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Commit 60fb75d5 authored by Dennis Müller's avatar Dennis Müller
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<?xml version="1.0" encoding="UTF-8"?>
<omdoc base="http://mathhub.info/MitM/Foundation/math.omdoc"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Foundation/math.mmt#0.0.0:11364.342.0"/><meta property="http://cds.omdoc.org/?metadata?importedby"><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMLIT type="http://www.openmath.org/cd?OpenMath?OMSTR" value="mmt-omdoc"/></om:OMOBJ></meta></metadata><instruction text="namespace http://mathhub.info/MitM/Foundation"/><instruction text="import rules scala://rules.mitm.mmt.kwarc.info"/><instruction text="import lf scala://lf.mmt.kwarc.info/"/><instruction text="import lfx scala://LFX.mmt.kwarc.info"/><instruction text="fixmeta http://cds.omdoc.org/mmt?mmt"/><mref name="[http://mathhub.info/MitM/Foundation?Metadata]" target="http://mathhub.info/MitM/Foundation?Metadata"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Foundation/math.mmt#217.8.0:231.8.14"/></metadata></mref><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Foundation/math.mmt#261.12.0:330.12.69"/></metadata>We define a formal language for basic mathematical objects in LF.</opaque><mref name="[http://mathhub.info/MitM/Foundation?Subtyping]" target="http://mathhub.info/MitM/Foundation?Subtyping"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Foundation/math.mmt#333.14.0:348.14.15"/></metadata></mref><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Foundation/math.mmt#420.18.0:442.18.22"/></metadata>First, some logic.</opaque><mref name="[http://mathhub.info/MitM/Foundation?Logic]" target="http://mathhub.info/MitM/Foundation?Logic"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Foundation/math.mmt#493.21.0:504.21.11"/></metadata></mref><mref name="[http://mathhub.info/MitM/Foundation?NaturalDeduction]" target="http://mathhub.info/MitM/Foundation?NaturalDeduction"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Foundation/math.mmt#2741.70.0:2763.70.22"/></metadata></mref><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Foundation/math.mmt#4563.108.0:4744.109.106"/></metadata>Now some theories that introduce primitive types and literals for them.
<omdoc base="http://mathhub.info/MitM/Foundation/math.omdoc"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Foundation/math.mmt#0.0.0:11364.342.0"/><meta property="http://cds.omdoc.org/?metadata?importedby"><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMLIT type="http://www.openmath.org/cd?OpenMath?OMSTR" value="mmt-omdoc"/></om:OMOBJ></meta></metadata><instruction text="namespace http://mathhub.info/MitM/Foundation"/><instruction text="import rules scala://rules.mitm.mmt.kwarc.info"/><instruction text="import lf scala://lf.mmt.kwarc.info"/><instruction text="import lfx scala://LFX.mmt.kwarc.info"/><instruction text="fixmeta http://cds.omdoc.org/mmt?mmt"/><mref name="[http://mathhub.info/MitM/Foundation?Metadata]" target="http://mathhub.info/MitM/Foundation?Metadata"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Foundation/math.mmt#217.8.0:231.8.14"/></metadata></mref><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Foundation/math.mmt#261.12.0:330.12.69"/></metadata>We define a formal language for basic mathematical objects in LF.</opaque><mref name="[http://mathhub.info/MitM/Foundation?Subtyping]" target="http://mathhub.info/MitM/Foundation?Subtyping"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Foundation/math.mmt#333.14.0:348.14.15"/></metadata></mref><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Foundation/math.mmt#420.18.0:442.18.22"/></metadata>First, some logic.</opaque><mref name="[http://mathhub.info/MitM/Foundation?Logic]" target="http://mathhub.info/MitM/Foundation?Logic"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Foundation/math.mmt#493.21.0:504.21.11"/></metadata></mref><mref name="[http://mathhub.info/MitM/Foundation?NaturalDeduction]" target="http://mathhub.info/MitM/Foundation?NaturalDeduction"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Foundation/math.mmt#2741.70.0:2763.70.22"/></metadata></mref><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Foundation/math.mmt#4563.108.0:4744.109.106"/></metadata>Now some theories that introduce primitive types and literals for them.
Because literals must modify the parser, they are supplied as rules that are implemented in a plugin.</opaque><mref name="[http://mathhub.info/MitM/Foundation?NatLiterals]" target="http://mathhub.info/MitM/Foundation?NatLiterals"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Foundation/math.mmt#4753.111.0:4770.111.17"/></metadata></mref><mref name="[http://mathhub.info/MitM/Foundation?IntLiterals]" target="http://mathhub.info/MitM/Foundation?IntLiterals"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Foundation/math.mmt#5609.139.0:5626.139.17"/></metadata></mref><mref name="[http://mathhub.info/MitM/Foundation?RealLiterals]" target="http://mathhub.info/MitM/Foundation?RealLiterals"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Foundation/math.mmt#5982.155.0:6000.155.18"/></metadata></mref><mref name="[http://mathhub.info/MitM/Foundation?Literals]" target="http://mathhub.info/MitM/Foundation?Literals"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Foundation/math.mmt#6558.176.0:6572.176.14"/></metadata></mref><mref name="[http://mathhub.info/MitM/Foundation?Trigonometry]" target="http://mathhub.info/MitM/Foundation?Trigonometry"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Foundation/math.mmt#7045.197.0:7063.197.18"/></metadata></mref><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Foundation/math.mmt#7466.217.0:7534.217.68"/></metadata>String literals are also needed occasionally, e.g., in the LMFDB.</opaque><mref name="[http://mathhub.info/MitM/Foundation?Strings]" target="http://mathhub.info/MitM/Foundation?Strings"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Foundation/math.mmt#7538.219.0:7551.219.13"/></metadata></mref><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Foundation/math.mmt#7670.226.0:7714.226.44"/></metadata>Now some more complex types. First lists.</opaque><mref name="[http://mathhub.info/MitM/Foundation?Lists]" target="http://mathhub.info/MitM/Foundation?Lists"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Foundation/math.mmt#7717.228.0:7728.228.11"/></metadata></mref><mref name="[http://mathhub.info/MitM/Foundation?InformalProofs]" target="http://mathhub.info/MitM/Foundation?InformalProofs"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Foundation/math.mmt#7807.232.0:7827.232.20"/></metadata></mref><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Foundation/math.mmt#8093.242.0:8331.250.0"/></metadata><scope>(Finite) sets ❙
theory Sets : ur:?LF =
include ?Logic❙
......
......@@ -35,8 +35,8 @@ DependsOn http://mathhub.info/MitM/Foundation?Logic?ImplicitProof?type http://cd
DependsOn http://mathhub.info/MitM/Foundation?Logic?ImplicitProof?type http://mathhub.info/MitM/Foundation?Logic?ded?type
DependsOn http://mathhub.info/MitM/Foundation?Logic?ImplicitProof?type http://mathhub.info/MitM/Foundation?Logic?prop?type
DependsOn http://mathhub.info/MitM/Foundation?Logic?ImplicitProof?type http://mathhub.info/MitM/Foundation?Logic?ded?definition
Declares http://mathhub.info/MitM/Foundation?Logic http://mathhub.info/MitM/Foundation?Logic?[scala://lf.mmt.kwarc.info/?TermIrrelevanceRule]/-975443801
constant http://mathhub.info/MitM/Foundation?Logic?[scala://lf.mmt.kwarc.info/?TermIrrelevanceRule]/-975443801
Declares http://mathhub.info/MitM/Foundation?Logic http://mathhub.info/MitM/Foundation?Logic?[scala://lf.mmt.kwarc.info?TermIrrelevanceRule]/-975443801
constant http://mathhub.info/MitM/Foundation?Logic?[scala://lf.mmt.kwarc.info?TermIrrelevanceRule]/-975443801
Declares http://mathhub.info/MitM/Foundation?Logic http://mathhub.info/MitM/Foundation?Logic?eq
constant http://mathhub.info/MitM/Foundation?Logic?eq
DependsOn http://mathhub.info/MitM/Foundation?Logic?eq?type http://mathhub.info/MitM/Foundation?Logic?prop?type
......
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