X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fhelp%2FC%2Fsec_terms.xml;h=945a43837bcfb79db57081fbb359579a1ec12be3;hb=8752fac73a864c821b6954f0572bce2052924183;hp=faa4f765fedbac4f32d2cb7007c105db6059c8f3;hpb=097487efb60f77326ea3959db169be9ee6c40da1;p=helm.git diff --git a/helm/software/matita/help/C/sec_terms.xml b/helm/software/matita/help/C/sec_terms.xml index faa4f765f..945a43837 100644 --- a/helm/software/matita/help/C/sec_terms.xml +++ b/helm/software/matita/help/C/sec_terms.xml @@ -5,65 +5,111 @@ 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 - first sequence in square brackets, that are followed by three dots. - E.g.: [and &term;]… + 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.: [<|>] + Repetitions of a sequence of elements are given by putting the + sequence in square brackets, that are followed by three dots. The empty + sequence is a valid repetition. + E.g.: [and &term;]… + Characters belonging to a set of characters are given + by listing the set elements in square brackets. Hyphens are used to + specify ranges of characters in the set. + E.g.: [a-zA-Z0-9_-] Terms & co. Lexical conventions - - - - - - &id; - ::= - 〈〈&TODO;〉〉 - - - -
- - - - - - &nat; - ::= - 〈〈&TODO;〉〉 - - - -
- - - - - - &uri; - ::= - 〈〈&TODO;〉〉 - - - -
+ + id + + + + &id; + ::= + 〈〈any sequence of letters, underscores or valid XML digits prefixed by a latin letter ([a-zA-Z]) and post-fixed by a possible empty sequence of decorators ([?'`])〉〉 + + + +
+ + nat + + + + &nat; + ::= + 〈〈any sequence of valid XML digits〉〉 + + + +
+ + char + + + + &char; + ::= + [a-zA-Z0-9_-] + + + +
+ + uri-step + + + + &uri-step; + ::= + &char;[&char;]… + + + +
+ + uri + + + + &uri; + ::= + [cic:/|theory:/]&uri-step;[/&uri-step;]….&id;[.&id;]…[#xpointer(&nat;/&nat;[/&nat;]…)] + + + +
Terms - + + + + + +
+ Terms - - &term; + &term; ::= &sterm; simple or delimited term @@ -107,11 +153,10 @@ | - let - [co]rec - &id; [&id;|(&id;[,&term;]… :&term;)]… [on &nat;] - [: &term;] - ≝ &term; + + let + [co]rec + &rec_def; (co)recursive definitions @@ -119,10 +164,7 @@ - [and - [&id;|(&id;[,&term;]… :&term;)]… [on &nat;] - [: &term;] - ≝ &term;]… + [and &rec_def;]… @@ -140,16 +182,34 @@ …user provided notation + + &rec_def; + ::= + + &id; [&id;|(&id;[,&term;]… :&term;)]… + + + + + + + + [on &nat;] + [: &term;] + ≝ &term;] + + +
- +
+ Simple terms - - &sterm; + &sterm; ::= (&term;) @@ -182,6 +242,12 @@ Set the impredicate sort of datatypes + + + | + CProp + one fixed predicative sort of constructive propositions + | @@ -218,11 +284,9 @@ [ - &match_pattern; ⇒ &term; - [ - | - &match_pattern; ⇒ &term; - ]…] + &match_branch;[|&match_branch;]… + ] + @@ -241,12 +305,12 @@
- +
+ Arguments - - &args; + &args; ::= _[: &term;] @@ -273,16 +337,8 @@ (&id;[,&id;]…[: &term;]) - - -
- - - - - - &args2; + &args2; ::= &id; @@ -297,12 +353,18 @@
- +
+ Pattern matching - - - &match_pattern; + + &match_branch; + ::= + &match_pattern; ⇒ &term; + + + + &match_pattern; ::= &id; 0-ary constructor @@ -316,6 +378,7 @@
+ @@ -344,7 +407,7 @@ [<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;]…] +[<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 inductive i x y z: S ≝ k1:T1 | … | kn:Tn with i' : S' ≝ k1':T1' | … | km':Tm' @@ -416,7 +479,7 @@ Notice that the command is equivalent to definition f: T ≝ t. - <emphasis role="bold">variant</emphasis> &id;[<emphasis role="bold">:</emphasis> &term;] [<emphasis role="bold">≝</emphasis> &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 @@ -443,5 +506,176 @@ + + Tactic arguments + This section documents the syntax of some recurring arguments for + tactics. + + + intros-spec + + intros-spec + + + + &intros-spec; + ::= + [&nat;] [([&id;]…)] + + + +
+ The natural number is the number of new hypotheses to be introduced. The list of identifiers gives the name for the first hypotheses. + + + + pattern + + pattern + + + + &pattern; + ::= + in + [&id;[: &path;]]… + [⊢ &path;]] + simple pattern + + + + | + in match &term; + [in + [&id;[: &path;]]… + [⊢ &path;]] + full pattern + + + +
+ + path + + + + &path; + ::= + 〈〈any &sterm; whithout occurrences of Set, Prop, CProp, Type, &id;, &uri; and user provided notation; however, % is now an additional production for &sterm;〉〉 + + + +
+ A path locates zero or more subterms of a given term by mimicking the term structure up to: + + Occurrences of the subterms to locate that are + represented by %. + Subterms without any occurrence of subterms to locate + that can be represented by ?. + + + For instance, the path + ∀_,_:?.(? ? % ?)→(? ? ? %) + locates at once the subterms + x+y and x*y in the + term ∀x,y:nat.x+y=1→0=x*y + (where the notation A=B hides the term + (eq T A B) for some type T). + + A simple pattern extends paths to locate + subterms in a whole sequent. In particular, the pattern + in H: p K: q ⊢ r locates at once all the subterms + located by the pattern r in the conclusion of the + sequent and by the patterns p and + q in the hypotheses H + and K of the sequent. + + If no list of hypotheses is provided in a simple pattern, no subterm + is selected in the hypothesis. If the ⊢ p + part of the pattern is not provided, no subterm will be matched in the + conclusion if at least one hypothesis is provided; otherwise the whole + conclusion is selected. + + Finally, a full pattern is interpreted in three + steps. In the first step the match T in + part is ignored and a set S of subterms is + located as for the case of + simple patterns. In the second step the term T + is parsed and interpreted in the context of each subterm + s ∈ S. In the last term for each + s ∈ S the interpreted term T + computed in the previous step is looked for. The final set of subterms + located by the full pattern is the set of occurrences of + the interpreted T in the subterms s. + + A full pattern can always be replaced by a simple pattern, + often at the cost of increased verbosity or decreased readability. + Example: the pattern + ⊢ in match x+y in ∀_,_:?.(? ? % ?) + locates only the first occurrence of x+y + in the sequent x,y: nat ⊢ ∀z,w:nat. (x+y) * (z+w) = + z * (x+y) + w * (x+y). The corresponding simple pattern + is ⊢ ∀_,_:?.(? ? (? % ?) ?). + + Every tactic that acts on subterms of the selected sequents have + a pattern argument for uniformity. To automatically generate a simple + pattern: + + Select in the current goal the subterms to pass to the + tactic by using the mouse. In order to perform a multiple selection of + subterms, hold the Ctrl key while selecting every subterm after the + first one. + From the contextual menu select "Copy". + From the "Edit" or the contextual menu select + "Paste as pattern" + + + + + reduction-kind + Reduction kinds are normalization functions that transform a term + to a convertible but simpler one. Each reduction kind can be used both + as a tactic argument and as a stand-alone tactic. + + reduction-kind + + + + &reduction-kind; + ::= + normalize + Computes the βδιζ-normal form + + + + | + reduce + Computes the βδιζ-normal form + + + + | + simplify + Computes a form supposed to be simpler + + + + | + unfold [&sterm;] + δ-reduces the constant or variable if specified, or that + in head position + + + + | + whd + Computes the βδιζ-weak-head normal form + + + +
+ + +