Coq 8.10 2020-02-08 15:15:38 -05:00
AbstractInterpretation.v More cleanup around addition of RuleInduction 2021-03-01 12:15:34 -05:00
BasicSyntax.v Push the last code change through a further copy-and-paste instance 2017-02-09 06:58:38 -05:00
BasicSyntax_template.v Small typo fix in BasicSyntax 2017-02-07 15:11:54 -05:00
CompilerCorrectness.v Revising before class 2021-03-21 10:14:31 -04:00
CompilerCorrectness_template.v Revising before class 2021-03-21 10:14:31 -04:00
ConcurrentSeparationLogic.v Chapter renumbering 2021-03-28 17:03:56 -04:00
ConcurrentSeparationLogic_template.v Small patch for Coq 8.13 2021-02-14 17:26:21 -05:00
Connecting.v Chapter renumbering 2021-03-28 17:03:56 -04:00
DataAbstraction.v Update for Coq 8.12.2 2021-01-03 14:56:39 -05:00
DataAbstraction_template.v Typo fixes 2018-02-25 19:40:10 -05:00
DeepAndShallowEmbeddings.v Chapter renumbering 2021-03-28 17:03:56 -04:00
DeepAndShallowEmbeddings_template.v First phase of update for Coq 8.10 2020-02-02 17:16:19 -05:00
DeeperInterp.ml Revising before class 2020-04-08 10:48:14 -04:00
DeeperWithFailInterp.ml Revising before class 2020-04-08 10:48:14 -04:00
DeepInterp.ml Revising before class 2020-04-08 10:48:14 -04:00
DependentInductiveTypes.v Merge 2020-02-02 17:19:40 -05:00
DependentInductiveTypes_template.v Merge 2020-02-02 17:19:40 -05:00
EvaluationContexts.v EvaluationContexts: exceptions 2021-03-28 15:33:23 -04:00
EvaluationContexts_template.v EvaluationContexts_template 2021-03-30 16:12:37 -04:00
FirstClassFunctions.v A little more text for the new FirstClassFunctions examples 2020-02-15 12:32:36 -05:00
FirstClassFunctions_template.v Update FirstClassFunctions_template from new source material 2020-02-12 14:03:15 -05:00
Frap.v SubsetTypes 2017-03-21 19:27:36 -04:00
frap_book.tex Typo fix 2021-03-29 09:35:17 -04:00
FrapWithoutSets.v Revising before class, including with an optimization to the model-checking engine 2020-04-20 11:56:23 -04:00
HoareLogic.v Make the ht1 tactic a bit more robust in HoareLogic.v 2021-04-12 15:07:34 -04:00
HoareLogic_template.v Make the ht1 tactic a bit more robust in HoareLogic.v 2021-04-12 15:07:34 -04:00
Imp.v Avoid a command only introduced in Coq 8.10, so that 8.9 keeps working 2020-02-10 13:44:35 -05:00
index.html New semester 2021-02-17 08:47:42 -05:00
Interpreters.v Truly building with Coq 8.9 again 2020-02-10 13:53:26 -05:00
Interpreters_template.v Avoid a command only introduced in Coq 8.10, so that 8.9 keeps working 2020-02-10 13:44:35 -05:00
IntroToProofScripting.v Revising for next lecture 2021-03-07 14:21:30 -05:00
IntroToProofScripting_template.v Revising for next lecture 2021-03-07 14:21:30 -05:00
Invariant.v Connecting: proved an invariant for a compilation result 2018-04-29 16:57:47 -04:00
LambdaCalculusAndTypeSoundness.v LambdaCalculusAndTypeSoundness: remove the other use of evaluation contexts 2021-03-27 18:57:03 -04:00
LambdaCalculusAndTypeSoundness_template.v LambdaCalculusAndTypeSoundness_template update 2021-03-27 19:15:05 -04:00
LICENSE Separate out library code with its own license 2020-03-17 09:22:06 -04:00
LogicProgramming.v Revising before tomorrow's lecture 2021-03-16 18:23:24 -04:00
LogicProgramming_template.v Revising before tomorrow's lecture 2021-03-16 18:23:24 -04:00
Makefile Separate out library code with its own license 2020-03-17 09:22:06 -04:00
Makefile.fraplib Separate out library code with its own license 2020-03-17 09:22:06 -04:00
Map.v Prevent more warnings for Coq 8.10 2020-02-08 15:15:38 -05:00
MessagesAndRefinement.v Chapter renumbering 2021-03-28 17:03:56 -04:00
ModelCheck.v Revising before class, including with an optimization to the model-checking engine 2020-04-20 11:56:23 -04:00
ModelChecking.v More cleanup around addition of RuleInduction 2021-03-01 12:15:34 -05:00
ModelChecking_sol.v Tweak files for ModelChecking in class 2017-03-06 09:44:29 -05:00
ModelChecking_template.v More cleanup around addition of RuleInduction 2021-03-01 12:15:34 -05:00
OperationalSemantics.v More cleanup around addition of RuleInduction 2021-03-01 12:15:34 -05:00
OperationalSemantics_template.v More cleanup around addition of RuleInduction 2021-03-01 12:15:34 -05:00
Polymorphism.v Avoid a command only introduced in Coq 8.10, so that 8.9 keeps working 2020-02-10 13:44:35 -05:00
Polymorphism_template.v Avoid a command only introduced in Coq 8.10, so that 8.9 keeps working 2020-02-10 13:44:35 -05:00
ProgramDerivation.v Chapter renumbering 2021-03-28 17:03:56 -04:00
ProgramDerivation_template.v Revising before class 2020-04-26 14:29:53 -04:00
ProofByReflection.v Revising before class 2020-05-10 14:10:01 -04:00
ProofByReflection_template.v Revising before class 2020-05-10 14:10:01 -04:00
README.md Fixed markdown inline 2020-03-28 15:07:21 -07:00
Relations.v Prevent more warnings for Coq 8.10 2020-02-08 15:15:38 -05:00
RuleInduction.v More cleanup around addition of RuleInduction 2021-03-01 12:15:34 -05:00
RuleInduction_template.v More space in template 2021-03-01 14:28:33 -05:00
SeparationLogic.v Chapter renumbering 2021-03-28 17:03:56 -04:00
SeparationLogic_template.v More revision before class 2020-04-13 09:27:45 -04:00
SepCancel.v Add missing parentheses in SepCancel's normalize2 tactic 2020-07-24 18:23:44 -07:00
SessionTypes.v Chapter renumbering 2021-03-28 17:03:56 -04:00
Sets.v Prevent more warnings for Coq 8.10 2020-02-08 15:15:38 -05:00
SharedMemory.v Chapter renumbering 2021-03-28 17:03:56 -04:00
SubsetTypes.v Proofreading SubsetTypes 2018-04-03 18:32:56 -04:00
SubsetTypes_template.v SubsetTypes_template 2017-03-22 09:15:33 -04:00
TransitionSystems.v Revising for today's lecture 2021-03-03 14:26:51 -05:00
TransitionSystems_template.v More cleanup around addition of RuleInduction 2021-03-01 12:15:34 -05:00
TypesAndMutation.v Chapter renumbering 2021-03-28 17:03:56 -04:00
Var.v Interpreters: factorial example 2016-02-06 22:09:37 -05:00

Formal Reasoning About Programs

This is an in-progress, open-source book by Adam Chlipala simultaneously introducing the Coq proof assistant and techniques for proving correctness of programs. That is, the game is doing completely rigorous, machine-checked mathematical proofs, showing that programs meet their specifications.

Just run make here to build everything, including the book frap_book.pdf and the accompanying Coq source modules. Alternatively, run make lib to build just the book library, not the chapter example files or PDF.

Code associated with the different chapters

The main narrative, also present in the book PDF, presents standard program-proof ideas, without rigorous proofs. Matching Coq files here show how to make it rigorous. Interleaved with that narrative, there are also other lectures' worth of material, for building up more practical background on Coq itself. That secondary track appears in this list, too, at a higher level of indentation.

  • Chapter 2: BasicSyntax.v
    • Polymorphism.v: polymorphism and generic data structures
  • Chapter 3: DataAbstraction.v
  • Chapter 4: Interpreters.v
    • FirstClassFunctions.v: functions as data; continuations and continuation-passing style
  • Chapter 5: TransitionSystems.v
    • IntroToProofScripting.v: writing scripts to find proofs in Coq
  • Chapter 6: ModelChecking.v
    • ProofByReflection.v: writing verified proof procedures in Coq
  • Chapter 7: OperationalSemantics.v
    • LogicProgramming.v: 'eauto' and friends, to automate proofs via logic programming
  • Chapter 8: AbstractInterpretation.v
  • Chapter 9: CompilerCorrectness.v
  • Chapter 10: LambdaCalculusAndTypeSoundness.v
  • Chapter 11: TypesAndMutation.v
  • Chapter 12: HoareLogic.v
  • Chapter 13: DeepAndShallowEmbeddings.v
  • Chapter 14: SeparationLogic.v
  • Chapter 15: Connecting.v
  • Chapter 16: ProgramDerivation.v
  • Chapter 17: SharedMemory.v
  • Chapter 18: ConcurrentSeparationLogic.v
  • Chapter 19: MessagesAndRefinement.v

There are also two supplementary files that are independent of the main narrative, for introducing programming with dependent types, a distinctive Coq feature that we neither use nor recommend for the problem sets, but which many students find interesting (and useful in other contexts).

  • SubsetTypes.v: a first introduction to dependent types by attaching predicates to normal types (used after CompilerCorrectness.v in the last course offering)
  • DependentInductiveTypes.v: building type dependency into datatype definitions (used after LambdaCalculusAndTypeSoundness.v in the last course offering)