compiler fails to reject a program about fricas HOT 4 OPEN

On Mon, Apr 08, 2024 at 06:03:06AM -0700, Ralf Hemmecke wrote: The following program is missing `==` at position (*), but still compiles fine. I only detected that problem, because, when I wanted to use `uNCoefficient`, the interpreter claimed that that function is not defined in `QEtaOneOverPi(Integer)`. The only hint I can see is: ``` Semantic Errors: [1] C is not a known type ``` I wonder by which reasoning the compiler is able to accept that program. Here is the program ``` PP ==> PositiveInteger ZZ ==> Integer MZZ ==> Matrix ZZ -- consider only 2x2 matricies )abbrev package Q1PI QEtaOneOverPi QEtaOneOverPi(C: IntegralDomain): Exports == Implementation where Exports ==> with uNCoefficient: (PP, MZZ, C) -> C if C has Field then moebiusTransform: (MZZ, C) -> C Implementation ==> add uNCoefficient(nn: PP, gamma: MZZ, tau: C): C -----------------------------(*) c: ZZ := gamma(2,1) d: ZZ := gamma(2,2) determinant(gamma) - nn*(c*tau+d)^2 if C has Field then moebiusTransform(gamma: MZZ, x: C): C == (gamma(1,1)*x+gamma(1,2)::C) / (gamma(2,1)*x+gamma(2,2)::C) ``` If you remove the last `iF` and all lines below, then the compiler says ``` QEtaOneOverPi has 1 precompilation error: Parsing error: Apparent indentation error following add >> Apparent user error: precompilation failed ```

On Mon, Apr 08, 2024 at 12:36:53PM -0700, Ralf Hemmecke wrote: Yes, syntacticallly it is C applied to the block and the whole thing is a declaration. However, with the information at hand, C is an integral domain and not a functor that can be applied to something. I do not quite understand the stuff with "disguises meaning as a

variable/parameter". I do not see how the compiler can generate reasonable code for this "declaration", because the compiler should be unable to figure out what "C(some_block)" means here.