X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fhelp%2FC%2Fsec_terms.xml;h=fbf8dd4ef9cb614c7dfb52eb4c2fa80e1ab210b2;hb=871ed1c297e8c929a8c4460162e8521c9656bbc0;hp=45459572bfc20affb08754727e141ba99d7f8474;hpb=b4fb4fa6c17945b70d821e2b31e6aca727bcf9d5;p=helm.git diff --git a/helm/software/matita/help/C/sec_terms.xml b/helm/software/matita/help/C/sec_terms.xml index 45459572b..fbf8dd4ef 100644 --- a/helm/software/matita/help/C/sec_terms.xml +++ b/helm/software/matita/help/C/sec_terms.xml @@ -5,62 +5,67 @@ Syntax To describe syntax in this manual we use the following conventions: - Non terminal symbols are emphasized and have a link to their definition. E.g.: &term; - Terminal symbols are in bold. E.g.: theorem - Optional sequences of elements are put in square brackets. - E.g.: [in &term;] - Alternatives are put in square brakets and they are separated - by vertical bars. E.g.: [<|>] - Repetition of sequences of elements are given by putting the + Non terminal symbols are emphasized and have a link to their + definition. E.g.: &term; + Terminal symbols are in bold. E.g.: + theorem + Optional sequences of elements are put in square brackets. + E.g.: [in &term;] + Alternatives are put in square brakets and they are + separated by vertical bars. E.g.: [<|>] + Repetition of sequences of elements are given by putting the first sequence in square brackets, that are followed by three dots. - E.g.: [and &term;]… + E.g.: [and &term;]… Terms & co. Lexical conventions - - - - - - &id; - ::= - 〈〈&TODO;〉〉 - - - -
- - - - - - &nat; - ::= - 〈〈&TODO;〉〉 - - - -
- - - - - - &uri; - ::= - 〈〈&TODO;〉〉 - - - -
+ + + id + + + + &id; + ::= + 〈〈&TODO;〉〉 + + + +
+ + nat + + + + &nat; + ::= + 〈〈&TODO;〉〉 + + + +
+ + uri + + + + &uri; + ::= + 〈〈&TODO;〉〉 + + + +
+ Terms - - - + +
+ Terms + &term; @@ -144,9 +149,9 @@
- - - +
+ Simple terms + &sterm; @@ -158,8 +163,8 @@ | &id;[\subst[ - &id;≝&term; - [;&id;≝&term;]… + &id;≔&term; + [;&id;≔&term;]… ]] identifier with optional explicit named substitution @@ -241,31 +246,65 @@
- - - +
+ Arguments + &args; ::= - [(]_[: &term;][)] + _[: &term;] ignored argument | - [(]&id;[,&id;]…[: &term;][)] + + (_[: &term;]) + + ignored argument + + + + | + &id;[,&id;]…[: &term;] + + + | + (&id;[,&id;]…[: &term;]) + + + + +
+ + + Miscellaneous arguments + + + + &args2; + ::= + &id; + + + + + | + (&id;[,&id;]…: &term;) + +
- - - +
+ Pattern matching + &match_pattern; @@ -282,6 +321,7 @@
+ @@ -289,13 +329,13 @@ Definitions and declarations - axiom &id;: &term; + <emphasis role="bold">axiom</emphasis> &id;<emphasis role="bold">:</emphasis> &term; axiom axiom H: P H is declared as an axiom that states P - definition &id;[: &term;] [≝ &term;] + <emphasis role="bold">definition</emphasis> &id;[<emphasis role="bold">:</emphasis> &term;] [<emphasis role="bold">≝</emphasis> &term;] definition definition f: T ≝ t f is defined as t; @@ -309,16 +349,63 @@ Notice that the command is equivalent to theorem f: T ≝ t. - [co]inductive &id; (of inductive types) + [<emphasis role="bold">inductive</emphasis>|<emphasis role="bold">coinductive</emphasis>] &id; [&args2;]… <emphasis role="bold">:</emphasis> &term; <emphasis role="bold">≝</emphasis> [<emphasis role="bold">|</emphasis>] [&id;<emphasis role="bold">:</emphasis>&term;] [<emphasis role="bold">|</emphasis> &id;<emphasis role="bold">:</emphasis>&term;]… +[<emphasis role="bold">with</emphasis> &id; <emphasis role="bold">:</emphasis> &term; <emphasis role="bold">≝</emphasis> [<emphasis role="bold">|</emphasis>] [&id;<emphasis role="bold">:</emphasis>&term;] [<emphasis role="bold">|</emphasis> &id;<emphasis role="bold">:</emphasis>&term;]…]… + (co)inductive types declaration - &TODO; + inductive i x y z: S ≝ k1:T1 | … | kn:Tn with i' : S' ≝ k1':T1' | … | km':Tm' + Declares a family of two mutually inductive types + i and i' whose types are + S and S', which must be convertible + to sorts. + The constructors ki of type Ti + and ki' of type Ti' are also + simultaneously declared. The declared types i and + i' may occur in the types of the constructors, but + only in strongly positive positions according to the rules of the + calculus. + The whole family is parameterized over the arguments x,y,z. + If the keyword coinductive is used, the declared + types are considered mutually coinductive. + Elimination principles for the record are automatically generated + by Matita, if allowed by the typing rules of the calculus according to + the sort S. If generated, + they are named i_ind, i_rec and + i_rect according to the sort of their induction + predicate. + + + <emphasis role="bold">record</emphasis> &id; [&args2;]… <emphasis role="bold">:</emphasis> &term; <emphasis role="bold">≝</emphasis><emphasis role="bold">{</emphasis>[&id; [<emphasis role="bold">:</emphasis>|<emphasis role="bold">:></emphasis>] &term;] [<emphasis role="bold">;</emphasis>&id; [<emphasis role="bold">:</emphasis>|<emphasis role="bold">:></emphasis>] &term;]…<emphasis role="bold">}</emphasis> + record + record id x y z: S ≝ { f1: T1; …; fn:Tn } + Declares a new record family id parameterized over + x,y,z. + S is the type of the record + and it must be convertible to a sort. + Each field fi is declared by giving its type + Ti. A record without any field is admitted. + Elimination principles for the record are automatically generated + by Matita, if allowed by the typing rules of the calculus according to + the sort S. If generated, + they are named i_ind, i_rec and + i_rect according to the sort of their induction + predicate. + For each field fi a record projection + fi is also automatically generated if projection + is allowed by the typing rules of the calculus according to the + sort S, the type T1 and + the definability of depending record projections. + If the type of a field is declared with :>, + the corresponding record projection becomes an implicit coercion. + This is just syntactic sugar and it has the same effect of declaring the + record projection as a coercion later on. Proofs - theorem &id;[: &term;] [≝ &term;] + <emphasis role="bold">theorem</emphasis> &id;[<emphasis role="bold">:</emphasis> &term;] [<emphasis role="bold">≝</emphasis> &term;] theorem theorem f: P ≝ p Proves a new theorem f whose thesis is @@ -335,7 +422,7 @@ Notice that the command is equivalent to definition f: T ≝ t. - variant &id;[: &term;] [≝ &term;] + <emphasis role="bold">variant</emphasis> &id;[<emphasis role="bold">:</emphasis> &term;] [<emphasis role="bold">≝</emphasis> &term;] variant variant f: T ≝ t Same as theorem f: T ≝ t, but it does not @@ -343,19 +430,19 @@ an alternative name or proof to a theorem. - lemma &id;[: &term;] [≝ &term;] + <emphasis role="bold">lemma</emphasis> &id;[<emphasis role="bold">:</emphasis> &term;] [<emphasis role="bold">≝</emphasis> &term;] lemma lemma f: T ≝ t Same as theorem f: T ≝ t - fact &id;[: &term;] [≝ &term;] + <emphasis role="bold">fact</emphasis> &id;[<emphasis role="bold">:</emphasis> &term;] [<emphasis role="bold">≝</emphasis> &term;] fact fact f: T ≝ t Same as theorem f: T ≝ t - remark &id;[: &term;] [≝ &term;] + <emphasis role="bold">remark</emphasis> &id;[<emphasis role="bold">:</emphasis> &term;] [<emphasis role="bold">≝</emphasis> &term;] remark remark f: T ≝ t Same as theorem f: T ≝ t