Library compcert.lib.Coqlib
- Useful tactics
- Definitions and theorems over the type positive
- Definitions and theorems over the type Z
- Definitions and theorems on the data types option, sum and list
- Definitions and theorems over boolean types
- Well-founded orderings
- Nonempty lists
Library compcert.lib.Maps
- The abstract signatures of trees
- The abstract signatures of maps
- An implementation of trees over type positive
- An implementation of maps over type positive
- An implementation of maps over any type that injects into type positive
- An implementation of maps over any type with decidable equality
- A partial implementation of trees over any type that injects into type positive
- Additional properties over trees
- Useful notations
Library compcert.common.Errors
Library compcert.flocq.Core.Fcore_Zaux
Library compcert.flocq.Core.Fcore_Raux
Library compcert.flocq.Core.Fcore_defs
Library compcert.flocq.Core.Fcore_float_prop
Library compcert.flocq.Core.Fcore_rnd
Library compcert.flocq.Core.Fcore_generic_fmt
Library compcert.flocq.Core.Fcore_ulp
Library compcert.flocq.Core.Fcore_rnd_ne
Library compcert.flocq.Core.Fcore_FIX
Library compcert.flocq.Core.Fcore_FLX
Library compcert.flocq.Core.Fcore_FLT
Library compcert.flocq.Core.Fcore
Library compcert.flocq.Core.Fcore_digits
Library compcert.flocq.Calc.Fcalc_digits
Library compcert.flocq.Calc.Fcalc_bracket
Library compcert.flocq.Calc.Fcalc_round
- Helper function for computing the rounded value of a real number.
- Instances of the theorems above, for the usual rounding modes.
Library compcert.flocq.Calc.Fcalc_ops
Library compcert.flocq.Calc.Fcalc_div
Library compcert.flocq.Calc.Fcalc_sqrt
Library compcert.flocq.Prop.Fprop_relative
Library compcert.flocq.Appli.Fappli_IEEE
Library compcert.flocq.Appli.Fappli_IEEE_bits
Library compcert.x86_64.Archi
Library compcert.lib.Integers
- Comparisons
- Parameterization by the word size, in bits.
- Representation of machine integers
- Arithmetic and logical operations over machine integers
- Properties of integers and integer arithmetic
- Properties of modulus, max_unsigned, etc.
- Modulo arithmetic
- Properties of the coercions between Z and int
- Properties of zero, one, minus one
- Properties of equality
- Properties of addition
- Properties of negation
- Properties of subtraction
- Properties of multiplication
- Properties of division and modulus
- Bit-level properties
- Properties of bit-level operations over Z
- Bit-level reasoning over type int
- Properties of bitwise and, or, xor
- Properties of shifts
- Properties of rotations
- Properties of Z_one_bits and is_power2.
- Relation between bitwise operations and multiplications / divisions by powers of 2
- Properties of shrx (signed division by a power of 2)
- Properties of integer zero extension and sign extension.
- Properties of one_bits (decomposition in sum of powers of two)
- Properties of comparisons
- Specialization to integers of size 8, 32, and 64 bits
- Specialization to offsets in pointer values
Library compcert.flocq.Prop.Fprop_Sterbenz
Library compcert.flocq.Appli.Fappli_rnd_odd
Library compcert.lib.Fappli_IEEE_extra
Library compcert.lib.Floats
Library compcert.common.AST
- Syntactic elements
- Generic transformations over programs
- External functions
- Register pairs
- Arguments and results to builtin functions
Library compcert.common.Values
Library compcert.lib.Axioms
Library compcert.common.Linking
- Syntactic linking
- Matching between two programs
- Commutation between linking and program transformations
- Linking a set of compilation units
- Linking and composition of compilation passes
Library compcert.lib.Intv
- Membership
- Emptyness
- Disjointness
- Shifting an interval by some amount
- Enumerating the elements of an interval
- Checking properties on all elements of an interval
- Folding a function over all elements of an interval
Library compcert.common.Memdata
- Properties of memory chunks
- Memory values
- Encoding and decoding integers
- Encoding and decoding values
- Compatibility with memory injections
- Breaking 64-bit memory accesses into two 32-bit accesses
Library compcert.common.Memtype
- Operations on memory states
- Permissions, block validity, access validity, and bounds
- Relating two memory states.
- Properties of the memory operations
- Properties of the initial memory state.
- Properties of load.
- Properties of loadbytes.
- Properties of store.
- Properties of storebytes.
- Properties of alloc.
- Properties of free.
- Properties of drop_perm.
- Properties of extends.
- Properties of magree.
- Properties of inject.
- Properties of inject_neutral
- Properties of unchanged_on and strong_unchanged_on
Library compcert.common.Memory
Library compcert.common.Globalenvs
- Symbol environments
- Global environments
- Construction of the initial memory state
- Commutation with program transformations
Library compcert.common.Events
- Events and traces
- Relating values and event values
- Matching traces.
- Semantics of volatile memory accesses
- Semantics of external functions
- Evaluation of builtin arguments
Library compcert.common.Smallstep
- Closures of transitions relations
- Transition semantics
- Forward simulations between two transition semantics.
- Receptiveness and determinacy
- Backward simulations between two transition semantics.
- Transforming a semantics into a single-event, equivalent semantics
- Connections with big-step semantics
Library compcert.cfrontend.Ctypes
- Syntax of types
- Operations over types
- Construction of the composite environment
- Programs and compilation units
- Separate compilation and linking
Library compcert.cfrontend.Cop
- Syntax of operators.
- Type classification and semantics of operators.
- Combined semantics of unary and binary operators
- Compatibility with extensions and injections
- Some properties of operator semantics
Library compcert.cfrontend.Clight
Library liblayers.lib.Decision
- MathClasses-style "Decision" class.
- Instances
- Decision procedures for lists
- Decision procedures from compare
Library coqrel.Delay
Library coqrel.RelDefinitions
Library coqrel.RelClasses
Library coqrel.Relators
Library coqrel.RelOperators
- Union of relations
- Intersection of relations
- Implication
- The bottom and top relations
- Relation equivalence
- Relation composition
- Pulling a relation along functions
- Pushing a relation along functions
- Relation currying
- The req relation
- Checking predicates on the left and right elements
- Relation versions of ex and all
- The rel_incr construction
Library coqrel.Monotonicity
Library coqrel.RDestruct
Library coqrel.MorphismsInterop
Library coqrel.Transport
Library coqrel.PreOrderTactic
Library coqrel.LogicalRelations
Library liblayers.logic.Structures
Library liblayers.logic.LayerData
Library liblayers.logic.PseudoJoin
- Pseudo-joins and some properties
- Data-indexed version
- Normalization procedure
- Booleans have a pseudo-join structure
- Product of pseudo-join structures
- Adjoining an extra element
Library liblayers.logic.PseudoJoinReflection
Library liblayers.lib.ExtensionalityAxioms
Library liblayers.lib.Functor
Library liblayers.lib.Monad
Library liblayers.lib.OptionMonad
Library liblayers.logic.OptionOrders
Library liblayers.compcertx.ErrorMonad
- res is a monad
- Lifting orders on res
- Orders for res ∘ option
- Decision-related definitions
- Miscellaneous helpers
- PseudoJoin structure for res (option -)
Library liblayers.logic.GlobalVars
Library liblayers.logic.Modules
Library liblayers.logic.Primitives
Library liblayers.logic.Layers
Library liblayers.logic.Semantics
Library liblayers.logic.PTrees
- Generic operations on PTrees
- Decidable properties of PTrees
- Applying a partial function to all data of a tree.
Library liblayers.logic.PTreeModules
Library liblayers.logic.PTreeLayers
Library liblayers.logic.PTreeSemantics
Library liblayers.compcertx.GenSem
Library compcertx.common.MemoryX
Library liblayers.lib.Lens
Library liblayers.lib.PowersetMonad
Library liblayers.lib.Lift
Library compcert.lib.Ordered
Library compcert.lib.Decidableplus
Library compcert.lib.BoolEqual
Library compcert.x86.Op
- Evaluation functions
- Static typing of conditions, operators and addressing modes.
- Manipulating and transforming operations
- Invariance and compatibility properties.
Library compcert.x86.Machregs
Library compcert.backend.Locations
Library compcert.common.Separation
Library compcert.x86.Conventions1
Library compcert.backend.Conventions
Library compcert.backend.LTL
Library compcert.backend.Linear
Library compcert.backend.Bounds
Library compcert.x86.Stacklayout
Library compcert.backend.EraseArgs
Library compcert.x86.Asm
Library liblayers.compcertx.CompcertStructures
- Prerequisites
- Relations on programs and global environments
- Clight signatures
- Injection-related properties
- Names of external functions
- Lists
Library liblayers.compcertx.LiftMem
Library liblayers.compcertx.LiftMemX
Library liblayers.simrel.AbstractData
Library liblayers.compcertx.InitMem
Library liblayers.simrel.MemWithData
Library coqrel.BoolRel
Library liblayers.simrel.SimrelDefinition
- Preliminaries
- Simulation relations blueprints
- Tactics
Library liblayers.simrel.SimrelEquivalence
Library liblayers.simrel.MemoryRel
Library liblayers.compcertx.MakeProgramSpec
Library liblayers.compcertx.InitMemRel
Library liblayers.simrel.SimrelInitMem
Library liblayers.simrel.MemOpv
Library liblayers.simrel.SimrelCategory
Library liblayers.simrel.SimrelFunctor
Library liblayers.simrel.SimulationRelation
Library liblayers.simrel.SimrelInvariant
Library liblayers.compcertx.SimValues
Library liblayers.compcertx.SimEvents
Library compcert.common.Switch
Library compcert.backend.Cminor
Library compcert.backend.CminorSel
Library compcert.driver.Compopts
Library compcert.x86.SelectOp
- Constants
- Integer logical negation
- Integer addition and pointer addition
- Opposite
- Integer and pointer subtraction
- Immediate shifts
- Integer multiply
- Bitwise and, or, xor
- Integer division and modulus
- General shifts
- Floating-point arithmetic
- Comparisons
- Integer conversions
- Addressing modes
- Arguments of builtins
Library compcert.x86.SelectOpproof
Library compcert.backend.SplitLong
Library compcert.backend.SplitLongproof
- Axiomatization of the helper functions
- Correctness of the instruction selection functions for 64-bit operators
Library compcert.x86.SelectLong
Library compcert.x86.SelectLongproof
Library compcertx.driver.CompCertBuiltins
Library liblayers.compcertx.SimCompCertBuiltins
Library liblayers.compcertx.SimCop
Library compcertx.common.EventsX
Library liblayers.compcertx.SimClight
Library liblayers.compcertx.CompCertGlobalVars
Library liblayers.compcertx.CGlobalVars
Library liblayers.simrel.SimrelLessdef
- lessdef (and Mem.extends) as a simulation relation
- Strong version of extends for ec_mem_extends. Coincidentally,
Library liblayers.simrel.SimrelInject
Library liblayers.compcertx.CPrimitives
Library liblayers.compcertx.CGenSem
Library liblayers.logic.Language
Library liblayers.logic.LayerLogicImpl
Library liblayers.compcertx.ClightModules
Library liblayers.compcertx.MakeProgramFacts
- Preliminaries
- Properties relating module-layer pairs with their global environments
- Alternative monotonicity theorems
- Other global properties
Library liblayers.compcertx.MakeProgramInv
Library liblayers.compcertx.MakeProgram
Library liblayers.compcertx.InitMemMakeProgram
Library liblayers.compcertx.ClightWellTyped
Library liblayers.compcertx.ClightXSemantics
Library liblayers.simrel.AbstractionRelation
Library tutorial.common.TutoLib
Library tutorial.container.ContainerType
Library tutorial.container.Container
Library tutorial.container.ContainerIntro
Library tutorial.queue.AbsQueue
Library tutorial.queue.Node
Library tutorial.queue.Queue
Library tutorial.queue.QueueData
Library tutorial.queue.QueueIntro
Library tutorial.stack.Stack
Library tutorial.stack.Counter
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