## PolyPaver | Documentation | .pp Language

Warning This file currently documents a subset of the language, some newer features are not yet included.

# Example

power.
H1: x <- [1 .. 10].
H2: n <- [1 .. 10].
H3: integer(n).
->
C1: x^2 <= x^(n+1) + 0.000000001.

# Grammar

## Top level

<conjecture>       ::= <identifier> "." [ { <hypothesis> } "->" ] <conclusion> { <conclusion> }
<hypothesis>       ::= "H" { <id> } ":" <predicate> "."
<conclusion>       ::= "C" { <id> } ":" <predicate> "."
<predicate>        ::= <type_declaration> | <expression> <relation_symbol> <expression> | ...
<type_declaration> ::= "integer(" <identifier> ")"

## Relations

Relation Explanation
<- element of / within interval / sub-interval of
<=, >=, ==, =, != = and == both denote equality

## Expressions

Constant Explanation
Pi
FepsAbs 2-126 (IEEE Single FP least non-zero number)
FepsiAbs The interval [ -2-126..2-126]
FepsRel 2-24 (IEEE Single FP machine epsilon)
FepsiRel The interval [ -2-24..2-24]
Exact operator IEEE-Single-rounded operator
+ (+)
- (-)
* (*)
/ (/)
^ rounded integer power not available
Function Explanation
Interval(x,y) the least interval covering x and y
Sqrt(x) exact square root of x
Exp(x) exact natural exponential (ex)
Sin(x) exact sine
Cos(x) exact cosine
Integral(a,b,f,x) exact integral from a to b of f(x)dx

Please note that in the above, x, y, a and b are arbitrary expressions.