X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=matita%2Fhelp%2FC%2Fsec_terms.xml;h=3cae2f84c1866ad13d858e14eb32953176c38c13;hb=84dbeab0a11aed6afb529b884bd796dec644c949;hp=d2594c718ba2c35d753c3e4c9c6a1edb1ab04039;hpb=3beaf3083a6677e1ea8228e618f385bef67b7f15;p=helm.git diff --git a/matita/help/C/sec_terms.xml b/matita/help/C/sec_terms.xml index d2594c718..3cae2f84c 100644 --- a/matita/help/C/sec_terms.xml +++ b/matita/help/C/sec_terms.xml @@ -26,78 +26,102 @@ Terms & co. Lexical conventions - - +
+ qstring + + + + &qstring; + ::= + "〈〈any sequence of characters excluded "〉〉" + + + +
+ id - &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 ([?'`])〉〉 + 〈〈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; + &nat; ::= - 〈〈any sequence of valid XML digits + 〈〈any sequence of valid XML digits〉〉
- +
char - &char; + &char; ::= [a-zA-Z0-9_-]
- +
uri-step - &uri-step; + &uri-step; ::= &char;[&char;]…
- +
uri - &uri; + &uri; ::= [cic:/|theory:/]&uri-step;[/&uri-step;]….&id;[.&id;]…[#xpointer(&nat;/&nat;[/&nat;]…)]
- Terms + + + + - +
Terms - &term; + &term; ::= &sterm; simple or delimited term @@ -141,11 +165,10 @@ | - let - [co]rec - &id; [&id;|(&id;[,&term;]… :&term;)]… [on &nat;] - [: &term;] - ≝ &term; + + let + [co]rec + &rec_def; (co)recursive definitions @@ -153,10 +176,7 @@ - [and - [&id;|(&id;[,&term;]… :&term;)]… [on &nat;] - [: &term;] - ≝ &term;]… + [and &rec_def;]… @@ -174,16 +194,34 @@ …user provided notation + + &rec_def; + ::= + + &id; [&id;|_|(&id;[,&id;]… :&term;)]… + + + + + + + + [on &id;] + [: &term;] + ≝ &term;] + + +
- +
Simple terms - &sterm; + &sterm; ::= (&term;) @@ -216,6 +254,12 @@ Set the impredicate sort of datatypes + + + | + CProp + one fixed predicative sort of constructive propositions + | @@ -241,7 +285,7 @@ | match &term; - [ in &term; ] + [ in &id; ] [ return &term; ] with @@ -252,11 +296,9 @@ [ - &match_pattern; ⇒ &term; - [ - | - &match_pattern; ⇒ &term; - ]…] + &match_branch;[|&match_branch;]… + ] + @@ -275,12 +317,12 @@
- +
Arguments - &args; + &args; ::= _[: &term;] @@ -307,16 +349,8 @@ (&id;[,&id;]…[: &term;]) - - -
- - - Miscellaneous arguments - - - &args2; + &args2; ::= &id; @@ -331,12 +365,18 @@
- +
Pattern matching + + &match_branch; + ::= + &match_pattern; ⇒ &term; + + - &match_pattern; + &match_pattern; ::= &id; 0-ary constructor @@ -347,6 +387,18 @@ (&id; &id; [&id;]…) n-ary constructor (binds the n arguments) + + + | + &id; &id; [&id;]… + n-ary constructor (binds the n arguments) + + + + | + _ + any remaining constructor (ignoring its arguments) +
@@ -377,6 +429,11 @@ f must be defined by means of tactics. Notice that the command is equivalent to theorem f: T ≝ t. + + <emphasis role="bold">letrec</emphasis> &TODO; + &TODO; + &TODO; + [<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;]…]… @@ -451,7 +508,7 @@ <para>Notice that the command is equivalent to <command>definition f: T ≝ t</command>.</para> </sect2> <sect2 id="variant"> - <title><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 @@ -485,12 +542,12 @@ intros-spec - +
intros-spec - &intros-spec; + &intros-spec; ::= [&nat;] [([&id;]…)] @@ -502,19 +559,125 @@ pattern -
+
pattern - &pattern; + &pattern; ::= - &TODO; + in + [&id;[: &path;]]… + [⊢ &path;]] + simple pattern + + + + | + in match &path; + [in + [&id;[: &path;]]… + [⊢ &path;]] + full pattern
- &TODO; + + path + + + + &path; + ::= + 〈〈any &sterm; without 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 ?. + + + Warning: the format for a path for a match … with + expression is restricted to: match &path; + with + [ + _ + ⇒ + &path; + | … + | + _ + ⇒ + &path; + ] + Its semantics is the following: the n-th + "_ + ⇒ + &path;" branch is matched against the n-th constructor of the + inductive data type. The head λ-abstractions of &path; are matched + against the corresponding constructor arguments. + + 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" + @@ -522,18 +685,13 @@ 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; + &reduction-kind; ::= - demodulate - - - - | normalize Computes the βδιζ-normal form @@ -553,8 +711,8 @@ | unfold [&sterm;] - δ-reduces the constant or variable specified, or that - in head position if none is specified + δ-reduces the constant or variable if specified, or that + in head position @@ -566,6 +724,36 @@
+ + + auto-params + &TODO; + + reduction-kind + + + + &autoparams; + ::= + depth=&nat; + &TODO; + + + + | + width=&nat; + &TODO; + + + + | + &TODO; + &TODO; + + + +
+