text stringlengths 157 7.64M | meta dict |
|---|---|
theory ResTerm
imports Main
begin
section‹Resource Terms›
text‹
Resource terms describe resources with atoms drawn from two types, linear and copyable, combined
in a number of ways:
▪ Parallel resources represent their simultaneous presence,
▪ Non-deterministic resource represent exactly one of two options,... | {
"path": "afp-2025-02-12/thys/ProcessComposition/ResTerm.thy",
"repo": "afp-2025-02-12",
"sha": "4303ec6b6de06ddbcb4307b2fea6343a1a9a63f1c6d986e8ed157063c01ff65b"
} |
(*
Title: Generalizations2.thy
Author: Jose Divasón <jose.divasonm at unirioja.es>
Author: Jesús Aransay <jesus-maria.aransay at unirioja.es>
*)
section‹Generalization of the Second Part of the Fundamental Theorem of Linear Algebra›
theory Generalizations2
imports
Rank_Nullity_Theor... | {
"path": "afp-2025-02-12/thys/QR_Decomposition/Generalizations2.thy",
"repo": "afp-2025-02-12",
"sha": "ad756ac6c1e9ca077f4d8f627b13b43cf57d2d4043068c9bf20400efa4eed625"
} |
(* Title: Infinite Matrix Model of Kleene Algebra
Author: Alasdair Armstrong, Georg Struth, Tjark Weber
Maintainer: Georg Struth <g.struth at sheffield.ac.uk>
Tjark Weber <tjark.weber at it.uu.se>
*)
section ‹Infinite Matrices›
theory Inf_Matrix
imports Finite_Suprema
begin
text ‹Matric... | {
"path": "afp-2025-02-12/thys/Kleene_Algebra/Inf_Matrix.thy",
"repo": "afp-2025-02-12",
"sha": "1f8f5cdb75fa1d7a6a1c14a928bb13a486533a75f03624b8fd5a35780cb5765f"
} |
section ‹Equalizers and Subobjects›
theory Equalizer
imports Terminal
begin
subsection ‹Equalizers›
definition equalizer :: "cset ⇒ cfunc ⇒ cfunc ⇒ cfunc ⇒ bool" where
"equalizer E m f g ⟷ (∃ X Y. (f : X → Y) ∧ (g : X → Y) ∧ (m : E → X)
∧ (f ∘⇩c m = g ∘⇩c m)
∧ (∀ h F. ((h : F → X) ∧ (f ∘⇩c h = g ∘⇩c h)) ... | {
"path": "afp-2025-02-12/thys/Category_Set/Equalizer.thy",
"repo": "afp-2025-02-12",
"sha": "35febde2d53f50b8c8974ba0ddad84afdf18778ed133ff85c34b34159b665633"
} |
section‹Homology, I: Simplices›
theory "Simplices"
imports
"HOL-Analysis.Function_Metric"
"HOL-Analysis.Abstract_Euclidean_Space"
"HOL-Algebra.Free_Abelian_Groups"
begin
subsection‹Standard simplices, all of which are topological subspaces of @{text"R^n"}. ›
type_synonym 'a chain = "((nat ⇒ real) ... | {
"path": "Isabelle2024/src/HOL/Homology/Simplices.thy",
"repo": "Isabelle2024",
"sha": "c85e6e253dac597180df293639c374c5f228e6198f57a9434927fd9f24ba84da"
} |
subsection‹ScottVariantHOMLAndersonQuant.thy (Figure 15 of \cite{J75})›
text‹Verification of Scottâs variant of Gödelâs argument with a mixed use of actualist and possibilist quantifiers
for entities; cf. Footnote 20 in \cite{J75}.›
theory ScottVariantHOMLAndersonQuant imports HOMLinHOL ModalFilter
begin
consts... | {
"path": "afp-2025-02-12/thys/Notes_On_Goedels_Ontological_Argument/ScottVariantHOMLAndersonQuant.thy",
"repo": "afp-2025-02-12",
"sha": "6e5c34d3ea2d0f2177f576191731caf60995a406a3a9b42071841e01ed32457e"
} |
(* Author: Tobias Nipkow *)
section ‹Association List Update and Deletion›
theory AList_Upd_Del
imports Sorted_Less
begin
abbreviation "sorted1 ps ≡ sorted(map fst ps)"
text‹Define own ‹map_of› function to avoid pulling in an unknown
amount of lemmas implicitly (via the simpset).›
hide_const (open) map_of
fun map... | {
"path": "Isabelle2024/src/HOL/Data_Structures/AList_Upd_Del.thy",
"repo": "Isabelle2024",
"sha": "980e53c817d0b020d3ad33516a358dd3a339ef6aa16ff47cd41bee42e5ba111e"
} |
theory Refine_Rigorous_Numerics_Aform
imports
Refine_Rigorous_Numerics
"HOL-Types_To_Sets.Types_To_Sets"
begin
lemma Joints_ne_empty[simp]: "Joints xs ≠ {}" "{} ≠ Joints xs"
(*goals:
1. ‹Joints xs ≠ {}›
2. ‹{} ≠ Joints xs›
discuss goal 1*)
apply ((auto simp: Joints_def (*‹Joints (?XS::(?... | {
"path": "afp-2025-02-12/thys/Ordinary_Differential_Equations/Numerics/Refine_Rigorous_Numerics_Aform.thy",
"repo": "afp-2025-02-12",
"sha": "67a8a0eb2c00086a29dcf83427be7b91bf3c1c32c862aa14c67963681e347ed3"
} |
(* Author: Alexander Maletzky *)
section ‹Ordered Associative Lists for Polynomials›
theory OAlist_Poly_Mapping
imports PP_Type MPoly_Type_Class_Ordered OAlist
begin
text ‹We introduce a dedicated type for ordered associative lists (oalists) representing polynomials.
To that end, we require the order relation th... | {
"path": "afp-2025-02-12/thys/Polynomials/OAlist_Poly_Mapping.thy",
"repo": "afp-2025-02-12",
"sha": "1f1af69e612dfa6a1048c0d9b1d28882333cca63b7468fba7fb21e394148beed"
} |
(***********************************************************************************
* Copyright (c) 2016-2020 The University of Sheffield, UK
* 2019-2020 University of Exeter, UK
*
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are per... | {
"path": "afp-2025-02-12/thys/Shadow_SC_DOM/tests/Shadow_DOM_Node_insertBefore.thy",
"repo": "afp-2025-02-12",
"sha": "00620014b4bf5191868181f80ad86f6d96935d45595bf448f5c8cd091dcc2773"
} |
(*
Title: Modal quantales
Author: Georg Struth
Maintainer: Georg Struth <g.struth at sheffield.ac.uk>
*)
section ‹Modal quantales›
theory Modal_Quantale
imports Quantales.Quantale_Star Modal_Kleene_Algebra_Var KAD.Modal_Kleene_Algebra
begin
subsection ‹Simplified modal semirings and Kleene algebras›
text ‹The pr... | {
"path": "afp-2025-02-12/thys/Quantales_Converse/Modal_Quantale.thy",
"repo": "afp-2025-02-12",
"sha": "58420d5511b39a0cebe9091a666ecadebe5b90b0500fdfb304210db2dced1330"
} |
(* Title: HOL/HOLCF/IOA/CompoScheds.thy
Author: Olaf Müller
*)
section ‹Compositionality on Schedule level›
theory CompoScheds
imports CompoExecs
begin
definition mkex2 :: "('a, 's) ioa ⇒ ('a, 't) ioa ⇒ 'a Seq →
('a, 's) pairs → ('a, 't) pairs → ('s ⇒ 't ⇒ ('a, 's × 't) pairs)"
where "mkex2 A B =
... | {
"path": "Isabelle2024/src/HOL/HOLCF/IOA/CompoScheds.thy",
"repo": "Isabelle2024",
"sha": "698deb08973b5e110e81b8da8f73d8584def88ae44484804a11e7db97d0468a1"
} |
(* Title: variants/a_norreqid/Seq_Invariants.thy
License: BSD 2-Clause. See LICENSE.
Author: Timothy Bourke, Inria
*)
section "Invariant proofs on individual processes"
theory A_Seq_Invariants
imports AWN.Invariants A_Aodv A_Aodv_Data A_Aodv_Predicates A_Fresher
begin
text ‹
The propositio... | {
"path": "afp-2025-02-12/thys/AODV/variants/a_norreqid/A_Seq_Invariants.thy",
"repo": "afp-2025-02-12",
"sha": "e22133f37891a231781ed44bd088b87eeb2bd21a3d2eea3dc47a332eb4ac26a3"
} |
section ‹General well-formedness of While CFG›
theory WellFormed imports
Interpretation
Labels
"../Basic/CFGExit_wf"
"../StaticIntra/CDepInstantiations"
begin
subsection ‹Definition of some functions›
fun lhs :: "cmd ⇒ vname set"
where
"lhs Skip = {}"
| "lhs (V:=e) = {V}"... | {
"path": "afp-2025-02-12/thys/Slicing/While/WellFormed.thy",
"repo": "afp-2025-02-12",
"sha": "4812130096493c57c694171eeacc9cfc7ab49e82815b6b46d7561d1448d8fada"
} |
(* Author: Tobias Nipkow *)
section "Deterministic List Update"
theory Move_to_Front
imports
Swaps
On_Off
Competitive_Analysis
begin
declare Let_def[simp]
subsection "Function ‹mtf›"
definition mtf :: "'a ⇒ 'a list ⇒ 'a list" where
"mtf x xs =
(if x ∈ set xs then x # (take (index xs x) xs) @ drop (index xs ... | {
"path": "afp-2025-02-12/thys/List_Update/Move_to_Front.thy",
"repo": "afp-2025-02-12",
"sha": "9058fb0f58d1ae7f722986a4b4e3c45d00c3106270fa903caf3c9dcbea564df7"
} |
(* Title: HOL/MicroJava/J/State.thy
Author: David von Oheimb
Copyright 1999 Technische Universitaet Muenchen
*)
section ‹Objects and the Heap›
theory Objects imports TypeRel Value begin
subsection‹Objects›
type_synonym
fields = "vname × cname ⇀ val" ― ‹field name, defining class, value›
type... | {
"path": "afp-2025-02-12/thys/Jinja/Common/Objects.thy",
"repo": "afp-2025-02-12",
"sha": "fb4509bd266f6604c2c7519bb7d5029d678de8d3c13dbb79610f988e6c5ebf8f"
} |
(*
Auction Theory Toolbox (http://formare.github.io/auctions/)
Authors:
* Marco B. Caminati http://caminati.co.nr
* Manfred Kerber <mnfrd.krbr@gmail.com>
* Christoph Lange <math.semantic.web@gmail.com>
* Colin Rowat <c.rowat@bham.ac.uk>
Dually licenced under
* Creative Commons Attribution (CC-BY) 3.0
* ISC License (1... | {
"path": "afp-2025-02-12/thys/Vickrey_Clarke_Groves/SetUtils.thy",
"repo": "afp-2025-02-12",
"sha": "b41bc7d210e1bb7e6c38c0acebbc1072deb33e704f3df7eabe93f1a6da600249"
} |
subsection "Proof"
theory Fun4_secure
imports Fun4
begin
(* THE PROOF OF SECURITY *)
definition "PC ≡ {0..6}"
(*For the counterparts, we chose i=0 to ensure going down the then branch*)
definition "same_xx_cp cfg1 cfg2 ≡
vstore (getVstore (stateOf cfg1)) xx = vstore (getVstore (stateOf cfg2)) xx
∧ vstore (getV... | {
"path": "afp-2025-02-12/thys/IMP_With_Speculation/Examples/Fun4_secure.thy",
"repo": "afp-2025-02-12",
"sha": "f048fe9c8fd3e0c870ae3e9bf8aee8248a8cffe28e647a3e5dc0f200a56bf51a"
} |
theory PNT_Subsummable
imports
"PNT_Remainder_Library"
begin
unbundle pnt_notation
definition has_subsum where "has_subsum f S x ≡ (λn. if n ∈ S then f n else 0) sums x"
definition subsum where "subsum f S ≡ ∑n. if n ∈ S then f n else 0"
definition subsummable (infix "subsummable" 50)
where "f subsummable S ≡ summ... | {
"path": "afp-2025-02-12/thys/PNT_with_Remainder/PNT_Subsummable.thy",
"repo": "afp-2025-02-12",
"sha": "8bb38532db8de0f002dbdb9c8bb619b5a0350fc4474d0837e0da85c406a4944d"
} |
(*************************************************************************
* Copyright (C)
* 2019 The University of Exeter
* 2018-2019 The University of Paris-Saclay
* 2018 The University of Sheffield
*
* License:
* This program can be redistributed and/or ... | {
"path": "afp-2025-02-12/thys/Isabelle_DOF/thys/RegExpInterface.thy",
"repo": "afp-2025-02-12",
"sha": "d670ae8f014aa415c781a41671b67cec074ac2ddb773c11a0b0f60276531cc2d"
} |
(* Title: Pre-Post Specifications and Modal Operators
Author: Walter Guttmann
Maintainer: Walter Guttmann <walter.guttmann at canterbury.ac.nz>
*)
section ‹Pre-Post Specifications and Modal Operators›
theory Pre_Post_Modal
imports Pre_Post Hoare_Modal
begin
class pre_post_spec_whiledo = pre_post_spe... | {
"path": "afp-2025-02-12/thys/Correctness_Algebras/Pre_Post_Modal.thy",
"repo": "afp-2025-02-12",
"sha": "a5046cf6a17f2921756d12a9f23dbf1a120642b1451dc12eb955b907315b45e4"
} |
theory SASP_Checker
imports SASP_Semantics
"HOL-Library.Code_Target_Nat"
begin
section ‹An Executable Checker for Multi-Valued Planning Problem Solutions›
subsection ‹Auxiliary Lemmas›
lemma map_of_leI:
assumes "distinct (map fst l)"
assumes "⋀k v. (k,v)∈set l ⟹ m k = Some v"
shows "map_of l ⊆⇩m m"... | {
"path": "afp-2025-02-12/thys/AI_Planning_Languages_Semantics/SASP_Checker.thy",
"repo": "afp-2025-02-12",
"sha": "c69da1afa368cc68c21cffdec6422b1e7a4e404d6442a39e8ce9b3d205657aee"
} |
(*
Author: Mohammad Abdulaziz, Fred Kurz
*)
theory STRIPS_Semantics
imports "STRIPS_Representation"
"List_Supplement"
"Map_Supplement"
begin
section "STRIPS Semantics"
text ‹ Having provided a concrete implementation of STRIPS and a corresponding locale ‹strips›, we
can now continue to define the semantics ... | {
"path": "afp-2025-02-12/thys/Verified_SAT_Based_AI_Planning/STRIPS_Semantics.thy",
"repo": "afp-2025-02-12",
"sha": "79dd3a05437f321f013673c4f393151fd5314e68a3ac1c9e580f74463a10c360"
} |
(* Title: Schutz_Spacetime/TemporalOrderOnPath.thy
Authors: Richard Schmoetten, Jake Palmer and Jacques D. Fleuriot
University of Edinburgh, 2021
*)
theory TemporalOrderOnPath
imports Minkowski "HOL-Library.Disjoint_Sets"
begin
text ‹
In Schutz \<^cite>‹‹pp.~18-30› in "schutz19... | {
"path": "afp-2025-02-12/thys/Schutz_Spacetime/TemporalOrderOnPath.thy",
"repo": "afp-2025-02-12",
"sha": "07d4b3e0867fce18333423d5fb2c0daaae4d9858c260d40fb290252bc16a7d20"
} |
(* Author: Tobias Nipkow, 2007 *)
section‹Presburger arithmetic›
theory PresArith
imports QE "HOL-Library.ListVector"
begin
declare iprod_assoc[simp]
subsection‹Syntax›
datatype atom =
Le int "int list" | Dvd int int "int list" | NDvd int int "int list"
fun divisor :: "atom ⇒ int" where
"divisor (Le i ks)... | {
"path": "afp-2025-02-12/thys/LinearQuantifierElim/Thys/PresArith.thy",
"repo": "afp-2025-02-12",
"sha": "830373c04ac558d846d8841f6c6f0dac70bf8a2f1c3371d416af86e1adf24303"
} |
(*
Title: Psi-calculi
Author/Maintainer: Jesper Bengtson (jebe@itu.dk), 2012
*)
theory Tau_Laws_Weak
imports Weaken_Bisimulation Weak_Congruence Tau_Sim Tau_Stat_Imp
begin
context weakTauLaws begin
lemma tauLaw1:
fixes Ψ :: 'b
and P :: "('a, 'b, 'c) psi"
shows "Ψ ⊳ τ.(P) ≈ P"
proof (-)
(*goal... | {
"path": "afp-2025-02-12/thys/Psi_Calculi/Tau_Laws_Weak.thy",
"repo": "afp-2025-02-12",
"sha": "94a5d1af9f5b8ce9fdc5c34e23e437845ae23a328434426ce94a52904b8fd798"
} |
(* Title: thys/DitherTM.thy
Author: Jian Xu, Xingyuan Zhang, and Christian Urban
Modifications: Sebastiaan Joosten
Further contributions by Franz Regensburger (FABR) 02/2022 :
* Re-ordering of sections;
Now, the dithering machine is discussed before the tm_copy machine
* Added comments
Editori... | {
"path": "afp-2025-02-12/thys/Universal_Turing_Machine/DitherTM.thy",
"repo": "afp-2025-02-12",
"sha": "76202fdd497982426276123e432a10a05dac0a53f64cb64bc9076b30366a76fb"
} |
(* Theory: Lovasz_Local_Lemma
Author: Chelsea Edmonds *)
section ‹Lovasz Local Lemma ›
theory Lovasz_Local_Lemma
imports
Basic_Method
"HOL-Real_Asymp.Real_Asymp"
Indep_Events
Digraph_Extensions
begin
subsection ‹Random Lemmas on Product Operator ›
lemma prod_constant_ge:
fixes y :: "'b :... | {
"path": "afp-2025-02-12/thys/Lovasz_Local/Lovasz_Local_Lemma.thy",
"repo": "afp-2025-02-12",
"sha": "7e8016e0212971e7c700260bf5f256d87498832679c0b1030ba1f2ebb5463df6"
} |
(*
Title: HOL/Analysis/FPS_Convergence.thy
Author: Manuel Eberl, TU München
Connection of formal power series and actual convergent power series on Banach spaces
(most notably the complex numbers).
*)
section ‹Convergence of Formal Power Series›
theory FPS_Convergence
imports
Generalised_Binomial_Th... | {
"path": "Isabelle2024/src/HOL/Analysis/FPS_Convergence.thy",
"repo": "Isabelle2024",
"sha": "cea1048a7a1e92c1f5a98a6e3582770d282c9d345169b866fc45dab95974aabc"
} |
(* The value setup for friendship status confidentiality *)
theory Friend_Value_Setup
imports "Friend_Openness"
begin
subsection ‹Value Setup›
context Friend
begin
datatype "value" =
FrVal bool ― ‹updated friendship status between ‹UID1› and ‹UID2››
| OVal bool ― ‹updated dynamic declassification trigger conditi... | {
"path": "afp-2025-02-12/thys/CoSMeDis/Friend_Confidentiality/Friend_Value_Setup.thy",
"repo": "afp-2025-02-12",
"sha": "97ecccc0075cac48e52167975623ed389c94c5370585173632268660d189fd47"
} |
theory Cones
imports
"HOL-Analysis.Analysis"
Triangle.Triangle
"../ODE_Auxiliarities"
begin
lemma arcsin_eq_zero_iff[simp]: "-1 ≤ x ⟹ x ≤ 1 ⟹ arcsin x = 0 ⟷ x = 0"
using sin_arcsin (*‹⟦- 1 ≤ ?y; ?y ≤ 1⟧ ⟹ sin (arcsin ?y) = ?y›*) by fastforce
definition conemem :: "'a::real_vector ⇒ 'a ⇒ real ⇒ 'a" where "co... | {
"path": "afp-2025-02-12/thys/Ordinary_Differential_Equations/IVP/Cones.thy",
"repo": "afp-2025-02-12",
"sha": "e36a2519331c2e0b88c9f1a721fba7bc0670e2e70a0afe1899297f3563a3a027"
} |
theory ResNormDirect
imports ResNormalForm
begin
section‹Direct Resource Term Normalisation›
text‹
In this section we define a normalisation procedure for resource terms that directly normalises a
term in a single bottom-up pass.
This could be considered normalisation by evaluation as opposed to by rewriting.... | {
"path": "afp-2025-02-12/thys/ProcessComposition/ResNormDirect.thy",
"repo": "afp-2025-02-12",
"sha": "7a88ceab69743083a589e19aad44a6996706e40d4474ceb0083580da5f6a8f22"
} |
(* Formalization adapted from:
Fabián Fernando Serrano Suárez, "Formalización en Isar de la
Meta-Lógica de Primer Orden." PhD thesis,
Departamento de Ciencias de la Computación e Inteligencia Artificial,
Universidad de Sevilla, Spain, 2012.
https://idus.us.es/handle/11441/57780. In Spanish *)
t... | {
"path": "afp-2025-02-12/thys/Prop_Compactness/PropCompactness.thy",
"repo": "afp-2025-02-12",
"sha": "f81d2369d200bd5c0e01105a931535aca3b923b3b37b906708baf2043a7da11c"
} |
(* Title: Quality_Increases.thy
License: BSD 2-Clause. See LICENSE.
Author: Timothy Bourke, Inria
*)
section "The quality increases predicate"
theory Quality_Increases
imports Aodv_Predicates Fresher
begin
definition quality_increases :: "state ⇒ state ⇒ bool"
where "quality_increases ξ ξ' ≡ ... | {
"path": "afp-2025-02-12/thys/AODV/Quality_Increases.thy",
"repo": "afp-2025-02-12",
"sha": "468208793b59d27d7ebfc79696bfbcffa2368c289ff3f955c55607cdcca43700"
} |
(* Title: HOL/Examples/Peirce.thy
Author: Makarius
*)
section ‹Peirce's Law›
theory Peirce
imports Main
begin
text ‹
We consider Peirce's Law: ‹((A ⟶ B) ⟶ A) ⟶ A›. This is an inherently
non-intuitionistic statement, so its proof will certainly involve some form
of classical contradiction.
Th... | {
"path": "Isabelle2024/src/HOL/Examples/Peirce.thy",
"repo": "Isabelle2024",
"sha": "c1c14c7e5141c72a5bc12290b60239518d75b39babcf85b608fe3ace9773f33e"
} |
(* Title: HOL/Induct/ABexp.thy
Author: Stefan Berghofer, TU Muenchen
*)
section ‹Arithmetic and boolean expressions›
theory ABexp
imports Main
begin
datatype 'a aexp =
IF "'a bexp" "'a aexp" "'a aexp"
| Sum "'a aexp" "'a aexp"
| Diff "'a aexp" "'a aexp"
| Var 'a
| Num nat
and 'a bexp =
... | {
"path": "Isabelle2024/src/HOL/Induct/ABexp.thy",
"repo": "Isabelle2024",
"sha": "a28bbcb56938dabc6422a814f11b7ef0cf1b4eac2af802c49f51e991cfe53250"
} |
(* Title: JinjaThreads/JVM/JVMDefensive.thy
Author: Andreas Lochbihler
*)
section ‹Instantiating the framework semantics with the JVM›
theory JVMThreaded
imports
JVMDefensive
"../Common/ConformThreaded"
"../Framework/FWLiftingSem"
"../Framework/FWProgressAux"
begin
primrec JVM_final :: "'addr j... | {
"path": "afp-2025-02-12/thys/JinjaThreads/JVM/JVMThreaded.thy",
"repo": "afp-2025-02-12",
"sha": "a1c13de5279af88b56b9e95009b5bca4e792072d65dca020eaaecf823833312c"
} |
section ‹The Free Group›
theory "FreeGroups"
imports
"HOL-Algebra.Group"
Cancelation
Generators
begin
text ‹
Based on the work in @{theory "Free-Groups.Cancelation"}, the free group is now easily defined
over the set of fully canceled words with the corresponding operations.
›
subsection ‹Inversion›
text ‹... | {
"path": "afp-2025-02-12/thys/Free-Groups/FreeGroups.thy",
"repo": "afp-2025-02-12",
"sha": "0e131fba3db27198a4ebcb55430002c3e39cd64b2175f4bd51a13955239115a4"
} |
theory Iterate_GPV imports
"HOL-Library.BNF_Axiomatization"
"HOL-Library.BNF_Corec"
begin
declare [[typedef_overloaded]]
datatype 'a spmf = return_spmf 'a
primrec (transfer) bind_spmf where
"bind_spmf (return_spmf a) f = f a"
datatype (generat_pures: 'a, generat_outs: 'b, generat_conts: 'c) generat
= Pure (... | {
"path": "Isabelle2024/src/HOL/Corec_Examples/Tests/Iterate_GPV.thy",
"repo": "Isabelle2024",
"sha": "93085e37fa14c0b4220d06434320ac4d3a9affcc0923ed2a8eadffe5e51c5da5"
} |
(*
Formalization by Cárolos Laméris
Note that
bojanczyk2014automata ~
BojaÅczyk, M., Klin, B., & Lasota, S. (2014).
Automata theory in nominal sets.
Logical Methods in Computer Science, 10.
( https://lmcs.episciences.org/1157 )
*)
section ‹
Myhill-Nerode Theorem for $G$-automata
›
text ... | {
"path": "afp-2025-02-12/thys/Nominal_Myhill_Nerode/Nominal_Myhill_Nerode.thy",
"repo": "afp-2025-02-12",
"sha": "7bfc6024b0d5427e02c3ae664fe4bc821257186a36d4d06cce070ba260782d2c"
} |
subsection ‹Monotone Convergence \label{sec:monconv}›
theory MonConv
imports Complex_Main
begin
text ‹A sensible requirement for an integral operator is that it be
``well-behaved'' with respect to limit functions. To become just a
little more
precise, it is expected that the limit operator may be interchanged
... | {
"path": "afp-2025-02-12/thys/Integration/MonConv.thy",
"repo": "afp-2025-02-12",
"sha": "feac20bb5b701a5d4037e26cf55c6dca7e57ca059b24a8c1d29bd8be7cf9def7"
} |
section ‹Static data dependence›
theory DataDependence imports "../Basic/DynDataDependence" begin
context CFG_wf begin
definition data_dependence :: "'node ⇒ 'var ⇒ 'node ⇒ bool"
("_ influences _ in _" [51,0])
where data_dependences_eq:"n influences V in n' ≡ ∃as. n influences V in n' via as"
lemma data_depende... | {
"path": "afp-2025-02-12/thys/Slicing/StaticIntra/DataDependence.thy",
"repo": "afp-2025-02-12",
"sha": "ceb817c2a681602a1a85737d1b549f7157ce23726380cd5a4935f872216b9cd4"
} |
(* Title: JinjaDCI/J/DefAss.thy
Author: Tobias Nipkow, Susannah Mansky
Copyright 2003 Technische Universitaet Muenchen, 2019-20 UIUC
Based on the Jinja theory J/DefAss.thy by Tobias Nipkow
*)
section ‹ Definite assignment ›
theory DefAss imports BigStep begin
subsection "Hypersets"
type_syn... | {
"path": "afp-2025-02-12/thys/JinjaDCI/J/DefAss.thy",
"repo": "afp-2025-02-12",
"sha": "7855f00146a1cf401480cde1fbf066807b5cf4e8702f93a51f3be507aa6d9a08"
} |
theory Interfaces_Normalize
imports Common_Primitive_Lemmas
begin
subsection‹Optimizing interfaces in match expressions›
(*returns: (list of positive interfaces × a list of negated interfaces)
it matches the conjunction of both
None if the expression cannot match*)
definition compress_interfaces :: "ifa... | {
"path": "afp-2025-02-12/thys/Iptables_Semantics/Primitive_Matchers/Interfaces_Normalize.thy",
"repo": "afp-2025-02-12",
"sha": "655aa6ce68b7cd94be7b5fd915381b9d5de011b36ff6f9954e54625d4c902ca8"
} |
(* Title: Isabelle Collections Library
Author: Peter Lammich <peter dot lammich at uni-muenster.de>
Maintainer: Peter Lammich <peter dot lammich at uni-muenster.de>
*)
section ‹\isaheader{Specification of Maps}›
theory MapSpec
imports ICF_Spec_Base
begin
text_raw‹\label{thy:MapSpec}›
(*@intf Map
... | {
"path": "afp-2025-02-12/thys/Collections/ICF/spec/MapSpec.thy",
"repo": "afp-2025-02-12",
"sha": "6568d5afacc0128c56e5fc6ca68e165b78186a8c64bd5a2ec7bbdbf839bcbc6b"
} |
(* Title: A locale for and a characterization of maximal normal subgroups
Author: Jakob von Raumer, Karlsruhe Institute of Technology
Maintainer: Jakob von Raumer <jakob.raumer@student.kit.edu>
*)
theory MaximalNormalSubgroups
imports "HOL-Algebra.Algebra"
begin
section ‹Facts about maximal normal s... | {
"path": "afp-2025-02-12/thys/Jordan_Hoelder/MaximalNormalSubgroups.thy",
"repo": "afp-2025-02-12",
"sha": "bd293331c18b54ddbe4d03192ff6ba3dcde4346905f9bf30211cc1d39c606117"
} |
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