plouf/doc

This is a reference for the language. It is for now in construction, messy and can change at any time.

• Comments are C style comments

Predicates

• You can create a predicate with let predicate_name = predicate
• You can create an implication with let predicate_name = conditions => result where conditions and result are predicates
• Predicates have to be proven with predicate : {proof} in order to be used in other proofs
• You can combine predicates with (predicate1; predicate2; predicate3)

Truths

• A truth is a predicate that has been proven to be true
• A predicate alone is interpreted as a truth : predicate;

Axioms

• You can use ax instead of let to define an axiom, or any externaly proven predicate
• Axioms are considered true without needing a proof

Proofs

• You can prove a new predicate by "running" a true predicate p1 on an other true predicate p2 that fulfill its conditions : let p = predicate : {p1(p2)}
• The verifier will do its best to prove your predicates automatically, and tell you were it has not been able to

Variables

• You have to define a set/type before doing anything with a variable : let x in set.R
• You can define multiple variable with the same type together : let a,b,c in set.N
• If you give a value to a variable, the type is implicit : let x = 3
• Variable definition is a predicate, but you don't have to prove it
• In a predicate combination, you can define a variable in a predicate and use it in another predicate : (n in set.N, n/2=0)
• If you define a variable with the same name as an other one, it will shadow it during the time of its existence

Expressions

• Expressions are OCamL style
• They are evaluated from left to right (generally)

Functions

• Predicates are functions that take truths as input and return a truth
• You can use _ instead of an argument and the verifier will try to deduce what didn't put. For example, if a truth is needed as an argument, the verifier will try to prove it itself