text stringlengths 157 7.64M | meta dict |
|---|---|
theory CFGExit_wf imports CFGExit CFG_wf begin
subsection ‹New well-formedness lemmas using ‹(_Exit_)››
locale CFGExit_wf =
CFG_wf sourcenode targetnode kind valid_edge Entry Def Use state_val +
CFGExit sourcenode targetnode kind valid_edge Entry Exit
for sourcenode :: "'edge ⇒ 'node" and targetnode :: "'edg... | {
"path": "afp-2025-02-12/thys/Slicing/Basic/CFGExit_wf.thy",
"repo": "afp-2025-02-12",
"sha": "e4690f98287425f8277b126fc011a4a29d03de2ebbe9202ed0f2f77c58ca28be"
} |
subsection ‹Formulation of a subject-subject communication policy and an information flow
policy, and showing both can be derived from subject-object configuration data›
theory Step_policies
imports Step_configuration
begin
subsubsection ‹Specification\label{sect:policy_specification}›
text ‹In order to use CISK,... | {
"path": "afp-2025-02-12/thys/CISC-Kernel/step/Step_policies.thy",
"repo": "afp-2025-02-12",
"sha": "7068dd63257fee546985eaf5592e6efe7318b0fb05aa1d728233bed450b7dbc6"
} |
(*
File: Symmetric_Polynomials.thy
Author: Manuel Eberl (TU München)
The definition of symmetric polynomials and the elementary symmetric polynomials.
Proof of the fundamental theorem of symmetric polynomials and its corollaries.
*)
section ‹Symmetric Polynomials›
theory Symmetric_Polynomials
imports
... | {
"path": "afp-2025-02-12/thys/Symmetric_Polynomials/Symmetric_Polynomials.thy",
"repo": "afp-2025-02-12",
"sha": "3d2d077f57ab8891f66e9c66ed6398987e606e75dc9e6dcbf8f007005abff0f7"
} |
section ‹Trees›
theory Tree imports Main begin
text ‹Sometimes it is nice to think of @{typ bool}s as directions in a binary tree›
hide_const (open) Left Right
type_synonym dir = bool
definition Left :: bool where "Left = True"
definition Right :: bool where "Right = False"
declare Left_def [simp]
declare Right_def [... | {
"path": "afp-2025-02-12/thys/Resolution_FOL/Tree.thy",
"repo": "afp-2025-02-12",
"sha": "5d5c8c86fc59af4f31425ca0ba8bc804784f7770901204414c36a82a0fec1e0b"
} |
section ‹Examples for the WS1S/Presburger Mixture›
(*<*)
theory WS1S_Presburger_Examples
imports
Formula_Derivatives.WS1S_Presburger_Equivalence
begin
(*>*)
lemma "check_eqv (Abs_idx (0, 0)) 0 (FEx SO (FBase (Eq_Presb None 0 42))) (FEx () (FBase (Eq [1] 42 0)))"
by (msorry)
lemma "check_eqv (Abs_idx (0, 1)) 1 ... | {
"path": "afp-2025-02-12/thys/Formula_Derivatives/Examples/WS1S_Presburger_Examples.thy",
"repo": "afp-2025-02-12",
"sha": "6488e5556ddde6e6efedf1a591322dd3de976ac0121be474d65b09e878c81375"
} |
(* Copyright 2021 (C) Mihails Milehins *)
section‹Subsemicategory›
theory CZH_SMC_Subsemicategory
imports
CZH_DG_Subdigraph
CZH_SMC_Semifunctor
begin
subsection‹Background›
named_theorems smc_sub_cs_intros
named_theorems smc_sub_bw_cs_intros
named_theorems smc_sub_fw_cs_intros
named_theorems smc_sub_bw_... | {
"path": "afp-2025-02-12/thys/CZH_Foundations/czh_semicategories/CZH_SMC_Subsemicategory.thy",
"repo": "afp-2025-02-12",
"sha": "3e1cef5168a1e82a2968c54dd58156f5dfc7e1e0c3a9805d8b9fc220216dfd36"
} |
section ‹Helpers›
theory Helpers imports Main begin
text ‹
First, we will prove a few lemmas unrelated to graphs or Menger's Theorem. These lemmas
will simplify some of the other proof steps.
›
text ‹
If two finite sets have different cardinality, then there exists an element in the larger set
that is not i... | {
"path": "afp-2025-02-12/thys/Menger/Helpers.thy",
"repo": "afp-2025-02-12",
"sha": "1d0853fdf6a1407f18a421681f9ef19f49bded774fa3a58451aa163322285a19"
} |
(*******************************************************************************
Project: IsaNet
Author: Tobias Klenze, ETH Zurich <tobias.klenze@inf.ethz.ch>
Version: JCSPaper.1.0
Isabelle Version: Isabelle2021-1
Copyright (c) 2022 Tobias Klenze
Licence: Mozilla Public License 2.0 (MPL) / BSD-3-Clause... | {
"path": "afp-2025-02-12/thys/IsaNet/instances/SCION_variant.thy",
"repo": "afp-2025-02-12",
"sha": "16e6f88b93cd1cf4e887ef9931521051d9debcc4089e68ae36f27364cc00a2a4"
} |
section ‹Lazy list monad›
theory Lazy_List_Monad
imports Monad_Zero_Plus
begin
text ‹To illustrate the general process of defining a new type
constructor, we formalize the datatype of lazy lists. Below are the
Haskell datatype definition and class instances.›
text_raw ‹
\begin{verbatim}
data List a = Nil | Cons a (L... | {
"path": "afp-2025-02-12/thys/Tycon/Lazy_List_Monad.thy",
"repo": "afp-2025-02-12",
"sha": "c7a8d39d00ddc9a18b58ce1df18e6241a548b7e562f6734c7bed9dd2a54fbe2a"
} |
(* Author: Alexander Bentkamp, Universität des Saarlandes
*)
section ‹Alternative Lebesgue Measure Definition›
theory Lebesgue_Functional
imports "HOL-Analysis.Lebesgue_Measure"
begin
text ‹Lebesgue\_Measure.lborel is defined on the typeclass euclidean\_space, which does not allow the
space dimension to be dependent... | {
"path": "afp-2025-02-12/thys/Deep_Learning/Lebesgue_Functional.thy",
"repo": "afp-2025-02-12",
"sha": "49570adf912a3050daa21c75156b8fe32738c3c4233119a473ef9689e7654b5e"
} |
subsection‹GoedelVariantHOML2possInS4.thy›
text‹The same as GoedelVariantHOML2poss, but now in logic S4, where the proof of theorem Th3 fails.›
theory GoedelVariantHOML2possInS4 imports HOMLinHOLonlyS4
begin
consts PositiveProperty::"(e⇒σ)⇒σ" ("P")
axiomatization where Ax1: "⌊P φ ❙∧ P ψ ❙⊃ P (φ ❙. ψ)⌋"
abbreviatio... | {
"path": "afp-2025-02-12/thys/Notes_On_Goedels_Ontological_Argument/GoedelVariantHOML2possInS4.thy",
"repo": "afp-2025-02-12",
"sha": "9ef4c67545e29be1efd290a9d2440a4b6392a2535ec9d5235b512110f3757d29"
} |
(* Title: JinjaThreads/J/WellType.thy
Author: Tobias Nipkow, Andreas Lochbihler
*)
section ‹Well-typedness of Jinja expressions›
theory WellType
imports
Expr
State
"../Common/ExternalCallWF"
"../Common/WellForm"
"../Common/SemiType"
begin
declare Listn.lesub_list_impl_same_size[simp del]
decl... | {
"path": "afp-2025-02-12/thys/JinjaThreads/J/WellType.thy",
"repo": "afp-2025-02-12",
"sha": "9feab26bdfce2bd533e11a7e93efe5064a7a36fc520f46ea2d34155d960f4e9d"
} |
(* Title: HOL/Computational_Algebra/Factorial_Ring.thy
Author: Manuel Eberl, TU Muenchen
Author: Florian Haftmann, TU Muenchen
*)
section ‹Factorial (semi)rings›
theory Factorial_Ring
imports
Main
"HOL-Library.Multiset"
begin
unbundle multiset.lifting
subsection ‹Irreducible and prime elem... | {
"path": "Isabelle2024/src/HOL/Computational_Algebra/Factorial_Ring.thy",
"repo": "Isabelle2024",
"sha": "0e2a08d88de5f807be7af6ca82e75aa7b9ba83c290b5ada4030cb0816471b95f"
} |
section ‹K-dimensional Region Trees - Nested Trees›
(*
Nested trees:
Each level of the k-d tree (kdt) is encapsulated in a separate splitting tree (tree1).
Experimental.
*)
theory KD_Region_Nested
imports "HOL-Library.NList"
begin
(* TODO: In Isabelle after 2023 - remove *)
lemma nlists_Suc: "nlists (Suc n) A = (⋃a∈... | {
"path": "afp-2025-02-12/thys/Region_Quadtrees/KD_Region_Nested.thy",
"repo": "afp-2025-02-12",
"sha": "28383d013450f511aadcf003c2575c2444849d3452b3f333dd3459bc0ed8de6c"
} |
(* Title: JinjaDCI/J/SmallStep.thy
Author: Tobias Nipkow, Susannah Mansky
Copyright 2003 Technische Universitaet Muenchen, 2019-20 UIUC
Based on the Jinja theory J/SmallStep.thy by Tobias Nipkow
*)
section ‹ Small Step Semantics ›
theory SmallStep
imports Expr State WWellForm
begin
fun block... | {
"path": "afp-2025-02-12/thys/JinjaDCI/J/SmallStep.thy",
"repo": "afp-2025-02-12",
"sha": "009b38880d264a4a4372e3ef774602b1cb38afc76f12d2c2da01d172ca72f43e"
} |
(*
* Copyright 2020, Data61, CSIRO (ABN 41 687 119 230)
* Copyright (c) 2022 Apple Inc. All rights reserved.
*
* SPDX-License-Identifier: BSD-2-Clause
*)
theory WhileLoopVarsPreserved imports
"AutoCorres2_Main.AutoCorres_Main"
begin
install_C_file "while_loop_vars_preserved.c"
autocorres [ts_force nondet = lo... | {
"path": "afp-2025-02-12/thys/AutoCorres2/tests/proof-tests/WhileLoopVarsPreserved.thy",
"repo": "afp-2025-02-12",
"sha": "a6ee078c9c8e8470f61525ae258ae6dbec830615a4d558a9c8418427812f3e6c"
} |
(* Title: Miscellanneous Definitions and Lemmas
Author: Peter Lammich <peter.lammich@uni-muenster.de>
Maintainer: Peter Lammich <peter.lammich@uni-muenster.de>
*)
section ‹Miscellanneous Definitions and Lemmas›
theory Misc
imports Main "HOL-Library.Multiset" "HOL-Library.Subseq_Order"
begin
text_... | {
"path": "afp-2025-02-12/thys/Program-Conflict-Analysis/Misc.thy",
"repo": "afp-2025-02-12",
"sha": "f0b526b9fb71dd8d8b2947a983130932a34aa282e07d93a8279a0ea50e403edf"
} |
theory Ground_Term_Extra
imports "Regular_Tree_Relations.Ground_Terms"
begin
lemma gterm_is_fun: "is_Fun (term_of_gterm t)"
apply (cases t)
(*goal: ‹is_Fun (term_of_gterm t)›*)
by simp
end
| {
"path": "afp-2025-02-12/thys/Superposition_Calculus/Ground_Term_Extra.thy",
"repo": "afp-2025-02-12",
"sha": "14245b375b6cc78630d31d93184d74d6ebd94e0aa2c4a65a9924da6bbfe51c3b"
} |
(* Title: HOL/MicroJava/BV/JVM.thy
Author: Tobias Nipkow, Gerwin Klein
Copyright 2000 TUM
*)
section ‹The Typing Framework for the JVM \label{sec:JVM}›
theory TF_JVM
imports "../DFA/Typing_Framework_err" EffectMono BVSpec
begin
definition exec :: "jvm_prog ⇒ nat ⇒ ty ⇒ ex_table ⇒ instr list ⇒ ty... | {
"path": "afp-2025-02-12/thys/Jinja/BV/TF_JVM.thy",
"repo": "afp-2025-02-12",
"sha": "08d4a9be37e2cab44f2a940acf335b98f2cb0dd62e0001fe929fd19a064661a7"
} |
(* Title: Safe OCL
Author: Denis Nikiforov, March 2019
Maintainer: Denis Nikiforov <denis.nikif at gmail.com>
License: LGPL
*)
(* TODO: There are a lot of similar lemmas in the theory.
They should be generalized *)
section ‹Tuples›
theory Tuple
imports Finite_Map_Ext Transitive_C... | {
"path": "afp-2025-02-12/thys/Safe_OCL/Tuple.thy",
"repo": "afp-2025-02-12",
"sha": "960b18884154ffac5f49de428a2a86bd38f79a4eacebec665782a9d3fdbeecf9"
} |
(*******************************************************************************
Project: IsaNet
Author: Tobias Klenze, ETH Zurich <tobias.klenze@inf.ethz.ch>
Version: JCSPaper.1.0
Isabelle Version: Isabelle2021-1
Copyright (c) 2022 Tobias Klenze
Licence: Mozilla Public License 2.0 (MPL) / BSD-3-Clause... | {
"path": "afp-2025-02-12/thys/IsaNet/instances/ICING_variant2.thy",
"repo": "afp-2025-02-12",
"sha": "0689510c4c94740ab99395a73e0529ad8de3c1f1efc7de881348b95b8da97d6c"
} |
(* Title: HOL/Library/While_Combinator.thy
Author: Tobias Nipkow
Author: Alexander Krauss
*)
section ‹A general ``while'' combinator›
theory While_Combinator
imports Main
begin
subsection ‹Partial version›
definition while_option :: "('a ⇒ bool) ⇒ ('a ⇒ 'a) ⇒ 'a ⇒ 'a option" where
"while_optio... | {
"path": "Isabelle2024/src/HOL/Library/While_Combinator.thy",
"repo": "Isabelle2024",
"sha": "9d15427766453eb6537b20fc988d028359de344478815ddbb855b5bf35cd28b4"
} |
section ‹Stochastic Dominance›
theory Stochastic_Dominance
imports
Complex_Main
"HOL-Probability.Probability"
Lotteries
Preference_Profiles
Utility_Functions
begin
subsection ‹Definition of Stochastic Dominance›
text ‹
This is the definition of stochastic dominance. It lifts a preference relation
on al... | {
"path": "afp-2025-02-12/thys/Randomised_Social_Choice/Stochastic_Dominance.thy",
"repo": "afp-2025-02-12",
"sha": "c072dd97f68dee8e4da5dfc4fb0bb4c82f6a59ae410ef75b1b2f22ab6725cf2d"
} |
(* Title: OAodv.thy
License: BSD 2-Clause. See LICENSE.
Author: Timothy Bourke, Inria
*)
section "The `open' AODV model"
theory OAodv
imports Aodv AWN.OAWN_SOS_Labels AWN.OAWN_Convert
begin
text ‹Definitions for stating and proving global network properties over individual processes.›
defini... | {
"path": "afp-2025-02-12/thys/AODV/OAodv.thy",
"repo": "afp-2025-02-12",
"sha": "0fc9422dd2a06b2f8dc8c03fdd7debcdc89c831c6371d08d818f4a6d598ec57e"
} |
(*
Title: Hermite_IArrays.thy
Author: Jose Divasón <jose.divasonm at unirioja.es>
Author: Jesús Aransay <jesus-maria.aransay at unirioja.es>
*)
section‹Hermite Normal Form refined to immutable arrays›
theory Hermite_IArrays
imports
Hermite
Echelon_Form.Echelon_Form_IArrays
begin
sub... | {
"path": "afp-2025-02-12/thys/Hermite/Hermite_IArrays.thy",
"repo": "afp-2025-02-12",
"sha": "ecaacf15d7855172d90ff480d9ea6366fb312c5bd09b51a28508ac75b7df88ca"
} |
section ‹Maximum Segment Sum›
theory Maximum_Segment_Sum
imports Main
begin
text ‹The \emph{maximum segment sum} problem is to compute, given a list of numbers,
the largest of the sums of the contiguous segments of that list. It is also known
as the \emph{maximum sum subarray} problem and has been considered many t... | {
"path": "afp-2025-02-12/thys/Maximum_Segment_Sum/Maximum_Segment_Sum.thy",
"repo": "afp-2025-02-12",
"sha": "250a799a8eb1acf6580f144b9ca21767ccd66b6cee3623ad015d97d66ed23836"
} |
(* Title: HOL/TLA/Buffer/Buffer.thy
Author: Stephan Merz, University of Munich
*)
section ‹A simple FIFO buffer (synchronous communication, interleaving)›
theory Buffer
imports "HOL-TLA.TLA"
begin
(* actions *)
definition BInit :: "'a stfun ⇒ 'a list stfun ⇒ 'a stfun ⇒ stpred"
where "BInit ic q oc =... | {
"path": "Isabelle2024/src/HOL/TLA/Buffer/Buffer.thy",
"repo": "Isabelle2024",
"sha": "03c485b71303648b2e083b26c3444daf5d2fbfe07450642578b90fbb1376b2dc"
} |
section ‹Missing Library Material›
theory Lambert_Series_Library
imports
"HOL-Complex_Analysis.Complex_Analysis"
"HOL-Library.Landau_Symbols"
"HOL-Real_Asymp.Real_Asymp"
begin
subsection ‹Miscellaneous›
lemma power_less_1_iff: "x ≥ 0 ⟹ (x :: real) ^ n < 1 ⟷ x < 1 ∧ n > 0"
by (metis not_gr_zero (*‹(¬ 0 < ?n... | {
"path": "afp-2025-02-12/thys/Lambert_Series/Lambert_Series_Library.thy",
"repo": "afp-2025-02-12",
"sha": "97ab03ec76d6650ed43454f9a26c087d53e4121369509302a59ecc5a69a2c464"
} |
theory Construction_Utility
imports
Fused_Resource
State_Isomorphism
begin
― ‹Dummy converters that return a constant value on their external interface›
primcorec
ldummy_converter :: "('a ⇒ 'b) ⇒ ('i_cnv, 'o_cnv, 'i_res, 'o_res) converter ⇒
('a + 'i_cnv, 'b + 'o_cnv, 'i_res, 'o_res) converter"
whe... | {
"path": "afp-2025-02-12/thys/Constructive_Cryptography_CM/Construction_Utility.thy",
"repo": "afp-2025-02-12",
"sha": "61a91baed3f7aeff3a0b34bf613e5f16166c9bda89b372f010bd2ee422a6daa8"
} |
section ‹Correctness Theorem of Partial Order Reduction›
theory Ample_Correctness
imports
Ample_Abstract
Formula
begin
locale ample_correctness =
S: transition_system_complete ex en init int +
R: transition_system_complete ex ren init int +
F: formula_next_free φ +
ample_abstract ex en init int ... | {
"path": "afp-2025-02-12/thys/Partial_Order_Reduction/Ample_Correctness.thy",
"repo": "afp-2025-02-12",
"sha": "5a7ba40299dbaf81fe44df7b75773bed2eef5a28cc698a0aa151ead27743d044"
} |
(*******************************************************************************
Project: Sumcheck Protocol
Authors: Azucena Garvia Bosshard <zucegb@gmail.com>
Christoph Sprenger, ETH Zurich <sprenger@inf.ethz.ch>
Jonathan Bootle, IBM Research Europe <jbt@zurich.ibm.com>
*******************... | {
"path": "afp-2025-02-12/thys/Sumcheck_Protocol/Instantiation_with_Polynomials/Roots_Bounds.thy",
"repo": "afp-2025-02-12",
"sha": "20541a7769d55eb15f8ab83e34b9d5014ea685d5f597811856ea22a96f7e9090"
} |
(* Title: AWN.thy
License: BSD 2-Clause. See LICENSE.
Author: Timothy Bourke
*)
section "Terms of the Algebra for Wireless Networks"
theory AWN
imports Lib
begin
subsection "Sequential Processes"
type_synonym ip = nat
type_synonym data = nat
text ‹
Most of AWN is independent of the type o... | {
"path": "afp-2025-02-12/thys/AWN/AWN.thy",
"repo": "afp-2025-02-12",
"sha": "54bc480f84d2bf58c02125b2daa43b4bef22bdbd6b17b82f90559c5afe0d7f45"
} |
section ‹The Euler--MacLaurin summation formula›
theory Euler_MacLaurin
imports
"HOL-Complex_Analysis.Complex_Analysis"
Bernoulli.Periodic_Bernpoly
Bernoulli.Bernoulli_FPS
begin
subsection ‹Auxiliary facts›
(* TODO Move? *)
lemma pbernpoly_of_int [simp]: "pbernpoly n (of_int a) = bernoulli n"
by (simp ad... | {
"path": "afp-2025-02-12/thys/Euler_MacLaurin/Euler_MacLaurin.thy",
"repo": "afp-2025-02-12",
"sha": "713ccf0ed7de5f1fed69a218203053c8b947027262aa35b715a6b950a755cd34"
} |
theory Get_Types_Verification
imports
"../abs-def/Abs_SAIS"
"../def/Get_Types"
begin
section "Suffix Types"
lemma get_suffix_types_step_r0_ret:
"∃xs' i'. get_suffix_types_step_r0 (xs, i) ys = (xs', i') ∧
length xs' = length xs ∧ (i = 0 ⟶ i' = 0) ∧ (∃j. i = Suc j ⟶ i' = j)"
apply (cases i)... | {
"path": "afp-2025-02-12/thys/SuffixArray/sais/proof/Get_Types_Verification.thy",
"repo": "afp-2025-02-12",
"sha": "9f4c4c1bb3e557dfcbf3e62170d55e36460ab330892758e5dd169819b5d68585"
} |
section ‹Absolute Retracts, Absolute Neighbourhood Retracts and Euclidean Neighbourhood Retracts›
theory Retracts
imports
Brouwer_Fixpoint
Continuous_Extension
begin
text ‹Absolute retracts (AR), absolute neighbourhood retracts (ANR) and also Euclidean neighbourhood
retracts (ENR). We define AR and ANR by special... | {
"path": "Isabelle2024/src/HOL/Analysis/Retracts.thy",
"repo": "Isabelle2024",
"sha": "45a0d3515ecd9ef13da35e9470024900d1c8ba956c0473e0e450501720586f77"
} |
(* Author: Maximilian Schäffeler *)
theory Policy_Iteration
imports "MDP-Rewards.MDP_reward"
begin
section ‹Policy Iteration›
text ‹
The Policy Iteration algorithms provides another way to find optimal policies under the expected
total reward criterion.
It differs from Value Iteration in that it continuously imp... | {
"path": "afp-2025-02-12/thys/MDP-Algorithms/Policy_Iteration.thy",
"repo": "afp-2025-02-12",
"sha": "4e1b57fd1783510b702d3cdbce14e3366543d7b74b81492715c51119600108cb"
} |
section ‹ Technical Lemmas ›
text ‹We show three lemmas used in the proof of both main theorems.›
theory Polygonal_Number_Theorem_Lemmas
imports "Three_Squares.Three_Squares"
begin
subsection ‹ Lemma 1.10 in \cite{nathanson1996} ›
text ‹This lemma is split into two parts. We modify the proof given in \cite{nathans... | {
"path": "afp-2025-02-12/thys/Polygonal_Number_Theorem/Polygonal_Number_Theorem_Lemmas.thy",
"repo": "afp-2025-02-12",
"sha": "67f36d3d18c1df66befe3f1204d5995c62e3fd87e6b9840d9fc8304c4b8aee26"
} |
(*
Title: Psi-calculi
Author/Maintainer: Jesper Bengtson (jebe@itu.dk), 2012
*)
theory Weaken_Transition
imports Weakening
begin
context weak
begin
definition weakenTransition :: "'b ⇒ ('a, 'b, 'c) psi ⇒ 'a action ⇒ ('a, 'b, 'c) psi ⇒ bool" ("_ ⊳ _ ⟹_ ≺ _" [80, 80, 80, 80] 80)
where
"Ψ ⊳ P ⟹α ≺ P' ≡ (∃P... | {
"path": "afp-2025-02-12/thys/Psi_Calculi/Weaken_Transition.thy",
"repo": "afp-2025-02-12",
"sha": "b3b69eadabd2756ac46be73ac12293e115fee66e4e13b2aa65d38fef5ceb02ae"
} |
(* Title: HOL/Auth/Guard/Guard_OtwayRees.thy
Author: Frederic Blanqui, University of Cambridge Computer Laboratory
Copyright 2002 University of Cambridge
*)
section‹Otway-Rees Protocol›
theory Guard_OtwayRees imports Guard_Shared begin
subsection‹messages used in the protocol›
abbreviation
ni... | {
"path": "Isabelle2024/src/HOL/Auth/Guard/Guard_OtwayRees.thy",
"repo": "Isabelle2024",
"sha": "1fe133cbc5b75252e628c98f186898e455fa119b316d8f2f8942ff3acac5dd90"
} |
(* Theory: Indep_Events.thy
Author: Chelsea Edmonds *)
section ‹ Independent Events ›
theory Indep_Events imports Cond_Prob_Extensions
begin
subsection ‹More bijection helpers›
lemma bij_betw_obtain_subsetr:
assumes "bij_betw f A B"
assumes "A' ⊆ A"
obtains B' where "B' ⊆ B" and "B' = f ` A'"
using assm... | {
"path": "afp-2025-02-12/thys/Lovasz_Local/Indep_Events.thy",
"repo": "afp-2025-02-12",
"sha": "beea1f945914d4cdd6425ed3a058932495b7249a68cc7cbe2c6421ded2917aa5"
} |
(* Title: Linear_Algebra_More
Author: Richard Schmoetten <richard.schmoetten@ed.ac.uk>, 2024
Maintainer: Richard Schmoetten <richard.schmoetten@ed.ac.uk>
*)
theory Linear_Algebra_More
imports
"HOL-Analysis.Analysis"
"Smooth_Manifolds.Smooth"
Transfer_Cayley_Hamilton
begin
section ‹Continui... | {
"path": "afp-2025-02-12/thys/Lie_Groups/Linear_Algebra_More.thy",
"repo": "afp-2025-02-12",
"sha": "4e1fdf5ba107f8699008bc7e18a32a0976f10b28e9c6bed5039364c7e9d4b6d0"
} |
(* Title: HOL/HOLCF/UpperPD.thy
Author: Brian Huffman
*)
section ‹Upper powerdomain›
theory UpperPD
imports Compact_Basis
begin
subsection ‹Basis preorder›
definition
upper_le :: "'a pd_basis ⇒ 'a pd_basis ⇒ bool" (infix "≤♯" 50) where
"upper_le = (λu v. ∀y∈Rep_pd_basis v. ∃x∈Rep_pd_basis u. x ⊑ y... | {
"path": "Isabelle2024/src/HOL/HOLCF/UpperPD.thy",
"repo": "Isabelle2024",
"sha": "e4b15b44997e4ff2e7cf5515887c13e1291bb3ecdc1441a5aaeffde7bd699444"
} |
(* Title: Free_Boolean_Algebra.thy
Author: Brian Huffman, Portland State University
*)
section ‹Free Boolean algebras›
theory Free_Boolean_Algebra
imports Main
begin
(*<*)
notation
bot ("⊥") and
top ("⊤") and
inf (infixl "⊓" 70) and
sup (infixl "⊔" 65)
lemma sup_conv_inf:
fixes x y :: "'a:... | {
"path": "afp-2025-02-12/thys/Free-Boolean-Algebra/Free_Boolean_Algebra.thy",
"repo": "afp-2025-02-12",
"sha": "33939ff3c52e54e39a25c82b3b9b586aac21cc458b98b1d1a996326c22a16566"
} |
(* Title: A Definitional Encoding of TLA in Isabelle/HOL
Authors: Gudmund Grov <ggrov at inf.ed.ac.uk>
Stephan Merz <Stephan.Merz at loria.fr>
Year: 2011
Maintainer: Gudmund Grov <ggrov at inf.ed.ac.uk>
*)
section ‹Representing Intensional Logic›
theory Intensional
imp... | {
"path": "afp-2025-02-12/thys/TLA/Intensional.thy",
"repo": "afp-2025-02-12",
"sha": "7f51d6c4dde2e2a400268a76fdb5cda86fd916084dbfc8a4e6eb1f2e7ed13e8d"
} |
theory Powers3844
imports Main Kyber_Values
begin
section ‹Checking Powers of Root of Unity›
text ‹In order to check, that $3844$ is indeed a root of unity, we need to calculate all powers
and show that they are not equal to one.›
fun fast_exp_7681 ::" int ⇒ nat ⇒ int" where
"fast_exp_7681 x 0 = 1" |
"fast_exp_7681 ... | {
"path": "afp-2025-02-12/thys/CRYSTALS-Kyber/Powers3844.thy",
"repo": "afp-2025-02-12",
"sha": "c75e5f5741987f06f1f35c79a8e8fdbc6f32a6cace6ef967c8d722655686d676"
} |
(*<*)
―‹ ********************************************************************
* Project : AGM Theory
* Version : 1.0
*
* Authors : Valentin Fouillard, Safouan Taha, Frederic Boulanger
and Nicolas Sabouret
*
* This file : AGM contraction
*
* Copyright (c) 2021 ... | {
"path": "afp-2025-02-12/thys/Belief_Revision/AGM_Contraction.thy",
"repo": "afp-2025-02-12",
"sha": "debf1610d2d43eb890d928cd9bd5540fe273a1ec30e7ee5df4617ff48653b122"
} |
(*******************************************************************************
Project: Refining Authenticated Key Agreement with Strong Adversaries
Module: sklvl3_symmetric.thy (Isabelle/HOL 2016-1)
ID: $Id: sklvl3_symmetric.thy 133183 2017-01-31 13:55:43Z csprenge $
Author: Joseph Lallemand, INRIA ... | {
"path": "afp-2025-02-12/thys/Key_Agreement_Strong_Adversaries/sklvl3_symmetric.thy",
"repo": "afp-2025-02-12",
"sha": "45c2c032b227c3762356c38a0db28104a10685deba5d574029ca80ad246fe365"
} |
(* Title: Group_Divisible_Designs.thy
Author: Chelsea Edmonds
*)
section ‹Group Divisible Designs›
text ‹Definitions in this section taken from the handbook \<^cite>‹"colbournHandbookCombinatorialDesigns2007"›
and Stinson \<^cite>‹"stinsonCombinatorialDesignsConstructions2004"››
theory Group_Divisible_Designs impor... | {
"path": "afp-2025-02-12/thys/Design_Theory/Group_Divisible_Designs.thy",
"repo": "afp-2025-02-12",
"sha": "1c01934525160b5bde5e85754ef4d82def8dee74ba3bbcc2fe175d7d25ad6e05"
} |
(* Title: HOL/Proofs/Lambda/NormalForm.thy
Author: Stefan Berghofer, TU Muenchen, 2003
*)
section ‹Inductive characterization of lambda terms in normal form›
theory NormalForm
imports ListBeta
begin
subsection ‹Terms in normal form›
definition
listall :: "('a ⇒ bool) ⇒ 'a list ⇒ bool" where
"lista... | {
"path": "Isabelle2024/src/HOL/Proofs/Lambda/NormalForm.thy",
"repo": "Isabelle2024",
"sha": "0e4026f44142b737f7eaa92340eb52c4c19af8bff3ae7596d7b0b16804e8facb"
} |
subsection‹ScottVariantHOMLposs.thy (Figure 19 of \cite{J75})›
text‹Scottâs variant of Gödelâs ontological proof is still valid when using possibilist quantifiers only.›
theory ScottVariantHOMLposs imports HOMLinHOL ModalFilter
begin
consts PositiveProperty::"(e⇒σ)⇒σ" ("P")
axiomatization where A1: "⌊❙¬P φ ❙↔ ... | {
"path": "afp-2025-02-12/thys/Notes_On_Goedels_Ontological_Argument/ScottVariantHOMLposs.thy",
"repo": "afp-2025-02-12",
"sha": "5d65ca116fc95244ff8ed5d290c57e02f1e2faebdb1067701fb66c4db604cd89"
} |
(* Title: HOL/MicroJava/DFA/LBVSpec.thy
Author: Gerwin Klein
Copyright 1999 Technische Universitaet Muenchen
*)
section ‹The Lightweight Bytecode Verifier›
theory LBVSpec
imports SemilatAlg Opt
begin
type_synonym 's certificate = "'s list"
primrec merge :: "'s certificate ⇒ 's binop ⇒ 's ord ... | {
"path": "Isabelle2024/src/HOL/MicroJava/DFA/LBVSpec.thy",
"repo": "Isabelle2024",
"sha": "688ba0438200aa63af7994c6eb1259cc2d4442bbc271c8e5eba4a451f3864c00"
} |
(* Title: variants/a_norreqid/Aodv_Message.thy
License: BSD 2-Clause. See LICENSE.
Author: Timothy Bourke, Inria
Author: Peter Höfner, NICTA
*)
section "AODV protocol messages"
theory A_Aodv_Message
imports A_Norreqid
begin
datatype msg =
Rreq nat ip sqn k ip sqn ip
| Rrep nat... | {
"path": "afp-2025-02-12/thys/AODV/variants/a_norreqid/A_Aodv_Message.thy",
"repo": "afp-2025-02-12",
"sha": "0a4470b0ae710960dc17279b39158893d31e1afb89f6d09f391e90975e683e57"
} |
theory PAC_Assoc_Map_Rel
imports PAC_Map_Rel
begin
section ‹Hash Map as association list›
type_synonym ('k, 'v) hash_assoc = ‹('k × 'v) list›
definition hassoc_map_rel_raw :: ‹(('k, 'v) hash_assoc × _) set› where
‹hassoc_map_rel_raw = br map_of (λ_. True)›
abbreviation hassoc_map_assn :: ‹('k ⇒ 'v option) ⇒ ('k... | {
"path": "afp-2025-02-12/thys/PAC_Checker/PAC_Assoc_Map_Rel.thy",
"repo": "afp-2025-02-12",
"sha": "1693005a4e6c4a4c0e4b4e76b7034a7a1dff3447a31f8c9fe8eda5c351e3613c"
} |
theory CHERI_C_Global_Environment
imports CHERI_C_Concrete_Memory_Model
begin
text ‹Here, we define the global environment. The Global Environment does the following:
\begin{enumerate}
\item Creates a mapping from variables to locations (or rather, the capabilities)
\item Sets global variables by invoking... | {
"path": "afp-2025-02-12/thys/CHERI-C_Memory_Model/CHERI_C_Global_Environment.thy",
"repo": "afp-2025-02-12",
"sha": "0a5c2b7de87f0dd745699b3a675d0cd49cef76ca50fc54597d639f58926de007"
} |
theory Invariants
imports SCL_FOL
begin
text ‹The following lemma restate existing invariants in a compact, paper-friendly way.›
lemma (in scl_fol_calculus) scl_state_invariants:
shows
inv_trail_lits_ground:
"trail_lits_ground initial_state"
"scl N β S S' ⟹ trail_lits_ground S ⟹ trail_lits_ground ... | {
"path": "afp-2025-02-12/thys/Simple_Clause_Learning/Invariants.thy",
"repo": "afp-2025-02-12",
"sha": "b8f7c19519f00c715342b6a55aec31e47b0a60685a21c5e899e9cd3ad51ec51e"
} |
section "Sorts"
(*
Some stuff on sorts. Mostly from Sort.ML I think.
*)
theory Sorts
imports Term
begin
definition [simp]: "empty_osig = ({}, Map.empty)"
definition "sort_les cs s1 s2 = (sort_leq cs s1 s2 ∧ ¬ sort_leq cs s2 s1)"
definition "sort_eqv cs s1 s2 = (sort_leq cs s1 s2 ∧ sort_leq cs s2 s1)"
lemmas cla... | {
"path": "afp-2025-02-12/thys/Metalogic_ProofChecker/Sorts.thy",
"repo": "afp-2025-02-12",
"sha": "ff9cf32010ff6bf6ce3e3fa9cb505f232c4e3f1ea2eab6facd5882c85e0debf8"
} |
theory Grounded_First_Order_Superposition
imports
First_Order_Superposition
Ground_Superposition_Completeness
begin
context ground_superposition_calculus
begin
abbreviation eq_resolution_inferences where
"eq_resolution_inferences ≡ {Infer [P] C | P C. ground_eq_resolution P C}"
abbreviation eq_factorin... | {
"path": "afp-2025-02-12/thys/Superposition_Calculus/Grounded_First_Order_Superposition.thy",
"repo": "afp-2025-02-12",
"sha": "c2422bc0a25449eecddd140b38799f7c85ec503b8f6d92b0ff3e30a4a2d7bd9e"
} |
(*
Title: 2-Catoids
Author: Georg Struth
Maintainer: Georg Struth <g.struth at sheffield.ac.uk>
*)
section ‹2-Catoids›
theory Two_Catoid
imports Catoids.Catoid
begin
text‹We define 2-catoids and in particular (strict) 2-categories as local functional 2-catoids. With Isabelle
we first need to make two copies of c... | {
"path": "afp-2025-02-12/thys/OmegaCatoidsQuantales/Two_Catoid.thy",
"repo": "afp-2025-02-12",
"sha": "ac6a9abb05ace6aa41af8bd45bcb8faf85f2b1692dbf9c690f5e46833fef9763"
} |
(*
File: Akra_Bazzi_Library.thy
Author: Manuel Eberl <manuel@pruvisto.org>
Lemma bucket for the Akra-Bazzi theorem.
*)
section ‹Auxiliary lemmas›
theory Akra_Bazzi_Library
imports
Complex_Main
"Landau_Symbols.Landau_More"
"Pure-ex.Guess"
begin
(* TODO: Move? *)
lemma ln_mono: "0 < x ⟹ 0 < y ⟹ x ≤ y ⟹... | {
"path": "afp-2025-02-12/thys/Akra_Bazzi/Akra_Bazzi_Library.thy",
"repo": "afp-2025-02-12",
"sha": "863cf3bd6cdfd428cceac420bc492da1e6876cbab16e4f668ce954591491bb3e"
} |
(*
* Copyright (C) 2014 NICTA
* All rights reserved.
*)
(* Author: David Cock - David.Cock@nicta.com.au *)
section "Structured Reasoning"
theory StructuredReasoning imports Algebra begin
text ‹By linking the algebraic, the syntactic, and the semantic views
of computation, we derive a set of rules for decomposi... | {
"path": "afp-2025-02-12/thys/pGCL/StructuredReasoning.thy",
"repo": "afp-2025-02-12",
"sha": "dc98056404baa5c7f6ddd31638757c2f1756fd5665fe76a29c9ce12b14d8e2b4"
} |
(*****************************************************************************
* Featherweight-OCL --- A Formal Semantics for UML-OCL Version OCL 2.5
* for the OMG Standard.
* http://www.brucker.ch/projects/hol-testgen/
*
* UML_String.thy --- Library definitions.
* This... | {
"path": "afp-2025-02-12/thys/Featherweight_OCL/basic_types/UML_String.thy",
"repo": "afp-2025-02-12",
"sha": "c3f9162bd478e65dfb9b7f9ec6157b17522b35e02e89745c8478faf6e9a94057"
} |
(* Title: Safe OCL
Author: Denis Nikiforov, March 2019
Maintainer: Denis Nikiforov <denis.nikif at gmail.com>
License: LGPL
*)
chapter ‹Normalization›
theory OCL_Normalization
imports OCL_Typing
begin
(*** Normalization Rules ****************************************************)
section... | {
"path": "afp-2025-02-12/thys/Safe_OCL/OCL_Normalization.thy",
"repo": "afp-2025-02-12",
"sha": "9e473953895e48e1813c04ae42527d27ba80a3a5f61a1713a00b92f801fdbdac"
} |
theory InductRules
imports Main
begin
lemma disjCases2[consumes 1, case_names 1 2]:
assumes AB: "A ∨ B"
and AP: "A ⟹ P"
and BP: "B ⟹ P"
shows "P"
proof (-)
(*goal: ‹P›*)
from AB (*‹A ∨ B›*) AP (*‹A ⟹ P›*) BP (*‹B ⟹ P›*) show "?thesis"
(*goal: ‹P::bool›*)
by blast
qed
lemma disjCases3[consumes 1, c... | {
"path": "afp-2025-02-12/thys/LocalLexing/InductRules.thy",
"repo": "afp-2025-02-12",
"sha": "1ab36d6cd27fcb09a3bcfc50ede8c3999a6a0ce9c242543e4f60bc0742525ea2"
} |
section ‹Counting Irreducible Polynomials \label{sec:card_irred}›
subsection ‹The polynomial $X^n - X$›
theory Card_Irreducible_Polynomials_Aux
imports
"HOL-Algebra.Multiplicative_Group"
Formal_Polynomial_Derivatives
Monic_Polynomial_Factorization
begin
lemma (in domain)
assumes "subfield K R"
assumes "f ∈... | {
"path": "afp-2025-02-12/thys/Finite_Fields/Card_Irreducible_Polynomials_Aux.thy",
"repo": "afp-2025-02-12",
"sha": "06eb303763faa5a2f4c8e27f8b99f35021fcd31f4944c7e30583a9459e356ca6"
} |
theory NDFS_Benchmark
imports
Collections_Examples.Nested_DFS
"../../../Examples/Sepref_NDFS"
Separation_Logic_Imperative_HOL.From_List_GA
begin
(* We re-do some of the refinement here, to have a more direct control
of the exact data-structures that are used *)
(* Purely functional version *)
locale... | {
"path": "afp-2025-02-12/thys/Refine_Imperative_HOL/benchmarks/NestedDFS/isabelle/NDFS_Benchmark.thy",
"repo": "afp-2025-02-12",
"sha": "7efea1f81a654fdc262ee33135c2bbbcbc43d4a4e74d70a53e5d55ef785dc58c"
} |
section‹The main theorem›
theory Forcing_Main
imports
Internal_ZFC_Axioms
Choice_Axiom
Ordinals_In_MG
Succession_Poset
begin
subsection‹The generic extension is countable›
(*
― ‹Useful missing lemma›
lemma surj_imp_well_ord:
assumes "well_ord(A,r)" "h ∈ surj(A,B)"
shows "∃s. well_ord(B,r)"
*)
definit... | {
"path": "afp-2025-02-12/thys/Forcing/Forcing_Main.thy",
"repo": "afp-2025-02-12",
"sha": "73c78e26c5e72cc5c455ce9ba942a89a1e60c6fad630350aa8581b064c86b1eb"
} |
theory EtaExpansion
imports Launchbury.Terms Launchbury.Substitution
begin
definition fresh_var :: "exp ⇒ var" where
"fresh_var e = (SOME v. v ∉ fv e)"
lemma fresh_var_not_free:
"fresh_var e ∉ fv e"
proof (-)
(*goal: ‹fresh_var e ∉ fv e›*)
obtain v :: var where "atom v ♯ e"
(*goal: ‹(⋀v::Vars.var. atom v ... | {
"path": "afp-2025-02-12/thys/Call_Arity/EtaExpansion.thy",
"repo": "afp-2025-02-12",
"sha": "1a92caebb16663e4552115dbf7cd10f7735ff2e4c5bb8a360482af7692866d02"
} |
(* Title: HOL/Int.thy
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Author: Tobias Nipkow, Florian Haftmann, TU Muenchen
*)
section ‹The Integers as Equivalence Classes over Pairs of Natural Numbers›
theory Int
imports Quotient Groups_Big Fun_Def
begin
subsection ‹Defin... | {
"path": "Isabelle2024/src/HOL/Int.thy",
"repo": "Isabelle2024",
"sha": "755ba7a1a30108f02b17618142a8cb1e6ba95d1df4f1d05d564398483aa17334"
} |
theory More_Missing_Multiset
imports
"HOL-Combinatorics.Permutations"
Polynomial_Factorization.Missing_Multiset
begin
lemma rel_mset_free:
assumes rel: "rel_mset rel X Y" and xs: "mset xs = X"
shows "∃ys. mset ys = Y ∧ list_all2 rel xs ys"
proof (-)
(*goal: ‹∃ys. mset ys = Y ∧ list_all2 rel xs ys›*)
... | {
"path": "afp-2025-02-12/thys/Berlekamp_Zassenhaus/More_Missing_Multiset.thy",
"repo": "afp-2025-02-12",
"sha": "80d40e0b45d7b21db2511a8b84671ef93caef8f636e32f3900859fb04ab0270d"
} |
section ‹Functions›
theory Functions
imports "../Extensions/Set_Extensions"
begin
locale bounded_function =
fixes A :: "'a set"
fixes B :: "'b set"
fixes f :: "'a ⇒ 'b"
assumes wellformed[intro?, simp]: "x ∈ A ⟹ f x ∈ B"
locale bounded_function_pair =
f: bounded_function A B f +
g: bounde... | {
"path": "afp-2025-02-12/thys/Partial_Order_Reduction/Basics/Functions.thy",
"repo": "afp-2025-02-12",
"sha": "bed49ed30693fbf9934ce027af0630e325a69997154d38d7be464e366e5958ac"
} |
theory Weak_Validity
imports
Weak_Formula
Validity
begin
section ‹Weak Validity›
text ‹Weak formulas are a subset of (strong) formulas, and the definition of validity is simply
taken from the latter. Here we prove some useful lemmas about the validity of weak modalities.
These are similar to corresponding lemmas... | {
"path": "afp-2025-02-12/thys/Modal_Logics_for_NTS/Weak_Validity.thy",
"repo": "afp-2025-02-12",
"sha": "404ad05a20be29add5165488279f3b3b1c17fe4786282ed1cd6ffc7175003562"
} |
(* Title: HOL/Bali/Decl.thy
Author: David von Oheimb and Norbert Schirmer
*)
subsection ‹Field, method, interface, and class declarations, whole Java programs
›
theory Decl
imports Term Table
(** order is significant, because of clash for "var" **)
begin
text ‹
improvements:
\begin{itemize}
\item clar... | {
"path": "Isabelle2024/src/HOL/Bali/Decl.thy",
"repo": "Isabelle2024",
"sha": "dfafb4961b1247163675611012744287cebdf0d51f431d1d2dbeda059760f593"
} |
theory "Ids"
imports Complex_Main
begin
section ‹Identifier locale›
text ‹The differential dynamic logic formalization is parameterized by the type of identifiers.
The identifier type(s) must be finite and have at least 3-4 distinct elements.
Distinctness is required for soundness of some axioms. ›
locale ids =
f... | {
"path": "afp-2025-02-12/thys/Differential_Dynamic_Logic/Ids.thy",
"repo": "afp-2025-02-12",
"sha": "7f5a227d2cc407d670d1d17fdb30783f1a7328f711a8d5b8ad0fc6cbd8927c69"
} |
(******************************************************************************)
(* Project: Isabelle/UTP Toolkit *)
(* File: List_Lexord_Alt.thy *)
(* Authors: Simon Foster and Frank Zeyda ... | {
"path": "afp-2025-02-12/thys/UTP/toolkit/List_Lexord_Alt.thy",
"repo": "afp-2025-02-12",
"sha": "2450d81fb08d9a1616d29659cc06178e7442ffc43b7c0e86d697b80ca7ed547f"
} |
chapter‹Uniqueness Results: Syntactic Relations are Functions›
theory Functions
imports Coding_Predicates
begin
subsection ‹SeqStTermP›
lemma not_IndP_VarP: "{IndP x, VarP x} ⊢ A"
proof (-)
(*goal: ‹{IndP x, VarP x} ⊢ A›*)
obtain m :: name where "atom m ♯ (x,A)"
(*goal: ‹(⋀m. atom m ♯ (x, A) ⟹ thesis) ⟹ thes... | {
"path": "afp-2025-02-12/thys/Goedel_HFSet_Semanticless/Functions.thy",
"repo": "afp-2025-02-12",
"sha": "37beb192d8d55036b5190d1cba5b488d66e4994f4927d78bad738b11f33d36b6"
} |
(*******************************************************************************
Project: Development of Security Protocols by Refinement
Module: Key_establish/m3_ds.thy (Isabelle/HOL 2016-1)
ID: $Id: m3_ds.thy 132890 2016-12-24 10:25:57Z csprenge $
Authors: Christoph Sprenger, ETH Zurich <sprenger@inf.... | {
"path": "afp-2025-02-12/thys/Security_Protocol_Refinement/Key_establish/m3_ds.thy",
"repo": "afp-2025-02-12",
"sha": "64174734e09c584a0c9345e810c75138d522b8dba656f1dba6a25d316258a185"
} |
section "Closest Pair Algorithm"
theory Closest_Pair
imports Common
begin
text‹
Formalization of a slightly optimized divide-and-conquer algorithm solving the Closest Pair Problem
based on the presentation of Cormen \emph{et al.} \<^cite>‹"Introduction-to-Algorithms:2009"›.
›
subsection "Functional Correctness... | {
"path": "afp-2025-02-12/thys/Closest_Pair_Points/Closest_Pair.thy",
"repo": "afp-2025-02-12",
"sha": "df4f1e70e8c8e4b03c7479c46382ee42ba9f8fe435236f4d8481444c3cdc6559"
} |
section ‹Tangent numbers›
theory Tangent_Numbers
imports
"HOL-Computational_Algebra.Computational_Algebra"
"Bernoulli.Bernoulli_FPS"
"Polynomial_Interpolation.Ring_Hom_Poly"
Boustrophedon_Transform_Library
Alternating_Permutations
begin
subsection ‹The higher derivatives of $\tan x$›
text ‹
The $n$-th de... | {
"path": "afp-2025-02-12/thys/Boustrophedon_Transform/Tangent_Numbers.thy",
"repo": "afp-2025-02-12",
"sha": "83f8318685d35ffd76a61f5039c45281ca4ff6ab582a0dab2faf6f9e5647f601"
} |
section ‹Finite State Machines›
text ‹This theory defines well-formed finite state machines and introduces various closely related
notions, as well as a selection of basic properties and definitions.›
theory FSM
imports FSM_Impl "HOL-Library.Quotient_Type" "HOL-Library.Product_Lexorder"
begin
subsection ‹W... | {
"path": "afp-2025-02-12/thys/FSM_Tests/FSM.thy",
"repo": "afp-2025-02-12",
"sha": "1f5167daef313fed6c49195d96db1738a47796498c0ffc5bbeab285dbf252cea"
} |
(* Author: Bernhard Stöckl *)
theory Graph_Additions
imports Complex_Main "Graph_Theory.Graph_Theory" "Shortest_Path_Tree"
begin
lemma two_elems_card_ge_2: "finite xs ⟹ x ∈ xs ∧ y ∈ xs ∧ x≠y ⟹ Finite_Set.card xs ≥ 2"
using card_gt_0_iff (*‹(0 < card ?A) = (?A ≠ {} ∧ finite ?A)›*) mk_disjoint_insert (*‹?a ∈ ?A ... | {
"path": "afp-2025-02-12/thys/Query_Optimization/Graph_Additions.thy",
"repo": "afp-2025-02-12",
"sha": "e873af5b9dd5db8f7bc700044a976fbf7fb172216f209ffd782dcabdf771fe37"
} |
(*
File: KD_Tree.thy
Author: Martin Rau, TU München
*)
section "Definition of the ‹k›-d Tree"
theory KD_Tree
imports
Complex_Main
"HOL-Analysis.Finite_Cartesian_Product"
"HOL-Analysis.Topology_Euclidean_Space"
begin
text ‹
A ‹k›-d tree is a space-partitioning data structure for organizing points ... | {
"path": "afp-2025-02-12/thys/KD_Tree/KD_Tree.thy",
"repo": "afp-2025-02-12",
"sha": "51ebf26b2462b9dfcfac404b1477d1051e16c41c88e74120442d5857325d6369"
} |
section‹Separative notions and proper extensions›
theory Proper_Extension
imports
Names
begin
text‹The key ingredient to obtain a proper extension is to have
a ∗‹separative preorder›:›
locale separative_notion = forcing_notion +
assumes separative: "p∈P ⟹ ∃q∈P. ∃r∈P. q ≼ p ∧ r ≼ p ∧ q ⊥ r"
begin
text‹For se... | {
"path": "afp-2025-02-12/thys/Forcing/Proper_Extension.thy",
"repo": "afp-2025-02-12",
"sha": "9c24bd61a89950dfcc445ebd248338596532b5949212d23fb698fbfaf5437fbd"
} |
(* Author: Tobias Nipkow *)
section ‹Multiset of Elements of Binary Tree›
theory Tree_Multiset
imports Multiset Tree
begin
text ‹
Kept separate from theory \<^theory>‹HOL-Library.Tree› to avoid importing all of theory \<^theory>‹HOL-Library.Multiset› into \<^theory>‹HOL-Library.Tree›. Should be merged if \<^theory... | {
"path": "Isabelle2024/src/HOL/Library/Tree_Multiset.thy",
"repo": "Isabelle2024",
"sha": "2e87f581435b2eb6eaf138189aec3073e81dd1d483f340cc7dccd5505dd4538e"
} |
(* Title: HOL/Algebra/Ideal.thy
Author: Stephan Hohe, TU Muenchen
*)
theory Ideal
imports Ring AbelCoset
begin
section ‹Ideals›
subsection ‹Definitions›
subsubsection ‹General definition›
locale ideal = additive_subgroup I R + ring R for I and R (structure) +
assumes I_l_closed: "⟦a ∈ I; x ∈ carrie... | {
"path": "Isabelle2024/src/HOL/Algebra/Ideal.thy",
"repo": "Isabelle2024",
"sha": "f7d3438c33b7f912c06a9f6f883b85c892c6a328fc29bba434e020622ad00c2f"
} |
(* Title: JinjaDCI/BV/TF_JVM.thy
Author: Tobias Nipkow, Gerwin Klein, Susannah Mansky
Copyright 2000 TUM, 2019-20 UIUC
Based on the Jinja theory BV/TF_JVM.thy by Tobias Nipkow and Gerwin Klein
*)
section ‹ The Typing Framework for the JVM \label{sec:JVM} ›
theory TF_JVM
imports Jinja.Typing_... | {
"path": "afp-2025-02-12/thys/JinjaDCI/BV/TF_JVM.thy",
"repo": "afp-2025-02-12",
"sha": "1ddbc55a290096b1f3cf72a445a1ca4758d8fa003eae8bc1504219896b156e5d"
} |
✐‹creator "Kevin Kappelmann"›
subsubsection ‹Connected›
theory Binary_Relations_Connected
imports
Binary_Relation_Functions
begin
consts connected_on :: "'a ⇒ 'b ⇒ bool"
overloading
connected_on_pred ≡ "connected_on :: ('a ⇒ bool) ⇒ ('a ⇒ 'a ⇒ bool) ⇒ bool"
begin
definition "connected_on_pred P R ≡ ∀x y : P... | {
"path": "afp-2025-02-12/thys/Transport/HOL_Basics/Binary_Relations/Properties/Binary_Relations_Connected.thy",
"repo": "afp-2025-02-12",
"sha": "1940c66c0f56624dcfb97b934c6404b0d87b6dd3b9c33cd66bf538e819842637"
} |
(* Title: ListSlice.thy
Date: Oct 2006
Author: David Trachtenherz
*)
section ‹Additional definitions and results for lists›
theory ListSlice
imports "List-Infinite.ListInf"
begin
subsection ‹Slicing lists into lists of lists›
definition ilist_slice :: "'a ilist ⇒ nat ⇒ 'a list ilist"
wher... | {
"path": "afp-2025-02-12/thys/AutoFocus-Stream/ListSlice.thy",
"repo": "afp-2025-02-12",
"sha": "27bb1632d3c02c6f3d0ec7431cedcebdcb8c1a1c0ff9aef5d5f9144e2bc467f7"
} |
section ‹Framework Graph Lifting for Noninterference›
theory LiftingInter
imports NonInterferenceInter
begin
text ‹In this section, we show how a valid CFG from the slicing framework in
\<^cite>‹"Wasserrab:08"› can be lifted to fulfil all properties of the
‹NonInterferenceIntraGraph› locale. Basically, we redefine... | {
"path": "afp-2025-02-12/thys/InformationFlowSlicing_Inter/LiftingInter.thy",
"repo": "afp-2025-02-12",
"sha": "1fe5c495a3fd478911af53a26606370366bbc5d4c45dfdf7d8aebad04ab9b99c"
} |
section ‹General Priority Search Trees›
theory PST_General
imports
"HOL-Data_Structures.Tree2"
Prio_Map_Specs
begin
text ‹\noindent
We show how to implement priority maps
by augmented binary search trees. That is, the basic data structure is some
arbitrary binary search tree, e.g.\ a red-black tree, imple... | {
"path": "afp-2025-02-12/thys/Priority_Search_Trees/PST_General.thy",
"repo": "afp-2025-02-12",
"sha": "39ccd27b89f9b0102b8f4c5cf791ac8645223d15c79092ef1ba35bb2b2790c47"
} |
(*
Author: René Thiemann
Akihisa Yamada
License: BSD
*)
subsection ‹Compare Instance for Complex Numbers›
text ‹We define some code equations for complex numbers, provide a comparator for complex
numbers, and register complex numbers for the container framework.›
theory Compare... | {
"path": "afp-2025-02-12/thys/Algebraic_Numbers/Compare_Complex.thy",
"repo": "afp-2025-02-12",
"sha": "a62481e902411d30dd04e568f52de3dbbfaf0062a9aa24ccfc300887dc226b77"
} |
theory SINVAR_BLPtrusted
imports "../TopoS_Helper"
begin
subsection ‹SecurityInvariant Basic Bell LaPadula with trusted entities›
type_synonym security_level = nat
record node_config =
security_level::security_level
trusted::bool
definition default_node_properties :: "node_config"
where "default_node_pr... | {
"path": "afp-2025-02-12/thys/Network_Security_Policy_Verification/Security_Invariants/SINVAR_BLPtrusted.thy",
"repo": "afp-2025-02-12",
"sha": "24d3c97797a72d59d6b7a45bb0f5ea36f9e43702d9c75a845c0d7eea544706b8"
} |
(*<*)
theory Regex
imports
"MFOTL_Monitor.Trace"
"HOL-Library.Extended_Nat"
begin
unbundle lattice_syntax
(*>*)
section ‹Regular expressions›
context begin
qualified datatype (atms: 'a) regex = Skip nat | Test 'a
| Plus "'a regex" "'a regex" | Times "'a regex" "'a regex" | Star "'a regex"
lemma finite... | {
"path": "afp-2025-02-12/thys/MFODL_Monitor_Optimized/Regex.thy",
"repo": "afp-2025-02-12",
"sha": "2cd268fb8701097fa021bd42a544774d66df50cb47be77a28ad930d54047a812"
} |
subsection‹Consistency›
text‹We follow the proofs by Melvin Fitting~\<^cite>‹"fitting1990first"›.›
theory Consistency
imports Sema
begin
definition "Hintikka S ≡ (
⊥ ∉ S
∧ (∀k. Atom k ∈ S ⟶ ❙¬ (Atom k) ∈ S ⟶ False)
∧ (∀F G. F ❙∧ G ∈ S ⟶ F ∈ S ∧ G ∈ S)
∧ (∀F G. F ❙∨ G ∈ S ⟶ F ∈ S ∨ G ∈ S)
∧ (∀F G. F ❙→ G ∈ S ⟶ ❙¬F ∈... | {
"path": "afp-2025-02-12/thys/Propositional_Proof_Systems/Consistency.thy",
"repo": "afp-2025-02-12",
"sha": "0df5b5641036760e98df7d307a1d51a18ff97737e12659c1f81302d080791f97"
} |
subsubsection‹Going back: CNFs to formulas›
theory CNF_To_Formula
imports CNF_Formulas "HOL-Library.List_Lexorder"
begin
text‹One downside of CNFs is that they cannot be converted back to formulas
as-is in full generality.
If we assume an order on the atoms, we can convert finite CNFs.›
(* This theory was written a... | {
"path": "afp-2025-02-12/thys/Propositional_Proof_Systems/CNF_To_Formula.thy",
"repo": "afp-2025-02-12",
"sha": "4e62b1985487b9c74e39664354559f894c849acf18145f81d787ac929c167477"
} |
section ‹Cheeger Inequality\label{sec:cheeger_ineq}›
text ‹The Cheeger inequality relates edge expansion (a combinatorial property) with the second
largest eigenvalue.›
theory Expander_Graphs_Cheeger_Inequality
imports Expander_Graphs_Eigenvalues
begin
unbundle intro_cong_syntax
hide_const Quantum.T
context regul... | {
"path": "afp-2025-02-12/thys/Expander_Graphs/Expander_Graphs_Cheeger_Inequality.thy",
"repo": "afp-2025-02-12",
"sha": "dbeb6bc4183a5cca61d70dbfc452d42c18032230781120d03f03287c7f95de80"
} |
theory Lib
imports
Ordinary_Differential_Equations.ODE_Analysis
begin
section ‹Generic Mathematical Lemmas›
text‹General lemmas that don't have anything to do with dL specifically and could be fit for
general-purpose libraries, mostly dealing with derivatives, ODEs and vectors.›
lemma vec_extensionality:"(⋀i. v$i... | {
"path": "afp-2025-02-12/thys/Differential_Dynamic_Logic/Lib.thy",
"repo": "afp-2025-02-12",
"sha": "f18524b348d58cd550a9856aa159a9629db16ccd00e7e49c2ca9a5e777fd617b"
} |
(*
Title: Example Completeness Proof for a Natural Deduction Calculus for Basic Hybrid Logic
Author: Asta Halkjær From
*)
chapter ‹Example: Hybrid Logic›
theory Example_Hybrid_Logic imports Derivations begin
section ‹Syntax›
datatype (nominals_fm: 'i, 'p) fm
= Fls (‹❙⊥›)
| Pro 'p (‹❙‡›)
| Nom 'i (‹❙⋅›)
... | {
"path": "afp-2025-02-12/thys/Synthetic_Completeness/Example_Hybrid_Logic.thy",
"repo": "afp-2025-02-12",
"sha": "796aaacbcbe334c96da37feeae622ef92172275c15219e547028e8a01a35015a"
} |
(* Title: Countable Ordinals
Author: Brian Huffman, 2005
Maintainer: Brian Huffman <brianh at cse.ogi.edu>
*)
section ‹Ordinal Arithmetic›
theory OrdinalArith
imports OrdinalRec
begin
subsection ‹Addition›
instantiation ordinal :: plus
begin
definition
"(+) = (λx. ordinal_rec x (λp. oSuc))"... | {
"path": "afp-2025-02-12/thys/Ordinal/OrdinalArith.thy",
"repo": "afp-2025-02-12",
"sha": "a3598b8dabe9d4a738618a245c247e1c031fc1ae7791047ba0f4d54df17b780d"
} |
section ‹Uniqueness of Laplace Transform›
theory Uniqueness
imports
"Existence"
"Lerch_Lemma"
begin
text ‹We show uniqueness of the Laplace transform for continuous functions.›
lemma laplace_transform_zero:― ‹should also work for piecewise continuous›
assumes cont_f: "continuous_on {0..} f"
assumes eo: ... | {
"path": "afp-2025-02-12/thys/Laplace_Transform/Uniqueness.thy",
"repo": "afp-2025-02-12",
"sha": "3c828a630f34db5f69f1fede7f383d8dce443d03e916f748b2e53025c9b74a7f"
} |
subsubsection ‹States›
theory SingleStepState
imports RegisterMachineSimulation
begin
lemma lm04_07_one_step_relation_state:
fixes d :: state
and c :: configuration
and p :: program
and t :: nat
and a :: nat
defines "r ≡ R c p"
defines "s ≡ S c p"
defines "z ≡ Z c p"
defines "cs ≡ fst (steps c p ... | {
"path": "afp-2025-02-12/thys/DPRM_Theorem/Register_Machine/SingleStepState.thy",
"repo": "afp-2025-02-12",
"sha": "f2d78ea3b0fda7dcc52e9c3cb2a826ae2a8b28eaf10134c25a074b98ddd66368"
} |
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