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Diffstat (limited to 'test-suite/output/Notations3.v')
| -rw-r--r-- | test-suite/output/Notations3.v | 260 |
1 files changed, 260 insertions, 0 deletions
diff --git a/test-suite/output/Notations3.v b/test-suite/output/Notations3.v index 4b8bfe31..876aaa39 100644 --- a/test-suite/output/Notations3.v +++ b/test-suite/output/Notations3.v @@ -1,4 +1,9 @@ (**********************************************************************) +(* Check precedence, spacing, etc. in printing with curly brackets *) + +Check {x|x=0}+{True/\False}+{forall x, x=0}. + +(**********************************************************************) (* Check printing of notations with several instances of a recursive pattern *) (* Was wrong but I could not trigger a problem due to the collision between *) (* different instances of ".." *) @@ -139,3 +144,258 @@ Notation "'tele' x .. z := b" := (at level 85, x binder, z binder). Check tele (t:Type) '((y,z):nat*nat) (x:t) := tt. + +(* Checking that "fun" in a notation does not mixed up with the + detection of a recursive binder *) + +Notation "[ x ;; .. ;; y ]" := ((x,((fun u => S u), .. (y,(fun u => S u,fun v:nat => v)) ..))). +Check [ fun x => x+0 ;; fun x => x+1 ;; fun x => x+2 ]. + +(* Cyprien's part of bug #4765 *) + +Section Bug4765. + +Notation foo5 x T y := (fun x : T => y). +Check foo5 x nat x. + +End Bug4765. + +(**********************************************************************) +(* Test printing of #5526 *) + +Notation "x === x" := (eq_refl x) (only printing, at level 10). +Check (fun x => eq_refl x). + +(* Test recursive notations with the recursive pattern repeated on the right *) + +Notation "{{ x , .. , y , z }}" := (pair x .. (pair y z) ..). +Check {{0,1}}. +Check {{0,1,2}}. +Check {{0,1,2,3}}. + +(* Test printing of #5608 *) + +Reserved Notation "'letpair' x [1] = { A } ; 'return' ( b0 , b1 , .. , b2 )" + (at level 200, format "'letpair' x [1] = { A } ; '//' 'return' ( b0 , b1 , .. , b2 )"). +Notation "'letpair' x [1] = { a } ; 'return' ( b0 , b1 , .. , b2 )" := + (let x:=a in ( .. (b0,b1) .., b2)). +Check letpair x [1] = {0}; return (1,2,3,4). + +(* Test spacing in #5569 *) + +Notation "{ { xL | xR // xcut } }" := (xL+xR+xcut) + (at level 0, xR at level 39, format "{ { xL | xR // xcut } }"). +Check 1+1+1. + +(* Test presence of notation variables in the recursive parts (introduced in dfdaf4de) *) +Notation "!!! x .. y , b" := ((fun x => b), .. ((fun y => b), True) ..) (at level 200, x binder). +Check !!! (x y:nat), True. + +(* Allow level for leftmost nonterminal when printing-only, BZ#5739 *) + +Notation "* x" := (id x) (only printing, at level 15, format "* x"). +Notation "x . y" := (x + y) (only printing, at level 20, x at level 14, left associativity, format "x . y"). +Check (((id 1) + 2) + 3). +Check (id (1 + 2)). + +(* Test contraction of "forall x, let 'pat := x in ..." into "forall 'pat, ..." *) +(* for isolated "forall" (was not working already in 8.6) *) +Notation "! x .. y , A" := (id (forall x, .. (id (forall y, A)) .. )) (at level 200, x binder). +Check ! '(x,y), x+y=0. + +(* Check that the terminator of a recursive pattern is interpreted in + the correct environment of bindings *) +Notation "'exists_mixed' x .. y , P" := (ex (fun x => forall z:nat, .. (ex (fun y => forall z:nat, z=0 /\ P)) ..)) (at level 200, x binder). +Check exists_mixed x y '(u,t), x+y=0/\u+t=0. +Check exists_mixed x y '(z,t), x+y=0/\z+t=0. + +(* Check that intermediary let-in are inserted inbetween instances of + the repeated pattern *) +Notation "'exists_true' x .. y , P" := (exists x, True /\ .. (exists y, True /\ P) ..) (at level 200, x binder). +Check exists_true '(x,y) (u:=0) '(z,t), x+y=0/\z+t=0. + +(* Check that generalized binders are correctly interpreted *) + +Module G. +Generalizable Variables A R. +Class Reflexive {A:Type} (R : A->A->Prop) := reflexivity : forall x : A, R x x. +Check exists_true `{Reflexive A R}, forall x, R x x. +Check exists_true x `{Reflexive A R} y, x+y=0 -> forall z, R z z. +End G. + +(* Allows recursive patterns for binders to be associative on the left *) +Notation "!! x .. y # A #" := (.. (A,(forall x, True)) ..,(forall y, True)) (at level 200, x binder). +Check !! a b : nat # True #. + +(* Examples where the recursive pattern refer several times to the recursive variable *) + +Notation "{{D x , .. , y }}" := ((x,x), .. ((y,y),(0,0)) ..). +Check {{D 1, 2 }}. + +Notation "! x .. y # A #" := + ((forall x, x=x), .. ((forall y, y=y), A) ..) + (at level 200, x binder). +Check ! a b : nat # True #. + +Notation "!!!! x .. y # A #" := + (((forall x, x=x),(forall x, x=0)), .. (((forall y, y=y),(forall y, y=0)), A) ..) + (at level 200, x binder). +Check !!!! a b : nat # True #. + +Notation "@@ x .. y # A # B #" := + ((forall x, .. (forall y, A) ..), (forall x, .. (forall y, B) ..)) + (at level 200, x binder). +Check @@ a b : nat # a=b # b=a #. + +Notation "'exists_non_null' x .. y , P" := + (ex (fun x => x <> 0 /\ .. (ex (fun y => y <> 0 /\ P)) ..)) + (at level 200, x binder). +Check exists_non_null x y z t , x=y/\z=t. + +Notation "'forall_non_null' x .. y , P" := + (forall x, x <> 0 -> .. (forall y, y <> 0 -> P) ..) + (at level 200, x binder). +Check forall_non_null x y z t , x=y/\z=t. + +(* Examples where the recursive pattern is in reverse order *) + +Notation "{{RL c , .. , d }}" := (pair d .. (pair c 0) ..). +Check {{RL 1 , 2}}. + +Notation "{{RR c , .. , d }}" := (pair .. (pair 0 d) .. c). +Check {{RR 1 , 2}}. + +Set Printing All. +Check {{RL 1 , 2}}. +Check {{RR 1 , 2}}. +Unset Printing All. + +Notation "{{RLRR c , .. , d }}" := (pair d .. (pair c 0) .., pair .. (pair 0 d) .. c, pair c .. (pair d 0) .., pair .. (pair 0 c) .. d). +Check {{RLRR 1 , 2}}. +Unset Printing Notations. +Check {{RLRR 1 , 2}}. +Set Printing Notations. + +(* Check insensitivity of "match" clauses to order *) + +Module IfPat. +Notation "'if' t 'is' n .+ 1 'then' p 'else' q" := + (match t with S n => p | 0 => q end) + (at level 200). +Check fun x => if x is n.+1 then n else 1. +End IfPat. + +(* Examples with binding patterns *) + +Check {'(x,y)|x+y=0}. + +Module D. +Notation "'exists2'' x , p & q" := (ex2 (fun x => p) (fun x => q)) + (at level 200, x pattern, p at level 200, right associativity, + format "'[' 'exists2'' '/ ' x , '/ ' '[' p & '/' q ']' ']'") + : type_scope. + +Check exists2' (x,y), x=0 & y=0. +End D. + +(* Ensuring for reparsability that printer of notations does not use a + pattern where only an ident could be reparsed *) + +Module E. +Inductive myex2 {A:Type} (P Q:A -> Prop) : Prop := + myex_intro2 : forall x:A, P x -> Q x -> myex2 P Q. +Notation "'myexists2' x : A , p & q" := (myex2 (A:=A) (fun x => p) (fun x => q)) + (at level 200, x ident, A at level 200, p at level 200, right associativity, + format "'[' 'myexists2' '/ ' x : A , '/ ' '[' p & '/' q ']' ']'") + : type_scope. +Check myex2 (fun x => let '(y,z) := x in y>z) (fun x => let '(y,z) := x in z>y). +End E. + +(* A canonical example of a notation with a non-recursive binder *) + +Parameter myex : forall {A}, (A -> Prop) -> Prop. +Notation "'myexists' x , p" := (myex (fun x => p)) + (at level 200, x pattern, p at level 200, right associativity). + +(* A canonical example of a notation with recursive binders *) + +Notation "∀ x .. y , P" := (forall x, .. (forall y, P) ..) + (at level 200, x binder, y binder, right associativity) : type_scope. + +(* Check that printing 'pat uses an "as" when the variable bound to + the pattern is dependent. We check it for the three kinds of + notations involving bindings of patterns *) + +Check fun '((x,y) as z) => x+y=0/\z=z. (* Primitive fun/forall *) +Check myexists ((x,y) as z), x+y=0/\z=z. (* Isolated binding pattern *) +Check exists '((x,y) as z), x+y=0/\z=z. (* Applicative recursive binder *) +Check ∀ '((x,y) as z), x+y=0/\z=z. (* Other example of recursive binder, now treated as the exists case *) + +(* Check parsability and printability of irrefutable disjunctive patterns *) + +Check fun '(((x,y),true)|((x,y),false)) => x+y. +Check myexists (((x,y),true)|((x,y),false)), x>y. +Check exists '(((x,y),true)|((x,y),false)), x>y. +Check ∀ '(((x,y),true)|((x,y),false)), x>y. + +(* Check Georges' printability of a "if is then else" notation *) + +Module IfPat2. +Notation "'if' c 'is' p 'then' u 'else' v" := + (match c with p => u | _ => v end) + (at level 200, p pattern at level 100). +Check fun p => if p is S n then n else 0. +Check fun p => if p is Lt then 1 else 0. +End IfPat2. + +(* Check that mixed binders and terms defaults to ident and not pattern *) +Module F. + (* First without an indirection *) +Notation "[ n | t ]" := (n, (fun n : nat => t)). +Check fun S : nat => [ S | S+S ]. +Check fun N : nat => (N, (fun n => n+0)). (* another test in passing *) + (* Then with an indirection *) +Notation "[[ n | p | t ]]" := (n, (fun p : nat => t)). +Notation "[[ n | t ]]" := [[ n | n | t ]]. +Check fun S : nat => [[ S | S+S ]]. +End F. + +(* Check parsability/printability of {x|P} and variants *) + +Check {I:nat|I=I}. +Check {'I:True|I=I}. +Check {'(x,y)|x+y=0}. + +(* Check exists2 with a pattern *) +Check ex2 (fun x => let '(y,z) := x in y>z) (fun x => let '(y,z) := x in z>y). + +Module Issue7110. +Open Scope list_scope. +Notation "[ :: x1 , x2 , .. , xn & s ]" := (x1 :: x2 :: .. (xn :: s) ..) + (at level 0). +Definition foo (l : list nat) := + match l with + | a :: (b :: l) as l1 => l1 + | _ => l +end. +Print foo. +End Issue7110. + +Module LocateNotations. +Locate "exists". +Locate "( _ , _ , .. , _ )". +End LocateNotations. + +Module Issue7731. + +Axiom (P : nat -> Prop). +Parameter (X : nat). +Notation "## @ E ^^^" := (P E) (at level 20, E at level 1, format "'[ ' ## '/' @ E '/' ^^^ ']'"). +Notation "%" := X. + +Set Printing Width 7. +Goal ## @ % ^^^. +Show. +Abort. + +End Issue7731. |