Commit e6a4c2ce by Pierre Letouzey

### typos

parent 9ede9f16
 ... ... @@ -37,7 +37,7 @@ A dot `.` is mandatory to end each Coq phrase. Define a function `compose : forall A B C, (B->C)->(A->B)->(A->C)`. Test it with functions `S` and `pred` on natural numbers (type `nat`). #### Exercise 2 : boolean ersatz #### Exercise 2 : Boolean ersatz Define (without using `bool` nor any other inductive type): ... ... @@ -54,7 +54,7 @@ More precisely, define (without using `nat` nor any other inductive type): - a type `church : Type` - two constant `zero` and `one` of type `church` - a function `succ` of type `church->church` - two fonctions `plus` and `mult` of type `church->church->church` - two functions `plus` and `mult` of type `church->church->church` - a function `power` - a test `iszero` ... ... @@ -62,16 +62,16 @@ Also define two functions `nat2church : nat -> church` and `church2nat : church ## Base types #### Exercise 4 : booleans #### Exercise 4 : Booleans - Write a function `checktauto : (bool->bool)->bool` which tests whether a boolean unary function always answers `true`. - Write a function `checktauto : (bool->bool)->bool` which tests whether a Boolean unary function always answers `true`. - Same for `checktauto2` et `checktauto3` for boolean fonctions expecting 2, then 3 arguments. This can be done by enumerating all cases, but there is a clever way to proceed (for instance by re-using `checktauto`. - Same for `checktauto2` and `checktauto3` for Boolean functions expecting 2, then 3 arguments. This can be done by enumerating all cases, but there is a clever way to proceed (for instance by re-using `checktauto`. - Check wether `fun a b c => a || b || c || negb (a && b) || negb (a && c)` is a tautology. - Check whether `fun a b c => a || b || c || negb (a && b) || negb (a && c)` is a tautology. Note : the command `Open Scope bool_scope.` activates notations `||` and `&&` (respectively for functions `orb` and `andb`). - Define some functions behavint like Coq standard functions `negb` and `orb` and `andb`. - Define some functions behaving like Coq standard functions `negb` and `orb` and `andb`. #### Exercise 5 : usual functions on natural numbers. ... ...
Markdown is supported
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!