predefined types: GrB_PLUS_BOOL, GrB_PLUS_INT8, GrB_PLUS_UINT8, GrB_PLUS_INT16, GrB_PLUS_UINT16, GrB_PLUS_INT32, GrB_PLUS_UINT32, GrB_PLUS_INT64, GrB_PLUS_UINT64, GrB_PLUS_FP32, GrB_PLUS_FP64. - There are predefined types: GrB_PLUS_BOOL, GrB_PLUS_INT8, GrB_PLUS_UINT8, GrB_PLUS_INT16, GrB_PLUS_UINT16, GrB_PLUS_INT32, GrB_PLUS_UINT32, GrB_PLUS_INT64, GrB_PLUS_UINT64, GrB_PLUS_FP32, GrB_PLUS_FP64. - There are predefined types: GrB_PLUS_BOOL, GrB_PLUS_INT8, GrB_PLUS_UINT8, GrB_PLUS_INT16, GrB_PLUS_UINT16, GrB_PLUS_INT32, GrB_PLUS_UINT32, GrB_PLUS_INT64, GrB_PLUS_UINT64, GrB_PLUS_FP32, GrB_PLUS_FP64. - There are

201 9.21.2 Détection de l’isolement de l’hôte . . . . . . . . . . . . . . . . . . . . . 202 9.21.3 Plus d’informations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 9.21.4 Linux : démarrer VirtualBox, facile à utiliser. Les chapitres suivants entreront beaucoup plus dans les détails en traitant d’outils and de fonctionnalités plus puissants, mais heureusement, il n’est pas nécessaire de lire tout scenari : • Lancer plusieurs systèmes d’exploitation en même temps. VirtualBox vous permet d’exécuter plus d’un système d’exploitation en même temps. De cette façon, vous pou- vez lancer des logiciels écrits

interactive theorem prover. First we define a module Foo.idr module Foo plusAssoc : plus n (plus m o) = plus (plus n m) o plusAssoc = ?rhs We wish to perform induction on n. First we load the file into :p rhs ---------- Goal: ---------- { hole 0 }: (n : Nat) -> (m : Nat) -> (o : Nat) -> plus n (plus m o) = plus (plus n m) o 2.2 Application of Intros We first apply the intros tactic: 7 Idris Tutorial Assumptions: ---------- n : Nat m : Nat o : Nat ---------- Goal: ---------- { hole 3 }: plus n (plus m o) = plus (plus n m) o 2.3 Induction on n Then apply induction on to n: -Foo.rhs> induction n ----------

interactive theorem prover. First we define a module Foo.idr module Foo plusAssoc : plus n (plus m o) = plus (plus n m) o plusAssoc = ?rhs We wish to perform induction on n. First we load the file into :p rhs ---------- Goal: ---------- { hole 0 }: (n : Nat) -> (m : Nat) -> (o : Nat) -> plus n (plus m o) = plus (plus n m) o 2.2 Application of Intros We first apply the intros tactic: 7 Idris Tutorial Assumptions: ---------- n : Nat m : Nat o : Nat ---------- Goal: ---------- { hole 3 }: plus n (plus m o) = plus (plus n m) o 2.3 Induction on n Then apply induction on to n: -Foo.rhs> induction n ----------

interactive theorem prover. First we define a module Foo.idr module Foo plusAssoc : plus n (plus m o) = plus (plus n m) o plusAssoc = ?rhs We wish to perform induction on n. First we load the file into :p rhs ---------- Goal: ---------- { hole 0 }: (n : Nat) -> (m : Nat) -> (o : Nat) -> plus n (plus m o) = plus (plus n m) o 2.2 Application of Intros We first apply the intros tactic: 7 Idris Tutorial Assumptions: ---------- n : Nat m : Nat o : Nat ---------- Goal: ---------- { hole 3 }: plus n (plus m o) = plus (plus n m) o 2.3 Induction on n Then apply induction on to n: -Foo.rhs> induction n ----------

interactive theorem prover. First we define a module Foo.idr module Foo plusAssoc : plus n (plus m o) = plus (plus n m) o plusAssoc = ?rhs We wish to perform induction on n. First we load the file into :p rhs ---------- Goal: ---------- { hole 0 }: (n : Nat) -> (m : Nat) -> (o : Nat) -> plus n (plus m o) = plus (plus n m) o 2.2 Application of Intros We first apply the intros tactic: 7 Idris Tutorial Assumptions: ---------- n : Nat m : Nat o : Nat ---------- Goal: ---------- { hole 3 }: plus n (plus m o) = plus (plus n m) o 2.3 Induction on n Then apply induction on to n: -Foo.rhs> induction n ----------

interactive theorem prover. First we define a module Foo.idr module Foo plusAssoc : plus n (plus m o) = plus (plus n m) o plusAssoc = ?rhs We wish to perform induction on n. First we load the file into :p rhs ---------- Goal: ---------- { hole 0 }: (n : Nat) -> (m : Nat) -> (o : Nat) -> plus n (plus m o) = plus (plus n m) o 2.2 Application of Intros We first apply the intros tactic: 7 Idris Tutorial Assumptions: ---------- n : Nat m : Nat o : Nat ---------- Goal: ---------- { hole 3 }: plus n (plus m o) = plus (plus n m) o 2.3 Induction on n Then apply induction on to n: -Foo.rhs> induction n ----------

interactive theorem prover. First we define a module Foo.idr module Foo plusAssoc : plus n (plus m o) = plus (plus n m) o plusAssoc = ?rhs We wish to perform induction on n. First we load the file into :p rhs ---------- Goal: ---------- { hole 0 }: (n : Nat) -> (m : Nat) -> (o : Nat) -> plus n (plus m o) = plus (plus n m) o 2.2 Application of Intros We first apply the intros tactic: 7 Idris Tutorial Assumptions: ---------- n : Nat m : Nat o : Nat ---------- Goal: ---------- { hole 3 }: plus n (plus m o) = plus (plus n m) o 2.3 Induction on n Then apply induction on to n: -Foo.rhs> induction n ----------

ar y : -- Unary addition plus : Nat -> Nat -> Nat plus Z y = y plus (S k) y = S (plus k y) -- Unary multiplication mult : Nat -> Nat -> Nat mult Z y = Z mult (S k) y = plus y (mult k y) T h e s t an on n am e s m u s t b e gi n w i t h a c ap i t al l e t t e r or n ot . F u n c t i on n am e s ( plus an d mult ab ov e ) , d at a c on s t r u c t or s ( Z, S, Nil an d ::) an d t y p e c on s t r u t t h e s e f u n c t i on s at t h e I d r i s p r om p t : Idris> plus (S (S Z)) (S (S Z)) 4 : Nat Idris> mult (S (S (S Z))) (plus (S (S Z)) (S (S Z))) 12 : Nat Not e : W h e n d i s p l ay i n g an

ar y : -- Unary addition plus : Nat -> Nat -> Nat plus Z y = y plus (S k) y = S (plus k y) -- Unary multiplication mult : Nat -> Nat -> Nat mult Z y = Z mult (S k) y = plus y (mult k y) T h e s t an on n am e s m u s t b e gi n w i t h a c ap i t al l e t t e r or n ot . F u n c t i on n am e s ( plus an d mult ab ov e ) , d at a c on s t r u c t or s ( Z, S, Nil an d ::) an d t y p e c on s t r u 6 C H A P T E R 1. T H E I D R I S T U T O R I A L v1. 3. 1 Idris> plus (S (S Z)) (S (S Z)) 4 : Nat Idris> mult (S (S (S Z))) (plus (S (S Z)) (S (S Z))) 12 : Nat Not e : W h e n d i s p l ay i n g an