From ae259df54be7d1281316fff682b8102a914b327a Mon Sep 17 00:00:00 2001 From: Inigo Incer Date: Fri, 17 Feb 2023 18:30:08 -0800 Subject: [PATCH 01/16] minor --- docs/uses.ipynb | 20 ++++++++++++++++++++ 1 file changed, 20 insertions(+) create mode 100644 docs/uses.ipynb diff --git a/docs/uses.ipynb b/docs/uses.ipynb new file mode 100644 index 00000000..35758c5e --- /dev/null +++ b/docs/uses.ipynb @@ -0,0 +1,20 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Pacti helps designers to manipulate and reason about specifications. These specifications are given as assume-guarantee contracts. Every contract is a pair of requiremems of the form (assumptions, guarantees). " + ] + } + ], + "metadata": { + "language_info": { + "name": "python" + }, + "orig_nbformat": 4 + }, + "nbformat": 4, + "nbformat_minor": 2 +} From 5c382104304d84e7394c010ed14a4939d2850e46 Mon Sep 17 00:00:00 2001 From: Inigo Incer Date: Sat, 18 Feb 2023 09:09:01 -0800 Subject: [PATCH 02/16] minor --- docs/uses.ipynb | 17 ++++++++++++++--- 1 file changed, 14 insertions(+), 3 deletions(-) diff --git a/docs/uses.ipynb b/docs/uses.ipynb index 35758c5e..7f079701 100644 --- a/docs/uses.ipynb +++ b/docs/uses.ipynb @@ -5,15 +5,26 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Pacti helps designers to manipulate and reason about specifications. These specifications are given as assume-guarantee contracts. Every contract is a pair of requiremems of the form (assumptions, guarantees). " + "Pacti helps designers to manipulate and reason about specifications. These specifications are given as assume-guarantee contracts. Every contract is a pair of requirements of the form (assumptions, guarantees). " ] } ], "metadata": { + "kernelspec": { + "display_name": ".venv", + "language": "python", + "name": "python3" + }, "language_info": { - "name": "python" + "name": "python", + "version": "3.10.7" }, - "orig_nbformat": 4 + "orig_nbformat": 4, + "vscode": { + "interpreter": { + "hash": "b282b3e35ff361393169c4f355db145ffcb63e574f57c9818c827b7c99ca9fc3" + } + } }, "nbformat": 4, "nbformat_minor": 2 From 31bf2143f4e34cf20d8aa9a929c1280b2a20ca48 Mon Sep 17 00:00:00 2001 From: Inigo Incer Date: Sat, 18 Feb 2023 12:25:15 -0800 Subject: [PATCH 03/16] rename --- docs/{uses.ipynb => getting_started.ipynb} | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename docs/{uses.ipynb => getting_started.ipynb} (100%) diff --git a/docs/uses.ipynb b/docs/getting_started.ipynb similarity index 100% rename from docs/uses.ipynb rename to docs/getting_started.ipynb From 311af3828abfae52b07a756bd85cf0b3384f9a3a Mon Sep 17 00:00:00 2001 From: Inigo Incer Date: Sat, 18 Feb 2023 17:17:18 -0800 Subject: [PATCH 04/16] minor --- docs/getting_started.ipynb | 8 +++++++- examples/wip/contract_satisfaction.py | 29 +++++++++++++++++++++++++++ mkdocs.yml | 3 ++- 3 files changed, 38 insertions(+), 2 deletions(-) create mode 100644 examples/wip/contract_satisfaction.py diff --git a/docs/getting_started.ipynb b/docs/getting_started.ipynb index 7f079701..38868846 100644 --- a/docs/getting_started.ipynb +++ b/docs/getting_started.ipynb @@ -5,7 +5,13 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Pacti helps designers to manipulate and reason about specifications. These specifications are given as assume-guarantee contracts. Every contract is a pair of requirements of the form (assumptions, guarantees). " + "Pacti helps designers to manipulate and reason about specifications. These specifications are given as assume-guarantee contracts. Every contract is a pair of requirements of the form (assumptions, guarantees). \n", + "\n", + "\n", + " \n", + " \n", + " \"Logo\n", + "\n" ] } ], diff --git a/examples/wip/contract_satisfaction.py b/examples/wip/contract_satisfaction.py new file mode 100644 index 00000000..e164d0e4 --- /dev/null +++ b/examples/wip/contract_satisfaction.py @@ -0,0 +1,29 @@ + +from pacti.terms.polyhedra import PolyhedralContract, PolyhedralTermList, PolyhedralTerm +from pacti.iocontract import Var + + +contract = PolyhedralContract.from_string( + InputVars=["x"], + OutputVars=["y"], + assumptions=["x <= 2"], + guarantees=["2x + 3y <= 7", "2y - 3x <= 8"]) +print(contract) + +x = Var("x") +y = Var("y") +print(contract.a.contains_behavior({x:5})) +print(contract.a.contains_behavior({x:0})) +print(contract.g.contains_behavior({x:0, y:2})) +print(contract.g.contains_behavior({x:0, y:5})) + + +# now verify component +t1 = PolyhedralTerm(variables={x:1},constant=3) +t2 = PolyhedralTerm(variables={x:-1},constant=-3) +t3 = PolyhedralTerm(variables={y:1},constant=2) +t4 = PolyhedralTerm(variables={y:-1},constant=-2) +component = PolyhedralTermList([t1,t2,t3,t4]) + +print(contract.contains_environment(component)) +print(contract.contains_implementation(component)) \ No newline at end of file diff --git a/mkdocs.yml b/mkdocs.yml index fddb1dc7..69669f54 100644 --- a/mkdocs.yml +++ b/mkdocs.yml @@ -10,6 +10,7 @@ nav: - Home: - Overview: index.md - Getting started: getting_started.md + - Features: getting_started.ipynb - Changelog: changelog.md - Credits: credits.md - License: license.md @@ -21,7 +22,7 @@ nav: - Multi-agent Coordination: _case_studies/multiagent_coordination/multiagent.ipynb - Signal Processing in Digital ICs: _case_studies/digital_signal_processing/dsp_wl.ipynb - Synthetic Biology: _case_studies/biocircuit_specifications/specification_based_synthetic_biology.ipynb -- Documentation: #reference/ +- API: #reference/ - IoContract: iocontract.md - PolyhedralTerms : Polyhedral.md - Development: From 1b84964e5a865c26146195d7229ba11ffa9a5e83 Mon Sep 17 00:00:00 2001 From: Inigo Incer Date: Sun, 19 Feb 2023 09:43:34 -0800 Subject: [PATCH 05/16] rename --- docs/{getting_started.md => installing.md} | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename docs/{getting_started.md => installing.md} (100%) diff --git a/docs/getting_started.md b/docs/installing.md similarity index 100% rename from docs/getting_started.md rename to docs/installing.md From cc28d7c20c47d5d31804cd975d64e7cbd69c32ee Mon Sep 17 00:00:00 2001 From: Inigo Incer Date: Sun, 19 Feb 2023 09:43:52 -0800 Subject: [PATCH 06/16] rename --- mkdocs.yml | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/mkdocs.yml b/mkdocs.yml index 69669f54..ac0a8ef1 100644 --- a/mkdocs.yml +++ b/mkdocs.yml @@ -9,8 +9,8 @@ watch: [README.md, CONTRIBUTING.md, CHANGELOG.md, src/pacti] nav: - Home: - Overview: index.md - - Getting started: getting_started.md - - Features: getting_started.ipynb + - Installing: installing.md + - Getting Started: getting_started.ipynb - Changelog: changelog.md - Credits: credits.md - License: license.md @@ -109,4 +109,4 @@ plugins: extra: social: - icon: fontawesome/brands/github - link: https://github.com/github_username + link: https://github.com/FormalSystems From acec452808cfe17c1ddadd281c8f2c6bf3272bc2 Mon Sep 17 00:00:00 2001 From: Inigo Incer Date: Sun, 19 Feb 2023 09:44:03 -0800 Subject: [PATCH 07/16] hide edit button from webpage --- docs/css/material.css | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/docs/css/material.css b/docs/css/material.css index 9e8c14a6..b5fb7fbf 100644 --- a/docs/css/material.css +++ b/docs/css/material.css @@ -2,3 +2,8 @@ .md-main__inner { margin-bottom: 1.5rem; } + + +.md-content__button { + display: none; +} \ No newline at end of file From 113510a2bc8d14b104a51d8a2ca357308bad85c2 Mon Sep 17 00:00:00 2001 From: Inigo Incer Date: Sun, 19 Feb 2023 15:47:07 -0800 Subject: [PATCH 08/16] Many edits --- docs/getting_started.ipynb | 207 ++- .../circuit_series_composition_background.ai | 1536 +++++++++++++++ .../circuit_series_quotient_background.ai | 1644 +++++++++++++++++ .../circuit_series_composition_background.svg | 1 + .../circuit_series_quotient_background.svg | 1 + 5 files changed, 3383 insertions(+), 6 deletions(-) create mode 100644 docs/source/_static/circuit_series_composition_background.ai create mode 100644 docs/source/_static/circuit_series_quotient_background.ai create mode 100644 docs/source/_static/exports/circuit_series_composition_background.svg create mode 100644 docs/source/_static/exports/circuit_series_quotient_background.svg diff --git a/docs/getting_started.ipynb b/docs/getting_started.ipynb index 38868846..48ce6bde 100644 --- a/docs/getting_started.ipynb +++ b/docs/getting_started.ipynb @@ -5,14 +5,201 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Pacti helps designers to manipulate and reason about specifications. These specifications are given as assume-guarantee contracts. Every contract is a pair of requirements of the form (assumptions, guarantees). \n", + "# Introduction\n", "\n", - "\n", - " \n", - " \n", - " \"Logo\n", - "\n" + "Pacti helps designers to reason about specifications and to manipulate them. These specifications are given to Pacti as assume-guarantee contracts, which are requirements of the form (assumptions, guarantees).\n", + "\n", + "For Pacti, every contract has four elements:\n", + "- Input variables\n", + "- Output variables\n", + "- Assumptions\n", + "- Guarantees\n", + "\n", + "The assumptions of a contract are only allowed to refer to the input variables. Guarantees are only allowed to refer to the input and output variables of the contract, i.e., no variables outside the interface of the contract may appear in the assumptions or guarantees.\n", + "\n", + "The algebra of contracts has been extensively researched. This algebra allows us to compute new specifications from existing contracts. For example,\n", + "- The operation of composition allows us to compute the specification of the system formed by composing subsystems obeying the specifications being composed. In other words, composition is the system-building operation.\n", + "- The operation of quotient allows us to compute the specification of a component that needs to be composed with an existing subsystem so that the resulting system meets a top-level specification. Quotient is used to find missing-component specifications.\n", + "- The operation of merging is used to generate a single contract that simultaneously enforces the assumptions and guarantees of the contracts being merged. This is used to fuse contract viewpoints in concurrent design.\n", + "\n", + "### Computing system specifications\n", + "\n", + "\n", + "Consider the following system:\n", + "\n", + "
\n", + "\n", + "
\n", + "\n", + "Components $M$ and $M'$ obey, respectively, contracts $C = (|i| \\le 2, o \\le i \\le 2o + 2)$ and $C' = (-1 \\le o \\le 1/5, o' \\le o)$. We can use Pacti to obtain the specification of the system that comprises these two components as follows: " + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "InVars: [i]\n", + "OutVars:[o_p]\n", + "A: [\n", + " i <= 0.19999999999999996\n", + " -0.5 i <= 0.0\n", + "]\n", + "G: [\n", + " -i + o_p <= 0.0\n", + "]\n" + ] + } + ], + "source": [ + "from pacti.terms.polyhedra import PolyhedralContract\n", + "\n", + "contract1 = PolyhedralContract.from_string(\n", + " InputVars=[\"i\"],\n", + " OutputVars=[\"o\"],\n", + " assumptions=[\"|i| <= 2\"],\n", + " guarantees=[\"o - i <= 0\", \"i - 2o <= 2\"])\n", + "\n", + "contract2 = PolyhedralContract.from_string(\n", + " InputVars=[\"o\"],\n", + " OutputVars=[\"o_p\"],\n", + " assumptions=[\"o <= 0.2\", \"-o <= 1\"],\n", + " guarantees=[\"o_p - o <= 0\"])\n", + "\n", + "system_contract = contract1.compose(contract2)\n", + "print(system_contract)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Pacti gives us the specification of the system. Note that the resulting contract only involves the top-level inputs and outputs.\n", + "\n", + "\n", + "### System diagnostics\n", + "\n", + "Suppose that we are trying to build a system as shown in the figure above with the same specification $C'$ for $M'$. Suppose that now the specification $C_n$ for $M$ is $(|i| <= 2, |o| <= 3)$." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "ename": "ValueError", + "evalue": "The guarantees \n[\n |o| <= 3.0\n]\nwere insufficient to abduce the assumptions \n[\n o <= 0.2\n -o <= 1.0\n]\nby eliminating the variables \n[, ]", + "output_type": "error", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[1;31mValueError\u001b[0m Traceback (most recent call last)", + "Cell \u001b[1;32mIn[2], line 7\u001b[0m\n\u001b[0;32m 1\u001b[0m contract1_n \u001b[39m=\u001b[39m PolyhedralContract\u001b[39m.\u001b[39mfrom_string(\n\u001b[0;32m 2\u001b[0m InputVars\u001b[39m=\u001b[39m[\u001b[39m\"\u001b[39m\u001b[39mi\u001b[39m\u001b[39m\"\u001b[39m],\n\u001b[0;32m 3\u001b[0m OutputVars\u001b[39m=\u001b[39m[\u001b[39m\"\u001b[39m\u001b[39mo\u001b[39m\u001b[39m\"\u001b[39m],\n\u001b[0;32m 4\u001b[0m assumptions\u001b[39m=\u001b[39m[\u001b[39m\"\u001b[39m\u001b[39m|i| <= 2\u001b[39m\u001b[39m\"\u001b[39m],\n\u001b[0;32m 5\u001b[0m guarantees\u001b[39m=\u001b[39m[\u001b[39m\"\u001b[39m\u001b[39m|o| <= 3\u001b[39m\u001b[39m\"\u001b[39m])\n\u001b[1;32m----> 7\u001b[0m contract_system \u001b[39m=\u001b[39m contract1_n\u001b[39m.\u001b[39;49mcompose(contract2)\n", + "File \u001b[1;32m~\\iir_repo\\pacti\\src\\pacti\\iocontract\\iocontract.py:458\u001b[0m, in \u001b[0;36mIoContract.compose\u001b[1;34m(self, other)\u001b[0m\n\u001b[0;32m 456\u001b[0m new_a \u001b[39m=\u001b[39m other\u001b[39m.\u001b[39ma\u001b[39m.\u001b[39mabduce_with_context(\u001b[39mself\u001b[39m\u001b[39m.\u001b[39ma \u001b[39m|\u001b[39m \u001b[39mself\u001b[39m\u001b[39m.\u001b[39mg, assumptions_forbidden_vars)\n\u001b[0;32m 457\u001b[0m \u001b[39mif\u001b[39;00m list_intersection(new_a\u001b[39m.\u001b[39mvars, assumptions_forbidden_vars):\n\u001b[1;32m--> 458\u001b[0m \u001b[39mraise\u001b[39;00m \u001b[39mValueError\u001b[39;00m(\n\u001b[0;32m 459\u001b[0m \u001b[39m\"\u001b[39m\u001b[39mThe guarantees \u001b[39m\u001b[39m\\n\u001b[39;00m\u001b[39m{}\u001b[39;00m\u001b[39m\\n\u001b[39;00m\u001b[39m\"\u001b[39m\u001b[39m.\u001b[39mformat(\u001b[39mself\u001b[39m\u001b[39m.\u001b[39mg)\n\u001b[0;32m 460\u001b[0m \u001b[39m+\u001b[39m \u001b[39m\"\u001b[39m\u001b[39mwere insufficient to abduce the assumptions \u001b[39m\u001b[39m\\n\u001b[39;00m\u001b[39m{}\u001b[39;00m\u001b[39m\\n\u001b[39;00m\u001b[39m\"\u001b[39m\u001b[39m.\u001b[39mformat(other\u001b[39m.\u001b[39ma)\n\u001b[0;32m 461\u001b[0m \u001b[39m+\u001b[39m \u001b[39m\"\u001b[39m\u001b[39mby eliminating the variables \u001b[39m\u001b[39m\\n\u001b[39;00m\u001b[39m{}\u001b[39;00m\u001b[39m\"\u001b[39m\u001b[39m.\u001b[39mformat(assumptions_forbidden_vars)\n\u001b[0;32m 462\u001b[0m )\n\u001b[0;32m 463\u001b[0m assumptions \u001b[39m=\u001b[39m new_a \u001b[39m|\u001b[39m \u001b[39mself\u001b[39m\u001b[39m.\u001b[39ma\n\u001b[0;32m 464\u001b[0m \u001b[39melif\u001b[39;00m other_helps_self \u001b[39mand\u001b[39;00m \u001b[39mnot\u001b[39;00m self_helps_other:\n", + "\u001b[1;31mValueError\u001b[0m: The guarantees \n[\n |o| <= 3.0\n]\nwere insufficient to abduce the assumptions \n[\n o <= 0.2\n -o <= 1.0\n]\nby eliminating the variables \n[, ]" + ] + } + ], + "source": [ + "contract1_n = PolyhedralContract.from_string(\n", + " InputVars=[\"i\"],\n", + " OutputVars=[\"o\"],\n", + " assumptions=[\"|i| <= 2\"],\n", + " guarantees=[\"|o| <= 3\"])\n", + "\n", + "contract_system = contract1_n.compose(contract2)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Pacti is unable to compute a system specification. In this case, this is due to the fact that our guarantee $|o| \\le 3$ for $M$ does not satisfy the assumptions of $C'$." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Quotient\n", + "\n", + "Now consider the situation shown in the following diagram:\n", + "\n", + "
\n", + "\n", + "
" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We wish to implement a system $M$ with specification $C = (|i| \\le 1, o' = 2i + 1)$, and to do this we have available a component $M'$ with specification $C' = (|i| \\le 2, o = 2i)$. We use the quotient operation in Pacti to obtain the specification of the component that we are missing--that would fill the question mark--so that the resulting object meets the specification $C$." ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "contract_top_level = PolyhedralContract.from_string(\n", + " InputVars=[\"i\"],\n", + " OutputVars=[\"o_p\"],\n", + " assumptions=[\"|i| <= 1\"],\n", + " guarantees=[\"o_p - 2i = 1\"])\n", + "\n", + "contract_existing_component = PolyhedralContract.from_string(\n", + " InputVars=[\"i\"],\n", + " OutputVars=[\"o\"],\n", + " assumptions=[\"|i| <= 2\"],\n", + " guarantees=[\"o - 2i = 0\"])\n", + "\n", + "contract_missing_object = contract_top_level.quotient(contract_existing_component)\n", + "print(contract_missing_object)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Observe that Pacti tells us that the missing component's specification has input $o$ and output $o'$. The resulting specification is guaranteed to implement the top-level system when composed with the contract of the existing component. We can verify this:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# compose quotient \n", + "new_system_object = contract_missing_object.compose(contract_existing_component)\n", + "print(new_system_object.refines(contract_top_level))" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### To learn more\n", + "\n", + "This introductory examples show some of the analysis tasks we can carry out with Pacti. We have developed several case studies that discuss the application of Pacti in various design disciplines." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [] } ], "metadata": { @@ -22,7 +209,15 @@ "name": "python3" }, "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", "version": "3.10.7" }, "orig_nbformat": 4, diff --git a/docs/source/_static/circuit_series_composition_background.ai b/docs/source/_static/circuit_series_composition_background.ai new file mode 100644 index 00000000..4602d876 --- /dev/null +++ b/docs/source/_static/circuit_series_composition_background.ai @@ -0,0 +1,1536 @@ +%PDF-1.6 % +1 0 obj <>/OCGs[23 0 R]>>/Pages 3 0 R/Type/Catalog>> endobj 2 0 obj <>stream + + + + + application/pdf + + + circuit_series_composition_background + + + Adobe Illustrator 26.5 (Windows) + 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GG$'N,~(@, zkWJ ʙ,uRS)7/I~$WJ \Ҋ@q +R-5!(LZQs<b\hmN/͸x0L3pn03UW~ +#?="t +})KBHmr Fv"uP +.Z +Ziwհ&$Ps2[/A/_ocR/HK/YQB,:T騄)wQ7.@eyYSh?}&܏aq[.1 "60!FmQ8米VS)V{~QV K (:M2R*$,ݮlaVr1elQȪWQpܚX,=-\UsƍMXwOފyݡF&߄QlCL!_2-9&9"pF6Rp9~(=kMLAnpU%PeNJD[cC@1vb^)E4>)Vߐ-/@4 f#(RL1S1diފbZ;w4TObv^,;X[=렏#N$ ;6X噪Nu?ew+-|$L*ǽ/NaצUOwͷ)ԐU_CBӯ +[TXQJN$|k+ 麱gFEweMPAΦT[jBwcg/DzS j텸q*  C~'\ SH'BR؟I$D.M N4šd;\* y+)tf  Һ 4Jb %4JU _P@ZB G9s\-HaUn +r <`6@AFݒ꒦GGƫ+l,&Mn]z [Mr$%S&kf)7V>Ѭ-v)FU= bF=^%Ui \Z 59 -蝦A"Sg%<ڭSIzI̸JPZ.5*xÏ2lHMYǶ[,nG\=n-t~2χkn~9a_LMMf/ۥBEɵS2M_-|S{p${)+ oE2R9&UZM̚Z\$S/xO+"A3qJASIUf@x'ݮ@ܢxy|PRFBWCF ۇ\Y"2hNS}mpCr9}WQ_exDn|Åe|KĔHAM-h뽎+Rł; %Fv&J;yUD)tiIp/@]GzpGYͬƏ$Օqwv\OqߗR>bPͤp{"j0&ne2zTx̀UqMUsdN wUgNcT. \C* 4*b#{^NRW/TNU.yeРN\ vr <#+6,)8ڠC,ZCg MC 4P瑣-zߛs3|!vzEeL5MAĶ{j=˿i:'9Q=4 +덵yѤLLyiExݼ:^RpS$\%C2y:p8_R+%\ʇ )/)~৹XR%kgB,KjVpL`4|SM蚆d b1>~`glUh񰶣)`6lg2 |P!R1uB n,sNw,ӶYE:XDfc"#E@H##!D$CwGDOζ6' B5̒H!&$; ^WܷG\b2 ܶƿUfn~,0gI;0(r|Fu7gì3w[ yHDNN>Se>VfrAO?6 ˩]I C2H"饌!9>TbR3Tڭ͠0G, FcIMx%H)uwUMJJ18P<&׹6NLDEw$ mk=9 d0rF6N޽Rӥ +?AqDE4:j +f]h>Xf[g"x*w+}`/n +uyhCDy_t*۴:: +no%Te\!s][Qp_s?퐳ȟ[MF7QAS9LxBoC!)Ae3L,ۈ0j + vh ƎdHGGOxP@s#S~۠[#|x(ujˈp3ē:jL+!`ʊO֚pLma!]&P I.+! m$FH+?H Y=7lkPrv(Sl<˱j#W]Tk:'ov5 nr.\2ܯ=*Z!DeR°K} +Xg;w`ʨ|6DV3Lp?N B:0ZNBEԸe%ėa"k-%<$;(娽 3U(Q3ՐZb:4u|ON]K~ta?R +5"B\'j?҂ +YQP4y}*(-C0MVayqѹYi4t!4HE!'K&ďGTq#>tOd-PvaC$G] '!6Vg+}^HǠwAWB`KUk .+_MP3!~g?-iTdz.U,KYI@QWߏxϊW%c9WZ;\ Ŵ_+<N *YG~݈φC0jMJ}yhMFY& RU>v<.;UcVQ霣cq(7Ǧ­(guM̽.ߵM` 6{I_<5}_}eR rgecW;(T!#g%w(*x%AIͱ8yc! qiyRRC(dDR# bgKYa:qKt9) &щFj(Sq3<\elmq&>3AMdN`ufƘ8. :upQ Vg[|q+Gkl~ 3Nkn0r$+c1% #d G KE ϼQx,y=в͂Bp.o[Ԝ-\& {2ۦ.2E'7Z)5+~ 3@]njN= hPTZ5q +{#N{M8KCS[EQ>&sY:}TF[?AeSOYD*y +bz +BɠlJ]k#}P {0/:é*S1ȓ?r+ôاv_RBDSUέ댭q\9HeExةVB{m3삀ͺ,c[q&jظ9d]cSMVI={:0{.:H1\ eϝǹ\\ӥyjN_5EvLA#C] 4c5Hg"9rF.|b4 .+}k*:|Yqme0yZ`Q  4PD% hj_o nUiA)#ZM6\"cmykpW $D \Hb3rbqwE'e? Rx|ǭ{M8B rvΘ+`w,&oc$F:P6yebng}n ynpڎ{/.vB>SEA~GXCOU3SQ8#Ha@).*p"P:2RyyxD/1>֌$ +'CI+w8za}+GSt (Mqٜ9:fw `ǥW*Zȥ9= y;~ ~Dlg׫Ph `SF̢F+"Z(rgÆaP grj_+3uQ +әT )YN%X{aڌaR;CZ.,~>g<ݬM6f{ySL|TU@qkI7|3\GɎ$U9WGjGnhn-^W\ @A1&VNטŤLXˎ5;űifC +s5Oh+ J*\Z2<E^7>DAľL|f]4s}=RIQKR#Ü>[]@]%Am> _A-+B{SE[q2VםޫJ dK_Ls iik$x>j@d]x?ږE 9(=r*`(榇AT MRa zlnrncjNcK袐NK {`bP+5=<㬊Ɇo[bP4v$ӣXÅ#,d/`y zź#t@2~sd 4;."6F-%ha˕]L?* >4? BpbwZјNqZȯE s&Ir"B%YgzpYaJnO*Ì )if(yIhóu|#pZbOzqUh]#,kZS]^Q0_(B fmFy*֙%G 䎏fpFjW8Rx۽ uj./$FA LZxTQ)c zh;Qe8Fbd\ǎp.o`:4RDޅ; +p%#8vfEp |kEtYZߠ + =I):~uR 2]O:\s\)mg6yZӹV Bbg&/x+^_PJߜ {_WH' rM~Y$DjO 2;`z F=*/~ʜN0* <~!iLږ#_oCgƽ?Ub>܋sa&e0-TԨWmnP\F-VwG s +F^&}1~ˡ!k @=V5zo#l8(RV:H6 ^H [5I}>9@L&=Ҙ"!>.٫H>r[衛#&I%~ QUїx(6UDqvf24 + +endstream endobj 25 0 obj [24 0 R] endobj 39 0 obj <> endobj xref +0 40 +0000000004 65535 f +0000000016 00000 n +0000000147 00000 n +0000042879 00000 n +0000000000 00000 f +0000042930 00000 n +0000000000 00000 f +0000087955 00000 n +0000000000 00000 f +0000000000 00000 f +0000000000 00000 f +0000000000 00000 f +0000000000 00000 f +0000000000 00000 f +0000000000 00000 f +0000000000 00000 f +0000088028 00000 n +0000088224 00000 n +0000089763 00000 n +0000155352 00000 n +0000220941 00000 n +0000000000 00000 f +0000045334 00000 n +0000045652 00000 n +0000045147 00000 n +0000264149 00000 n +0000043365 00000 n +0000085271 00000 n +0000085158 00000 n +0000043982 00000 n +0000044585 00000 n +0000044633 00000 n +0000045218 00000 n +0000045249 00000 n +0000066734 00000 n +0000045818 00000 n +0000046085 00000 n +0000067010 00000 n +0000085306 00000 n +0000264174 00000 n +trailer +<<54DF59721EB1C942AB0B96144E75D385>]>> +startxref +264386 +%%EOF diff --git a/docs/source/_static/exports/circuit_series_composition_background.svg b/docs/source/_static/exports/circuit_series_composition_background.svg new file mode 100644 index 00000000..e022a88e --- /dev/null +++ b/docs/source/_static/exports/circuit_series_composition_background.svg @@ -0,0 +1 @@ + \ No newline at end of file diff --git a/docs/source/_static/exports/circuit_series_quotient_background.svg b/docs/source/_static/exports/circuit_series_quotient_background.svg new file mode 100644 index 00000000..28567136 --- /dev/null +++ b/docs/source/_static/exports/circuit_series_quotient_background.svg @@ -0,0 +1 @@ + \ No newline at end of file From 61aaf7247b6d8ca2f3282b6072240daa8d7511d1 Mon Sep 17 00:00:00 2001 From: Inigo Incer Date: Sun, 19 Feb 2023 16:02:51 -0800 Subject: [PATCH 09/16] minor --- docs/getting_started.ipynb | 46 +- .../circuit_series_composition_background.ai | 1642 ++++++++-------- .../circuit_series_quotient_background.ai | 1679 +++++++++-------- .../circuit_series_composition_background.svg | 2 +- .../circuit_series_quotient_background.svg | 2 +- 5 files changed, 1697 insertions(+), 1674 deletions(-) diff --git a/docs/getting_started.ipynb b/docs/getting_started.ipynb index 48ce6bde..626693ba 100644 --- a/docs/getting_started.ipynb +++ b/docs/getting_started.ipynb @@ -27,34 +27,17 @@ "\n", "Consider the following system:\n", "\n", - "

\n", + "\n", + "![image](source/_static/exports/circuit_series_composition_background.svg)\n", "\n", "Components $M$ and $M'$ obey, respectively, contracts $C = (|i| \\le 2, o \\le i \\le 2o + 2)$ and $C' = (-1 \\le o \\le 1/5, o' \\le o)$. We can use Pacti to obtain the specification of the system that comprises these two components as follows: " ] }, { "cell_type": "code", - "execution_count": 1, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "InVars: [i]\n", - "OutVars:[o_p]\n", - "A: [\n", - " i <= 0.19999999999999996\n", - " -0.5 i <= 0.0\n", - "]\n", - "G: [\n", - " -i + o_p <= 0.0\n", - "]\n" - ] - } - ], + "outputs": [], "source": [ "from pacti.terms.polyhedra import PolyhedralContract\n", "\n", @@ -89,22 +72,9 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "ename": "ValueError", - "evalue": "The guarantees \n[\n |o| <= 3.0\n]\nwere insufficient to abduce the assumptions \n[\n o <= 0.2\n -o <= 1.0\n]\nby eliminating the variables \n[, ]", - "output_type": "error", - "traceback": [ - "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[1;31mValueError\u001b[0m Traceback (most recent call last)", - "Cell \u001b[1;32mIn[2], line 7\u001b[0m\n\u001b[0;32m 1\u001b[0m contract1_n \u001b[39m=\u001b[39m PolyhedralContract\u001b[39m.\u001b[39mfrom_string(\n\u001b[0;32m 2\u001b[0m InputVars\u001b[39m=\u001b[39m[\u001b[39m\"\u001b[39m\u001b[39mi\u001b[39m\u001b[39m\"\u001b[39m],\n\u001b[0;32m 3\u001b[0m OutputVars\u001b[39m=\u001b[39m[\u001b[39m\"\u001b[39m\u001b[39mo\u001b[39m\u001b[39m\"\u001b[39m],\n\u001b[0;32m 4\u001b[0m assumptions\u001b[39m=\u001b[39m[\u001b[39m\"\u001b[39m\u001b[39m|i| <= 2\u001b[39m\u001b[39m\"\u001b[39m],\n\u001b[0;32m 5\u001b[0m guarantees\u001b[39m=\u001b[39m[\u001b[39m\"\u001b[39m\u001b[39m|o| <= 3\u001b[39m\u001b[39m\"\u001b[39m])\n\u001b[1;32m----> 7\u001b[0m contract_system \u001b[39m=\u001b[39m contract1_n\u001b[39m.\u001b[39;49mcompose(contract2)\n", - "File \u001b[1;32m~\\iir_repo\\pacti\\src\\pacti\\iocontract\\iocontract.py:458\u001b[0m, in \u001b[0;36mIoContract.compose\u001b[1;34m(self, other)\u001b[0m\n\u001b[0;32m 456\u001b[0m new_a \u001b[39m=\u001b[39m other\u001b[39m.\u001b[39ma\u001b[39m.\u001b[39mabduce_with_context(\u001b[39mself\u001b[39m\u001b[39m.\u001b[39ma \u001b[39m|\u001b[39m \u001b[39mself\u001b[39m\u001b[39m.\u001b[39mg, assumptions_forbidden_vars)\n\u001b[0;32m 457\u001b[0m \u001b[39mif\u001b[39;00m list_intersection(new_a\u001b[39m.\u001b[39mvars, assumptions_forbidden_vars):\n\u001b[1;32m--> 458\u001b[0m \u001b[39mraise\u001b[39;00m \u001b[39mValueError\u001b[39;00m(\n\u001b[0;32m 459\u001b[0m \u001b[39m\"\u001b[39m\u001b[39mThe guarantees \u001b[39m\u001b[39m\\n\u001b[39;00m\u001b[39m{}\u001b[39;00m\u001b[39m\\n\u001b[39;00m\u001b[39m\"\u001b[39m\u001b[39m.\u001b[39mformat(\u001b[39mself\u001b[39m\u001b[39m.\u001b[39mg)\n\u001b[0;32m 460\u001b[0m \u001b[39m+\u001b[39m \u001b[39m\"\u001b[39m\u001b[39mwere insufficient to abduce the assumptions \u001b[39m\u001b[39m\\n\u001b[39;00m\u001b[39m{}\u001b[39;00m\u001b[39m\\n\u001b[39;00m\u001b[39m\"\u001b[39m\u001b[39m.\u001b[39mformat(other\u001b[39m.\u001b[39ma)\n\u001b[0;32m 461\u001b[0m \u001b[39m+\u001b[39m \u001b[39m\"\u001b[39m\u001b[39mby eliminating the variables \u001b[39m\u001b[39m\\n\u001b[39;00m\u001b[39m{}\u001b[39;00m\u001b[39m\"\u001b[39m\u001b[39m.\u001b[39mformat(assumptions_forbidden_vars)\n\u001b[0;32m 462\u001b[0m )\n\u001b[0;32m 463\u001b[0m assumptions \u001b[39m=\u001b[39m new_a \u001b[39m|\u001b[39m \u001b[39mself\u001b[39m\u001b[39m.\u001b[39ma\n\u001b[0;32m 464\u001b[0m \u001b[39melif\u001b[39;00m other_helps_self \u001b[39mand\u001b[39;00m \u001b[39mnot\u001b[39;00m self_helps_other:\n", - "\u001b[1;31mValueError\u001b[0m: The guarantees \n[\n |o| <= 3.0\n]\nwere insufficient to abduce the assumptions \n[\n o <= 0.2\n -o <= 1.0\n]\nby eliminating the variables \n[, ]" - ] - } - ], + "outputs": [], "source": [ "contract1_n = PolyhedralContract.from_string(\n", " InputVars=[\"i\"],\n", @@ -132,9 +102,7 @@ "\n", "Now consider the situation shown in the following diagram:\n", "\n", - "
\n", - "\n", - "
" + "![image](source/_static/exports/circuit_series_quotient_background.svg)" ] }, { diff --git a/docs/source/_static/circuit_series_composition_background.ai b/docs/source/_static/circuit_series_composition_background.ai index 4602d876..1bbd6782 100644 --- a/docs/source/_static/circuit_series_composition_background.ai +++ b/docs/source/_static/circuit_series_composition_background.ai @@ -1,5 +1,5 @@ %PDF-1.6 % -1 0 obj <>/OCGs[23 0 R]>>/Pages 3 0 R/Type/Catalog>> endobj 2 0 obj <>stream +1 0 obj <>/OCGs[23 0 R]>>/Pages 3 0 R/Type/Catalog>> endobj 2 0 obj <>stream @@ -23,23 +23,23 @@ Adobe Illustrator 26.5 (Windows) - 2023-02-19T13:40:51-07:00 - 2023-02-19T13:40:52-08:00 - 2023-02-19T13:40:52-08:00 + 2023-02-19T15:55:14-07:00 + 2023-02-19T15:55:14-08:00 + 2023-02-19T15:55:14-08:00 256 80 JPEG - /9j/4AAQSkZJRgABAgEASABIAAD/7QAsUGhvdG9zaG9wIDMuMAA4QklNA+0AAAAAABAASAAAAAEA AQBIAAAAAQAB/+4ADkFkb2JlAGTAAAAAAf/bAIQABgQEBAUEBgUFBgkGBQYJCwgGBggLDAoKCwoK 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n(FRM&#ỴZst&I`>bLs^<3Dps8U%tK&8>7A򽝿lz^\Ӓ?y9{&~)KXrÛ4(T +]8{'kQq\|q{mxկ>o^e1m}TQ=/)|h;l\jC$7*r"n'v) gG'k㊶V8@+($8APEyKic *.SV\\Cx^ j\Zq?\ZsJES?!o.86~^JJ# '5My@>Yu4Ϸ&]7&JU2ivo dpFf 7u JV@P $ v|Vن|dq0[B ,ϗ'pCTJB{7z0Y8JƆ+!2jůDV'û:1}=6#W@r(4|.i5Re 3-Gld`-%NJ +d1o +b8_ATB> ld1@e$0fKT0;Eպ vxh?WE#|f[*s]/KoUwmTvpKtCvx #D2J`TE fAKmMz˂|m.$>6.VZ#j̋GO%aY)qoĚiTyliM63qΌZM<}>9R`/b6(|uchȡ^rm%jg׷FgѿSGr+^V~!w;M"yCNJJw}S*9Ogj;1M`Zrr: +&y"p{}O#RY]J<-LKĥ{1}Nd5îaϪ1$/+c +:* +=Ϸ8v` Ci1nE>sQHO)Ep\4#qiIkqUΥв[wֲC wƒ~F^ܕ}P&X`.J'?NRptSH?bh!9L|wa̫!W"7yX#0ۨiׯ7kC249i3B@<,&@LЖ<7?Xb?HAː"]*2fUVNCF_p3 HEXjƜmVM;,{1Q2kY峽;åH- Y +ƘtuN!KrMzU2\۩{p&(^q6RRAٰ07נޔKqAX:dr[k2>\NA+A]״6p)>ʥs5Eh"P-Gq)׏jUwG7RoCL]_n&?N.RբO.M w;:M[KsP_AP3#ck7wNi~9zX#aT6!nWA` 8u5Cw3P|% +jʬ_q(*_&Dn|Kس~a+]0KXYps% Ԅu +(^dxt6:OG}_1mI_ު9/x-z0M^0'УaYėhUG <{%jOZFeP|zLMe hf 0xR9"Nb;sY"/@ۏ!;m4F>=S +endstream endobj 24 0 obj [23 0 R] endobj 36 0 obj <> endobj xref 0 37 0000000004 65535 f 0000000016 00000 n 0000000147 00000 n -0000041156 00000 n +0000041981 00000 n 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a/docs/source/_static/exports/circuit_series_composition_background.svg b/docs/source/_static/exports/circuit_series_composition_background.svg index e022a88e..95d24907 100644 --- a/docs/source/_static/exports/circuit_series_composition_background.svg +++ b/docs/source/_static/exports/circuit_series_composition_background.svg @@ -1 +1 @@ - \ No newline at end of file + \ No newline at end of file diff --git a/docs/source/_static/exports/circuit_series_quotient_background.svg b/docs/source/_static/exports/circuit_series_quotient_background.svg index 28567136..14a8e62a 100644 --- a/docs/source/_static/exports/circuit_series_quotient_background.svg +++ b/docs/source/_static/exports/circuit_series_quotient_background.svg @@ -1 +1 @@ - \ No newline at end of file + \ No newline at end of file From 8a4bd5165d0ccf2da031beac6008321108c7bca1 Mon Sep 17 00:00:00 2001 From: Inigo Incer Date: Sun, 19 Feb 2023 16:25:16 -0800 Subject: [PATCH 10/16] minor --- docs/getting_started.ipynb | 2 +- .../circuit_series_composition_background.png | Bin 0 -> 9232 bytes .../circuit_series_quotient_background.png | Bin 0 -> 11685 bytes 3 files changed, 1 insertion(+), 1 deletion(-) create mode 100644 docs/source/_static/exports/circuit_series_composition_background.png create mode 100644 docs/source/_static/exports/circuit_series_quotient_background.png diff --git a/docs/getting_started.ipynb b/docs/getting_started.ipynb index 626693ba..9b6d1f54 100644 --- a/docs/getting_started.ipynb +++ b/docs/getting_started.ipynb @@ -102,7 +102,7 @@ "\n", "Now consider the situation shown in the following diagram:\n", "\n", - "![image](source/_static/exports/circuit_series_quotient_background.svg)" + "![image](source/_static/exports/circuit_series_quotient_background.png)" ] }, { diff --git a/docs/source/_static/exports/circuit_series_composition_background.png b/docs/source/_static/exports/circuit_series_composition_background.png new file mode 100644 index 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"![image](data:image/png;base64,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)\n", "\n", "Components $M$ and $M'$ obey, respectively, contracts $C = (|i| \\le 2, o \\le i \\le 2o + 2)$ and $C' = (-1 \\le o \\le 1/5, o' \\le o)$. We can use Pacti to obtain the specification of the system that comprises these two components as follows: " ] @@ -102,7 +101,7 @@ "\n", "Now consider the situation shown in the following diagram:\n", "\n", - "![image](source/_static/exports/circuit_series_quotient_background.png)" + "![image](data:image/png;base64,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)" ] }, { From 4c963d67c8ac8c1c695fbbe24d91ea6e4367d5ed Mon Sep 17 00:00:00 2001 From: Inigo Incer Date: Sun, 19 Feb 2023 16:34:33 -0800 Subject: [PATCH 12/16] saving outputs --- docs/getting_started.ipynb | 37 +++++++++++++++++++++++++++++++++---- 1 file changed, 33 insertions(+), 4 deletions(-) diff --git a/docs/getting_started.ipynb b/docs/getting_started.ipynb index 3d9e8c00..dc929736 100644 --- a/docs/getting_started.ipynb +++ b/docs/getting_started.ipynb @@ -34,9 +34,25 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "InVars: [i]\n", + "OutVars:[o_p]\n", + "A: [\n", + " i <= 0.19999999999999996\n", + " -0.5 i <= 0.0\n", + "]\n", + "G: [\n", + " -i + o_p <= 0.0\n", + "]\n" + ] + } + ], "source": [ "from pacti.terms.polyhedra import PolyhedralContract\n", "\n", @@ -71,9 +87,22 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": {}, - "outputs": [], + "outputs": [ + { + "ename": "ValueError", + "evalue": "The guarantees \n[\n |o| <= 3.0\n]\nwere insufficient to abduce the assumptions \n[\n o <= 0.2\n -o <= 1.0\n]\nby eliminating the variables \n[, ]", + "output_type": "error", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[1;31mValueError\u001b[0m Traceback (most recent call last)", + "Cell \u001b[1;32mIn[2], line 7\u001b[0m\n\u001b[0;32m 1\u001b[0m contract1_n \u001b[39m=\u001b[39m PolyhedralContract\u001b[39m.\u001b[39mfrom_string(\n\u001b[0;32m 2\u001b[0m InputVars\u001b[39m=\u001b[39m[\u001b[39m\"\u001b[39m\u001b[39mi\u001b[39m\u001b[39m\"\u001b[39m],\n\u001b[0;32m 3\u001b[0m OutputVars\u001b[39m=\u001b[39m[\u001b[39m\"\u001b[39m\u001b[39mo\u001b[39m\u001b[39m\"\u001b[39m],\n\u001b[0;32m 4\u001b[0m assumptions\u001b[39m=\u001b[39m[\u001b[39m\"\u001b[39m\u001b[39m|i| <= 2\u001b[39m\u001b[39m\"\u001b[39m],\n\u001b[0;32m 5\u001b[0m guarantees\u001b[39m=\u001b[39m[\u001b[39m\"\u001b[39m\u001b[39m|o| <= 3\u001b[39m\u001b[39m\"\u001b[39m])\n\u001b[1;32m----> 7\u001b[0m contract_system \u001b[39m=\u001b[39m contract1_n\u001b[39m.\u001b[39;49mcompose(contract2)\n", + "File \u001b[1;32m~\\iir_repo\\pacti\\src\\pacti\\iocontract\\iocontract.py:458\u001b[0m, in \u001b[0;36mIoContract.compose\u001b[1;34m(self, other)\u001b[0m\n\u001b[0;32m 456\u001b[0m new_a \u001b[39m=\u001b[39m other\u001b[39m.\u001b[39ma\u001b[39m.\u001b[39mabduce_with_context(\u001b[39mself\u001b[39m\u001b[39m.\u001b[39ma \u001b[39m|\u001b[39m \u001b[39mself\u001b[39m\u001b[39m.\u001b[39mg, assumptions_forbidden_vars)\n\u001b[0;32m 457\u001b[0m \u001b[39mif\u001b[39;00m list_intersection(new_a\u001b[39m.\u001b[39mvars, assumptions_forbidden_vars):\n\u001b[1;32m--> 458\u001b[0m \u001b[39mraise\u001b[39;00m \u001b[39mValueError\u001b[39;00m(\n\u001b[0;32m 459\u001b[0m \u001b[39m\"\u001b[39m\u001b[39mThe guarantees \u001b[39m\u001b[39m\\n\u001b[39;00m\u001b[39m{}\u001b[39;00m\u001b[39m\\n\u001b[39;00m\u001b[39m\"\u001b[39m\u001b[39m.\u001b[39mformat(\u001b[39mself\u001b[39m\u001b[39m.\u001b[39mg)\n\u001b[0;32m 460\u001b[0m \u001b[39m+\u001b[39m \u001b[39m\"\u001b[39m\u001b[39mwere insufficient to abduce the assumptions \u001b[39m\u001b[39m\\n\u001b[39;00m\u001b[39m{}\u001b[39;00m\u001b[39m\\n\u001b[39;00m\u001b[39m\"\u001b[39m\u001b[39m.\u001b[39mformat(other\u001b[39m.\u001b[39ma)\n\u001b[0;32m 461\u001b[0m \u001b[39m+\u001b[39m \u001b[39m\"\u001b[39m\u001b[39mby eliminating the variables \u001b[39m\u001b[39m\\n\u001b[39;00m\u001b[39m{}\u001b[39;00m\u001b[39m\"\u001b[39m\u001b[39m.\u001b[39mformat(assumptions_forbidden_vars)\n\u001b[0;32m 462\u001b[0m )\n\u001b[0;32m 463\u001b[0m assumptions \u001b[39m=\u001b[39m new_a \u001b[39m|\u001b[39m \u001b[39mself\u001b[39m\u001b[39m.\u001b[39ma\n\u001b[0;32m 464\u001b[0m \u001b[39melif\u001b[39;00m other_helps_self \u001b[39mand\u001b[39;00m \u001b[39mnot\u001b[39;00m self_helps_other:\n", + "\u001b[1;31mValueError\u001b[0m: The guarantees \n[\n |o| <= 3.0\n]\nwere insufficient to abduce the assumptions \n[\n o <= 0.2\n -o <= 1.0\n]\nby eliminating the variables \n[, ]" + ] + } + ], "source": [ "contract1_n = PolyhedralContract.from_string(\n", " InputVars=[\"i\"],\n", From 0661f84fcd8fc8316138aed7bfc3b6ed32158aed Mon Sep 17 00:00:00 2001 From: Inigo Incer Date: Sun, 19 Feb 2023 16:37:05 -0800 Subject: [PATCH 13/16] now saving ALL outputs --- docs/getting_started.ipynb | 37 ++++++++++++++++++++++++++++++------- 1 file changed, 30 insertions(+), 7 deletions(-) diff --git a/docs/getting_started.ipynb b/docs/getting_started.ipynb index dc929736..86ab268c 100644 --- a/docs/getting_started.ipynb +++ b/docs/getting_started.ipynb @@ -34,7 +34,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 3, "metadata": {}, "outputs": [ { @@ -87,7 +87,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 4, "metadata": {}, "outputs": [ { @@ -97,7 +97,7 @@ "traceback": [ "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[1;31mValueError\u001b[0m Traceback (most recent call last)", - "Cell \u001b[1;32mIn[2], line 7\u001b[0m\n\u001b[0;32m 1\u001b[0m contract1_n \u001b[39m=\u001b[39m PolyhedralContract\u001b[39m.\u001b[39mfrom_string(\n\u001b[0;32m 2\u001b[0m InputVars\u001b[39m=\u001b[39m[\u001b[39m\"\u001b[39m\u001b[39mi\u001b[39m\u001b[39m\"\u001b[39m],\n\u001b[0;32m 3\u001b[0m OutputVars\u001b[39m=\u001b[39m[\u001b[39m\"\u001b[39m\u001b[39mo\u001b[39m\u001b[39m\"\u001b[39m],\n\u001b[0;32m 4\u001b[0m assumptions\u001b[39m=\u001b[39m[\u001b[39m\"\u001b[39m\u001b[39m|i| <= 2\u001b[39m\u001b[39m\"\u001b[39m],\n\u001b[0;32m 5\u001b[0m guarantees\u001b[39m=\u001b[39m[\u001b[39m\"\u001b[39m\u001b[39m|o| <= 3\u001b[39m\u001b[39m\"\u001b[39m])\n\u001b[1;32m----> 7\u001b[0m contract_system \u001b[39m=\u001b[39m contract1_n\u001b[39m.\u001b[39;49mcompose(contract2)\n", + "Cell \u001b[1;32mIn[4], line 7\u001b[0m\n\u001b[0;32m 1\u001b[0m contract1_n \u001b[39m=\u001b[39m PolyhedralContract\u001b[39m.\u001b[39mfrom_string(\n\u001b[0;32m 2\u001b[0m InputVars\u001b[39m=\u001b[39m[\u001b[39m\"\u001b[39m\u001b[39mi\u001b[39m\u001b[39m\"\u001b[39m],\n\u001b[0;32m 3\u001b[0m OutputVars\u001b[39m=\u001b[39m[\u001b[39m\"\u001b[39m\u001b[39mo\u001b[39m\u001b[39m\"\u001b[39m],\n\u001b[0;32m 4\u001b[0m assumptions\u001b[39m=\u001b[39m[\u001b[39m\"\u001b[39m\u001b[39m|i| <= 2\u001b[39m\u001b[39m\"\u001b[39m],\n\u001b[0;32m 5\u001b[0m guarantees\u001b[39m=\u001b[39m[\u001b[39m\"\u001b[39m\u001b[39m|o| <= 3\u001b[39m\u001b[39m\"\u001b[39m])\n\u001b[1;32m----> 7\u001b[0m contract_system \u001b[39m=\u001b[39m contract1_n\u001b[39m.\u001b[39;49mcompose(contract2)\n", "File \u001b[1;32m~\\iir_repo\\pacti\\src\\pacti\\iocontract\\iocontract.py:458\u001b[0m, in \u001b[0;36mIoContract.compose\u001b[1;34m(self, other)\u001b[0m\n\u001b[0;32m 456\u001b[0m new_a \u001b[39m=\u001b[39m other\u001b[39m.\u001b[39ma\u001b[39m.\u001b[39mabduce_with_context(\u001b[39mself\u001b[39m\u001b[39m.\u001b[39ma \u001b[39m|\u001b[39m \u001b[39mself\u001b[39m\u001b[39m.\u001b[39mg, assumptions_forbidden_vars)\n\u001b[0;32m 457\u001b[0m \u001b[39mif\u001b[39;00m list_intersection(new_a\u001b[39m.\u001b[39mvars, assumptions_forbidden_vars):\n\u001b[1;32m--> 458\u001b[0m \u001b[39mraise\u001b[39;00m \u001b[39mValueError\u001b[39;00m(\n\u001b[0;32m 459\u001b[0m \u001b[39m\"\u001b[39m\u001b[39mThe guarantees \u001b[39m\u001b[39m\\n\u001b[39;00m\u001b[39m{}\u001b[39;00m\u001b[39m\\n\u001b[39;00m\u001b[39m\"\u001b[39m\u001b[39m.\u001b[39mformat(\u001b[39mself\u001b[39m\u001b[39m.\u001b[39mg)\n\u001b[0;32m 460\u001b[0m \u001b[39m+\u001b[39m \u001b[39m\"\u001b[39m\u001b[39mwere insufficient to abduce the assumptions \u001b[39m\u001b[39m\\n\u001b[39;00m\u001b[39m{}\u001b[39;00m\u001b[39m\\n\u001b[39;00m\u001b[39m\"\u001b[39m\u001b[39m.\u001b[39mformat(other\u001b[39m.\u001b[39ma)\n\u001b[0;32m 461\u001b[0m \u001b[39m+\u001b[39m \u001b[39m\"\u001b[39m\u001b[39mby eliminating the variables \u001b[39m\u001b[39m\\n\u001b[39;00m\u001b[39m{}\u001b[39;00m\u001b[39m\"\u001b[39m\u001b[39m.\u001b[39mformat(assumptions_forbidden_vars)\n\u001b[0;32m 462\u001b[0m )\n\u001b[0;32m 463\u001b[0m assumptions \u001b[39m=\u001b[39m new_a \u001b[39m|\u001b[39m \u001b[39mself\u001b[39m\u001b[39m.\u001b[39ma\n\u001b[0;32m 464\u001b[0m \u001b[39melif\u001b[39;00m other_helps_self \u001b[39mand\u001b[39;00m \u001b[39mnot\u001b[39;00m self_helps_other:\n", "\u001b[1;31mValueError\u001b[0m: The guarantees \n[\n |o| <= 3.0\n]\nwere insufficient to abduce the assumptions \n[\n o <= 0.2\n -o <= 1.0\n]\nby eliminating the variables \n[, ]" ] @@ -143,9 +143,24 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "InVars: [o]\n", + "OutVars:[o_p]\n", + "A: [\n", + " |o| <= 2.0\n", + "]\n", + "G: [\n", + " -o + o_p = 1.0\n", + "]\n" + ] + } + ], "source": [ "contract_top_level = PolyhedralContract.from_string(\n", " InputVars=[\"i\"],\n", @@ -173,9 +188,17 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "True\n" + ] + } + ], "source": [ "# compose quotient \n", "new_system_object = contract_missing_object.compose(contract_existing_component)\n", From acbc695d0d232dcfe712cbd1e6b1f7ef4b7a7167 Mon Sep 17 00:00:00 2001 From: Inigo Incer Date: Sun, 19 Feb 2023 16:45:15 -0800 Subject: [PATCH 14/16] typo --- docs/getting_started.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/getting_started.ipynb b/docs/getting_started.ipynb index 86ab268c..75898c42 100644 --- a/docs/getting_started.ipynb +++ b/docs/getting_started.ipynb @@ -212,7 +212,7 @@ "source": [ "### To learn more\n", "\n", - "This introductory examples show some of the analysis tasks we can carry out with Pacti. We have developed several case studies that discuss the application of Pacti in various design disciplines." + "These introductory examples show some analysis tasks we can carry out with Pacti. The `case_studies` folder contains several case studies that discuss the application of Pacti in various design disciplines." ] }, { From 5fd8a454634ed8b3a433f194b29ffe09ae62c46e Mon Sep 17 00:00:00 2001 From: Inigo Incer Date: Sun, 19 Feb 2023 16:48:42 -0800 Subject: [PATCH 15/16] header change --- docs/getting_started.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/getting_started.ipynb b/docs/getting_started.ipynb index 75898c42..aa30b04d 100644 --- a/docs/getting_started.ipynb +++ b/docs/getting_started.ipynb @@ -5,7 +5,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Introduction\n", + "# Getting started\n", "\n", "Pacti helps designers to reason about specifications and to manipulate them. These specifications are given to Pacti as assume-guarantee contracts, which are requirements of the form (assumptions, guarantees).\n", "\n", From 27cd94652d45f38a37c5c1c40c6bd4f56a13f6fe Mon Sep 17 00:00:00 2001 From: Inigo Incer Date: Sun, 19 Feb 2023 16:53:23 -0800 Subject: [PATCH 16/16] minor --- docs/command-line-interface.md | 45 ++++++++++++++++++++++++++++++++++ docs/index.md | 44 --------------------------------- 2 files changed, 45 insertions(+), 44 deletions(-) create mode 100644 docs/command-line-interface.md diff --git a/docs/command-line-interface.md b/docs/command-line-interface.md new file mode 100644 index 00000000..0ed7c54e --- /dev/null +++ b/docs/command-line-interface.md @@ -0,0 +1,45 @@ +## Examples + + +### Composition + + +Suppose we have the following system: + +Buffers connected in series + + +Components $M$ and $M'$ obey, respectively, contracts $C = (|i| \le 2, o \le i \le 2o + 2)$ and $C' = (-1 \le o \le 1/5, o' \le o)$. We can use Pacti to obtain the specification of the system by executing the command + +`pacti examples/example.json result.json` + +Pacti places the result of composition in the file result.json. The output is + +``` + Composed contract: + InVars: [] + OutVars:[] + A: 5*i <= 1, -1/2*i <= 0 + G: -1*i + 1*o_p <= 0 +``` + +### Quotient + + +Now we consider an example of quotient. Consider the following circuits: + +Buffers connected in series + +We wish to implement a system $M$ with specification $C = (|i| \le 1, o' = 2i + 1)$, and to do this we have available a component $M'$ with specification $C' = (|i| \le 2, o = 2i)$. We use the quotient operation in Pacti to obtain the specification of the component that we are missing so that the resulting object meets the specification $C$. We run the command + +`pacti examples/example_quotient.json result.json` + +And Pacti outputs + +``` + Contract quotient: + InVars: [] + OutVars:[] + A: 1*o <= 2, -1*o <= 2 + G: -1*o + 1*o_p <= 1, 1*o + -1*o_p <= -1 +``` \ No newline at end of file diff --git a/docs/index.md b/docs/index.md index ec08973e..52ce6657 100644 --- a/docs/index.md +++ b/docs/index.md @@ -10,48 +10,4 @@ system using assume-guarantee specifications, or contracts. Pacti's capabilities - Computing specifications of subsystems that need to be added to a design in order to meet an objective. - Verifying whether a component meets a specification. -## Examples - -### Composition - - -Suppose we have the following system: - -Buffers connected in series - - -Components $M$ and $M'$ obey, respectively, contracts $C = (|i| \le 2, o \le i \le 2o + 2)$ and $C' = (-1 \le o \le 1/5, o' \le o)$. We can use Pacti to obtain the specification of the system by executing the command - -`pacti examples/example.json result.json` - -Pacti places the result of composition in the file result.json. The output is - -``` - Composed contract: - InVars: [] - OutVars:[] - A: 5*i <= 1, -1/2*i <= 0 - G: -1*i + 1*o_p <= 0 -``` - -### Quotient - - -Now we consider an example of quotient. Consider the following circuits: - -Buffers connected in series - -We wish to implement a system $M$ with specification $C = (|i| \le 1, o' = 2i + 1)$, and to do this we have available a component $M'$ with specification $C' = (|i| \le 2, o = 2i)$. We use the quotient operation in Pacti to obtain the specification of the component that we are missing so that the resulting object meets the specification $C$. We run the command - -`pacti examples/example_quotient.json result.json` - -And Pacti outputs - -``` - Contract quotient: - InVars: [] - OutVars:[] - A: 1*o <= 2, -1*o <= 2 - G: -1*o + 1*o_p <= 1, 1*o + -1*o_p <= -1 -```