+ +

Library mathcomp.ssreflect.ssrnotations

+ +

+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria.
+ Distributed under the terms of CeCILL-B. *)
+ +
+

+ +

Reserved notation for various arithmetic and algebraic operations: + e. [a1, ..., a_n] evaluation (e.g., polynomials). + e`i indexing (number list, integer pi-part). + x^-1 inverse (group, field). + x *+ n, x *- n integer multiplier (modules and rings). + x ^+ n, x ^- n integer exponent (groups and rings). + x *: A, A :* x external product (scaling/module product in rings, + left/right cosets in groups). + A :&: B intersection (of sets, groups, subspaces, ...). + A :|: B, a |: B union, union with a singleton (of sets). + A :\: B, A :\ b relative complement (of sets, subspaces, ...). + A, < [a]> generated group/subspace, generated cycle/line. + 'C[x], 'C_A[x] point centralisers (in groups and F-algebras). + 'C(A), 'C_B(A) centralisers (in groups and matrix and F_algebras). + 'Z(A) centers (in groups and matrix and F-algebras). + m %/ d, m %% d Euclidean division and remainder (nat, polynomials). + d %| m Euclidean divisibility (nat, polynomial). + m = n % [mod d] equality mod d (also defined for <>, ==, and !=). + e^`(n) nth formal derivative (groups, polynomials). + e^` simple formal derivative (polynomials only). + `|x| norm, absolute value, distance (rings, int, nat). + x <= y ?= iff C x is less than y, and equal iff C holds (nat, rings). + x <= y :> T, etc cast comparison (rings, all comparison operators). + [rec a1, ..., an] standard shorthand for hidden recursor (see prime.v). + The interpretation of these notations is not defined here, but the + declarations help maintain consistency across the library. +

+ + Reserved notation for evaluation +

+ +

+
+Reserved Notation "e .[ x ]"
+  (at level 2, left associativity, format "e .[ x ]").
+ +
+Reserved Notation "e .[ x1 , x2 , .. , xn ]" (at level 2, left associativity,
+  format "e '[ ' .[ x1 , '/' x2 , '/' .. , '/' xn ] ']'").
+ +
+
+ +
+ Reserved notation for subscripting and superscripting +
+
+Reserved Notation "s `_ i" (at level 3, i at level 2, left associativity,
+  format "s `_ i").
+Reserved Notation "x ^-1" (at level 3, left associativity, format "x ^-1").
+ +
+
+ +
+ Reserved notation for integer multipliers and exponents +
+
+Reserved Notation "x *+ n" (at level 40, left associativity).
+Reserved Notation "x *- n" (at level 40, left associativity).
+Reserved Notation "x ^+ n" (at level 29, left associativity).
+Reserved Notation "x ^- n" (at level 29, left associativity).
+ +
+
+ +
+ Reserved notation for external multiplication. +
+
+Reserved Notation "x *: A" (at level 40).
+Reserved Notation "A :* x" (at level 40).
+ +
+
+ +
+ Reserved notation for set-theretic operations. +
+
+Reserved Notation "A :&: B" (at level 48, left associativity).
+Reserved Notation "A :|: B" (at level 52, left associativity).
+Reserved Notation "a |: A" (at level 52, left associativity).
+Reserved Notation "A :\: B" (at level 50, left associativity).
+Reserved Notation "A :\ b" (at level 50, left associativity).
+ +
+
+ +
+ Reserved notation for generated structures +
+
+Reserved Notation "<< A >>" (at level 0, format "<< A >>").
+Reserved Notation "<[ a ] >" (at level 0, format "<[ a ] >").
+ +
+
+ +
+ Reserved notation for centralisers and centers. +
+
+Reserved Notation "''C' [ x ]" (at level 8, format "''C' [ x ]").
+Reserved Notation "''C_' A [ x ]"
+  (at level 8, A at level 2, format "''C_' A [ x ]").
+Reserved Notation "''C' ( A )" (at level 8, format "''C' ( A )").
+Reserved Notation "''C_' B ( A )"
+  (at level 8, B at level 2, format "''C_' B ( A )").
+Reserved Notation "''Z' ( A )" (at level 8, format "''Z' ( A )").
+
+ +
+ Compatibility with group action centraliser notation. +
+
+Reserved Notation "''C_' ( A ) [ x ]" (at level 8, only parsing).
+Reserved Notation "''C_' ( B ) ( A )" (at level 8, only parsing).
+ +
+
+ +
+ Reserved notation for Euclidean division and divisibility. +
+
+Reserved Notation "m %/ d" (at level 40, no associativity).
+Reserved Notation "m %% d" (at level 40, no associativity).
+Reserved Notation "m %| d" (at level 70, no associativity).
+Reserved Notation "m = n %[mod d ]" (at level 70, n at next level,
+  format "'[hv ' m '/' = n '/' %[mod d ] ']'").
+Reserved Notation "m == n %[mod d ]" (at level 70, n at next level,
+  format "'[hv ' m '/' == n '/' %[mod d ] ']'").
+Reserved Notation "m <> n %[mod d ]" (at level 70, n at next level,
+  format "'[hv ' m '/' <> n '/' %[mod d ] ']'").
+Reserved Notation "m != n %[mod d ]" (at level 70, n at next level,
+  format "'[hv ' m '/' != n '/' %[mod d ] ']'").
+ +
+
+ +
+ Reserved notation for derivatives. +
+
+Reserved Notation "a ^` " (at level 8, format "a ^` ").
+Reserved Notation "a ^` ( n )" (at level 8, format "a ^` ( n )").
+ +
+
+ +
+ Reserved notation for absolute value. +
+
+Reserved Notation "`| x |" (at level 0, x at level 99, format "`| x |").
+ +
+
+ +
+ Reserved notation for conditional comparison +
+
+Reserved Notation "x <= y ?= 'iff' c" (at level 70, y, c at next level,
+  format "x '[hv' <= y '/' ?= 'iff' c ']'").
+ +
+
+ +
+ Reserved notation for cast comparison. +
+
+Reserved Notation "x <= y :> T" (at level 70, y at next level).
+Reserved Notation "x >= y :> T" (at level 70, y at next level, only parsing).
+Reserved Notation "x < y :> T" (at level 70, y at next level).
+Reserved Notation "x > y :> T" (at level 70, y at next level, only parsing).
+Reserved Notation "x <= y ?= 'iff' c :> T" (at level 70, y, c at next level,
+  format "x '[hv' <= y '/' ?= 'iff' c :> T ']'").
+
+