1 <?xml version="1.0" encoding="UTF-8"?>
3 <page xmlns="http://lambdadelta.info/"
4 description = "\lambda\delta home page"
5 title = "\lambda\delta home page"
7 head = "The Formal Systems of the λδ (\lambda\delta) Family"
9 <sitemap name="sitemap"/>
11 <section15 name="specifications">Computer-checked formal specifications</section15>
13 The systems of the λδ family are developed as machine-checked digital specifications,
14 and are listed in the next table, which includes the major milestones.
17 The life cycle of a specification consists of four periods.
18 <notice class="alpha" text="Alpha:"/>
19 the definitions are designed and the major propositions are proved,
20 then the calculus is announced with a presentation.
21 <notice class="beta" text="Beta:"/>
22 major changes and additions may occur before the calculus is released on paper.
23 <notice class="gamma" text="Gamma:"/>
24 subsequent improvements occur until the specification is completed or superseded,
25 while major changes and additions are announced and reported on paper.
26 <notice class="delta" text="Delta:"/>
27 after its conclusion, the specification is modified just for maintenance.
29 <table name="versions"/>
32 <notice class="alpha" text="Change logs: "/>
33 <rlink to="html/changes.html">System and Specification</rlink>
34 (updated <notice class="gamma" notice="2019-12"/>).
38 Informational pages on the specifications are provided.
40 <topitem name="notice1">
41 <notice class="alpha" text="Notice on displayed numerical acounts:"/>
42 nodes are counted according to the "intrinsic complexity measure"
43 [F. Guidi: "Procedural Representation of CIC Proof Terms"
44 Journal of Automated Reasoning 44(1-2), Springer (February 2010), pp. 53-78].
46 <topitem name="notice2">
47 <notice class="alpha" text="Notice on displayed logical structures:"/>
48 from the logical standpoint, the source scripts are grouped in "planes"
49 and these are grouped in "components";
50 the notation for the relations or functions
51 introduced in each script, is shown in parentheses (? are placeholders).
54 <!-- VERSION 3 =========================================================== -->
56 <subsection name="v3"><img logo="ld3"/>λδ version 3 (proposed)</subsection>
58 The formal specification of λδ version 3
62 <!-- VERSION 2 =========================================================== -->
64 <subsection name="v2"><img logo="ld2"/>λδ version 2 (active)</subsection>
66 The formal specification of λδ version 2
67 is available in the following formats.
71 <notice class="alpha" text="Notice:"/>
72 the scripts are checked by the latest version of Matita from
73 <link to="http://matita.cs.unibo.it/gitweb/?p=helm.git;a=summary">HELM Git repository</link>.
76 <topitem name="source2B">
78 <rlink to="download/lambdadelta_2B.tar.bz2">lambdadelta_2B for Matita 0.99.4</rlink>
79 (revised <notice class="gamma" text="2020-02"/>).
81 <rlink to="html/documentation.html#ldJ2a">Documentation (J2a)</rlink>.
83 <notice class="gamma" text="2020-02-27."/>
84 repackaged without λδ-ground-2.
86 <notice class="gamma" text="2019-11-19."/>
87 released [Git revision: 2019-11-19 20:45:15].
91 Informational pages on the parts of the specification:
92 <rlink to="html/ground_2.html">Background</rlink>,
93 <rlink to="html/static_2.html">Syntax</rlink>,
94 <rlink to="html/basic_2.html">Core</rlink>,
95 <rlink to="html/apps_2.html">Applications</rlink>.
99 <topitem name="source2A">
101 <rlink to="download/lambdadelta_2A.tar.bz2">lambdadelta_2A for Matita 0.99.2</rlink>
102 (revised <notice class="delta" text="2020-02"/>).
104 <rlink to="html/documentation.html#ldR2c">Documentation (R2c)</rlink>.
106 <notice class="delta" text="2020-02-27."/>
107 repackaged on the basis of λδ-ground-2.
109 <notice class="delta" text="2019-11-20."/>
110 repackaged (was lambdadelta_2A1).
112 <notice class="gamma" text="2014-10-28."/>
113 released [Git revision: 2014-10-28 17:46:26].
117 Informational pages on the parts of the specification:
118 <rlink to="html/basic_2A.html">Core</rlink>.
122 <topitem name="source2g">
124 <rlink to="download/lambdadelta_ground.tar.bz2">lambdadelta_ground for Matita 0.99.4</rlink>
125 (revised <notice class="gamma" text="2020-02"/>).
128 <notice class="gamma" text="2020-02-27."/>
129 released [Git revision: 2014-10-28 17:46:26].
133 Informational pages on the parts of the specification:
134 <rlink to="html/ground_2.html">Core</rlink>.
139 <!-- VERSION 1 =========================================================== -->
141 <subsection name="v1"><img logo="ld1"/>λδ version 1 (superseded)</subsection>
143 The formal specification of λδ version 1
144 is available in the following formats.
147 <topitem name="source1A">
149 <rlink to="download/lambdadelta_1A.tar.bz2">lambdadelta_1A for Coq 7.3.1</rlink>
150 (revised <notice class="delta" text="2019-11"/>).
152 <rlink to="html/documentation.html#ldJ1a">Documentation (J1a)</rlink>.
154 <notice class="delta" text="2019-11-20."/>
155 repackaging (was lambdadelta_1).
157 <notice class="delta" text="2015-01-15."/>
158 17 new lemmas and former lemma "eq_nat_dec" renamed as "nat_dec_neg".
162 Informational pages on the parts of the specification:
163 <rlink to="html/ground_1.html">Background</rlink>,
164 <rlink to="html/basic_1.html">Core</rlink>.
168 <topitem name="static1A">
169 <rlink to="static/matita/lambdadelta/">lambdadelta_1A for Matita 0.5</rlink>
170 (revised <notice class="delta" text="2019-11"/>).
171 Static HTML pages generated by the <link to="http://helm.cs.unibo.it/">HELM</link> rendering engine.
173 <rlink to="static/matita/lambdadelta/basic_1/pr3/pr3/pr3_confluence.con.html">
174 Confluence of reduction</rlink>
175 (Church-Rosser property).
177 <rlink to="static/matita/lambdadelta/basic_1/ty3/props/ty3_correct.con.html">
178 Correctness of types</rlink>.
180 <rlink to="static/matita/lambdadelta/basic_1/ty3/props/ty3_unique.con.html">
181 Uniqueness of types up to conversion</rlink>.
183 <rlink to="static/matita/lambdadelta/basic_1/ty3/pr3/ty3_sred_pr3.con.html">
184 Subject reduction of the type assignment</rlink>.
186 <rlink to="static/matita/lambdadelta/basic_1/ty3/arity_props/ty3_sn3.con.html">
187 Strong normalization of the typed terms</rlink>.
189 <rlink to="static/matita/lambdadelta/basic_1/ty3/dec/ty3_inference.con.html">
190 Decidability of the type inference problem</rlink>.
194 <topitem name="dynamic1A">
195 <link to="http://mowgli.cs.unibo.it:58080/apply?keys=RT&xmluri=http://helm.cs.unibo.it/helm//html/folder/index.html&prop.media-type=text/html&param.thmedia-type=text/html&param.thkeys=T1%2CT2%2CL%2CE&param.embedkeys=d_c%2CTC1%2CHC2%2CL&param.thencoding=UTF-8&prop.encoding=UTF-8&prop.doctype-public=-//W3C//DTD%20XHTML%201.0%20Transitional//EN&param.doctype-public=-//W3C//DTD%20XHTML%201.0%20Transitional//EN&param.encoding=UTF-8&param.media-type=text/html&param.keys=d_c%2CC1%2CHC2%2CL&profile=default&param.profile=default&param.CICURI=theory:/matita/lambdadelta/">
196 lambdadelta_1A for Matita 0.5</link>
197 (revised <notice class="delta" text="2019-11"/>).
198 <link to="http://helm.cs.unibo.it/">HELM</link> directory.
199 <notice class="alpha" text="Notice: the HELM rendering engine is offline."/>